Seismic Design Guide for Metal Building Systems

Seismic Design Guide for Metal Building Systems: Based on the 2006 IBC

ISBN 978-1-58001-762-6

Copyright by MBMA 1300 Sumner Ave. Cleveland, OH 44115-2851

COPYRIGHT 2008 Published by the International Code Council®

ALL RIGHTS RESERVED. This publication is a copyrighted work owned by the Metal Building Manufacturers Association. Without advance written permission from the copyright owner, no part of this book may be reproduced, distributed, or transmitted in any form or by any means, including, without limitation, electronic, optical, or mechanical means (by way of example and not limitation, photocopying or recording by or in an information storage and retrieval system). For information on permission to copy material exceeding fair use, please contact MBMA at 1300 Sumner Ave., Cleveland, OH 44115-2851. Phone: (216) 241-7333.

The information contained in this document is believed to be accurate; however, it is being provided for informational purposes only and is intended for use only as a guide. Publication of this document by the International Code Council should not be construed as the ICC or MBMA engaging in or rendering engineering, legal, or other professional services. Use of the information contained in this workbook should not be considered by the user as a substitute for the advice of a registered professional engineer, attorney, or other professional. If such advice is required, you should seek the services of a registered professional engineer, licensed attorney, or other professional. Cover photographs provided by MBMA. Publication date: November, 2008 First printing Printed in the United States of America

Seismic Design Guide For Metal Building Systems

TABLE OF CONTENTS

Introduction I.

BACKGROUND ...............................................................................................................1 A. PURPOSE................................................................................................................1 B. STYLE AND ORGANIZATION ..................................................................................1 C. MBMA SEISMIC GUIDE STEERING COMMITTEE....................................................2 D. AUTHORS ..............................................................................................................2 II. TECHNICAL BASIS..........................................................................................................3 A. CODES AND STANDARDS USED AS THE DESIGN GUIDE BASIS ...............................3 B. BASIC CONCEPT OF SEISMIC CODE REDUCED FORCES ...........................................4 C. METAL BUILDING STANDARD DESIGN AND ANALYSIS PRACTICE/ECONOMY .......5 D. APPROACH TO METAL BUILDING ROOF DIAPHRAGM RIGIDITY (FLEXIBLE VS. RIGID) AND ACCIDENTAL TORSION .......................................................................6 E. LOWER SEISMIC AREA DESIGN ALTERNATIVE ......................................................9 F. STABILITY ANALYSIS AND DESIGN .......................................................................9 III. OTHER SIGNIFICANT ISSUES ........................................................................................11 A. ADVANTAGES IN PERFORMING A GEOTECHNICAL INVESTIGATION .....................11 B. RELATIONSHIP AND ISSUES BETWEEN THE METAL BUILDING SUPPLIER AND THE BUILDING SPECIFYING ENGINEER .......................................................................11 C. RELATIONSHIP AND ISSUES BETWEEN THE METAL BUILDING SUPPLIER AND FOUNDATION/HARDWALL ENGINEER ..................................................................12 D. HARDWALL DETAILING AND ACTUAL BEHAVIOR ...............................................13

Design Example 1 Determination of Seismic Design Forces PROBLEM STATEMENT ................................................................................................ 1-2 DESIGN EXAMPLE OBJECTIVE ..................................................................................... 1-3 1. DETERMINE EARTHQUAKE DESIGN FORCES ............................................................... 1-4 1.1. COMPUTE SITE GROUND MOTION DESIGN VALUES .......................................... 1-4 1.2. DETERMINE THE OCCUPANCY CATEGORY, IMPORTANCE FACTOR, AND SEISMIC DESIGN CATEGORY FOR EACH SITE BUILDING .................................................. 1-7 1.3. DETERMINE THE SEISMIC BASE SHEAR, V, FOR EACH BUILDING ....................... 1-8 1.4. DETERMINE THE SEISMIC LOAD EFFECTS E AND EM FOR EACH BUILDING IN EACH DIRECTION ...................................................................................................... 1-24

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Seismic Design Guide For Metal Building Systems

Design Example 2 Design of Frames, Columns, Bracing and Other Elements of the Lateral-Force-Resisting System PROBLEM STATEMENT ................................................................................................ 2-3 DESIGN EXAMPLE OBJECTIVE ..................................................................................... 2-4 2. DESIGN OF TYPICAL MEMBERS AND CONNECTIONS .................................................. 2-5 2.1. GENERAL DESIGN GUIDANCE – TYPICAL MEMBERS AND CONNECTIONS .......... 2-5 2.2. DESIGN BUILDING A (R > 3)............................................................................ 2-13 2.3. DESIGN BUILDING A – ALTERNATE DESIGN (R = 3)........................................ 2-42 2.4. DESIGN BUILDING B........................................................................................ 2-69 2.5. BEAM-TO-COLUMN CONNECTION DESIGN ...................................................... 2-99 2.6. COLUMN BASE AND ANCHOR BOLT DESIGN ................................................. 2-108 2.7. FUNDAMENTAL FORCES FOR FOUNDATION DESIGN ...................................... 2-110 2.8. WELDING ISSUES AND QUALITY ASSURANCE REQUIREMENTS...................... 2-115 2.9. APPROVED STEEL AND WELDING MATERIAL ................................................ 2-118

Design Example 3 Evaluation of Design Options for a Metal Building System with a Concrete Deck Mezzanine 3. BACKGROUND ............................................................................................................. 3-2 3.1. CASE 1 – SMALL INTERIOR MEZZANINE ............................................................ 3-4 3.2. CASE 2 – SMALL MEZZANINE FULL LENGTH OF BUILDING ............................... 3-8 3.3. CASE 3 – LARGE MEZZANINE AS SEPARATE STORY ........................................ 3-12

Design Example 4 Determination of Seismic Design Forces and Detailing Requirements for a Metal Building with Concrete or Masonry Walls PROBLEM STATEMENT ................................................................................................ 4-2 DESIGN EXAMPLE OBJECTIVE ..................................................................................... 4-2 4. DISTRIBUTION OF SEISMIC DESIGN LOADS ................................................................. 4-3 4.1. DETERMINE EARTHQUAKE DESIGN FORCES ...................................................... 4-3 4.2. WALL DESIGN AND WALL TO METAL CONNECTION ....................................... 4-12 4.3. SIDE WALL GIRTS ........................................................................................... 4-23

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Seismic Design Guide for Metal Building Systems

Seismic Design Guide for Metal Building Systems 2006 IBC Edition

INTRODUCTION

I.

Background A.

Purpose The purpose of this publication is to provide a comprehensive guide, referred to herein as the Guide, for the practical seismic design of metal building systems, which results in designs that are compliant with the seismic requirements of the 2006 International Building Code£ (2006 IBC£). This publication is an update of an earlier edition of this Guide that was based on the 2000 IBC. The Metal Building Manufacturers Association (MBMA) intends for this to be a useful tool for engineers, building officials and plan checkers. It should be noted that the design procedures provided in this Guide are not the only way to achieve compliance with the code; they merely represent one way that has been deemed to be the most appropriate by the authors.

B.

Style and Organization There are two primary parts to this Guide. In the first part, the background and organization of the Guide are described, along with the technical basis and the approach used to establish a consensus on judgment issues. In the second part, four design examples are provided. The examples are in narrative form and are intended to illustrate acceptable approaches to deal with the most common seismic design issues encountered in the design of metal building systems. The examples represent realistic design situations for metal building systems. Throughout the design examples, commentary is provided as italicized notes, as shown in this paragraph.

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Seismic Design Guide for Metal Building Systems

The comments are intended to provide the reader with insights and background, and to point out the impact of more recent code revisions on specific seismic requirements, as appropriate in the design example. The four design examples that are provided are:

C.

•

Design Example 1 - Determination of Seismic Design Forces

•

Design Example 2 - Design of Frames, Columns, Bracing and other Elements of the Lateral Force-Resisting System

•

Design Example 3 – Evaluation of Design Options for a Metal Building System with a Concrete Deck Mezzanine (Rigid Diaphragm)

•

Design Example 4 - Determination of Seismic Design Forces and Detailing Requirements for a Metal Building with Concrete or Masonry Walls (Hardwalls)

MBMA Seismic Design Guide Steering Committee The Metal Building Manufacturers Association (MBMA) commissioned the authors to develop the first Guide (IBC 2000 version) to achieve the abovestated purpose. This updated edition of the Guide (IBC 2006 version) was carried out by a steering committee under the direction of the lead author, Robert Bachman. The original authors then worked with the steering committee to develop the final updated Guide. The steering committee consisted of the following individuals: Mike Pacey, S.E. Division Engineer Andy Jaworski, P.E. Senior Research and Design Engineer Allen Hurtz, S.E. Manager of Engineering Igor Marinovic, P.E. Senior Research Engineer Jim Miller, S.E. CEO

Butler Manufacturing Company Nucor Building Systems Star Building Systems VP Buildings J.R. Miller & Associates

W. Lee Shoemaker, P.E., Ph.D., director of research and engineering for MBMA, acted as the facilitator for the Guide D.

Authors The following individuals authored and assisted with the IBC 2006 design guide updates:

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Seismic Design Guide for Metal Building Systems

Robert E. Bachman, S.E. Principal Richard M. Drake, S.E. Director, Design Engineering Martin W. Johnson, S.E. Project Manager Thomas M. Murray, Ph.D., P.E. Montague Betts Professor of Structural Steel Design

R.E. Bachman Consulting Structural Engineer Fluor Corporation ABS Consulting Virginia Polytechnic Institute and State University

Each of these individuals provided special expertise to the Guide.

II.

•

Bachman provided expertise in IBC and ASCE 7-05 Seismic Requirements and served as the lead Guide author for coordinating its development.

•

Drake provided expertise on the AISC Seismic Provisions (AISC 341) and served as the publication consultant.

•

Johnson provided expertise on seismic design issues associated with metal buildings.

•

Murray provided expertise on the seismic design of beam-tocolumn moment connections.

Technical Basis A.

Codes and Standards Used as the Design Guide Basis The design recommendations in this Guide are based on the 2006 International Building Code£ (2006 IBC£) and the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures ASCE/SEI Standard 7-05 including Supplement No. 1 (referred herein as ASCE 7-05). Structural steel design is based on AISC 360-05 American Institute of Steel Construction Specification for Structural Steel Buildings, March 9, 2005, and AISC 341-05 American Institute of Steel Construction Seismic Provisions for Steel Buildings, March 9, 2005, including Supplement No. 1, November 16, 2005 (note that this was referred to in the previous Guide as the AISC Seismic Provisions, but is now referred to as AISC 341-05), and standard industry practice. AISC 341-05 is composed of two parts. Part I is Structural Steel Buildings and Part II is Composite Structural Steel and Reinforced Concrete Buildings. In this Guide, all references are to Part I, unless otherwise noted.

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Seismic Design Guide for Metal Building Systems

AISC 341-05 is written in a unified format that addresses both Load Resistance Factor Design (LRFD) and Allowable Strength Design (ASD). This Guide focuses on Allowable Strength Design (ASD) but points out differences and/or advantages of Load and Resistance Factor Design (LRFD) when appropriate. Note that in the previous edition of this Guide the strength design load factors were used because the previous version of AISC Seismic Provisions (1997) did not allow choice between design methods for steel structures assigned to high SDC. LRFD was the only method permitted. For users of the Allowable Stress Design format, which is no longer supported or permitted by AISC 360-05, AISC provided the conversion factors in Part III of the Seismic Provisions, so the allowable stress capacities in the AISC Seismic Provisions (1997) would be calibrated to strength load combinations. In AISC 341-05, Part III was eliminated since the allowable strength capacities have been calibrated to the basic allowable stress combinations of the 2006 IBC and ASCE 7-05. While either LRFD or Allowable Strength Design (ASD) is permitted, for this example ASD design is utilized. Therefore, the 2006 IBC Allowable Stress Design load combinations are presented instead of LRFD load combinations that were presented in the previous Guide and are further discussed in Sections 2.1.4 and 2.1.8. It should be noted that the 2006 IBC references ASCE 7 for its seismic criteria requirements and AISC 341-05 for its steel seismic detailing requirements. The 2006 IBC, ASCE 7-05 and AISC 341-05 are fully compatible through a significant coordination that took place between the various code and standard writing committees. B.

Basic Concept of Seismic Code Reduced Forces The 2006 IBC requires that all structures, in most parts of the United States, be designed to resist design earthquake ground motions. As currently defined, these design earthquake motions have average return periods of between 300 and 800 years and are quite severe. In regions of high seismicity in the United States it would be economically prohibitive to design structures to remain elastic for these motions (as is done for wind loads). Therefore, the seismic design for resisting earthquake motions is based on the concept of inelastic design. Over the past 60 years, earthquake engineering has evolved to allow for inelastic yielding to accommodate seismic loadings as long as such yielding does not impair the vertical load capacity of the structure. To reconcile with the allowance of damage from inelastic response, forces determined by linear analysis are reduced to a design earthquake force level through the introduction of the seismic force reduction factor, R.

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Seismic Design Guide for Metal Building Systems

Various magnitudes of R, based on the inelastic absorption of structure types, have been defined. The larger the value of R, the lower the design earthquake force, and more detailing requirements are imposed to assure that the structure will perform inelastically as intended. Larger R-values also result in more restrictions regarding the proportioning of members and their connections. In addition, there are limitations on the types of structural systems that can utilize a high R-value. In this Guide, the seismic force reduction factors that are used are consistent with the structural systems found in metal buildings. Because reduced forces are used, special design and detailing is required for some members and connections. The design examples clearly illustrate where these special connection forces are required and how they should be applied. The user is cautioned that application of reduced seismic forces in design without the corresponding application of seismic detailing will likely result in a design that does not comply with the 2006 IBC. C.

Metal Building Standard Design and Analysis Practice/Economy The metal building systems concept rose to significance during World War II in response to the U.S. military’s needs for light, economical structures that could be easily transported and quickly assembled using unskilled labor. Although today’s modern systems bear little resemblance to the Quonset huts of those days, metal buildings remain the most practical, economical solution for many low-rise structures. The economies associated with metal building systems come from a variety of factors. First, through years of improvements and innovations, the metal building industry has consistently produced lighter structures than typically found in conventional construction. This is achieved through the use of built-up web-tapered “primary” framing members and cold-formed “secondary” structural members, including roof purlins and wall girts. Another economical aspect of metal building systems is the combination of mass-produced components with custom-designed and fabricated structural members. To achieve this efficiency, the metal building industry has developed computer software that performs structural analyses, determines member and connection sizes, selects mass-produced components when appropriate, and produces shop and erection drawings. Metal buildings are typically analyzed based on the assumption that the roof acts as a flexible diaphragm and distributes loads to each line of resistance based on the tributary area. Frames and longitudinal bracing are then designed using two-dimensional models. Seismic design presents a challenge for metal building systems due to the many special seismic detailing requirements that are not otherwise required.

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Seismic Design Guide for Metal Building Systems

In some cases, this requires the manufacturer to prepare extensive calculations and details in addition to the calculations and details typically produced by its proprietary software. Because metal building structures are typically single story, they are exempted from drift criteria (ASCE 7 Table 12.12-1, Footnote c) provided they meet the requirements so noted. Typically, the engineer for the metal building manufacturer designs only the steel building structure. Another engineer normally performs the design of the remainder of the structure, including foundations and concrete or masonry walls. This is further discussed in Section III.C. D.

Approach to Metal Building Roof Diaphragm Rigidity (Flexible vs. Rigid) and Accidental Torsion Diaphragm Flexibility Applied forces are distributed within any building in a direct relationship to the rigidity of the structural elements of that building. A significant factor is the rigidity of structural elements that transfer forces horizontally, relative to elements that transfer force vertically. For either extreme of this relative rigidity between horizontal and vertical elements, engineers have developed simplified design approaches to determine force distributions. The two extremes are defined as follows: •

Flexible Diaphragm: The rigidity of the horizontal diaphragm is very small relative to the rigidity of the vertical systems.

•

Rigid Diaphragm: The rigidity of the horizontal diaphragm is very large compared to the rigidity of the vertical systems.

Analysis using either of these bounding assumptions produces results that vary in accuracy depending upon how closely the actual structure matches the simplifying assumptions. Although many (perhaps most) structures fall somewhere between these extremes, more accurate analysis can only be done by using complex finite-element models that are generally not practical to use for ordinary building designs. 2006 IBC Section 1602.1 defines a flexible diaphragm as having a lateral deflection of more than two times the average story drift of the vertical elements supporting the diaphragm, and a rigid diaphragm as everything else. This definition requires calculation of diaphragm deflection, which is complex and imprecise for many types of diaphragm construction. Therefore, it is important to be able to select and use appropriate simplified assumptions to obtain rapid structural design solutions. Diaphragm deflection varies, depending upon the materials used, the type and spacing of fasteners used in the construction, the depth of the diaphragm in 6

Seismic Design Guide for Metal Building Systems

the direction of deformation, and the width or span of the diaphragm transverse to the direction of deformation. Horizontal diaphragm systems in metal buildings might consist of either the metal cladding of the roof itself or horizontal bracing systems installed beneath the roof alone. Examples of horizontal bracing systems used include rods, angles, cables, or other structural members and are often tension-only bracing. Metal Roof Systems Metal roof cladding typically consists of either standing seam metal panels or through-fastened roof panels. •

In standing seam roof (SSR) systems, the formed roof sheets are restrained against uplift but are free to slide against each other (float) along the length of the joining seams. Side seam resistance to slip varies. The panel clips allow for relative movement between the panels and their supporting structure to accommodate thermal expansion. The resulting roof systems vary in the strength and stiffness required to transfer horizontal forces, and in general they are considered to be flexible for any type of construction. Therefore, separate horizontal bracing systems that are designed to resist the full wind and earthquake demands usually need to be provided. Friction caused by sliding of panels at the attachments along seams probably provides energy dissipation (damping) to the structure that is beneficial to earthquake response, but is usually ignored in the design. There are exceptions to this typical presumed behavior. Standing seam roof systems, with documented diaphragm strength and stiffness values, may be sufficient to act as subdiaphragms for the distribution of portions of the lateral forces to the main diaphragm cross-ties, i.e. strut purlins.

•

Through-fastened roof (TFR) systems come in many types. Some systems use screws that fasten through only one sheet of adjoining roof panels, while an overlapping rib holds down the adjacent sheet. This roofing type, like a standing seam roof, is presumed to be flexible for all types of construction. Other TFR systems use concealed or exposed screws that fasten through both metal sheets along an overlapping edge. The rigidity of these systems varies depending upon the type and spacing of fasteners, the profile and thickness of the joining metal roofing sheets, and the overall depth and width of the diaphragm.

It has been a traditional metal building design practice to assume that diaphragms of all types are flexible, regardless of the size or shape of the building or the type and relative rigidity of the vertical structural elements. For the most part, this assumption is reasonably correct and appropriate. A typical metal building that is relatively square in plan view, with either an SSR or TFR roof system, a series of moment frames in the transverse

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Seismic Design Guide for Metal Building Systems

directions, and several bays of tension-rod bracing in the longitudinal direction, would be expected to meet the deflection check as a flexible diaphragm system. However, the design engineer should be aware that some structural geometries might be better classified as having rigid diaphragms: •

As an example, a warehouse building with a TFR roof system that has a series of moment (portal) frames instead of bracing along the walls of the longitudinal axis, in order to provide a continuous line of loading docks along the walls of the building. The relatively flexible moment frames are likely to experience deflections equal to or greater than the TFR system. Note that an SSR roof system would still be considered flexible for this building.

•

Structures using relatively flexible cable bracing systems as vertical bracing, in conjunction with relatively more rigid tensionrod horizontal bracing or a TFR roof system might be considered as having rigid diaphragms.

In a recent development, ASCE 7-05 has adopted a new provision found in Section 12.3.1.1 of ASCE 7-05 which states that untopped steel decking is permitted to be considered as a flexible diaphragm in structures in which the vertical elements of the lateral force resisting system are structural steel braced frames or concrete, masonry, steel or composite shear frames. Inherent and Accidental Torsion ASCE 7-05 Section 12.8.4.1 requires, for diaphragms which are rigid (i.e. not flexible), that the distribution of base shear forces should consider the inherent torsional moment caused by difference in location between the center of mass and center of stiffness of the structure. In addition, ASCE 705 Section 12.8.4.2 requires, for rigid diaphragms, that an additional “accidental” torsional moment be added to the inherent torsion defined by ASCE 7-05 Section 12.8.4.1. Further, ASCE 7-05 Section 12.8.4.3 requires that in some instances the combined inherent and accidental torsional moment must be multiplied by a dynamic amplification factor. Unique Structure Geometries Many buildings have geometries that complicate the picture when considering horizontal force distribution. A common instance is for buildings that contain partial mezzanine floor levels. These floors might be clearly rigid by inspection, such as when consisting of concrete-topped metal decking supported by steel beams, or they might be of more questionable rigidity, such as when plywood floor sheathing is used. In either instance, the design of the overall building would need to include the forces generated by the weight of the floor system, and appropriate structural elements would need to be provided to resist these forces. The method used to distribute these forces to the building system, whether flexible, rigid or envelope would

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Seismic Design Guide for Metal Building Systems

be determined based on comparison of the relative rigidity of the horizontal floor system versus the rigidity of the resisting vertical elements. Because of new limitations placed on ordinary steel systems found in ASCE 7-05 for structures assigned to Seismic Design Categories D, E and F, there are significant changes on what is permitted for metal buildings with more than one floor or with mezzanines. Therefore Example 3 has been completely reworked from that presented in the previous and focuses primarily under what conditions mezzanines of various sizes are permitted with ordinary steel systems. The option of using intermediate moment frames instead of ordinary moment frames is also discussed further in Design Example 3. One option, that is not discussed in Example 3 but which is also permitted, is to design the building and mezzanine as structurally independent structures. Example 3 has provides guidance on when torsional rigidity analysis should be performed to distribute lateral forces but details of the torsional rigidity analysis procedure are not provided. E.

Lower Seismic Area Design Alternative The approach provided in this Guide assumes that the design will utilize the largest R value that is permitted for the structural system being utilized, resulting in the lowest seismic design forces. This means that specific and somewhat stringent detailing requirements of AISC 341-05 are imposed. In the lower areas of seismicity for structures that are classified as Seismic Design Category B or C, the steel building design engineer has the option to design for somewhat higher seismic forces assuming an R = 3 , but ignoring the special detailing requirements. There are several special requirements embedded in the 2006 IBC. These are discussed in Section 1.4.4 of Design Example 1. The advantage of the R = 3 option might be that other loads (such as wind) may govern the design. The R = 3 option may perhaps result in a much simpler design and analysis for such cases without any reduction in economy. In this edition, an R =3 option is provided as one of the approaches described in Design Example 2 which is identified as Design Building A Alternate. 2006 IBC Section 2205.2.2 requires that all structural steel structures assigned to SDC D, E, or F be designed and detailed in accordance with AISC 341-05.

F.

STABILITY ANALYSIS AND DESIGN AISC 360 Chapter C addresses general requirements for the stability analysis and design of members and frames. Any method of analysis and design that considers the following effects is permissible: •

P- effects (frame deformations)

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Seismic Design Guide for Metal Building Systems

•

P- effects (member deformations)

•

Member flexural, shear, and axial deformations

•

Geometric imperfections due to initial frame out-of-plumbness (o)

•

Geometric imperfections due to initial member out-of-straightness (o)

•

Member stiffness reduction from residual stresses

Three approaches are presented for the determination of required strength of member, connections, and other elements: •

Section C2.2a – Second-Order Analysis

•

Section C2.2b – First-Order Analysis

•

Appendix 7 – Direct Analysis

All frame analyses in this document meet the requirements of AISC 360 Section C2.1a, General Second-Order Elastic Method. All frame designs in this document meet the requirements of AISC 360 Section C2.2a, Design By Second-Order Analysis. These requirements should be familiar as the traditional effective length factor (K) approach, with an additional requirement for a minimum lateral load. They are characterized by the following features: •

Notional loads equal to 0.2% of the gravity loads are added to all gravity-only load combinations to account for the initial structure outof-plumbness and to insure that there is some amplification of moments in symmetrical systems.

•

This method may be used as long as 2nd-order / 1sr-order is less than or equal to 1.5. Otherwise, the Direct Analysis Method of AISC 360 Appendix 7 must be used.

•

Columns and beam-columns in moment frames shall be design using an effective length factor (K) greater than 1.0. If 2nd-order / 1sr-order is less than or equal to 1.1, the effective length factor (K) may be taken as 1.0.

•

Columns in braced frames shall be designed for an effective length factor (K) less than or equal to 1.0.

Frame analysis meeting the requirements of AISC 360 Appendix 7, Direct Analysis Method, would also be acceptable.

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Seismic Design Guide for Metal Building Systems

III. Other Significant Issues A.

Advantages in Performing a Geotechnical Investigation For many constructed metal buildings, geotechnical investigations are not performed, and the minimum soil allowables are used for foundation design. However, there may be advantages of performing a geotechnical investigation for a project site, including: •

Determination of the site class of the soil profile of the site. Without this determination, the default value of Site Class D is generally assumed per code, which could result in earthquake design forces being over two times greater than that required if the site class was actually Site Class B. A lower site class may also result in a reduction in a seismic design category for a particular structure, which in turn may mean less restrictive detailing requirements and height limitations. This would result in a lower cost structure and foundation.

•

Determination of site-specific soil bearing values. This determination would usually result in higher allowable bearing pressures than the default values provided in the code, resulting in more economical foundation designs.

•

Detection of soil or foundation problems, which could adversely affect the construction or structural performance of the metal building. These problems could include subsurface areas of weakness, expansive soils, corrosive soils and water table issues. Mitigating these problems, if present, would likely result in a building that performs better over its life.

Note that according to 2006 IBC Section 1613.5.5 (ASCE 7-05 Section 20.1), the site classification is ideally based on site specific soil data to a depth of 100 feet. However, in lieu of data available to that depth, IBC permits the “soil properties to be estimated by the registered design professional preparing the soils report based on known geologic conditions.” Therefore, it is important to request that borings be taken to the necessary depth to comply with this requirement. B.

Relationship and Issues between the Metal Building Supplier and the Building Specifying Engineer Metal building systems are designed and fabricated by manufacturers, then typically sold through franchised builders (or dealers) who also provide erection services. In most cases it is the builder, and not the manufacturer’s engineer, who has a direct relationship with the end customer and the other project designers. This creates a line of communication that often includes

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Seismic Design Guide for Metal Building Systems

nontechnical personnel, a situation that can lead to designs that do not fully satisfy project needs. To avoid such problems, it is vitally important that all project requirements, including design specifications, special loading and applicable code provisions, are clearly communicated to the metal building design engineer. It is equally important that all of the metal building design engineer’s assumptions and output data are communicated to the end customer, the project architect, and the foundation engineer. Furthermore, 2006 IBC Section 1603 requires that the construction documents clearly indicate pertinent structural design information, including earthquake design data. Typically, due to lack of direct contact with the end user, the metal building manufacturer’s engineer is not in a position to serve as the design professional of record for a project. This function must be served by a registered design professional who prepares the design for the foundation and any other structural components or systems and who has a direct relationship with the lead designer or end customer. Additionally the design professional of record has the responsibility to coordinate dimensions and the layout of grid lines, frame lines, and building lines. C.

Relationship and Issues between the Metal Building Supplier and Foundation/Hardwall Engineer As previously stated, it is typical practice to have the foundation and concrete or masonry walls of metal buildings designed by a separate registered design professional. It is very important that the loads imposed by the metal building to a foundation or hardwall are clearly identified to the engineer responsible for their design. Also, the interface details between the building, walls and foundation (bolt type, size, location, spacing and connection details) need to be clearly identified. It is also very important that the hardwall design engineer clearly communicate all applicable design criteria to the metal building engineer. For example if the wall engineer’s design assumes that hardwalls do not behave as shear walls, then special connections need to be provided between the hardwall and the building to accommodate the building lateral in-plane displacement. Conversely, if the wall engineer’s design assumes a hardwall is a shear wall, the shear wall loads imposed by the building need to be communicated to the hardwall engineer so he or she can engineer the hardwall and its foundation for these loads. In general, if hardwalls are being used, they will usually have more than adequate strength to act as shear walls if designed to do so. This would mean different seismic design assumptions and building/wall interface details. It is also important that consistent R values are used between the metal building designer and hardwall engineer. The choice of R affects the seismic 12

Seismic Design Guide for Metal Building Systems

force levels in the overall structure and detailing requirements for the hardwall engineer. This subject is covered in more detail in Design Example 4. Additionally, it must be understood who is taking overall responsibility for the building design for purposes of sealing of drawings and submission to the authority having jurisdiction. The engineer’s seal on the metal building drawings normally only applies to the products furnished or specified by the metal building manufacturer. In general, the wall and foundation engineer acts as the design professional of record and accepts responsibility for the overall work product which includes approval of all building/wall interface details. D.

Hardwall Detailing and Actual Behavior Clear and complete communication between the wall design engineer and the metal building system design engineer are imperative in order to ensure building/wall compatibility and achieve the desired building performance. For example, if a building is located in an area with a relatively high level of seismicity and the hardwalls are not designed as shear walls, building-to-wall connection details must be designed to accommodate the relative displacement between the building and hardwall. Failure to coordinate this issue will almost certainly result in “accidental” loading of building components that were not designed for the resulting level of force. This is not an acceptable situation. The building will resist seismic loads along the stiffest lines of resistance regardless of inconsistent assumptions that may be made by the building and hardwall design engineers. If an earthquake occurs and the connections between the building and hardwall cannot accommodate the relative displacement and do not have the necessary strength and displacement compatibility, the connections will likely fail, creating a falling hazard from the walls and perhaps causing severe torsional problems in the metal building’s lateral load path. This is the reason that there needs to be one engineer who takes overall responsibility for such a building so that assumptions at interfaces are aligned. It is recommended that this person be the wall design engineer, since he or she is the most familiar with the wall design criteria and limitations and is responsible for the wall and foundation design. A common hardwall application in metal buildings is to use a partial height hardwall, sometimes called a wainscot wall. This provides a more durable wall where it might be subject to impacts from vehicles or machinery. This type of hardwall also needs to be properly detailed with regard to seismic loads. If the wall is less than approximately 8 feet in height, it is normally designed as a cantilevered element and is only tied to the wall panel. Taller walls are tied structurally to the frames, but care must be taken to ensure that the wall doesn’t unintentionally brace the building. This can usually be done

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Seismic Design Guide for Metal Building Systems

with simple span girts and oversize holes for the bolts that tie the girt to the wall.

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Seismic Design Guide for Metal Building Systems

DESIGN EXAMPLE 1 Determination of Seismic Design Forces Refer to 2006 IBC, Section 1613, and ASCE/SEI 7-05 including Supplement No. 1, Chapters 11 and 12 for seismic load provisions. The following example looks at a building located in three different geographic sites.

Problem Statement: ....................................................................................................................................... 1-2 Design Example Objective:........................................................................................................................... 1-3 1

Determine Earthquake Design Forces.................................................................................................. 1-4 1.1 Compute Site Ground Motion Design Values ............................................................................ 1-4 1.1.1 Determine the Latitude and Longitude Coordinates for each Site Address............................ 1-4 1.1.2 Determine the Site Class for each Site ................................................................................... 1-5 1.1.3 Determine the Maximum Considered Earthquake Ground Motion Values for each Site....... 1-5 1.1.4 Determine the Site Design Spectral Response Acceleration Parameters................................ 1-6 1.2

Determine the Occupancy Category, Importance Factor, and Seismic Design Category for each Site Building .............................................................................................................................. 1-7 1.2.1 Determine the Building Occupancy Category and Importance Factor................................... 1-7 1.2.2 Determine the Seismic Design Category (SDC) for each Building........................................ 1-7

1.3 Determine the Seismic Base Shear, V, for each Building .......................................................... 1-8 1.3.1 Determine the Approximate Fundamental Period, Ta, for the Example Building .................. 1-8 1.3.2 Determine the Initial Effective Seismic Weight, W, of the Building. .................................... 1-9 1.3.3 Select Design Coefficients and Factors and System Limitations for Basic Seismic-ForceResisting Systems................................................................................................................. 1-11 1.3.4 Determine the Seismic Base Shear, V, for Two-Dimensional Model at each Site............... 1-16 1.4 Determine the Seismic Load Effects, E and Em, for each Building in each Direction.............. 1-24 1.4.1 Determine the Redundancy Coefficient, , for each Direction, at each Site. ....................... 1-24 1.4.2 Determine the Seismic Load Effect, E, for each Building Site and each Direction ............. 1-26 1.4.3 Determine the Maximum Seismic Load Effect, Em, for each Building Site and Direction .. 1-29

1-1

Seismic Design Guide for Metal Building Systems

Problem Statement: Warehouse building, normal occupancy Collateral load = 1.5 psf Ordinary steel concentrically braced frame end walls − w/ tension-only brace rods Ordinary steel concentrically braced frame side walls − w/ tension-only brace rods Ordinary steel moment frame interior frames − w/interior columns No rigid interior partitions or ceilings 65 F

T. 70 F

RO

20 FT.

ROOF SLOPE 1/2 : 12

RO

8@

OF

ROO

BRA CIN

25 F T. =

200

GT HIS

BAY

(NO

FB R AC

TS HO

ING

WN )

T. 65 F T.

OF

TH I SB

BRA

AY (N

CIN G

OT

TH I SB AY

(NO

TS HO

S HO WN )

10

@

25

. FT

=

25

T. 0F

FT.

Metal Building Framing – Design Example 1

Weights for Initial Seismic Loads Roof panel and insulation = 1.5 psf Roof purlin

= 1.0 psf

Wall (including girts)

= 3.0 psf

Frame

= 2.0 psf

1-2

WN )

Seismic Design Guide for Metal Building Systems

Locations Site 1: 67 Winthrop Drive, Chester, CT 06412 Site 2: 2630 East Holmes Road, Memphis, TN 38118 Site 3: 1500 W. Rialto Ave., San Bernardino, CA 92410 Soils Properties Site 1: Unknown, no geotechnical report available Site 2: Unknown, no geotechnical report available Site 3: Geotechnical report is available Design Example Objective: Determine earthquake design forces for the given building.

1-3

Seismic Design Guide for Metal Building Systems

1 1.1

DETERMINE EARTHQUAKE DESIGN FORCES COMPUTE SITE GROUND MOTION DESIGN VALUES On most projects, the end customer or his or her design professional has the responsibility to provide the site ground motion design values. The procedure provided in this section may be used to determine the site ground motion design values by those responsible for making that determination.

1.1.1

Determine the Latitude and Longitude Coordinates for each Site Address The latitude and longitude used in this example were obtained using a website that provides this data for a given address in the United States. A search for current websites that provide this data is recommended because availability and features of these sites change periodically. It is recommended that the latitude and longitude be determined to at least three digits beyond the decimal point (which is accurate to a few hundred feet).

1.1.1.1 Site 1 67 Winthrop Drive, Chester, CT 06412 Latitude

= 41.387 degrees

Longitude = −72.508 degrees 1.1.1.2 Site 2 2630 East Holmes Road, Memphis, TN 38118 Latitude

= 35.007 degrees

Longitude = −89.976 degrees 1.1.1.3 Site 3 1500 W. Rialto Ave., San Bernardino, CA 92410 Latitude

= 34.101 degrees

Longitude = −117.319 degrees

1-4

Seismic Design Guide for Metal Building Systems

1.1.2

Determine the Site Class for each Site

1.1.2.1 Site 1 Soil properties not known Therefore use default – Site Class D as required per IBC Section 1613.5.2 (also in ASCE 7 Section 11.4.2). 1.1.2.2 Site 2 Soil properties not known Therefore use default – Site Class D as required per IBC Section 1613.5.2 (also in ASCE 7 Section 11.4.2). 1.1.2.3 Site 3 A soils report was prepared in accordance with the 1997 UBC and the soil profile was determined to be SD, which is referred to as Site Class D in the IBC and ASCE 7. Note that the 1997 UBC soil profile, the IBC site class, and ASCE 7 site class use the same soil profile classification system. See Section IIIA in the Introduction for more information regarding the potential advantages for performing a geotechnical investigation. 1.1.3

Determine the Maximum Considered Earthquake (MCE) Ground Motion Values for each Site Values of the mapped spectral accelerations for short periods and a 1-second period, SS and S1, can be obtained from either the maps in IBC Figures 1613.5(1) through 1613.5(14), or more accurately from the United States Geological Survey (USGS) website. The website location, http://earthquake.usgs.gov/research/hazmaps/design/, provides a Java Ground Motion Parameter Calculator. This tool utilizes the Java Application language and computes mapped spectral acceleration values for user entered latitude and longitude coordinates. When selecting the parameters to be calculated, the user should select International Building Code as the Analysis Option, and then select the 2006 International Building Code as the Data Edition. The values of SDS and SD1 may be obtained directly from this website. It should be noted that even though one may obtain the calculated values of SDS and SD1 directly from the website in lieu of calculating these values from SS and S1, the procedure for calculating SDS and SD1 is shown below for completeness. Also, if the zip code is used in lieu of more specific latitude and longitude location, the user is cautioned against using the centroid values which may be unconservative. Alternately, it is recommended that the maximum value be used.

1-5

Seismic Design Guide for Metal Building Systems

Also note that a pulldown menu for Geographic Region lets the user select either one of the “48 conterminous states”, Alaska, Hawaii, or other U.S. Territories. Based on the site class, the adjusted maximum considered earthquake spectral response acceleration parameters for short periods, SMS, and at 1-second period, SM1, are defined in IBC Section 1613.5.3 as follows: SMS = FaSS

(IBC Equation 16-37)

SM1 = FvS1

(IBC Equation 16-38)

Where, Fa is the site coefficient defined in IBC Table 1613.5.3(1) Fv is the site coefficient defined in IBC Table 1613.5.3(2) The long-period transition period, TL, is obtained from ASCE 7 Figures 22-15 through 22-20. 1.1.3.1 Site 1 coordinates and Site Class D SS = 22.5%

Fa = 1.60

SMS = 36.0%

S1 = 6.0%

Fv = 2.40

SM1 = 14.4%

TL= 6 seconds 1.1.3.2 Site 2 coordinates and Site Class D SS = 104.9%

Fa = 1.08

SMS = 113.3%

S1 = 29.3%

Fv = 1.81

SM1 = 53.0%

TL= 12 seconds 1.1.3.3 Site 3 coordinates and Site Class D SS = 183.4%

Fa = 1.00

SMS = 183.4%

S1 = 64.8%

Fv = 1.50

SM1 = 97.2%

TL= 8 seconds 1.1.4

Determine the Site Design Spectral Response Acceleration Parameters From IBC Equations 16-39 and 16-40 in Section 1613.5.4 (also in ASCE 7 Equations 11.4-3 and 11.4-4) determine SDS and SD1. The value of the ground motion, expressed as a percentage of g, needs to be converted to a fraction of g at this step by dividing by 100.

1.1.4.1 Site 1

S DS =

2 2 § 36.0 · S MS = ¨ ¸ = 0.240 3 3 © 100 ¹

1-6

Seismic Design Guide for Metal Building Systems

S D1 =

2 2 § 14.4 · SM1 = ¨ ¸ = 0.096 3 3 © 100 ¹

1.1.4.2 Site 2

S DS =

2 2 § 113.3 · S MS = ¨ ¸ = 0.755 3 3 © 100 ¹

S D1 =

2 2 § 53.0 · SM1 = ¨ ¸ = 0.353 3 3 © 100 ¹

1.1.4.3 Site 3

S DS =

2 2 § 183.4 · S MS = ¨ ¸ = 1.223 3 3 © 100 ¹

S D1 =

2 2 § 97.2 · SM1 = ¨ ¸ = 0.648 3 3 © 100 ¹

1.2

DETERMINE THE OCCUPANCY CATEGORY, IMPORTANCE FACTOR, AND SEISMIC DESIGN CATEGORY FOR EACH SITE BUILDING

1.2.1

Determine the Building Occupancy Category and Importance Factor

The building occupancy category is determined per IBC 2006 Table 1604.5 and the importance factor is based on ASCE 7 Section 11.5. Based on the problem description, the buildings at all three sites are warehouses with normal occupancy. Therefore at all sites the building occupancy category is “II” and the seismic importance factor, I, is 1.0. ASCE 7-05 and 2006 IBC use the same notation for the importance factor, I, for earthquake, wind and other loads. Although the importance factors are different, subscripts are not used to distinguish them as has been done in the past. 1.2.2

Determine the Seismic Design Category (SDC) for each Building

The seismic design category (SDC) is based on IBC Tables 1613.5.6(1) and 1613.5.6(2), with occupancy category = II (also in ASCE 7 Tables 11.6-1 and 11.6-2), and the SDS and SD1 site values. The SDC in both tables needs to be determined and the highest SDC is required to be taken as the SDC for the building. 1.2.2.1 Site 1

From IBC Table 1613.5.6(1): SDC = B From IBC Table 1613.5.6(2): SDC = B Therefore the SDC is B 1-7

Seismic Design Guide for Metal Building Systems

1.2.2.2 Site 2

From IBC Table 1613.5.6(1): SDC = D From IBC Table 1613.5.6(2): SDC = D Therefore the SDC is D 1.2.2.3 Site 3

From IBC Table 1613.5.6(1): SDC = D From IBC Table 1613.5.6(2): SDC = D Therefore the SDC is D 1.3

DETERMINE THE SEISMIC BASE SHEAR, V, FOR EACH BUILDING

1.3.1

Determine the Approximate Fundamental Period, Ta, for the Example Building

The approximate fundamental period, Ta, is determined in accordance with ASCE 7 Section 12.8.2.1. The approximate formula given in ASCE 7 Equation 12.8-7 is based on the height of the building. For purposes of this equation, for a building with a sloping roof, the height at the eave of the building should be used. Since the same building configuration is used at all three sites, the approximate fundamental periods are the same at the three sites. The ASCE 7 empirical equation below was developed to provide a lower bound on the structure fundamental period, resulting in a conservative base shear. Ta = CT hnx

(ASCE 7 Eq. 12.8-7)

Where: CT and x are determined from Table 12.8-2 CT = 0.028 and x = 0.8 in the transverse direction where the structural system is steel moment frame. CT = 0.020 and x = 0.75 in the longitudinal direction and the transverse end walls because the structural systems are ordinary steel concentrically braced frames and not ordinary moment frames or ordinary steel eccentrically braced frames. They are therefore classified as “other.” hn = 20 feet, eave height for all frames. Typically in metal buildings, the interior bays are laterally supported in the transverse direction by moment frames and the end walls in the transverse direction are either braced frames or moment frames. In cases where a flexible diaphragm exists between the end walls and the first interior moment frame, separate end wall moment frame periods may be computed. 1-8

Seismic Design Guide for Metal Building Systems

In situations where the exterior walls are hardwalls, designed to be the primary lateral force resisting system (i.e. shear walls), the value of CT and x should be selected based on the hardwall system.

Transverse direction moment frames: Ta = 0.028(20 feet )

0.8

= 0.308 seconds

Transverse direction end walls: Ta = 0.020(20 feet )0.75 = 0.189 seconds

Longitudinal direction: Ta = 0.020(20 feet )0.75 = 0.189 seconds In metal building design, it is common practice to use the above code equations rather than performing a dynamic analysis to determine the building fundamental periods. However, it is also permissible to determine the fundamental periods by dynamic methods or the Rayleigh Method (ASCE 7 Equation 15.4-6). When dynamic analysis methods or Rayleigh methods are used, the resulting period used for determining seismic design base shear forces is limited and cannot be taken as greater than the factor Cu (obtained from ASCE 7 Table 12.8.1) times the approximate period Ta. This limitation on dynamic analysis period does not apply when one is determining drift. Therefore, in certain instances, there may be advantages in obtaining the building fundamental periods using dynamic analysis methods. An approximate dynamic method, treating the moment frame or braced frame as a single degree of freedom system, might be considered to determine the fundamental period: T = 2

m k

where, m is the building mass associated with that frame (expressed as W/g) and k is the lateral stiffness of the frame, calculated by applying a unit load at the eave. The same limitation on T, discussed above, would apply when computing seismic design shear base forces, but not drift. 1.3.2

Determine the Initial Effective Seismic Weight, W, of the Building

The initial effective seismic weight, W, is determined in accordance with ASCE 7 Section 12.7.2. As recommended practice for metal buildings, the effective seismic weights will be determined with the collateral load included. For an initial estimate of the effective seismic weight, either: (1) assume weights per square foot based on historical data or (2) perform an initial trial design where other loads such as wind or snow have been considered and 1-9

Seismic Design Guide for Metal Building Systems

members sized on a preliminary basis. It is usual design practice to proceed with design based on these preliminary weights and to check during the final calculations whether the member weights have changed enough to require a redesign. For this example it is assumed that the initial assumed weights are the same for all three sites. At all sites, the flat roof snow load determined in accordance with ASCE 7 Section 7.3 was less than or equal to 30 psf. Therefore, per subparagraph 4 of ASCE 7 Section 12.7.2, the snow may be neglected when determining the effective seismic weight of the structure. Where the flat roof snow load is greater than 30 psf, the effective seismic weight shall include 20 percent (or as specified by the local building official) of the flat roof snow load added to the weight per square foot of the roof. In this example, the assumed weights per square foot are based on the following provided data.

Assumed Weights for Initial Seismic Loads Roof panel and insulation = 1.5 psf Roof purlin

= 1.0 psf

Wall (including girts)

= 3.0 psf

Frame

= 2.0 psf

Collateral load

= 1.5 psf

It is common practice in metal building design to model the structural system as a series of two-dimensional models. Therefore, separate twodimensional base shears are determined for the typical transverse frame, end walls, and side walls. To accommodate these separate base shears, effective weights have been determined for each frame and wall type. It is also common practice to assume that half of the wall weight acts at the roof level and half at the ground level. It should be noted that wall weight in the direction parallel to the lateral load system being evaluated can be excluded, provided the wall is concrete or masonry and is designed to resist in-plane loads. In other words, the weight of a concrete or masonry side wall can be excluded from the seismic load calculations for longitudinal bracing, provided that details permit unrestrained longitudinal movement of the longitudinal bracing relative to the wall. On the other hand, this exclusion does not apply to metal panel walls, steel studs, wood, EIFS, or other flexible wall systems that are attached to the building frame at several points along the height of the framing system. In this example, metal panel side walls and end walls are used. 1.3.2.1 Transverse Moment Frame Model (One Frame)

Roof Area = (200 ft ) (25 ft ) = 5,000 ft 2 Wall Area = 2(20 ft ) (25 ft ) = 1,000 ft 2 1-10

Seismic Design Guide for Metal Building Systems

Roof Weight = (5,000 ft 2 ) (1.5 + 1.0 + 2.0 + 1.5 psf ) = 30,000 lbs = 30.0 kips

(1,000 ft ) (3.0 psf ) = 1,500 lbs = 1.5 kips 2

Wall Weight =

2

Total Effective Seismic Weight = 30.0 + 1.5 = 31.5 kips 1.3.2.2 Transverse End Wall Model (One End Wall)

§ 25 ft · 2 Roof Area = (200 ft ) ¨ ¸ = 2,500 ft © 2 ¹ § 20 + 24.17 ft · § 25 ft · 2 Wall Area = (200 ft ) ¨ ¸ + 2(20 ft ) ¨ ¸ = 4,917 ft 2 © ¹ © 2 ¹ Roof Weight = (2,500 ft 2 ) (1.5 + 1.0 + 2.0 + 1.5 psf ) = 15,000 lbs = 15.0 kips

(4,917 ft ) (3.0 psf ) = 7,376 lbs = 7.4 kips Wall Weight = 2

2

Total Effective Seismic Weight = 15.0 + 7.4 = 22.4 kips 1.3.2.3 Longitudinal Side Wall Model (One Side Wall)

The longitudinal side wall effective seismic weight is the total of all the transverse frame weights divided by two. Total Effective Seismic Weight = 1.3.3

9(31.5 kips ) + 2(22.4 kips ) = 164.2 kips 2

Select Design Coefficients and Factors and System Limitations for Basic Seismic-Force-Resisting Systems

The design coefficients and factors and system limitations for the basic seismicforce-resisting systems are selected from ASCE 7 Table 12.2-1. In metal buildings, transverse moment frames are typically designed and detailed as ordinary steel moment frames where the basic seismic-forceresisting system is primarily moment frames. Transverse end walls are typically designed as either moment frames or ordinary steel concentrically braced frames. Longitudinal side walls are typically designed as ordinary steel concentrically braced frames, where the basic seismic-force-resisting system is composed of brace rods, cables or braces. Other structural systems could be utilized if conditions warrant. It should be noted that unless the bracing carries gravity loads other than its own weight, a building frame-type system and not a bearing wall-type system should be selected. Minor eccentricities of connections of the type 1-11

Seismic Design Guide for Metal Building Systems

typically found in metal buildings are typically considered as acceptable as ordinary steel concentrically braced frame systems. Some structural systems, particularly cable bracing systems, are quite flexible and may result in drifts that exceed the limits of ASCE 7 Table 12.12-1. Under certain conditions drift limits may be exceeded; see Note “c” of Table 12.12-1. When drift limits are exceeded, seismic detailing of architectural components is required to demonstrate that the anticipated seismic drift can be accommodated. A significant alternative structural system may be considered for buildings assigned to SDC A, B or C, which will be examined for comparison as Site 1 Alternate. These buildings can be designed as “Structural Systems not specifically detailed for seismic resistance” which are identified in ASCE 7 Table 12.2-1, Line H. This option requires using a value of R = 3. While the design seismic forces are higher, the advantage of this alternative is to be able to ignore the AISC 341 seismic design and detailing provisions and to have the option to use the same AISC 360 design provisions that are used for wind load. Note that this option is not permitted for SDC D, E, or F. For this example, the same structural systems are used at all three sites, except for the site 1 alternate values. In previous editions of ASCE 7 and the IBC, for structures assigned to SDC D, E or F restrictions were provided on the values one could use if there were different system on different lines of resistance or in different directions. Section 12.2.3.2 of ASCE 7 now permits separate values to be used on each line of all resistance provided the structure meets the following requirements: 1) Occupancy Category I or II, 2) Two stories or less in height, 3) Utilizes a flexible diaphragm Since the example satisfies all conditions, separate values may be used for the transverse ordinary moment frames and the ordinary concentrically braced frames used for the endwalls. 1.3.3.1 Transverse Direction (Moment Frames)

For ordinary steel moment frames, select from ASCE 7 Table 12.2-1 the following: R = 3.5

Ωo = 3

Cd = 3

Because the metal building diaphragms are typically flexible, Note g of Table 12.2-1 allows for a reduction of Ωo for moment frames. Note g of Table 12.2-1 states that the tabulated value of the overstrength factor, Ωo, may be reduced by subtracting ½ for structures with flexible diaphragms, but shall not be taken as less than 2.0 for any structure. Using this note, one obtains: 1-12

Seismic Design Guide for Metal Building Systems

R = 3.5 Ωo = 2.5 Cd = 3 The beam-to-column connections in ordinary steel moment frames are required to be designed for the lesser of either the flexural strength of the beam or girder (1.1 RyMp) or the “maximum moment that can be delivered by the system.” Alternatively, the connections may meet the requirements for intermediate or special steel moment frames. Since the AISC introduction of the above requirement in 1997 there was no guidance in the AISC or FEMA resources on how to apply it to moment frames with web tapered members. Several rational, yet simple approaches were developed over the years, either to define the maximum moment by using the maximum design earthquake force, Em, provided that the overstrength factor Ωo is taken as 3.0, or by establishing an upper limit on the moment that can be delivered by the system. The 2005 edition of the AISC Seismic Provisions (AISC 341-05) represents a step forward from the previous editions: the User Note clarifies some limits of applicability of the OMF provisions (but not all) while the Commentary provides additional guidance. Of three factors that may limit the maximum moment that can be developed in the beam (Commentary C11.2a.), the third listed option (R = 1) has the most practical value. The approach where the required moment is calculated from seismic forces using the system modification factor R=1 has the same meaning as using the amplified force Em, although the solution with R=1 will produce slightly larger moment (ER=1 / ΩoER=3.5 =1.0 E / (3.0 E/3.5) = 1.167). In either case, the overstrength would be accounted for and the desired frame behavior achieved (primarily elastic, with only minimum inelastic deformations expected). Due to simplicity, this approach with R=1 will be used throughout this manual. Another practical alternative, such as determining the maximum moment from the known strength of the column, or foundation to resist uplift, may be more feasible in other cases. Hence, for optimum design all three options listed in the Commentary could be investigated. MBMA is currently sponsoring research on the seismic behavior of moment frames utilized in metal buildings that is expected to provide additional data that will lead to development of better and more realistic provisions for moment frames that use web-tapered members. 1.3.3.2 Transverse Direction End Walls (Brace Rods)

For ordinary steel concentrically braced frames, select from ASCE 7 Table 12.2-1 the following: R = 3.25

Ωo = 2

Cd = 3.25 1-13

Seismic Design Guide for Metal Building Systems

Note that AISC 341-05, Section 14.2, does not allow tension-only bracing in K, V, or inverted V configurations in ordinary steel concentrically braced frames. 1.3.3.3 Longitudinal Direction Side Walls (Brace Rods)

For ordinary steel concentrically braced frames, select from ASCE 7 Table 12.2-1 the following: R = 3.25

Ωo = 2

Cd = 3.25

Note that AISC 341-05, Section 14.2, does not allow tension-only bracing in K, V, or inverted V configurations in ordinary steel concentrically braced frames 1.3.3.4 Determine Design Coefficients, Factors and System Limitations (height limits) for each Building at each Site Transverse Direction (Moment Frames)

Site 1 Alternate**

Site 1

Site 2

Site 3

*

Max. Height

No Limit

No Limit

65 ft.

65 ft.*

SDC

B

B

D

D

R

3.5

3

3.5

3.5

Ωo

2.5

2.5

2.5

2.5

Cd

3

3

3

3

ASCE 7 Section 12.2.5.6 states: *

Ordinary steel moment frames assigned to Seismic Design Category D or E are permitted in single story buildings to a height of 65 feet where the dead load of the roof does not exceed 20 psf. In addition, the dead weight portion of walls more than 35 feet above the base shall not exceed 20 psf. If these conditions do not exist, such as discussed in Example 3 with a large mezzanine, the structure is not permitted if assigned to Seismic Design Category D or E unless designed as a seismically separate structure or as an intermediate steel moment frame.

The Guide authors interpret the 20 psf roof criteria as the total roof weight divided by the surface area of the roof and the 20 psf wall criteria as the total wall weight above 35 feet divided by the surface area of walls above 35 feet. Also, it is the opinion of the authors that the 20 psf roof criteria is only intended to be compared to dead loads, and not roof load combinations that may include snow loads or live loads. ** ASCE 7 Table 12.2-1 and Section 14.1.2 allows an alternative set of design coefficients and factors for buildings assigned to SDC A, B or C. The last entry in Table 12.2-1, structural steel systems not specifically detailed for seismic resistance excluding cantilever column systems, permits a value of 3 1-14

Seismic Design Guide for Metal Building Systems

to be used for R, Ωo, and Cd. The value of o may be taken as 2.5 since metal building systems are assumed to have flexible diaphragms as noted in Section 1.3.3.1. Using this option, structural steel systems not specifically detailed for seismic resistance, means that AISC 341-05 is not required. This has the significant trade-off benefit of reducing connection seismic design forces while only slightly increasing member seismic design forces. Site 1 of this example will compare both options. Transverse Direction End Walls (Brace Rods)

Site 1

Site 1 Alternate**

Site 2

Site 3

Max. Height

No Limit

No Limit

65 ft.*

65 ft.*

SDC

B

B

D

D

R

3.25

3

3.25

3.25

Ωo

2

2.5

2

2

Cd

3.25

3

3.25

3.25

Longitudinal Direction Side Walls (Brace Rods)

Site 1

Site 1 Alternate**

Site 2

Site 3

*

Max. Height

No Limit

No Limit

65 ft.

65 ft.*

SDC

B

B

D

D

R

3.25

3

3.25

3.25

Ωo

2

2.5

2

2

Cd

3.25

3

3.25

3.25

For gable roofs, a judgment is required as to what building height should be used when comparing to the prescribed height limits. In the previous edition of this Guide, it was suggested that if the roof slope is less than or equal to 10 degrees, it would be permissible to use the eave height, similar to what is done for determining pressure coefficients for wind load design. The eave height is most representative of the point of rigidity in the moment frame. This is also consistent with the assumption made in Section 1.3.1 for determining the fundamental period of the building. For roof slopes greater than 10 degrees, a mean roof height would be more appropriate. It should also be noted that building height is defined in Chapter 5 of IBC for fire classification as “the vertical distance from grade plane to the average height of the highest roof surface,” regardless of roof slope.

1-15

Seismic Design Guide for Metal Building Systems

In this example, since the eave height, 20 ft, is less than the height limits, the basic force resisting systems selected are allowed for all buildings at all sites. 1.3.4

Determine the Seismic Base Shear, V, for Two-Dimensional Model at each Site

V = C sW

(ASCE 7 Eq. 12.8-1)

Where: Cs =

S DS §R· ¨ ¸ ¨I ¸ © ¹

(ASCE 7 Eq. 12.8-2)

Except Cs need not exceed: for T ≤ TL C s =

S D1 §R· T¨ ¸ ©I¹

Cs =

for T > TL

(ASCE 7 Eq. 12.8-3)

S D1TL §R· T 2¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-4)

and Cs shall not be taken less than: C s = 0.01

(ASCE 7 Eq. 12.8-5)

The 2007 Supplement to the 2006 IBC adopted Supplement 2 to ASCE 7-05. Supplement 2 revises ASCE 7-05 Eq. 12-8-5 to now be Cs = 0.44SDSI .

and in addition, if S1 ≥ 0.6, then Cs shall not be taken as less than: Cs =

0.5S1 §R· ¨ ¸ ¨I ¸ © ¹

(ASCE 7 Eq. 12.8-6)

1.3.4.1 Site 1 Summarize Design Parameters

SDS = 0.240 SD1 = 0.096 I = 1.0 TL = 6 seconds

1-16

Seismic Design Guide for Metal Building Systems

Transverse Direction (Moment Frame)

T = Ta = 0.308 seconds W = 31.5 kips R = 3.5 Cs =

S DS 0.240 = = 0.069 § R · § 3.5 · ¸ ¨ ¸ ¨ ¨I ¸ © 1 ¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

S D1 0.096 = = 0.089 §R· § 3.5 · T ¨ ¸ (0.308 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.069 V = C sW = (0.069) (31.5 kips ) = 2.17 kips

(ASCE 7 Eq. 12.8-1)

Transverse Direction End Walls (Brace Rods)

T = Ta = 0.189 seconds W = 22.4 kips R = 3.25 Cs =

S DS 0.240 = = 0.074 § R · § 3.25 · ¸ ¨ ¸ ¨ ¨I ¸ © 1 ¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

0.096 S D1 = = 0.156 § 3.25 · §R· T ¨ ¸ (0.189 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.074 V = C sW = (0.074) (22.4 kips ) = 1.66 kips 1-17

(ASCE 7 Eq. 12.8-1)

Seismic Design Guide for Metal Building Systems

Longitudinal Direction Side Walls (Brace Rods)

T = Ta = 0.189 seconds W = 164.2 kips R = 3.25 Cs =

S DS 0.240 = = 0.074 § R · § 3.25 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

S D1 0.096 = = 0.156 §R· § 3.25 · T ¨ ¸ (0.189 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.074 V = C sW = (0.074) (164.2 kips ) = 12.15 kips

(ASCE 7 Eq. 12.8-1)

1.3.4.2 Site 1 Alternate (Steel Systems Not Specifically Detailed For Seismic Resistance) Summarize Design Parameters

SDS = 0.240 SD1 = 0.096 I = 1.0 TL = 6 seconds Transverse Direction (Moment Frame)

T = Ta = 0.308 seconds W = 31.5 kips R=3 Cs =

S DS 0.240 = = 0.080 § 3· §R· ¨ ¸ ¨ ¸ ¨I ¸ ©1¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL,

1-18

Seismic Design Guide for Metal Building Systems

C s (max ) =

0.096 S D1 = = 0.104 § 3· §R· T ¨ ¸ (0.308 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.080 V = C sW = (0.080) (31.5 kips ) = 2.52 kips

(ASCE 7 Eq. 12.8-1)

Transverse Direction End Walls (Brace Rods)

T = Ta = 0.189 seconds W = 22.4 kips R=3 Cs =

S DS 0.240 = = 0.080 § 3· §R· ¨ ¸ ¨ ¸ ¨I ¸ ©1¹ © ¹

C s (max ) =

(ASCE 7 Eq. 12.8-2)

0.096 S D1 = = 0.169 § 3· §R· T ¨ ¸ (0.189 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.080 V = C sW = (0.080) (22.4 kips ) = 1.79 kips

(ASCE 7 Eq. 12.8-1)

Longitudinal Direction Side Walls (Brace Rods)

T = Ta = 0.189 seconds W = 164.2 kips R=3 Cs =

S DS 0.240 = = 0.080 §R· § 3· ¨ ¸ ¨ ¸ ©I¹ ©1¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL,

1-19

Seismic Design Guide for Metal Building Systems

C s (max ) =

0.096 S D1 = = 0.169 § 3· §R· T ¨ ¸ (0.189 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 1 because S1 < 0.6. Cs = 0.080 V = C sW = (0.080) (164.2 kips ) = 13.14 kips

(ASCE 7 Eq. 12.8-1)

1.3.4.3 Site 2 Summarize Design Parameters

SDS = 0.755 SD1 = 0.353 I = 1.0 TL = 12 seconds Transverse Direction (Moment Frame)

T = Ta = 0.308 seconds W = 31.5 kips R = 3.5 Cs =

S DS 0.755 = = 0.216 § R · § 3.5 · ¸ ¨ ¸ ¨ ¨I ¸ © 1 ¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

S D1 0.353 = = 0.328 §R· § 3.5 · T ¨ ¸ (0.308 sec ) ¨ ¸ ©I¹ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 2 because S1 < 0.6. Cs = 0.216 V = C sW = (0.216) (31.5 kips ) = 6.80 kips Transverse Direction End Walls (Brace-Rods)

T = Ta = 0.189 seconds W = 22.4 kips 1-20

(ASCE 7 Eq. 12.8-1)

Seismic Design Guide for Metal Building Systems

R = 3.25 Cs =

S DS 0.755 = = 0.232 § R · § 3.25 · ¸ ¨ ¸ ¨ ¨I ¸ © 1 ¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

0.353 S D1 = = 0.575 § 3.25 · §R· T ¨ ¸ (0.189 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 2 because S1 < 0.6. Cs = 0.232 V = C sW = (0.232) (22.4 kips ) = 5.20 kips

(ASCE 7 Eq. 12.8-1)

Longitudinal Direction Side Walls (Brace Rods)

T = Ta = 0.189 seconds W = 164.2 kips R = 3.25 Cs =

S DS 0.755 = = 0.232 § R · § 3.25 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL,

C s (max ) =

S D1 0.353 = = 0.575 §R· § 3.25 · T ¨ ¸ (0.189 sec ) ¨ ¸ ©I¹ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for Site 2 because S1 < 0.6. Cs = 0.232 V = C sW = (0.232) (164.2 kips ) = 38.09 kips 1.3.4.4 Site 3 Summarize Design Parameters

SDS = 1.223 SD1 = 0.648 1-21

(ASCE 7 Eq. 12.8-1)

Seismic Design Guide for Metal Building Systems

I = 1.0 TL = 8 seconds Check for limits on Ss from ASCE 7 Section 12.8.1.3.

Note that these limits should be routinely checked, but that it was noted by inspection that they did not govern for Sites 1 or 2. T  0.5 seconds Regular structure less than 5 stories Therefore,

S S = 1.5 , S MS = 1.5 , S DS = 1.00 ≤ SDS = 1.223 It should also be noted that these permitted upper limits for S1 and SDS only apply when determining the base shear and not when determining the seismic design category. Transverse Direction (Moment Frame)

T = Ta = 0.308 seconds W = 31.5 kips R = 3.5 Cs =

S DS 1.00 = = 0.286 § R · § 3.5 · ¸ ¨ ¸ ¨ ¨I ¸ © 1 ¹ © ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL, C s (max ) =

S D1 0.648 = = 0.602 §R· § 3.5 · T ¨ ¸ (0.308 sec ) ¨ 1 ¸ ¨I ¸ © ¹ © ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is applicable for Site 3 because S1 ≥ 0.6. C s (min ) =

0.5S1 0.5(0.648) = = 0.093 §R· § 3.5 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-6)

C s = 0.286 V = C sW = (0.286 ) (31.5 kips ) = 9.01 kips Transverse Direction End Walls (Brace-Rods)

T = Ta = 0.189 seconds 1-22

(ASCE 7 Eq. 12.8-1)

Seismic Design Guide for Metal Building Systems

W = 22.4 kips R = 3.25 Cs =

S DS 1.00 = = 0.308 § R · § 3.25 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL,

C s (max ) =

0.648 S D1 = = 1.057 §R· § 3.25 · T ¨ ¸ (0.189 sec ) ¨ ¸ ©I¹ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is applicable for Site 3 because S1 ≥ 0.6. C s (min ) =

0.5S1 0.5(0.648) = = 0.100 §R· § 3.25 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-6)

C s = 0.308 V = C sW = (0.308) (22.4 kips ) = 6.90 kips

(ASCE 7 Eq. 12.8-1)

Longitudinal Direction Side Walls (Brace Rods)

T = Ta = 0.189 seconds W = 164.2 kips R = 3.25 Cs =

S DS 1.00 = = 0.308 § R · § 3.25 · ¸ ¨ ¸ ¨ ©I¹ © 1 ¹

(ASCE 7 Eq. 12.8-2)

Since T ≤ TL,

C s (max ) =

0.648 S D1 = = 1.057 §R· § 3.25 · T ¨ ¸ (0.189 sec ) ¨ ¸ ©I¹ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is applicable for Site 3 because S1 ≥ 0.6. C s (min ) =

0.5S1 0.5(0.648) = 0.100 = § 3.25 · §R· ¸ ¨ ¨ ¸ © 1 ¹ ©I¹ 1-23

(ASCE 7 Eq. 12.8-6)

Seismic Design Guide for Metal Building Systems

C s = 0.308 V = C sW = (0.308) (164.2 kips ) = 50.57 kips

(ASCE 7 Eq. 12.8-1)

1.4

DETERMINE THE SEISMIC LOAD EFFECTS, E AND EM, FOR EACH BUILDING IN EACH DIRECTION

1.4.1

Determine the Redundancy Coefficient, , for each Direction, at each Site

The redundancy coefficient, , for each direction, at each site, is based on ASCE 7 Section 12.3.4. Therefore,  will be calculated in the longitudinal and transverse directions. In ASCE 7-05, the redundancy coefficient is a function of the percentage loss of lateral story strength assuming a single member or connection loses its lateral seismic force carrying capacity as compared to story strength with all members retaining their capacity. For buildings that have rigid and semi-rigid diaphragms, it is also a function of whether the loss of a single member would result in an extreme torsional irregularity. Since metal buildings are deemed to have flexible diaphragms, a determination of torsional irregularity if a member or connection loses its lateral load carrying capacity is not required. However, since the flexible diaphragm assumption assumes that each line of resistance is independent of the others, it is the interpretation of the guide authors that the redundancy coefficient needs to be determined for each line of resistance, as if that line of resistance was a story. It should be noted that if the roof were designed as a rigid or semi-rigid diaphragm, all seismic force resisting members in all lines of resistance could be considered in the redundancy evaluation. This would more likely result in a lower redundancy factor in some situations but it will mean that all rigid diaphragm analysis considerations would need to be made including torsional analysis. For this guideline document, the diaphragms have been assumed to be flexible. Also note that the redundancy coefficient determination is not required if the SDC assigned to the building is A, B or C, and therefore ρ is taken as 1.0 as noted in ASCE 7, Section 12.3.4.1. The redundancy coefficient determination is no longer a function of the maximum force in any one member; therefore it is no longer a function of transverse frame column fixity conditions except for the situation when there are only one or two bays in the transverse direction. 1.4.1.1 Site 1

SDC B. Per ASCE 7-05 Section 12.3.4.1, the redundancy coefficient, , is 1.0 in both directions. 1-24

Seismic Design Guide for Metal Building Systems

1.4.1.2 Site 2 Transverse Direction – End Walls

SDC D. In the transverse direction, the redundancy coefficient, , is 1.0 if the removal of one diagonal member does not reduce the strength of an end wall line of resistance by more than 33%. Otherwise the redundancy coefficient, , is 1.3. For a metal building system with braced end walls, the situation where  is 1.0 would arise if there were four or more bays of tension-only cross bracing on the line of resistance. For the example building, there are only 2 bays of cross bracing, therefore the redundancy coefficient, , is 1.3. Transverse Direction – Moment Frames

SDC D. In the transverse direction, the redundancy coefficient, , is 1.0 if making one moment connection pinned does not reduce the strength of the moment frame line by more than 33%. Otherwise the redundancy coefficient, , is 1.3. For metal building systems with moment frame lines of resistance, the situation where  is 1.0 would arise if there were four or more moment connections in the line of resistance including column fixity at the base of the columns. For the case where the columns are fixed at the base and assuming one of the beam column joints is pinned, the expected reduction in story strength would be less than 33%. Therefore, a good rule of thumb is if there are four or more moment connections in the line of resistance, the redundancy coefficient, , can be taken as 1.0; otherwise it is 1.3. For the example building, there are only two moment connections in the line of resistance so the redundancy coefficient, , is 1.3. The above rule of thumb is based on the assumption that all moment connections in a line of resistance contribute approximately the same to the story strength. It is generally assumed that for columns fixed at the top and bottom, non-tapered columns will be used, and therefore the rule of thumb above is applicable. Longitudinal Direction – Side Wall

SDC D. In the longitudinal direction, the redundancy coefficient, , is 1.0 if the removal of one diagonal member does not reduce the strength of a side wall line of resistance by more than 33%. Otherwise the redundancy coefficient, , is 1.3. For a metal building system, with braced side walls, the situation where  is 1.0 would arise if there were four or more bays of tension-only cross bracing on the line of resistance. For the example there are only three bays of tensiononly cross bracing. Therefore, the redundancy coefficient, , is 1.3.

1-25

Seismic Design Guide for Metal Building Systems

1.4.1.3 Site 3

SDC D. Determination of the redundancy coefficient, , is the same as for Site 2. 1.4.2

Determine the Seismic Load Effect, E, for each Building Site and each Direction

E h = ρQE

(ASCE 7 Eq. 12.4-

E v = 0.2S DS D

(ASCE 7 Eq. 12.4-

3) 4) Stated in more commonly used terms: E = Eh + Ev

(ASCE 7 Eq. 12.4-

E = E h − Ev

(ASCE 7 Eq. 12.4-

1) 2) Where: Eh = the effect of horizontal seismic forces Ev = the effect of vertical seismic forces QE = V or Fp as defined in Chapter 12 of ASCE 7. (Note in the sections that follow, V is substituted for QE) Note that Ev is permitted to be taken as zero when SDS ≤ 0.125 per ASCE 7 Section 12.4.2.2. Strictly speaking, E (and for that matter Em) is not actually a load which is applied to a structure like V, but the resultant effect of combined earthquake loads (an effect is an internal member force, stress, unity ratio, etc.). This combination of earthquake load effects is to be combined with the effects from other loads, such as dead and live loads, in accordance with the load combinations of Chapter 2 of ASCE 7-05. However, from a user standpoint, since we typically do elastic static analysis for all loads, the combined effect can be treated as either a load or load combination because by elastic superposition the results will be the same. This is the approach the authors have adopted in this Guide. 1.4.2.1 Site 1

Summarize Design Parameters On One Frame Line Seismic Design Category = B (ρ = 1.0) SDS = 0.240 V transverse direction (moment frame) = 2.17 kips 1-26

Seismic Design Guide for Metal Building Systems

V transverse direction end walls (brace rods) = 1.66 kips V longitudinal direction side walls (brace rods) = 12.15 kips

ρ transverse end wall = 1.0 ρ transverse moment frame = 1.0 ρ longitudinal = 1.0 Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

E h = ρV = (1.0) (2.17 kips ) = 2.17 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

E h = ρV = (1.0) (1.66 kips) = 1.66 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Longitudinal Direction Side Walls (Brace Rods) Applied Horizontal Force:

E h = ρV = (1.0) (12.15 kips) = 12.15 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

1.4.2.2 Site 1 Alternate (Steel Systems Not Specifically Detailed For Seismic Resistance)

Summarize Design Parameters On One Frame Line Seismic Design Category = B (ρ = 1.0) SDS = 0.240 V transverse direction (moment frame) = 2.52 kips V transverse direction end walls (brace rods) = 1.79 kips V longitudinal direction side walls (brace rods) = 13.14 kips

ρ transverse end wall = 1.0 ρ transverse moment frame = 1.0 ρ longitudinal = 1.0 Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

E h = ρV = (1.0 ) (2.52 kips ) = 2.52 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

1-27

Seismic Design Guide for Metal Building Systems

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

E h = ρV = (1.0) (1.79 kips) = 1.79 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Longitudinal Direction Side Walls (Brace Rods) Applied Horizontal Force:

E h = ρV = (1.0) (13.14 kips) = 13.14 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

1.4.2.3 Site 2

Summarize Design Parameters On One Frame Line Seismic Design Category = D SDS = 0.755 V transverse direction (moment frame) = 6.80 kips V transverse direction end walls (brace rods) = 5.20 kips V longitudinal direction side walls (brace rods) = 38.09 kips

ρ transverse end wall = 1.3 ρ transverse moment frame = 1.3 ρ longitudinal = 1.3 Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

E h = ρV = (1.30) (6.80 kips ) = 8.84 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

E h = ρV = (1.30) (5.20 kips) = 6.76 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

Longitudinal Side Wall Model (One Side Wall) Applied Horizontal Force:

E h = ρV = (1.30) (38.09 kips) = 49.52 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

1.4.2.4 Site 3

Summarize Design Parameters On One Frame Line Seismic Design Category = D

1-28

Seismic Design Guide for Metal Building Systems

SDS = 1.00 V transverse direction (moment frame) = 9.01 kips V transverse direction end walls (brace rods) = 6.90 kips V longitudinal direction side walls (brace rods) = 50.57 kips

ρ transverse end wall = 1.3 ρ transverse moment frame = 1.3 ρ longitudinal = 1.3 Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

E h = ρV = (1.30) (9.01 kips ) = 11.71 kips

Applied Vertical Force:

Ev = ±0.2 S DS D = ±0.2(1.00)D = ±0.200 D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

E h = ρV = (1.30) (6.90 kips) = 8.97 kips

Applied Vertical Force:

Ev = ±0.2 S DS D = ±0.2(1.00)D = ±0.200 D

Longitudinal Side Wall Model (One Side Wall)

1.4.3

Applied Horizontal Force:

E h = ρV = (1.30) (50.57 kips) = 65.74 kips

Applied Vertical Force:

Ev = ±0.2 S DS D = ±0.2(1.00)D = ±0.200 D

Determine the Maximum Seismic Load Effect, Em, for each Building Site and each Direction

Em = Emh + Ev = Ω o QE + 0.2S DS D

(ASCE 7 Eq. 12.4-5)

Em = Emh − Ev = Ω o QE − 0.2 S DS D

(ASCE 7 Eq. 12.4-6)

Where: Emh = the maximum effect of horizontal seismic forces with overstrength factor included Ev =

the effect of vertical seismic forces

In the previous edition of the AISC Seismic Provisions, the maximum seismic load effect load combinations were different than the IBC. In AISC 341-05 this has been changed to make it clear that the load combinations in the applicable building codes shall be used. Note that for buildings in SDC A, B, or C, the maximum seismic load effects, Em, are not required except for the following: 1-29

Seismic Design Guide for Metal Building Systems

•

IBC 1605.1, which references ASCE 7 Section 12.10.2.1, requires Em for collectors in SDC C, D, E, and F.

•

IBC 1605.1, which references ASCE 7 Section 12.3.3.3, requires Em for elements supporting discontinuous walls or frames in SDC B, C, D, E, and F.

The above requirements apply regardless of the R factor used in the design. Summarize Design Parameters

Ωo transverse direction (moment frame) = 2.5* Ωo transverse direction end walls (brace rods) = 2.0 (2.5 for Site 1 Alternate) Ωo longitudinal direction side walls (brace rods) = 2.0 (2.5 for Site 1 Alternate) *

For determining the “the maximum force that can be delivered by the system” for purposes of designing the beam-to-column moment connection, the value of Ωo shall be taken as 3.5 (see the discussion in Sections 1.3.3.1 and 1.4.4.2). 1.4.3.1 Site 1

Summarize Design Parameters On One Frame Line SDS = 0.240 V transverse direction (moment frame) = 2.17 kips V transverse direction end walls (brace rods) = 1.66 kips V longitudinal direction side walls (brace rods) = 12.15 kips Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

Emh = Ω oV = (2.5) (2.17 kips ) = 5.43 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

Emh = Ω oV = (2.0) (1.66 kips) = 3.32 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Longitudinal Side Wall Model (One Side Wall)

Applied Horizontal Force:

Emh = Ω oV = (2.0) (12.15 kips ) = 24.30 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

1-30

Seismic Design Guide for Metal Building Systems

1.4.3.2 Site 1 Alternate

Summarize Design Parameters On One Frame Line SDS = 0.240 V transverse direction (moment frame) = 2.52 kips V transverse direction end walls (brace rods) = 1.79 kips V longitudinal direction side walls (brace rods) = 13.14 kips Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

Emh = Ω oV = (2.5) (2.52 kips ) = 6.30 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.240 )D = ±0.048D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

Emh = Ω oV = (2.5) (1.79 kips) = 4.48 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

Longitudinal Side Wall Model (One Side Wall)

Applied Horizontal Force:

Emh = Ω oV = (2.5) (13.14 kips) = 32.85 kips

Applied Vertical Force:

E v = ±0.2S DS D = ±0.2(0.240)D = ±0.048D

1.4.3.3 Site 2

Summarize Design Parameters On One Frame Line SDS = 0.755 V transverse direction (moment frame) = 6.80 kips V transverse direction end walls (brace rods) = 5.20 kips V longitudinal direction side walls (brace rods) = 38.09 kips Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

Emh = ΩoV = (2.5) (6.80 kips ) = 17.00 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

Emh = ΩoV = ( 2.0) (5.20 kips ) = 10.40 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

1-31

Seismic Design Guide for Metal Building Systems

Longitudinal Side Wall Model (One Side Wall) Applied Horizontal Force:

Emh = Ω oV = (2.0) (38.09kips) = 76.18 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(0.755)D = ±0.151D

1.4.3.4 Site 3

Summarize Design Parameters On One Frame Line SDS = 1.00 V transverse direction (moment frame) = 9.01 kips V transverse direction end walls (brace rods) = 6.90 kips V longitudinal direction side walls (brace rods) = 50.57 kips Transverse Moment Frame Model (One Frame) Applied Horizontal Force:

Emh = Ω oV = (2.5) (9.01kips ) = 22.53 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(1.00)D = ±0.200 D

Transverse End Wall Model (One End Wall) Applied Horizontal Force:

E mh = Ω oV = (2.0) (6.90 kips) = 13.80 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(1.00)D = ±0.200 D

Longitudinal Side Wall Model (One Side Wall)

1.4.4

Applied Horizontal Force:

E mh = Ω oV = (2.0) (50.57 kips) = 101.14 kips

Applied Vertical Force:

Ev = ±0.2S DS D = ±0.2(1.00)D = ±0.200 D

Elements Designed Using Seismic Force Effects, E and Em

The seismic force effects, E and Em, defined in Sections 1.4.2 and 1.4.3 should be used to design the following elements for all seismic design categories except SDC A (all 3 sites). 1.4.4.1 ASCE 7 Sections Requiring Use of the Em Load Combination

The following ASCE 7-05 Sections require the use of the Em load combination: 1. ASCE 7 Section 12.10.2.1 − Collector elements, splices, and their connections to resisting elements. 2. ASCE 7 Section 12.3.3.3 − Elements supporting discontinuous walls or frames.

1-32

Seismic Design Guide for Metal Building Systems

1.4.4.2 AISC Seismic Provisions (341-05) Requiring Use of the Em Load Combination

AISC 341-05 applies where the code specified seismic response modification coefficient, R, for steel structures is greater than 3.0, unless specifically required by the IBC. It should be noted that AISC 341-05 would also apply for cantilever column systems where R is less than 3 for SDC B, C, D, E or F. Note that AISC 341-05 eliminated Part III which contained the rules for Allowable Stress Design to LRFD (strength) conversion. This latest edition still allows two strength based design methods; Allowable Strength Design (new ASD) and LRFD. However, all affected provisions in Part I were rewritten in the dual format (new ASD and LRFD), which assumes the use of the matching load combinations from the Applicable Building Code (e.g. 2006 IBC). If the option is taken to design the structure using R = 3 and Ωo = 3, and to not include seismic detailing, then the additional requirements of AISC 341-05 do not apply, but the ASCE 7 Sections 12.10.2.1 and 12.3.3.3 noted above must still be included in the design. The following provisions of AISC 341-05 require the use of the Em load combination: 1. AISC 341-05, Section 8.3 − Column Strength The following provisions for column axial strength (shown here in the ΩP ASD format) are only required to be met when c a > 0.4. Note that Ωc Pn is 1.67 for ASD and Pa is the required axial strength of a column using ASD load combinations (without consideration of the amplified seismic load). a) Axial tensile strength, considered in the absence of any applied moment, except that it need not exceed the maximum expected strength of the foundation to resist uplift, as stated in Section 8.3(2) (b). Note that this provision inherently presumes that the tensile strength of the foundation anchor rods is sufficient to carry the full foundation weight. A separate provision in Section 8.5 specifies that anchor rods should be designed using the same load combinations used for the attached structure elements, including amplified seismic loads for shear, if applicable. b) Axial compressive strength, considered in the absence of any applied moment, except that it need not exceed the limits on the required compressive strength based on the nominal strengths of the connecting beam or brace elements, as stated in Section 8.3(2)(a). 1-33

Seismic Design Guide for Metal Building Systems

2. AISC 341-05, Section 8.4a – Column Splices. A column splice is a field connection which is either bolted, welded, or a combination of both. These splices need to be designed for the amplified forces determined at the location of the splice. 3. AISC 341-05, Section 8.5b – Required Shear Strength of Columns at Column Bases. Note that this provision applies to both pinned and fixed base columns. 4. AISC 341-05, Section 8.5c – Required Flexural Strength of Columns at Column Bases. Note that this provision only applies to fixed base columns. 5. AISC 341-05, Section 14.4 – Ordinary Steel Concentrically Braced Frames Ordinary steel concentrically braced frame systems, for the connections of braces, as stated in Section 14.4. However, the force need not exceed the maximum force that can be transferred by either the brace or structure system (see Exceptions in Section 14.4). 6. AISC 341-05, Section 11.2a - Ordinary Steel Moment Frame Beam-toColumn Connections The beam-to-column connections of ordinary steel moment frames are required to be designed for the lesser of either the flexural strength of the beam or girder (1.1RyMp) or the maximum moment that can be delivered by the system (See Section 1.3.3.1 for further discussion). Alternatively, the connections may meet the requirements for intermediate or special steel moment frames. 1.4.4.3 Elements Designed Using Seismic Load Effects, E

The seismic load effects, E, defined in Section 1.4.2, should be used to design all other elements, not listed above in Section 1.4.4.2, for all seismic design categories except SDC A (all 3 sites). However, in AISC 341-05, Sections 13.4a and 14.4a, only the special design requirements apply for beams intersected by bracing members.

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Seismic Design Guide for Metal Building Systems

DESIGN EXAMPLE 2 Design of Frames, Columns, Bracing and Other Elements of the Lateral-Force-Resisting System This example illustrates how the seismic design loads developed in Design Example 1 are applied for the design of frames, columns, bracing and other elements of the lateral-forceresisting system.

Problem Statement: ..................................................................................................................................... 2-3 Design Example Objective .......................................................................................................................... 2-4 2 Design of Typical Members and Connections........................................................................................ 2-5 2.1 General Design Guidance – Typical Members and Connections ............................................. 2-5 2.1.1 Structural Analysis .............................................................................................................. 2-5 2.1.2 Diaphragm Flexibility and Torsion...................................................................................... 2-6 2.1.3 Alternate Bracing Concepts and Modeling.......................................................................... 2-6 2.1.4 2006 IBC Load Combinations ............................................................................................. 2-8 2.1.5 Determination of the Earthquake Loads, E and Em.............................................................. 2-8 2.1.6 AISC Seismic Provisions (341-05)...................................................................................... 2-9 2.1.7 Treatment of Collateral Loads, C ...................................................................................... 2-10 2.1.8 Allowable Strength Load Combinations............................................................................ 2-10 2.1.9 Alternate Basic ASD Load Combinations ......................................................................... 2-11 2.2 Design Building A (R > 3) ..................................................................................................... 2-13 2.2.1 Structural Analysis Models ................................................................................................ 2-13 2.2.2 Design Earthquake Forces.................................................................................................. 2-14 2.2.3 Member Forces................................................................................................................... 2-15 2.2.4 Seismic Analysis Results Summary for Horizontal Displacements ................................... 2-17 2.2.5 Basic Load Case Analysis Results Summary for Member Forces ..................................... 2-17 2.2.6 Story Drift Checks.............................................................................................................. 2-18 2.2.7 Basic Load Combinations .................................................................................................. 2-22 2.2.8 Allowable Strength Seismic Load Combinations with Overstrength Factor...................... 2-22 2.2.9 Design of Diaphragm Systems Including Horizontal Roof Bracing .................................. 2-23 2.2.10 Determination of Diaphragm Seismic Weights Including Horizontal Bracing .................. 2-26 2.2.11 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-27 2.2.12 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-27 2.2.13 Design of Side Wall OCBF................................................................................................ 2-31 2.2.14 Design of End Wall OCBF................................................................................................. 2-36 2.2.15 Design of Ordinary Moment Frames.................................................................................. 2-39 2.3 Design Building A – Alternate Design (R = 3) ...................................................................... 2-42 2.3.1 Structural Analysis Models ................................................................................................ 2-42 2.3.2 Design Earthquake Forces.................................................................................................. 2-43 2.3.3 Member Forces................................................................................................................... 2-44 2.3.4 Seismic Analysis Results Summary for Horizontal Displacements ................................... 2-46 2.3.5 Basic Load Case Analysis Results Summary for Member Forces ..................................... 2-46 2.3.6 Story Drift Checks.............................................................................................................. 2-46 2.3.7 Basic Load Combinations .................................................................................................. 2-50

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Seismic Design Guide for Metal Building Systems

2.3.8 Allowable Strength Seismic Load Combinations With Overstrength Factor..................... 2-51 2.3.9 Design of Diaphragm Systems Including Horizontal Roof Bracing .................................. 2-51 2.3.10 Determination of Diaphragm Seismic Weights Including Horizontal Bracing .................. 2-54 2.3.11 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-55 2.3.12 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-55 2.3.13 Design of Side Wall ........................................................................................................... 2-60 2.3.14 Design of End Wall ............................................................................................................ 2-64 2.3.15 Design of Moment Frames ................................................................................................. 2-66 Final Drift Check ............................................................................................................................. 2-68 2.4 Design Building B .................................................................................................................. 2-69 2.4.1 Structural Analysis Models ................................................................................................ 2-69 2.4.2 Design Earthquake Forces.................................................................................................. 2-70 2.4.3 Member Forces................................................................................................................... 2-71 2.4.4 Seismic Analysis Results Summary for Horizontal Displacements ................................... 2-72 2.4.5 Basic Load Case Analysis Results Summary for Member Forces ..................................... 2-73 2.4.6 Story Drift Checks.............................................................................................................. 2-73 2.4.7 Basic Load Combinations .................................................................................................. 2-77 2.4.8 Allowable Strength Seismic Load Combinations with Overstrength Factor...................... 2-78 2.4.9 Design of Diaphragm Systems Including Horizontal Roof Bracing .................................. 2-78 2.4.10 Determination of Diaphragm Seismic Weights Including Horizontal Bracing .................. 2-81 2.4.11 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-82 2.4.12 Determination of Diaphragm Element Design Forces Including Horizontal Bracing........ 2-82 2.4.13 Design of Side Wall OCBF................................................................................................ 2-87 2.4.14 Design of End Wall OCBF................................................................................................. 2-91 2.4.15 Design of Ordinary Moment Frames.................................................................................. 2-95 2.5 Beam-to-Column Connection Design .................................................................................... 2-99 2.5.1 Design Building A ........................................................................................................... 2-100 2.5.2 Design Building B ........................................................................................................... 2-107 2.6

Column Base and Anchor Bolt Design................................................................................. 2-108

2.7 Foundation Forces for Foundation Design ........................................................................... 2-110 2.7.1 End Wall Columns with Bracing Connected to the Top and Bottom .............................. 2-111 2.7.2 End Wall Columns without Bracing Connected to the Top and Bottom ......................... 2-111 2.7.3 Exterior Rigid Frame Columns with Bracing Connected to the Top and Bottom .......... 2-112 2.7.4 Exterior Rigid Frame Columns without Bracing Connected to the Top and Bottom ...... 2-113 2.7.5 Interior Rigid Frame Columns......................................................................................... 2-114 2.8 Welding Issues and Quality Assurance Requirements ......................................................... 2-115 2.8.1 Welding Issues................................................................................................................. 2-115 2.8.2 Quality Assurance............................................................................................................ 2-116 2.9

Approved Steel and Welding Material ................................................................................. 2-118

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Seismic Design Guide for Metal Building Systems

Problem Statement: The building configuration and matches that provided in Design Example 1.

Metal Building Framing – Design Example 2 Two sets of building designs from Design Example 1 are further developed. Design Building A Design Building A is located at Site 1: 67 Winthrop Drive, Chester CT 06412. Note that since Design Building A has been identified as SDC B in Example 1, it will be evaluated using two options: a. Using seismic force resisting systems with R > 3.0 and AISC 341-05 b. Alternate Design – Using structural steel systems not specifically detailed for seismic resistance with R = 3.0, and AISC 341-05 is not required Note that Design Building A is identical to the building used in Example 1. Design Building B Design Building B is located at Site 3: 1500 W. Rialto Ave., San Bernardino, CA 92410.

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Seismic Design Guide for Metal Building Systems

Note that Design Building B is different with respect to the building used in Example 1 in that the interior columns are fixed at the base, affecting the redundancy factor. Material properties of steel plate and sheet used in this example for primary beams and columns have a minimum specified yield stress of 50 ksi, except, HSS columns have a minimum specified yield stress of 46 ksi, and rod bracing has a minimum specified yield stress of 50 ksi. For a discussion on approved steels and weld material for seismic forceresisting systems, see Section 2.14. Design Example Objective: Using the seismic design loads developed in Design Example 1, show how the design loads are applied for the design of frames, bracing and other typical members of a seismic force-resisting system. In addition, design typical members and connections in accordance with 2006 IBC and AISC 341-05.

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Seismic Design Guide for Metal Building Systems

2

DESIGN OF TYPICAL MEMBERS AND CONNECTIONS

2.1

GENERAL DESIGN GUIDANCE – TYPICAL MEMBERS AND CONNECTIONS

2.1.1

Structural Analysis The analysis procedures that are permitted for structural design are specified in Section 12.6 and Table 12.6-1 of ASCE 7. For structures assigned to SDC A, B, and C, there are no restrictions on analysis procedures. For some structures assigned to SDC D, E, and F, depending upon the height, occupancy, period, or system regularity of the structure, dynamic analysis procedures may be required. For the typical metal building configurations, such as found in this example, equivalent lateral force analyses are permitted by Section 12.6. It is common practice in metal building design to model the structural system as a series of two-dimensional models, i.e. flexible diaphragm assumption (See Subsection II.D of the Introduction to this Guide for further discussion). Separate models are typically developed for individual transverse moment frames, and end wall and side wall braced frames. Additional models may be developed if the structural systems of the frames or walls vary. For this example it is assumed the systems are the same.

2.1.1.1 Transverse Moment Frame Models (Interior Frames 2-10) Because there are two interior moment frame designs (Design Building A and B) being considered, i.e. frames without and with interior column fixity, respectively, two different frame models are required. The seismic load is applied at both ends of the frame because it more closely portrays the actual locations of the seismic inertial forces. An even more accurate application would be to apply tributary loads at discrete points along the member. Applying the seismic load at one end only is overly conservative, and will result in very conservative beam axial loads. 2.1.1.2 Transverse End Wall Model (Frames 1 and 11) The end walls of both Design Buildings A and B have the same basic structural system; therefore, the same analysis model can be used for both designs. The seismic load is applied at both sides of the end wall because it more closely portrays the actual locations of the seismic inertial forces. An even more accurate application would be to apply tributary loads at discrete points along the member. Applying the seismic load at one side only is overly conservative and will result in very conservative beam axial loads. 2.1.1.3 Longitudinal Side Wall Model The seismic load is applied at both ends of the side wall because it more closely portrays the actual locations of the seismic inertial forces. Applying the seismic load at one end only is overly conservative and will result in very conservative

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Seismic Design Guide for Metal Building Systems

beam axial loads. An even more accurate application would be to apply tributary loads at each frame line. 2.1.2

Diaphragm Flexibility and Torsion The approach used for roof diaphragm rigidity (flexible vs. rigid) and torsion (both inherent and accidental) is discussed in Subsection II.D of the Introduction to this Guide. Since a flexible diaphragm assumption is used in this example, redistribution of horizontal forces associated with torsional effects is not applicable per ASCE 7 Section 12.8.4.

2.1.3

Alternate Bracing Concepts and Modeling In some cases, it may be necessary or desirable to utilize alternative bracing concepts for metal building lateral-force-resisting systems. Alternative concepts include moment frames instead of x-bracing, fixed base columns instead of xbracing, cable x-bracing instead of rod x-bracing, and metal wall panels instead of rod x-bracing. This section provides discussion on how the structural models would be modified for these different alternatives.

2.1.3.1 Moment Frames Instead of X-Bracing If one uses different structural systems, the earthquake design forces need to be reevaluated to determine whether they are still valid. The structural period, Rvalues and redundancy factor may all change, causing a change in the earthquake design forces.

V/2

V/2

OR

OR

Eh/2

Eh/2

OR

OR

Emh/2

Emh/2

Figure 2.1-1 End Wall Moment Frame Alternative V/2

V/2

OR

OR

Eh/2

Eh/2

OR

OR

Emh/2

Emh/2

Figure 2.1-2 Side Wall Moment Frame Alternative 2.1.3.2 Fixed Base Columns Instead of X-Bracing If one uses different structural systems, the earthquake design forces need to be reevaluated to determine whether they are still valid. The structural period, R-

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Seismic Design Guide for Metal Building Systems

values and redundancy factor may all change, causing a change in the earthquake design forces.

V/2

V/2

OR

OR

Eh/2

Eh/2

OR

OR

Emh/2

Emh/2

Figure 2.1-3 End Wall Fixed Base Column Alternative V/2

V/2

OR

OR

Eh/2

Eh/2

OR

OR

Emh/2

Emh/2

Figure 2.1-4 Side Wall Fixed Base Column Alternative

2.1.3.3 Cable X-Bracing Instead of Rod X-Bracing The structural model for cable x-bracing is essentially identical as rod xbracing. AISC 341-05 does not list steel cable as an approved material, as noted in the User Note of Section 6.1, because AISC only covers the material properties of those steel components included in the definition of structural steel in the AISC Code of Standard Practice. However, this does not preclude the use of cable x-bracing as part of the seismic-forceresisting-system, as noted in the AISC 341-05 User Note of Section 14.2. However, it is the opinion of the authors that restrictions should be placed on using cable bracing in areas of high seismicity because of the lack of inelastic behavior inherent in steel cables. Therefore, the recommendation is to limit cable bracing in SDC D or E to buildings with heights less than 15 feet, and to use an R = 0.5. Cable bracing should not be used in buildings in SDC F. 2.1.3.4 Metal Wall Panels Instead of Rod X-Bracing Some metal building manufacturers elect to use metal wall panels as shear panels instead of rod x-bracing for end walls and/or side walls. The IBC does not currently include metal wall panels as seismic resisting systems except as provided for in Section 2211 for light-framed, cold-formed steel walls.

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Seismic Design Guide for Metal Building Systems

Therefore, unless the construction is as defined in Section 2211, metal wall panels may only be used as shear panels in Seismic Design Categories A, B, or C with the structural system specified as one not specifically detailed for seismic design resistance, with the R-value equal to 3. The structural model should be identical to that used for wind loads. While not specifically permitted, it is the opinion of the authors that metal wall panels may be used in structures assigned to SDC D and E provided an R = 1 is used in the design and the height is limited to 15 feet. It would be prudent to have this option reviewed and approved by the authority having jurisdiction. 2.1.4

2006 IBC Load Combinations In the 2006 IBC, load combinations are defined in Section 1605. There is one set of load combinations to be used with Load Resistance and Factor Design (LRFD). There are two sets of load combinations that are provided for use with ASD. Note that IBC and ASCE 7 refer to Allowable Stress Design with regard to these combinations, whereas AISC 341-05 is now based on Allowable Strength Design. The ASD load combinations in Section 1605.3.1 are more compatible with the AISC Allowable Strength Design than are the ASD load combinations in Section 1605.3.2, because AISC ASD does not permit increases in allowables. In addition there is one set of special seismic load combinations in IBC Section 1605.4 that is to be used with both LRFD and ASD for the design of certain elements and components. Note that the 2006 IBC provides only the provisions up to the determination of the Seismic Design Category, and all other provisions are referenced to ASCE 7. It should be noted that for this example, roof live loads were not provided since they are not required to be included in load combinations which include seismic loads. Roof live loads are not required in either the LRFD load combinations or the alternate ASD load combinations because of the low probability of roof live loads occurring simultaneously with earthquake loads. The authors are of the opinion that the basic ASD load combinations currently provided in IBC and ASCE 7 need to be revised to reflect this same logic.

2.1.5

Determination of the Earthquake Loads, E and Em In the IBC load combinations, the earthquake loads are defined by two load effects, E and Em. These load effects are defined in IBC Section 1602, and further cross-referenced to ASCE 7 Sections 12.4.2 and 12.4.3, respectively. They also were previously defined in Design Example 1 and are repeated below: E = ρQ E ± 0.2S DS D

(ASCE 7 Eqs. 12.4-1 through 12.4-4)

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Seismic Design Guide for Metal Building Systems

E m = Ω o QE ± 0.2 S DS D

(ASCE 7 Eqs. 12.4-5 through 12.4-7)

The second term is actually a vertically applied load and should be added to the dead load. To provide clarity for this example, the seismic load definitions, E and Em have been defined in more commonly understood terms as E = E h + Ev E m = E mh + E mv The values of the above terms, determined in Design Example 1, have been repeated in Design Example 2 in Sections 2.2.2, 2.3.2, and 2.4.2. The lateral load analysis for member forces is done based on Eh and Emh. 2.1.6

AISC Seismic Provisions (341-05) AISC 341-05 is written in a unified format that addresses both Load Resistance Factor Design (LRFD) and Allowable Strength Design (ASD). Note that in the previous edition of this Guide the strength design load factors were used because the AISC Seismic Provisions (1997) did not allow choice between design methods for steel structures assigned to high SDC. LRFD was the only method permitted. For users of ASD format, AISC provided the conversion factors in Part III of the Seismic Provisions, so the allowable stress capacities in the AISC Seismic Provisions (1997) would be calibrated to strength load combinations. In the 2005 AISC Seismic Provisions, Part III was eliminated since the allowable strength capacities have been calibrated to the basic allowable stress combinations of the 2006 IBC and ASCE 7-05. While either LRFD or ASD design is permitted, for this example ASD design is utilized. Therefore, the ASD load combinations are presented instead of LRFD load combinations that were presented in the previous Guide. AISC 341-05 provides the nominal strength, and then the appropriate required strength is determined, depending on the design method used. For LRFD, the design shall be performed in accordance with: Ru ≤ φRn where Ru = required strength (LRFD) Rn = nominal strength

φ = resistance factor For ASD, the design shall be performed in accordance with: Ra ≤ Rn / Ω where 2-9

Seismic Design Guide for Metal Building Systems

Ra = required strength (ASD) Rn = nominal strength

Ω = safety factor Recognizing that most metal buildings are currently design using ASD, this Guide will use that design basis of AISC 341-05, where appropriate. 2.1.7

Treatment of Collateral Loads, C For metal building seismic designs, collateral loads are treated as follows: 1. The collateral load is treated as a dead load for load combinations where the maximum downward load is required, or 2. The collateral load is treated as a live load for load combinations where the minimum downward load is required.

2.1.8

Allowable Strength Load Combinations As previously discussed in Section 2.1.4, IBC Basic Allowable Stress Design Load Combinations are compatible with the AISC Allowable Strength Design. These load combinations are listed in this section and are used as the basis for design in this document. It should be noted that only the load combinations that include seismic loads are included and that other load combinations may govern the design.

2.1.8.1 Basic Load Combinations The ASCE 7 allowable strength seismic load combinations in Section 12.4.2.3 are identical to those in IBC, but presented in a more user friendly format. The applicable ASCE 7 load combinations 5, 6 and 8 from Section 12.4.2.3 are as follows: (1.0 + 0.14 S DS ) ( D + C ) ± 0.7 ρQ E

Eq. 5

(1.0 + 0.105S DS ) ( D + C ) ± 0.525ρQE + 0.75S

Eq. 6

(0.6 − 0.14 S DS ) D ± 0.7 ρQE

Eq. 8

The ± was added to the above load combinations to make it understood that load combinations should be checked for earthquake loads in all orthogonal horizontal directions. 2.1.8.2 Allowable Strength Seismic Load Combinations with Overstrength Factor In AISC 341-05, ASD and LRFD are fully integrated (all equations are shown in dual format) in Part I. Therefore Part III of the 2002 Seismic Provisions (ASD-to-LRFD conversion) was eliminated. Either design method is valid provided that the load combination is consistent. The 2006 IBC Special Seismic Combinations (using overstrength factor) in

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Seismic Design Guide for Metal Building Systems

section 1605.4 are complete for the LRFD design method, but not for the ASD design method. The 2006 IBC does not include ASD-compliant special seismic combinations. The 2007 Supplement to the IBC deletes the special seismic load combinations in IBC Section 1605.4, and instead provides a cross-reference to the load combinations in ASCE 7-05 Section 12.4.3.2. Section 12.4.3.2 of ASCE 7-05 provides the correct special load combinations (or overstrength factor load combinations) to use with ASD. Therefore, this Guide is recommending the use of the load combinations in ASCE 7-05 Section 12.4.3.2. The ASCE 7 Section 12.4.2.3 allowable strength seismic load combinations with overstrength factor load combinations 5, 6 and 8 from Section 12.4.3.1 are as follows:

2.1.9

(1.0 + 0.14 S DS ) ( D + C ) ± 0.7Ω oQ E

Eq. 5

(1.0 + 0.105S DS ) ( D + C ) ± 0.525Ω oQE + 0.75S

Eq. 6

(0.6 − 0.14 S DS ) D ± 0.7Ω o QE

Eq. 8

Alternate Basic ASD Load Combinations There are two sets of ASD load combinations in the IBC. 1. The first set is called the basic load combinations and is based on the ASD load combinations found in ASCE 7. 2. The second set is called the alternate basic load combinations, which was first created for the 1997 UBC to make the seismic provisions consistent with current steel design practice at that time. Both load combination sets were adopted into the IBC. The alternate basic ASD load combinations are not currently in ASCE 7. The alternate ASD load combinations are included in this Guide for completeness, and because they may be used in building foundation design which is typically done on an ASD basis. They may also be used for structures assigned to Seismic Design Categories A, B, or C if R = 3 is used for design, i.e. the “not detailed for seismic” option. However, when using the alternate ASD load combinations with the AISC Specification (AISC 360-05), an increase in allowables is not permitted. Therefore, these alternate basic load combinations will not likely provide the most economic solution. The nonseismic ASD load combinations may be used for ASD design of buildings in all seismic design categories.

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Seismic Design Guide for Metal Building Systems

For this design example, the alternate set of the basic load combinations of IBC Section 1605.3.2 are as follows. The two ASD load combinations that contain seismic loads are:

D+L+S ±

0.9 D ±

E 1.4

(IBC Eq. 16-20)

E 1.4

(IBC Eq. 16-21)

It should be noted that in these two load combinations, the roof live load, Lr, is not included. The collateral load, C, which for metal building seismic design is treated as a dead load, is included in the first combination. However, the collateral load is treated as a live load in the second combination and therefore is not included. The ASD load combinations can be restated as: D+C + L+S ± 0.9 D ±

E 1.4

(Eq. 2.1.9-1)

E 1.4

(Eq. 2.1.9-2)

Substituting E, defined previously: D+C + L+S ± 0 .9 D ±

Eh Ev + 1 .4 1.4

Eh Ev − 1 .4 1 .4

(Eq. 2.1.9-3) (Eq. 2.1.9-4)

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Seismic Design Guide for Metal Building Systems

2.2

DESIGN BUILDING A (R > 3)

The building configuration and initial trial moment frame and brace rod sizes are shown in the following figure. The brace rods for the end wall are initially assumed to be 0.5 inch diameter while the brace rods for the side wall are initially assumed to be 0.625 inch diameter.

O.F.

5X0.25

WEB THK.

0.1780

I.F.

5X0.25

5X0.25

5X0.25

0.25

0.1780

6X0.3125

6X0.3125

6X0.375

0.1780

0.125

5X0.25

5X0.375

16'-0"

8.281'

10'-0"

10'-0"

6.240'

20'-0"

16'-0"

10'-1"

0.1489

0.1489

0.1489

5X0.3125

5X0.25

6X0.3125

6X0.3125

6X0.3125

5X0.25

5X0.25

Symm. C L Frame

0.50 12

20' E.H.

SS

SS

SS

SS

SS

S

SS

SS

SS

11

21'-3 3/8"

PIPE 6-5/8 X 10.78

H

16'-10 3/4"

0.125

WEB THK.

1

6X0.25

O.F.

S

6.896' 10'-0"

0.1489

6X0.25 6X0.25

6X0.25

2

12

3

SS

SS

HH

SS

SS

10

9

8

7

6 5

4

0.4170'

I.F.

65'

35'

CONNECTION DETAILS : Location

1

2

Web Dep.

8.0

34.0

BASE

Type Plate Plate(DN)

HORZ STF

4

5

6

7

8

9

10

11

12

30.0

22.0

22.0

22.0

33.0

25.5

25.5

6.625

6.625

2E/2E

CAP (EXT)

3E/2E

SPLICE

SPLICE

SPLICE

2E/2E

2E/2E

8.0X0.375

2.75X0.25

6.0X0.25

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

6.0X0.5

N/A

N/A

N/A

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

6.0X0.5

(4)-3/4

N/A

N/A

(10)-3/4

N/A

(8)-3/4

N/A

N/A

(8)-3/4

(8)-3/4

Plate Plate(UP) Bolts

3 N/A

BASE

CAP/STF

8.0X0.5

8.0X0.375

N/A

2.75X0.25

(4)-3/4

(4)-1/2

Figure 2.2-1 Design Building A – Trial Moment Frame

2.2.1

Structural Analysis Models Transverse Moment Frame Model

Exterior Frame Columns: Fixed Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Eh/2 19 FT.

7

6

5

OR

Emh/2

H

G

F

E

1

3 A

J

8

B 64 FT.

V/2

I 9

23 FT.

OR

Eh/2

10

OR

2

4 C

70 FT.

OR

K 19 FT.

V/2

Emh/2

D 64 FT.

Figure 2.2-2 Design Building A – Transverse Frame Analysis Model

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Seismic Design Guide for Metal Building Systems

Transverse End Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.2-3 Design Building A – Transverse End Wall Analysis Model Longitudinal Side Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.2-4 Design Building A – Longitudinal Side Wall Analysis Model 2.2.2

Design Earthquake Forces

The design earthquake forces on individual frame or brace lines based on Design Example 1 are as follows: Design Building A Site 1

Transverse Moment Frame Transverse End Wall Longitudinal Side Wall

V

Eh

Ev

Emh*

(kips) 2.17 1.66 12.15

(kips) 2.17 1.66 12.15

(kips) 0.048D 0.048D 0.048D

(kips) 5.43 3.32 24.30

The values of Emh in the table are based on Ωo = 2.5 for transverse moment frames and Ωo = 2.0 for the transverse end wall and longitudinal side wall. *

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Seismic Design Guide for Metal Building Systems

2.2.3

Member Forces

For Design Building A, the dead, collateral, and earthquake forces on individual frame or brace lines based on Design Example 1 using AISC 341-05, and the requirements of AISC 360-05 Section C2.1b (second order analysis by amplified first-order elastic analysis) are as follows:

Dead Load

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

2-15

Axial (kips) −3.08 −2.73 −6.20 −5.98 −1.55 −1.33 −1.45 0 −0.90 0 0 −3.08 0

Moment (ft-kips) 0 −21.3 0 0 −19.8 −37.8 13.4 0 0 0 0 0 0

Shear (kips) −1.45 −1.45 0 0 2.39 −2.98 −0.06 0 0 −0.45 0 0 −0.09

Seismic Design Guide for Metal Building Systems

Collateral Load

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam Earthquake Loads, Eh

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

2-16

Axial (kips) −1.18 −1.18 −2.57 −2.57 −0.66 −0.57 −0.62 0 −0.47 0 0 −1.18 0

Moment (ft-kips) 0 −9.15 0 0 −8.48 −16.2 5.72 0 0 0 0 0 0

Shear (kips) −0.62 −0.62 0 0 1.02 −1.28 −0.03 0 0 −0.24 0 0 −0.05

Axial (kips) 0.45 0.45 −0.72 −0.72 0.02 0.02 −0.01 1.08 −0.70 0.83 5.09 −3.08 4.05

Moment (ft-kips) 0 17.83 0 0 18.51 −9.31 0 0 0 0 0 0 0

Shear (kips) 1.09 1.09 0 0 −0.45 −0.46 0.27 0 0 0 0 0 0

Seismic Design Guide for Metal Building Systems

Maximum Earthquake Loads, Emh1

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top End Wall Brace Rod (Ωo = 2.0) End Wall Brace Column (Ωo = 2.0) End Wall Beam (Ωo = 2.0) Side Wall Brace Rod (Ωo = 2.0) Side Wall Brace Column (Ωo = 2.0) Side Wall Beam (Ωo = 2.0) 1

2.2.4

Axial (kips) 1.13 1.13 −1.80 −1.80 2.16 −1.40 1.66 10.18 −6.16 8.10

Moment (ft-kips) 0 44.58 0 0 0 0 0 0 0 0

Shear (kips) 2.73 2.73 0 0 0 0 0 0 0 0

Ωo = 2.5, unless otherwise noted.

Seismic Analysis Results Summary for Horizontal Displacements

In this section, the horizontal displacement results are presented for Design Building A for each of the structural analysis models. The actual twodimensional linear elastic analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier. The seismic displacement results are based on the applied frame line base shear, V, using unfactored load values (i.e. E, not 0.7E). Horizontal Displacements at the Eave Height Resulting from Applying the Frame Line Base Shear, V

2.2.5

Transverse Moment Frame

0.742 in

Transverse End Wall Braced Frames

0.102 in

Longitudinal Side Wall Braced Frames

0.169 in

Basic Load Case Analysis Results Summary for Member Forces

In this example, the member forces are presented for each of the basic load cases. Two seismic load cases are included. One seismic load case is for Eh and the other is for Emh. For the examples presented here, Eh and V are identical but since this is not always the case, separate basic load cases have been identified for the purposes of this document. The actual two-dimensional analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier.

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Seismic Design Guide for Metal Building Systems

2.2.6

Story Drift Checks

Story drift is evaluated based on ASCE 7-05 Section 12.8.6. Typically for metal buildings, three story drifts are calculated corresponding to the three structural models. The story drifts are calculated using ASCE 7 Equation 12.815. They are increased by an incremental factor to account for P-delta effects. For this example, three sets of drift checks will be made for each design. Note that footnote a of ASCE 7 Table 12.12-1 states “there shall be no drift limit for single-story structures with interiors walls, partitions, ceilings, and exterior walls that have been designed to accommodate the story drifts.” If this exception is utilized, it would be prudent to communicate this on the contract documents (i.e. the interior walls, partitions and ceilings should be detailed to accommodate drift). For illustrative purposes, this Guide provides drift calculations, even though it could be argued that they are unnecessary. 2.2.6.1 Determine Story Drift without P-Delta Effects

δx =

C d δ xe I

(ASCE Eq. 12.8-15)

Where: Cd = the deflection amplification factor from Design Example 1, i.e.: Cd = 3, for the transverse moment frame Cd = 3.25, for the transverse end wall Cd = 3.25, for the longitudinal side wall I = the occupancy importance factor from Design Example 1 = 1.0

δxe = the elastic horizontal deflections resulting from applying the base shear V to an elastic structural analysis model of the building seismic-force-resisting system. For this example, these analyses were performed by others and the results provided in Section 2.1.4 of this example. Note that the base shear V of this example and Design Example 1 were determined using the simplified code period formulas. Alternatively, if a dynamic analysis (or Rayleigh equation) is performed and used for design and analysis, as discussed in Section 1.3.1, the upper bound period limits of ASCE 7 Section 12.8.2 are not used when calculating drift. Substituting the above values and the previous displacement into ASCE 7 Equation 12.8-15:

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Seismic Design Guide for Metal Building Systems

Story Drift w/o P-Delta Effects, δx Transverse Moment Frame

3(0.742 in ) = 2.23 in 1.0

Transverse End Wall

3.25(0.102 in ) = 0.33 in 1.0

Longitudinal Side Wall

3.25(0.169 in ) = 0.55 in 1.0

2.2.6.2 Determine P-Delta Incremental Factor in Accordance with ASCE 7 Section 12.8.7

For each seismic load combination, ASCE 7 Section 12.8.7 requires that the story drift, δx, be increased by a factor relating to the P-delta effects. This Pdelta incremental factor is defined as: Incremental Factor =

1.0 1−θ

Where the stability coefficient,θ , is determined in accordance with ASCE 7 Section 12.8.7. It should be noted that in ASCE Section 12.8.7, it states that if θ ≤ 0.10 , the P-delta effects can be ignored, which is the same as stating that the incremental factor may be taken as 1.0.

θ=

Px Δ V x hsx C d

(ASCE 7 Eq. 12.8-16)

Where: Px = the total unfactored vertical load at and above Level x; where computing Px, tributary to the frame line under consideration

Δ = the design story drift occurring simultaneously with Vx, inches (Note that for a single story building that Δ is equal to δx) Vx = the seismic shear force acting between level x and level x-1 hsx = the story height below level x (for buildings with pitched roof, the story height is taken as the eave height), inches Cd = deflection amplification factor in ASCE 7 Table 12.2-1 In addition, per ASCE 7 Section 12.8.7, θ shall not exceed θmax.

θ max =

0.5 ≤ 0.25 βC d

(ASCE 7 Eq. 12.8-17)

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Seismic Design Guide for Metal Building Systems

β = the ratio of the shear demand to capacity between level x and level x-1. Where the ratio is not calculated, β = 1.0 can conservatively be used. Note that ASCE 7 permits that where the P-delta effect is included in an automated (second order) analysis, Eq. 12.8-17 shall still be satisfied. However, the value of θ computed from Eq. 12.8-16, using the results of the P-delta analysis, is permitted to be divided by (1 +θ) before checking Eq. 12.8-17. For initial design calculations, it is typical to assume β = 1.0 and determine θmax based on that assumption, since member capacities have yet to be calculated. Once a design has been established, if the drift is greater than allowable, the β factor along with the P-delta incremental factor should be reevaluated based on actual shear demand to actual capacity and the drift rechecked. For this example, separate values of θ, θmax and the P-delta incremental factor are determined for each of the seismic-force-resisting systems (along each brace/frame line). The value of Px is the total vertical load obtained previously in this design example and is the sum of all unfactored column axial loads (including gravity only columns with axial loads taken at the top of the columns) resulting from dead load, floor live load and collateral load tributary to the frame line under consideration. Note that if the flat roof snow load is greater than 30 psf, Px would also include 20 percent of the snow load, unless otherwise required by the authority having jurisdiction. However it should also be noted that Px need never include the roof live load. For the example, the end wall Px is taken as the end wall brace column load multiplied times 8, while the side wall Px is taken as half of the total of all moment frame and end wall column loads. The following calculations illustrate the determination of Px for two example building designs. 2.2.6.3 Determination of Px

In the following calculations, the negative sign indicating compression has been ignored for simplicity in presentation. Transverse Moment Frame

Px = 2(3.08 + 6.20 + 1.18 + 2.57 ) = 26.06 kips Transverse End Wall

Px = 8(0.90 + 0.47 ) = 10.96 kips Longitudinal Side Wall

Px = 0.5[9(26.06) + 2(10.96 )] = 128.2 kips

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Seismic Design Guide for Metal Building Systems

2.2.6.4 Determine the P-Delta Incremental Factors

Vx is taken from the problem statement for this design example and hx is taken as the eave height of 240 inches. Cd and δx are indicated previously in this design example. β is not calculated and is therefore taken as 1.0. Substituting the above data into the P-delta equations, one obtains: Story Drift Parameters θmax Incremental factor

Px

θ

Transverse Moment Frame

26.06

0.020

0.17

1.0

Transverse End Wall

10.96

0.0028

0.15

1.0

Longitudinal Side Wall

128.2

0.0074

0.15

1.0

Note, if θ > θmax in any of the above cases, either the seismic-forceresisting system would need to be redesigned or β would need to be calculated in order to determine if adequate shear capacity was present in the design. It should be noted that in this example P-delta effects could be ignored in all frame lines. 2.2.6.5 Determine the Design Story Drift with P-Delta Effects and Compare with IBC Drift Allowables of ASCE 7 Section 12.12

The design story drift with P-delta effects, Δ, is determined by simply multiplying the story drift without P-delta effects by the P-delta incremental factor. The design story drift is compared with the allowable story drift, Δa, specified in ASCE 7 Table 12.12-1. The allowable story drift is a function of occupancy category and building types. In Design Example 1, it was determined that the occupancy category was II. From ASCE 7 Table 12.12-1, the allowable drift for this example is 0.025hsx provided the interior walls, partitions, ceilings, and exterior wall systems have been designed to accommodate the story drift and the building is four stories or less in height. Note that the allowable drift would be 0.020hsx, if the aforementioned conditions are not met. hsx is taken as the eave height, equal to 20 feet for this example. It is recommended that the building first be checked for the value of 0.020hsx. If it is acceptable, then no special detailing of architectural components will be required beyond that already specified.

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Seismic Design Guide for Metal Building Systems

For this design example, separate drift check calculations are made for each of the seismic forces resisting systems.

Design Story Drifts

Δ

0.020hsx

0.025hsx

Transverse Moment Frame

2.23 in

4.8 in

6.0 in

Transverse End Wall

0.33 in

4.8 in

6.0 in

Longitudinal Side Wall

0.55 in

4.8 in

6.0 in

In the example, all the design story drifts are less than the 0.020hsx design allowables; therefore, no special detailing of architectural components is required beyond that already specified. 2.2.7

Basic Load Combinations

The basic load combinations are discussed in Section 2.1.8.1. From the problem statement and Design Example 1, Ev = 0.048D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0 . Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable basic load combinations are: (1.0 + 0.14 S DS ) ( D + C ) ± 0.7 ρQ E

Eq. 5

(0.6 − 0.14 S DS ) D ± 0.7 ρQE

Eq. 8

Substituting SDS = 0.240 yields the following:

2.2.8

1.0336( D + C ) ± 0.7 ρQE

Eq. 5

0.566 D ± 0.7 ρQE

Eq. 8

Allowable Strength Seismic Load Combinations with Overstrength Factor

The load combinations with overstrength factor are discussed in Section 2.1.8.2. From the problem statement and Design Example 1, Ev = 0.048D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0. Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable load combinations with overstrength factors are:

2-22

Seismic Design Guide for Metal Building Systems

(1.0 + 0.14 S DS ) ( D + C ) ± 0.7Ω oQ E

Eq. 5

(0.6 − 0.14S DS ) D ± 0.7Ω o QE

Eq. 8

Substituting SDS = 0.240 yields the following:

2.2.9

1.0336( D + C ) ± 0.7Ω o QE

Eq. 5

0.566 D ± 0.7Ω o QE

Eq. 8

Design of Diaphragm Systems Including Horizontal Roof Bracing

The example buildings contain three sets of horizontal roof bracing that transfer wind and seismic forces from the end walls and roof to the sets of vertical bracing that are provided along the longitudinal walls of the buildings. These horizontal roof bracing systems are acting as diaphragms in transferring horizontally applied loads to the seismic force resisting elements, consistent with the definition of a diaphragm in 2006 IBC Section 1602.1. Each set of horizontal bracing is laid out between adjacent transverse moment frames that are spaced 25 feet apart, with bracing work points spaced at 25 foot centers across the building width, so as to align with the vertical columns that are spaced along each end wall of the building. Thus, wind against the end walls and seismic forces are transferred from the end wall columns at the roof, through roof purlins that act as struts, to the work points of the horizontal roof bracing. In the transverse direction (assuming flexible diaphragm behavior), each frame resists a tributary portion of the roof seismic force. Typically, the roof spans the short distance between each frame without bracing; however, experience has shown that horizontal bending of purlins and girts in conjunction with the stiffness of roof panels are adequate to resist the marginal forces that develop over this short distance. Horizontal seismic load effects, Eh, and component forces, Fp, shown in subsequent sections are unfactored. Note that in allowable strength design load combinations used in conjunction with AISC 341-05, these seismic loads are factored by either 0.7 or 0.525. 2.2.9.1 Determination of Diaphragm Design Force Coefficients Including Horizontal Bracing

Diaphragms, including horizontal bracing requirements, are specified in ASCE Section 12.10. Design forces are calculated by the following: n

Fpx =

¦F

i

i=x n

¦ wi

wpx

ASCE Eq. 12.10-1

i= x

where

2-23

Seismic Design Guide for Metal Building Systems

Fpx

= diaphragm design force

Fi

= design force at level i (determined by ASCE 7 Eq. 12.8-11)

wi

= weight tributary to level i

wpx

= weight tributary to diaphragm at level x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx Note that for a one-story building, the equation for Fpx simplifies to the following:

Fpx = V but is still subject to the maximum and minimum limitations above. Per ASCE 7 Section 12.3.4.1, the redundancy factor, ρ, that is applied to diaphragms (including horizontal bracing systems) is 1.0 for all Seismic Design Categories, when the loads are determined in accordance with ASCE 7, Eq. 12.10.1. The load combinations to be used for the design of members and connections in the horizontal bracing system need not consider special seismic load combinations with the overstrength factor except where the members also serve as collectors or are common to the vertical seismic force resisting system (See Section 1.4.3 for further discussion). Design Building A is required to be designed using SDC B requirements. Roof bracing/diaphragm design forces in the longitudinal axis of the building are based on the design forces used for the bracing of the longitudinal side walls. Substituting the following values determined in Section 1.3.4.1:

wpx = wi = W = 164.2 kips Fi = V = 12.15 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,longitudinal =

i= x n

¦w

w px =

12.15kips wroof = 0.074wroof,longitudinal 164.2kips

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx 0.048wpx ≤ Fpx ≤ 0.096 wpx

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Seismic Design Guide for Metal Building Systems

Therefore, use Fpx = 0.074wroof,longitudinal Diaphragm design forces for the metal roof deck that spans the short 25-foot dimension between transverse frames is based on the design forces used for the transverse frames. For a typical interior bay, substituting in the values from Section 1.3.4.1:

wpx = wi = W = 31.5 kips Fi = V = 2.17 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i= x n

¦w

w px =

2.17kips wroof = 0.069wroof,transverse 31.5kips

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx 0.048wpx ≤ Fpx ≤ 0.096wpx Therefore, use Fpx = 0.069wroof, transverse For the two end bays, the average of the two adjacent frame design forces is used. Substituting in the values from Section 1.3.4.1:

wpx = wi = W = 31.5 kips + 22.4 kips = 53.9 kips Fi = V = 2.17 kips + 1.66 kips = 3.83 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i=x n

¦w

i

w px =

(2.17kips + 1.66kips ) w (31.5kips + 22.4kips ) roof

i=x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx

2-25

= 0.071wroof,transverse

Seismic Design Guide for Metal Building Systems

(0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx 0.048wpx ≤ Fpx ≤ 0.096 wpx Therefore, use Fpx = 0.071wroof, transverse The controlling diaphragm design force in the longitudinal direction, is the largest of the three forces calculated above, resulting in:

Fpx = 0.074wroof,longitudinal 2.2.10

Determination of Diaphragm Seismic Weights Including Horizontal Bracing

Seismic forces resulting from the roof and wall weight are resisted in the longitudinal direction by three bays of horizontal roof bracing that collect and transfer these forces to the vertical side wall bracing. The following calculations consider only diaphragm forces in the longitudinal building axis. In the longitudinal direction, the horizontal roof bracing resists forces resulting from both the roof and frame weights:

Roof panel and insulation Roof purlin Frame Collateral Load Total

1.5 psf 1.0 psf 2.0 psf 1.5 psf 6.0 psf × roof area

= = = = =

In the longitudinal direction, the diaphragm also resists tributary forces for the end walls, at a weight of 3.0 psf times the tributary wall area. The resulting seismic weights are equal to: Roof Weight = (200 ft ) (250 ft ) (6 psf ) = 300,000 lbs = 300 kips

End Wall Weight = 2 ×

(200 ft ) (22.09 ft ) × 3.0 psf 2

= 13,254 lbs = 13.3 kips

Where, 22.09 feet is the average height of the end walls.

Total Seismic Weight roof ,longit = 300.0 + 13.3 = 313.3 kips

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Seismic Design Guide for Metal Building Systems

2.2.11

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

For Design Building A, the diaphragm design force in the longitudinal direction becomes: Froof = 0.074wroof (from Section 2.2.9.1) Froof, longitudinal = 0.074(313.3 kips) = 23.19 kips Froof ,longitudinal = 2.2.12

(23.19kips ) (1000lbs / kip ) = 200 ft

116 lb/ft

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

Each building has three sets of horizontal roof bracing which combine to resist the longitudinal forces. Distribution of the total applied forces to each set of bracing may be subject to differing opinions. For simplicity’s sake and to promote a more uniform roof bracing design, it is preferred to assume that forces are distributed equally between each set of bracing. 2.2.12.1 Horizontal Bracing Systems

For Design Building A, the seismic design force applied at each work point of the roof bracing is:

(116 lb/ft ) (25 ft ) = 967 lbs 3 sets of bracing

The reaction force at each end of the truss is equal to:

(200 ft − 25 ft ) (116 lb/ft ) = 3,384 2 × 3 sets of bracing

lbs

The 25 feet is deducted because the last 12.5 feet at each end of the span is assumed to load the eave strut and vertical bracing directly. 967 lb

1

967 lb

2 A

967 lb

3 B

967 lb

4

967 lb

5 D

C

967 lb

6 E

967 lb

7 F

8 G

8 @ 25 ft = 200 ft

3,384 lb

3,384 lb

Figure 2.2-5 Plan View of Typical Roof Bracing – Design Building A 2-27

Seismic Design Guide for Metal Building Systems

The actual design forces in each brace element must reflect the member orientation and the tension-only nature of the rod bracing used. For this example, the lateral spacing of bracing points (25 ft) is equal to the longitudinal column spacing; thus, each rod is oriented at 45 degrees. Design Load Combination

IBC and AISC 341-05 are nonspecific but imply an inherent difference between vertical braced frames and horizontal bracing systems that are used as diaphragms. Although vertical tension-only bracing is permitted, connections are designed using the load combination with overstrength, Em = ΩoQE (see Section 2.3.1), horizontal tension-only bracing systems are permitted to be designed using the normal Eh = ρQE load combinations. From Figure 2.2-5, the rod tension and connection seismic design force in Rod (1) is: QE =

3,384 lbs 3,384 lbs = = 4,785 lbs = 4.79 kips cos(45°) 0.707

The maximum seismic design force in the horizontal bracing rods is: E h = ρQE = (1.0) (4.79 kips) = 4.79 kips where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 Note that the required design force is computed for Rod 1 in Figure 2.2-5, while the design forces for Rods 2, 3, and 4 are smaller. The analysis to determine these smaller forces is not included in this example.

Brace rods are designed using AISC 360-05. The compression members of the horizontal truss system (at the most heavily loaded strut that is not a collector, shown as Member “A” in Figure 2.2-6) must be designed for a seismic design force equal to: Eh = ρQE = (1.0) (3,384 lbs) = 3,384 lbs

where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 AISC 360-05 is also used for the design of the compression struts. The design of these struts should consider applicable vertical loads plus any bending moment that may result from eccentricity between the location of horizontal bracing forces and the center of the compression member. Special strut members as shown in Figure 2.2-7 may be needed when cold-formed purlin section cannot be shown to be adequate to resist the resulting stresses.

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Seismic Design Guide for Metal Building Systems

In addition, the tension/compression chord seismic design force must be resisted by the roof beams and splices of the main building frames at braced bays as shown in Figure 2.2-6 and is equal to: Chord Force =

(3,384 lbs ) (100 ft ) − 967 lbs(25 + 50 + 75 ft ) = 7,734 lbs = 7.73 kips 25 ft

967 lb

967 lb

967 lb

483 lb

7,734 lb 2

3

A

4

B

C

RIDGE

EAVE

1

7,734 lb

3,384 lb

Figure 2.2-6 Design Building A, Free Body Diagram Showing Bracing Chord Seismic Design Force at Mid-Span

purlin

P strut

2.2-7. Positioning the Roof Bracing and Struts to Minimize Eccentricity

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Seismic Design Guide for Metal Building Systems

2.2.12.2 Eave Struts

The eave struts are the members at each eave of the roof that form the intersection of roof and wall. The eave struts often serve as collector elements for earthquake forces along the building length and transfer them to the vertical bracing systems. The applied eave strut seismic design forces, for Design Building A, are calculated as follows: From end wall:

(20 ft ) (25 ft ) (3 psf ) (0.074) = 28 lbs 4

From tributary roof and side wall: ª§ 25 ft · º § 20 ft · «¨ 2 ¸ (6 psf ) + ¨ 2 ¸ (3 psf )» (0.074) = 8 lb / ft ¹ ¹ © ¬© ¼

The resulting applied forces and internal forces for Design Building A are shown in Figure 2.2-8. 8 lb/ft 28 lb

28 lb BRACED 50 ft BAY

BRACED BAY

100 ft

75 ft

BRACED BAY

685.4 lb TO WALL BRACING

685.4 lb TO WALL BRACING

25 ft 685.4 lb TO WALL BRACING

APPLIED FORCES

542.6 lb

428 lb

457.2 lb

COMPRESSION

28 lb

28 lb

TENSION

142.8 lb

257.4 lb

228 lb

Figure 2.2-8 Eave Strut Applied and Internal Forces – Design Building A

The resulting seismic design forces for the eave struts are as follows: Eh = ρQE = (1.0) (542.6 lbs) = 543 lbs

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Seismic Design Guide for Metal Building Systems

It should be noted that appropriate load factors need to be applied to the above loads when added to load combinations. An additional strut force is required to transfer the forces from the horizontal to the vertical bracing. Depending upon the positioning of the horizontal roof and vertical rod bracing, the eave strut might also act as a strut to transfer both the forces shown above, as well as the forces from the roof bracing to the wall bracing. Alternatively, a separate strut member could be provided at the bracing, similar to the situation shown in Figure 2.2-7. As a separate strut, the required seismic design force from the roof to the wall bracing would be as follows: Eh = ρ QE = (1.0) (3,384 lbs) = 3,384 lbs

If only a single eave strut is provided to resist both forces, then the member seismic design force would be the following: Eh = 543 lbs + 3,384 lbs = 3,927 lbs Eave struts often serve as collectors or drag elements. ASCE 7 Section 12.10.2.1 requires collector elements, splices, and their connections in Seismic Design Categories C, D, E, and F to be designed using the special Em load combination forces. Eave struts become collectors when forces from the horizontal roof bracing systems are required to be transferred through a length of strut to the location of vertical braced frames. This becomes a particular design consideration when the location of roof bracing bays does not match the location of bays containing vertical braced frames. In this example, the bays align, therefore only a single span of strut at each braced frame acts as a collector element. Note that in this example, that is SDC B, only Eh forces are required for the design of the collectors. Other tributary seismic forces carried by the eave strut are small in magnitude due to the typically small tributary width of roof and wall that attaches to the strut. Because the eave strut carries no more seismic forces in this regard than many other roof purlins, it was considered appropriate to design for this portion of the force in the same manner as other similar elements are designed. 2.2.13

Design of Side Wall OCBF

Ordinary concentrically braced frame member design is covered in AISC 34105, Section 14. Brace members are designed using Eh, while the required strength of brace connections need not exceed either the maximum force that

2-31

Seismic Design Guide for Metal Building Systems

can be developed by the system or a load effect based upon using the amplified seismic load, Emh (i.e. the load combination using overstrength factors). The member design follows similar procedures as shown for the roof bracing in Section 2.2.9. Member Forces

Seismic forces resisted by the side wall bracing can be calculated two ways. (1) As the sum of the forces from the roof bracing plus the eave struts: V = 3(3,384 lbs + 685 lbs ) = 12,207 lbs

(2) As the total calculated building seismic force (from Example 1, Section 1.4.2.1):

V = 12,150 lbs The difference is not significant and is primarily due to round-off of numbers in the analysis. For this example the total calculated building seismic forces from Example 1 will be used. Design forces for the horizontal beam at the braced bay were described in the preceding section. Forces in the bracing and adjacent columns are calculated in this section.

Figure 2.2-9 Longitudinal Side Wall Analysis Model

Horizontal Force per Longitudinal Braced Bay, QE: QE =

12,150 lbs = 4,050 lb/bay = 4.05 kips 3 bays

Brace Rod Length =

(25 ft )2 + (19 ft )2

Brace Rod Force: § 31.4 ft · ¸¸ (4.05 kips ) = 5.09 kips QE = ¨¨ © 25 ft ¹

2-32

= 31.4 ft

Seismic Design Guide for Metal Building Systems

Column Force: § 19 ft · ¸¸ (4.05 kips ) = 3.08 kips QE = ¨¨ © 25 ft ¹ 2.2.13.1 Design of Side Wall Brace Rods Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P M Side Wall Brace Rod Design Forces (kips) (ft-kips) Dead (D) 0.00 0.00 Collateral (C) 0.00 0.00 5.09 0.00 Earthquake (Eh = ρQE) 0.00 Earthquake w/overstrength (Emh = ΩoQE) 10.2 Pa Ma ASD Load Combinations (kips) (ft-kips) 1.0336( D + C ) + 0.7 ρQE 3.56 0.00 1.0336( D + C ) − 0.7 ρQE 0.00 −3.56 0.566 D + 0.7 ρQE 3.56 0.00 0.566 D − 0.7 ρQE 0.00 −3.56 Pa Ma ASD Load Combinations 1 (kips) (ft-kips) w/overstrength 1.0336( D + C ) + 0.7Ω o QE 7.13 0.00

V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−7.13

0.00

0.00

0.566 D + 0.7Ω o QE

7.13

0.00

0.00

0.566 D − 0.7Ω o QE

−7.13

0.00

0.00

1

Note that the ASD Load Combinations w/overstrength are only used for the brace rod connection design.

2.2.13.2 Design of Side Wall Brace Columns

Side wall brace columns must meet the requirements of Section 8.3 of AISC 341-05. Note that these columns are elements of the building moment frames. Design of these columns may have to include the simultaneous orthogonal column forces caused by dead and collateral load conditions depending on the seismic design category. In metal building designs, orthogonal effects are typically found in columns and column bases which are elements of the seismic force resisting systems in each direction. For example, a column which serves as part of a transverse moment frame in one direction and as part of a concentrically braced frame in the other direction is subject to orthogonal effects.

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Seismic Design Guide for Metal Building Systems

In accordance with ASCE 7 Section 12.5.2, orthogonal effects need not be investigated for buildings assigned to SDC B. For SDC C, the orthogonal effects are required only when Type 5 structural plan irregularity is present, i.e. nonparallel systems (see ASCE 7 Table 12.3-1). For high seismic applications (SDC D, E, or F) the orthogonal effects must be considered in all cases. ASCE 7 Section 12.5.3 lists two possible solutions (1) Apply 100 percent of the design force in one direction and 30% in the other, and (2) Simultaneous application of orthogonal ground motion. While either option is sufficient to satisfy this code requirement, the first approach is commonly used for design of metal building systems because the other approach is tied with the more complex methods such as time-history analysis. Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P Side Wall Brace Column Design Forces (kips) Dead (D) −3.08 Collateral (C) −1.18 Earthquake (Eh = ρQE) −3.08 Earthquake w/overstrength (Emh = ΩoQE) −6.16 Pa ASD Load Combinations (kips) 1.0336( D + C ) + 0.7 ρQE −6.56 1.0336( D + C ) − 0.7 ρQE −2.25 0.566 D + 0.7 ρQE −3.90 0.566 D − 0.7 ρQE 0.41 Pa ASD Load Combinations 1 (kips) w/overstrength 1.0336( D + C ) + 0.7Ω o QE −8.72

M (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−0.09

0.00

0.00

0.566 D + 0.7Ω o QE

−6.06

0.00

0.00

0.566 D − 0.7Ω o QE

2.57

0.00

0.00

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

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Seismic Design Guide for Metal Building Systems

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with the 2005 AISC Specification (360-05) Sections D and E, using the ASD provisions. 2.2.13.3 Design of Side Wall Brace Beams

Side wall brace beams must meet the requirements of Section 8.3 of AISC 34105. Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P Side Wall Brace Beam Design Forces (kips) Dead (D) 0.00 Collateral (C) 0.00 4.05 Earthquake (Eh = ρQE) 8.10 Earthquake w/overstrength (Emh = ΩoQE) Pa ASD Load Combinations (kips) 1.0336( D + C ) + 0.7 ρQE 2.84 1.0336( D + C ) − 0.7 ρQE −2.84 0.566 D + 0.7 ρQE 2.84 0.566 D − 0.7 ρQE −2.84 Pa ASD Load Combinations (kips) w/overstrength1 1.0336( D + C ) + 0.7Ω o QE 5.67

M (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

V (kips) −0.09 −0.05 0.00 0.00 Va (kips) −0.14 −0.14 −0.05 −0.05 Va (kips) −0.14

1.0336( D + C ) − 0.7Ω o QE

−5.67

0.00

−0.14

0.566 D + 0.7Ω o QE

5.67

0.00

−0.05

0.566 D − 0.7Ω o QE

−5.67

0.00

−0.05

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

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Seismic Design Guide for Metal Building Systems

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. 2.2.14

Design of End Wall OCBF

Ordinary concentrically braced frame member design is covered in AISC 34105, Section 14. Brace members are designed using Eh, while the required strength of brace connections need not exceed either the maximum force that can be developed by the system or a load effect based upon using the amplified seismic load (i.e. the load combination using overstrength factors). The member design follows similar procedures as shown for the roof bracing in Section 2.2.9. Member Forces

A calculation, as shown below, can be made to obtain the brace rod and column forces. Alternatively, the forces from the frame analysis based on more accurate geometry can be used. From Example 1, Section 1.4.3.1, the total seismic design force for each end frame is: V = 1.66 kips

Figure 2.2-10 – Transverse End Wall Framing

Horizontal Force per End Wall Braced Bay, QE:

QE =

1,660 lbs = 830 lb/bay = 0.83 kips 2 bays

Brace Rod Length =

(25 ft )2 + (21 ft )2

Brace Rod Force:

2-36

= 32.6 ft (using avg. ht. of 21 ft)

Seismic Design Guide for Metal Building Systems

§ 32.6 ft · ¸¸ (0.83 kips ) = 1.08 kips QE = ¨¨ © 25 ft ¹

Column Force: § 21 ft · ¸¸ (0.83 kips ) = 0.70 kips QE = ¨¨ © 25 ft ¹ 2.2.14.1 Design of End Wall Brace Rods Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P M End Wall Brace Rod Design Forces (kips) (ft-kips) Dead (D) 0.00 0.00 Collateral (C) 0.00 0.00 1.08 0.00 Earthquake (Eh = ρQE) 0.00 Earthquake w/overstrength (Emh = ΩoQE) 2.16

V (kips) 0.00 0.00 0.00 0.00

1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) 0.76 −0.76 0.76 −0.76 Pa (kips) 1.51

Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−1.51

0.00

0.00

0.566 D + 0.7Ω o QE

1.51

0.00

0.00

0.566 D − 0.7Ω o QE

−1.51

0.00

0.00

ASD Load Combinations

1

Note that the ASD Load Combinations w/overstrength are only used for the brace rod connection design. 2.2.14.2 Design of End Wall Brace Columns End wall brace columns must meet the requirements of Section 8.3 of AISC 341-05. Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P End Wall Brace Column Design Forces (kips) Dead (D) −0.90 Collateral (C) −0.47 Earthquake (Eh = ρQE) −0.70 Earthquake w/overstrength (Emh = ΩoQE) −1.40 2-37

M (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE

Pa (kips) −1.91 −0.93

Ma (ft-kips) 0.00 0.00

Va (kips) 0.00 0.00

0.566 D + 0.7 ρQE

−1.00

0.00

0.00

0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

−0.02 Pa (kips) −2.39

0.00 Ma (ft-kips) 0.00

0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−0.44

0.00

0.00

0.566 D + 0.7Ω o QE

−1.49

0.00

0.00

0.566 D − 0.7Ω o QE

0.47

0.00

0.00

ASD Load Combinations

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. For allowable strength design, if

Ω c Pa Pn

> 0.4 , the requirements of AISC 341-

05, Section 8.3 must be satisfied. There are no additional requirements specific to column members in Section 14 of Part I, AISC 341-05 for OCBF.

2.2.14.3 Design of End Wall Beam

End wall brace beams must meet the requirements of Section 8.3 of AISC 34105. Loads and Load Combinations (ρ = 1.0, Ωo = 2.0) P End Wall Brace Beam Design Forces (kips) Dead (D) 0.00 Collateral (C) 0.00 0.83 Earthquake (Eh = ρQE) 1.66 Earthquake w/overstrength (Emh = ΩoQE)

2-38

M (ft-kips) 0.00 0.00 0.00 0.00

V (kips) −0.45 −0.24 0.00 0.00

Seismic Design Guide for Metal Building Systems

1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) 0.58 −0.58 0.58 −0.58 Pa (kips) 1.16

Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

Va (kips) −0.71 −0.71 −0.25 −0.25 Va (kips) −0.71

1.0336( D + C ) − 0.7Ω o QE

−1.16

0.00

−0.71

0.566 D + 0.7Ω o QE

1.16

0.00

−0.25

0.566 D − 0.7Ω o QE

−1.16

0.00

−0.25

ASD Load Combinations

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. 2.2.15

Design of Ordinary Moment Frames

2.2.15.1 OMF Columns

Moment frame columns must meet the requirements of AISC 341-05. Loads and Load Combinations (ρ = 1.0, Ωo = 2.5) Top of Interior Columns Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE 2-39

P (kips) −5.98 −2.57 −0.72 −1.80 Pa (kips) −9.34 −8.33 −3.89 −2.88

M (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa Ma (kips) (ft-kips) 0.00 −10.10

Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−7.58

0.00

0.00

0.566 D + 0.7Ω o QE

−4.64

0.00

0.00

0.566 D − 0.7Ω o QE

−2.12

0.00

0.00

Bottom of Interior Columns

0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

P M (kips) (ft-kips) 0.00 −6.20 0.00 −2.57 0.00 −0.72 0.00 −1.80 Ma Pa (kips) (ft-kips) 0.00 −9.57 0.00 −8.56 0.00 −4.01 0.00 −3.01 Pa Ma (kips) (ft-kips) 0.00 −10.32

V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−7.80

0.00

0.00

0.566 D + 0.7Ω o QE

−4.77

0.00

0.00

0.566 D − 0.7Ω o QE

−2.25

0.00

0.00

P (kips) −2.73 −1.18 0.45 1.13

M (ft-kips) −21.3 −9.15 17.83 44.58

V (kips) −1.45 −0.62 1.09 2.73

Pa (kips) −3.73 −4.36 −1.23 −1.86

Ma (ft-kips) −18.99 −43.95 0.43

Va (kips) −1.38 −2.90 −0.06 −1.58

Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE

Top of Exterior Columns Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

2-40

−24.54

Seismic Design Guide for Metal Building Systems

1

ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) −3.25

Ma (ft-kips) −0.27

Va (kips) −0.23

1.0336( D + C ) − 0.7Ω o QE

−4.83

−62.68

−4.05

0.566 D + 0.7Ω o QE

−0.75

19.15

1.09

0.566 D − 0.7Ω o QE

−2.34

−43.26

−2.73

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial, shear, and flexural strength of the moment frame columns are calculated in accordance with AISC 360-05 Sections D, E, F, G and H, using the ASD provisions.

Ω c Pa

> 0.4 , the requirements of AISC 341Pn 05, Section 8.3 must be satisfied. Flexure need not be combined with axial forces when considering this provision.

For allowable strength design, if

There are no additional requirements specific to column members of ordinary moment frames in Section 11, of AISC 341-05 beyond the AISC 360-05 requirements. Final Drift Check

The previously calculated drift checks were based on displacements using the initial trial member sizes. None of the trial member sizes changed as a result of the design of the moment frame beams and columns. As a result, the previously calculated drift checks are appropriate. Had the initial trial sizes for the moment frame beams and/or columns been changed, the drift calculations might need to be repeated. If the initial trial sizes for the moment frame beams and/or columns increased in flexural stiffness, the previously calculated drift checks would be conservative and not require recalculation. 2.2.15.2 Design of OMF Beams

There are no additional requirements specific to beam members beyond the AISC 360-05 requirements.

2-41

Seismic Design Guide for Metal Building Systems

2.3

DESIGN BUILDING A – ALTERNATE DESIGN (R = 3)

An attractive alternative approach to the design of steel structures is permitted by the 2006 IBC and ASCE 7-05 for structures assigned to SDC A, B, and C. With this approach, steel structures may be designed without consideration of the seismic detailing requirements of AISC 341, provided R=3 is used when determining seismic forces. This means that members and connections are designed without consideration of the overstrength factor, with the exceptions noted in Section 1.4.4.1 of this guide. This example illustrates the use of this alternative approach. The building configuration and initial trial moment frame and brace rod sizes is shown in the following figure. The brace rods for the end wall are initially assumed to be 0.5 inch diameter while the brace rods for the side wall are initially assumed to be 0.625 inch diameter.

O.F.

5X0.25

WEB THK.

0.1780

I.F.

5X0.25

0.1780

6X0.3125

6X0.3125

6X0.375

0.1489

0.1489

5X0.25

5X0.25

10'-0"

10'-0"

6.240'

20'-0"

16'-0"

10'-1"

0.1489

0.25

5X0.3125

5X0.25

6X0.3125

6X0.3125

6X0.3125

5X0.25

5X0.25

0.1780

0.125

5X0.25

5X0.375

16'-0"

8.281'

Symm. C L Frame

0.50 12

20' E.H.

SS

SS

SS

SS

SS

SS

HH

SS

10 S

SS

SS

SS

11

21'-3 3/8"

PIPE 6-5/8 X 10.78

H

16'-10 3/4"

0.125

WEB THK.

1

6X0.25

O.F.

S

6.896' 10'-0"

0.1489

6X0.25 6X0.25

6X0.25

2

12

3

SS

SS

9

8

7

6 5

4

0.4170'

I.F.

65'

35'

CONNECTION DETAILS : Location Web Dep. Type Plate Plate(DN) Plate Plate(UP) Bolts

1

2

8.0

34.0

3 N/A

4

5

6

7

8

9

10

11

12

30.0

22.0

22.0

22.0

33.0

25.5

25.5

6.625

6.625

2E/2E

CAP (EXT)

3E/2E

SPLICE

SPLICE

SPLICE

2E/2E

2E/2E

8.0X0.375

2.75X0.25

6.0X0.25

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

6.0X0.5

N/A

N/A

N/A

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

(4)-3/4

N/A

N/A

(10)-3/4

N/A

(8)-3/4

N/A

N/A

(8)-3/4

BASE

HORZ STF

6.0X0.5

(8)-3/4

Figure 2.3-1 Design Building A – Trial Moment Frame 2.3.1

Structural Analysis Models Transverse Moment Frame Model

Exterior Frame Columns: Fixed Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

2-42

BASE

CAP/STF

8.0X0.5

8.0X0.375

N/A

2.75X0.25

(4)-3/4

(4)-1/2

Seismic Design Guide for Metal Building Systems

Figure 2.3-2 Design Building A – Transverse Frame Analysis Model Transverse End Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.3-3 Design Building A – Transverse End Wall Analysis Model Longitudinal Side Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.3-4 Design Building A – Longitudinal Side Wall Analysis Model 2.3.2

Design Earthquake Forces

The design earthquake forces on individual frame or brace lines based on Design Example 1 are as follows:

2-43

Seismic Design Guide for Metal Building Systems

Design Building A Site 1 Alternate

Transverse Moment Frame Transverse End Wall Longitudinal Side Wall

V (kips) 2.52 1.79 13.14

Eh (kips) 2.52 1.79 13.14

Ev (kips) 0.048D 0.048D 0.048D

Emh (kips) * * *

*

No value is given for Emh because AISC 341-05 is not required when the alternate design (R = 3) option is used for SDC A, B, or C structures. However, for SDC C, Emh loads are required for the design of collectors as discussed in Section 1.4.4.1 of Example 1. 2.3.3

Member Forces

For Design Building A Alternate, the dead, collateral, and earthquake forces on individual frame or brace lines based on Design Example 1 using the “not detailed for seismic” provisions, and the requirements of AISC 360-05 Section C2.1b (second order analysis by amplified first-order elastic analysis) are as follows:

Dead Load

Axial (kips)

Moment Frame Ext. Columns – Bottom Moment Frame Ext. Columns – Top Moment Frame Int. Columns – Bottom Moment Frame Int. Columns – Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

−3.08 −2.73 −6.20 −5.98 −1.55 −1.33 −1.45 0 −0.90 0 0 −3.08 0

2-44

Moment (ft-kips) 0 −21.3 0 0 −19.8 −37.8 13.4 0 0 0 0 0 0

Shear (kips) −1.45 −1.45 0 0 2.39 −2.98 −0.06 0 0 −0.45 0 0 −0.09

Seismic Design Guide for Metal Building Systems

Collateral Load

Axial (kips)

Moment Frame Ext. Columns – Bottom Moment Frame Ext. Columns – Top Moment Frame Int. Columns – Bottom Moment Frame Int. Columns – Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

Earthquake Loads, Eh

Moment Frame Ext. Columns – Bottom Moment Frame Ext. Columns – Top Moment Frame Int. Columns – Bottom Moment Frame Int. Columns – Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

Maximum Earthquake Loads, Emh

−1.18 −1.18 −2.57 −2.57 −0.66 −0.57 −0.62 0 −0.47 0 0 −1.18 0

Moment (ft-kips) 0 −9.15 0 0 −8.48 −16.2 5.72 0 0 0 0 0 0

Shear (kips) −0.62 −0.62 0 0 1.02 −1.28 −0.03 0 0 −0.24 0 0 −0.05

Axial

Moment

Shear

(kips)

(ft-kips)

(kips)

0.53 0.53 −0.84 −0.84 0.02 0.02 −0.01 1.17 −0.76 0.90 5.50 −3.33 4.38

0 20.72 0 0 21.49 −10.81 0 0 0 0 0 0 0

1.26 1.26 0 0 −0.53 −0.53 0.32 0 0 0 0 0 0

Axial

Moment

Shear

(kips)

(ft-kips)

(kips)

Not required for the alternate design (R=3)* *

No values have been computed for Emh (i.e. Emh taken as zero) because AISC 341-05 is not required when the alternate design (R = 3) option is used for Seismic Design Categories A, B, or C. However, for SDC C, Emh loads are

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Seismic Design Guide for Metal Building Systems

required for the design of collectors as discussed in Section 1.4.4.1 of Example 1. 2.3.4

Seismic Analysis Results Summary for Horizontal Displacements

In this section, the horizontal displacement results are presented for Design Building A Alternate for each of the structural analysis models. The actual twodimensional linear elastic analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier. The seismic displacement results are based on the applied frame line base shear, V, using unfactored load values (i.e. E, not 0.7E).

Transverse Moment Frame Transverse End Wall Braced Frames Longitudinal Side Wall Braced Frames 2.3.5

Horizontal Displacements at the Eave Height Resulting from Applying the Frame Line Base Shear, V 0.860 in 0.111 in 0.183 in

Basic Load Case Analysis Results Summary for Member Forces

In this example, the member forces are presented for each of the basic load cases. One seismic load case for Eh is included. The seismic load case using Emh is not required for the alternate design (R=3). For the examples presented here, Eh and V are identical but since this is not always the case, separate basic load cases have been identified for the purposes of this document. The actual two-dimensional analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier. 2.3.6

Story Drift Checks

Story drift is evaluated based on ASCE 7-05 Section 12.8.6. Typically for metal buildings, three story drifts are calculated corresponding to the three structural models. The story drifts are calculated using ASCE 7 Equation 12.815. They are increased by an incremental factor to account for P-delta effects. For this example, three sets of drift checks will be made for each design. Note that footnote a of ASCE 7 Table 12.12-1 states “there shall be no drift limit for single-story structures with interiors walls, partitions, ceilings, and exterior walls that have been designed to accommodate the story drifts.” If this exception is utilized, it would be prudent to communicate this on the contract documents (i.e. the interior walls, partitions and ceilings should be detailed to accommodate drift). For illustrative purposes, this Guide provides drift calculations, even though it could be argued that they are unnecessary.

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2.3.6.1 Determine Story Drift without P-Delta Effects

δx =

C d δ xe I

(ASCE Eq. 12.8-15)

Where: Cd = the deflection amplification factor from Design Example 1, i.e.: Cd = 3, for the transverse moment frame Cd = 3.25, for the transverse end wall Cd = 3.25, for the longitudinal side wall I = the occupancy importance factor from Design Example 1 = 1.0

δxe = the elastic horizontal deflections resulting from applying the base shear V to an elastic structural analysis model of the building seismic-force-resisting system. For this example, these analyses were performed by others and the results provided in Section 2.1.4 of this example. Note that the base shear V of this example and Design Example 1 were determined using the simplified code period formulas. Alternatively, if a dynamic analysis (or Rayleigh equation) is performed and used for design and analysis, as discussed in Section 1.3.1, the upper bound period limits of ASCE 7 Section 12.8.2 are not used when calculating drift. Substituting the above values and the previous displacement into ASCE 7 Equation 12.8-15: Story Drift w/o P-Delta Effects, δx Transverse Moment Frame

3(0.860 in ) = 2.58 in 1.0

Transverse End Wall

3.25(0.111in ) = 0.36 in 1.0

Longitudinal Side Wall

3.25(0.183 in ) = 0.59 in 1.0

2.3.6.2 Determine P-Delta Incremental Factor in Accordance with ASCE 7 Section 12.8.7

For each seismic load combination, ASCE 7 Section 12.8.7 requires that the story drift, δx, be increased by a factor relating to the P-delta effects. This Pdelta incremental factor is defined as:

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Seismic Design Guide for Metal Building Systems

Incremental Factor =

1.0 1−θ

Where the stability coefficient,θ , is determined in accordance with ASCE 7 Section 12.8.7. It should be noted that in ASCE Section 12.8.7, it states that if θ ≤ 0.10 , the P-delta effects can be ignored, which is the same as stating that the incremental factor may be taken as 1.0.

θ=

Px Δ V x hsx C d

(ASCE 7 Eq. 12.8-16)

Where: Px = the total unfactored vertical load at and above Level x; where computing Px, tributary to the frame line under consideration

Δ = the design story drift occurring simultaneously with Vx, inches (Note that for a single story building that Δ is equal to δx) Vx = the seismic shear force acting between level x and level x-1 hsx = the story height below level x (for buildings with pitched roof, the story height is taken as the eave height), inches Cd = deflection amplification factor in ASCE 7 Table 12.2-1 In addition, per ASCE 7 Section 12.8.7, θ shall not exceed θmax.

θ max =

0.5 ≤ 0.25 βC d

(ASCE 7 Eq. 12.8-17)

β = the ratio of the shear demand to capacity between level x and level x-1. Where the ratio is not calculated, β = 1.0 can conservatively be used. Note that ASCE 7 permits that where the P-delta effect is included in an automated (second order) analysis, Eq. 12.8-17 shall still be satisfied. However, the value of θ computed from Eq. 12.8-16, using the results of the P-delta analysis, is permitted to be divided by (1 + θ) before checking Eq. 12.8-17. For initial design calculations, it is typical to assume β = 1.0 and determine θmax based on that assumption, since member capacities have yet to be calculated. Once a design has been established, if the drift is greater than allowable, the β factor along with the P-delta incremental factor should be reevaluated based on actual shear demand to actual capacity and the drift rechecked. For this example, separate values of θ, θmax and the P-delta incremental factor are determined for each of the seismic-force-resisting systems (along each brace/frame line). The value of Px is the total vertical load obtained previously in this design example and is the sum of all unfactored column axial loads (including gravity only columns with axial loads taken at the top of the

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columns) resulting from dead load, floor live load and collateral load tributary to the frame line under consideration. Note that if the flat roof snow load is greater than 30 psf, Px would also include 20 percent of the snow load, unless otherwise required by the authority having jurisdiction. However it should also be noted that Px need never include the roof live load. For the example, the end wall Px is taken as the end wall brace column load multiplied times 8, while the side wall Px is taken as half of the total of all moment frame and end wall column loads. The following calculations illustrate the determination of Px for two example building designs. 2.3.6.3 Determination of Px

In the following calculations, the negative sign indicating compression has been ignored for simplicity in presentation. Transverse Moment Frame

Px = 2(3.08 + 6.20 + 1.18 + 2.57 ) = 26.06 kips Transverse End Wall

Px = 8(0.90 + 0.47 ) = 10.96 kips Longitudinal Side Wall

Px = 0.5[9(26.06) + 2(10.96 )] = 128.2 kips 2.3.6.4 Determine the P-Delta Incremental Factors

Vx is taken from the problem statement for this design example and hx is taken as the eave height of 240 inches. Cd and δx are indicated previously in this design example. β is not calculated and is therefore taken as 1.0. Substituting the above data into the P-delta equations, one obtains:

Px

Story Drift Parameters θ θmax Incremental factor

Transverse Moment Frame

26.06

0.037

0.17

1.0

Transverse End Wall

10.96

0.0028

0.15

1.0

Longitudinal Side Wall

128.2

0.0074

0.15

1.0

Note, if θ > θmax in any of the above cases, either the seismic-forceresisting system would need to be redesigned or β would need to be calculated in order to determine if adequate shear capacity was present in the design. It should be noted that in this example P-delta effects could be ignored in all frame lines.

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Seismic Design Guide for Metal Building Systems

2.3.6.5 Determine the Design Story Drift with P-Delta Effects and Compare with IBC Drift Allowables of ASCE 7 Section 12.12

The design story drift with P-delta effects, Δ, is determined by simply multiplying the story drift without P-delta effects by the P-delta incremental factor. The design story drift is compared with the allowable story drift, Δa, specified in ASCE 7 Table 12.12-1. The allowable story drift is a function of occupancy category and building types. In Design Example 1, it was determined that the occupancy category was II. From ASCE 7 Table 12.12-1, the allowable drift for this example is 0.025hsx provided the interior walls, partitions, ceilings, and exterior wall systems have been designed to accommodate the story drift and the building is four stories or less in height. Note that the allowable drift would be 0.020hsx, if the aforementioned conditions are not met. hsx is taken as the eave height, equal to 20 feet for this example. It is recommended that the building first be checked for the value of 0.020hsx. If it is acceptable, then no special detailing of architectural components will be required beyond that already specified. For this design example, separate drift check calculations are made for each of the seismic forces resisting systems for each design.

Design Story Drifts

Δ

0.020hsx

0.025hsx

Transverse Moment Frame

2.58 in

4.8 in

6.0 in

Transverse End Wall

0.36 in

4.8 in

6.0 in

Longitudinal Side Wall

0.59 in

4.8 in

6.0 in

In the example, all the design story drifts are less than the 0.020hsx design allowables; therefore, no special detailing of architectural components is required beyond that already specified. 2.3.7

Basic Load Combinations

The basic load combinations are discussed in Section 2.1.8.1. From the problem statement and Design Example 1, Ev = 0.048D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0 . Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable basic load combinations are:

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Seismic Design Guide for Metal Building Systems

(1.0 + 0.14 S DS ) ( D + C ) ± 0.7 ρQ E

Eq. 5

(0.6 − 0.14S DS ) D ± 0.7 ρQE

Eq. 8

Substituting SDS = 0.240 yields the following:

2.3.8

1.0336( D + C ) ± 0.7 ρQE

Eq. 5

0.566 D ± 0.7 ρQE

Eq. 8

Allowable Strength Seismic Load Combinations With Overstrength Factor

The load combinations with overstrength factor are discussed in Section 2.1.8.2. From the problem statement and Design Example 1, Ev = 0.048D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0 . Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable load combinations with overstrength factors are: (1.0 + 0.14 S DS ) ( D + C ) ± 0.7Ω oQ E

Eq. 5

(0.6 − 0.14S DS ) D ± 0.7Ω o QE

Eq. 8

Substituting SDS = 0.240 yields the following:

2.3.9

1.0336( D + C ) ± 0.7Ω o QE

Eq. 5

0.566 D ± 0.7Ω o QE

Eq. 8

Design of Diaphragm Systems Including Horizontal Roof Bracing

The example buildings contain three sets of horizontal roof bracing that transfer wind and seismic forces from the end walls and roof to the sets of vertical bracing that are provided along the longitudinal walls of the buildings. These horizontal roof bracing systems are acting as diaphragms in transferring horizontally applied loads to the seismic force resisting elements, consistent with the definition of a diaphragm in 2006 IBC Section 1602.1. Each set of horizontal bracing is laid out between adjacent transverse moment frames that are spaced 25 feet apart, with bracing work points spaced at 25 foot centers across the building width, so as to align with the vertical columns that are spaced along each end wall of the building. Thus, wind against the end walls and seismic forces are transferred from the end wall columns at the roof, through roof purlins that act as struts, to the work points of the horizontal roof bracing. In the transverse direction (assuming flexible diaphragm behavior), each frame resists a tributary portion of the roof seismic force. Typically, the roof spans the short distance between each frame without bracing; however, experience has shown that horizontal bending of purlins and girts in conjunction with the

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Seismic Design Guide for Metal Building Systems

stiffness of roof panels are adequate to resist the marginal forces that develop over this short distance. Horizontal seismic load effects, Eh, and component forces, Fp, shown in subsequent sections are unfactored. Note that in allowable strength design load combinations used in conjunction with AISC 341-05, these seismic loads are factored by either 0.7 or 0.525. 2.3.9.1 Determination of Diaphragm Design Force Coefficients Including Horizontal Bracing

Diaphragms, including horizontal bracing requirements, are specified in ASCE Section 12.10. Design forces are calculated by the following: n

Fpx =

¦F

i

i=x n

¦ wi

wpx

ASCE Eq. 12.10-1

i= x

where Fpx

= diaphragm design force

Fi

= design force at level i (determined by ASCE 7 Eq. 12.8-11)

wi

= weight tributary to level i

wpx

= weight tributary to diaphragm at level x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx Note that for a one-story building, the equation for Fpx simplifies to the following: Fpx = V but is still subject to the maximum and minimum limitations above. Per ASCE 7 Section 12.3.4.1, the redundancy factor, ρ, that is applied to diaphragms (including horizontal bracing systems) is 1.0 for all Seismic Design Categories, when the loads are determined in accordance with ASCE 7, Eq. 12.10.1. The load combinations to be used for the design of members and connections in the horizontal bracing system need not consider special seismic load combinations with the overstrength factor except where the members also serve as collectors or are common to the vertical seismic force resisting system (See Section 1.4.3 for further discussion). Design Building A Alternate is also required to be designed using SDC B requirements. Substituting in the values calculated in Section 1.3.4.2 yields slightly more load than if the system was detailed for seismic loads as in 2.4.1.1.

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Seismic Design Guide for Metal Building Systems

Roof bracing/diaphragm design forces in the longitudinal axis of the building are based on the design forces used for the bracing of the longitudinal side walls. Substituting in the values calculated in Section 1.3.4.2: wpx = wi = W = 164.2 kips Fi = V = 13.14 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,longitudinal =

i= x n

¦w

13.14kips wroof = 0.080wroof,longitudinal 164.2kips

w px =

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx 0.048wpx ≤ Fpx ≤ 0.096wpx Therefore, use Fpx = 0.080wroof,longitudinal Diaphragm design forces for the metal roof deck that spans the short 25-foot dimension between transverse frames is based on the design forces used for the transverse frames. For a typical interior bay, substituting in the values from Section 1.3.4.2: wpx = wi = W = 31.5 kips Fi = V = 2.52 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i= x n

¦w

w px =

2.52kips wroof = 0.080wroof,transverse 31.5kips

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx

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Seismic Design Guide for Metal Building Systems

0.048wpx ≤ Fpx ≤ 0.096wpx Therefore, use Fpx = 0.080wroof, transverse For the two end bays, the average of the two adjacent frame design forces is used. Substituting in the values from Section 1.3.4.2: wpx = wi = W = 31.5 kips + 22.4 kips = 53.9 kips Fi = V = 2.52 kips + 1.79 kips = 4.31 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i= x n

¦w

w px =

i

(2.52 kips + 1.79 kips ) w (31.5 kips + 22.4 kips ) roof

= 0.080wroof,transverse

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (0.240) (1.00)wpx ≤ Fpx ≤ (0.4) (0.240) (1.00)wpx 0.048wpx ≤ Fpx ≤ 0.096wpx Therefore, use Fpx = 0.080wroof, transverse The controlling diaphragm design force in the longitudinal direction, is the largest of the three forces calculated above, resulting in: Fpx = 0.080wroof,longitudinal 2.3.10

Determination of Diaphragm Seismic Weights Including Horizontal Bracing

Seismic forces resulting from the roof and wall weight are resisted in the longitudinal direction by three bays of horizontal roof bracing that collect and transfer these forces to the vertical side wall bracing. The following calculations consider only diaphragm forces in the longitudinal building axis. In the longitudinal direction, the horizontal roof bracing resists forces resulting from both the roof and frame weights:

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Seismic Design Guide for Metal Building Systems

Roof panel and insulation Roof purlin Frame Collateral Load Total

1.5 psf 1.0 psf 2.0 psf 1.5 psf 6.0 psf × roof area

= = = = =

In the longitudinal direction, the diaphragm also resists tributary forces for the end walls, at a weight of 3.0 psf times the tributary wall area. The resulting seismic weights are equal to: Roof Weight = (200 ft ) (250 ft ) (6 psf ) = 300,000 lbs = 300 kips

End Wall Weight = 2 ×

(200 ft ) (22.09 ft ) × 3.0 psf 2

= 13,254 lbs = 13.3 kips

Where, 22.09 feet is the average height of the end walls. Total Seismic Weight roof ,longit = 300.0 + 13.3 = 313.3 kips 2.3.11

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

For Design Building A Alternate, the diaphragm design force in the longitudinal direction becomes: Froof = 0.080wroof (from Section 2.3.9.1) Froof, longitudinal = 0.080(313.3 kips) = 25.1 kips Froof ,longitudinal = 2.3.12

(25.1 kips) (1000 lbs / kip ) = 200 ft

125.5 lb/ft

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

Each building has three sets of horizontal roof bracing which combine to resist the longitudinal forces. Distribution of the total applied forces to each set of bracing may be subject to differing opinions. For simplicity’s sake and to promote a more uniform roof bracing design, it is preferred to assume that forces are distributed equally between each set of bracing. 2.3.12.1 Horizontal Bracing Systems

For Design Building A Alternate, the seismic design force applied at each work point of the roof bracing is:

(125.5 lb) (25 ft ) 3 sets of bracing

= 1,046 lbs

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Seismic Design Guide for Metal Building Systems

The reaction force at each end of the truss is equal to:

(200 ft − 25 ft ) (125.5 lb/ft ) = 3,661 lbs 2 × 3 sets of bracing

The 25 feet is deducted because the last 12.5 feet at each end of the span is assumed to load the eave strut and vertical bracing directly.

1,046 lb

1

1,046 lb

2 A

1,046 lb

3 B

1,046 lb

4

1,046 lb

5 D

C

1,046 lb

6 E

1,046 lb

7 F

8 G

8 @ 25 ft = 200 ft

3,661 lb

3,661 lb

Figure 2.3-5 Plan View of Typical Roof Bracing – Design Building A Alternate

The actual design forces in each brace element must reflect the member orientation and the tension-only nature of the rod bracing used. For this example, the lateral spacing of bracing points (25 ft) is equal to the longitudinal column spacing; thus, each rod is oriented at 45 degrees. Design Load Combination

IBC and AISC 341-05 are nonspecific but imply an inherent difference between vertical braced frames and horizontal bracing systems that are used as diaphragms. Although vertical tension-only bracing is permitted, connections are designed using the load combination with overstrength, Em = ΩoQE (see Section 2.3.1), horizontal tension-only bracing systems are permitted to be designed using the normal Eh = ρQE load combinations. For Figure 2.3-5, the rod tension and connection seismic design force in Rod (1) is:

QE =

3,661 lbs 3,661 lbs = = 5,177 lbs = 5.18 kips cos(45°) 0.707

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Seismic Design Guide for Metal Building Systems

The maximum seismic design force in the horizontal bracing rods is: E h = ρQ E = (1.0) (5.18 kips ) = 5.18 kips where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 Note that the required design force is computed for Rod 1 in Figure 2.3-5, while the design forces for Rods 2, 3, and 4 are smaller. The analysis to determine these smaller forces is not included in this example. Brace rods are designed using the same procedures as shown for Design Building A. The compression members of the horizontal truss system (at the most heavily loaded strut that is not a collector) must be designed for a seismic design force equal to: E h = ρQE = (1.0) (3,661 lbs ) = 3,661 lbs where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 AISC 360-05 is also used for the design of the compression struts. The design of these struts should consider applicable vertical loads plus any bending moment that may result from eccentricity between the location of horizontal bracing forces and the center of the compression member. Special strut members as shown in Figure 2.3-7 may be needed when cold-formed purlin section cannot be shown to be adequate to resist the resulting stresses. In addition, the tension/compression chord seismic design force must be resisted by the roof beams and splices of the main building frames at braced bays as shown in Figure 2.3-6 and is equal to: AAltchordforce =

(3,661 lbs ) (100 ft ) − (1,046 lbs ) ( 25 + 50 + 75 ft ) = 8,368 lbs = 8.37 kips 25 ft

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Seismic Design Guide for Metal Building Systems

1,046 lb

1,046 lb

523 lb

1,046 lb

8,368 lb 2

3

A

4

B

C

RIDGE

EAVE

1

8,368 lb

3,661 lb

Figure 2.3-6 Design Building A Alternate, Free Body Diagram Showing Bracing Chord Seismic Design Force at Mid-Span

purlin

P strut

2.3-7. Positioning the Roof Bracing and Struts to Minimize Eccentricity 2.3.12.2 Eave Struts

The eave struts are the members at each eave of the roof that form the intersection of roof and wall. The eave struts often serve as collector elements for earthquake forces along the building length and transfer them to the vertical bracing systems. The applied eave strut seismic design forces are calculated in the same fashion as for Design Building A as:

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From end wall: ( 20 ft ) ( 25 ft ) (3 psf ) (0.080) = 30 lbs 4 From tributary roof and side wall: ª§ 25 ft · º § 20 ft · «¨ 2 ¸ (6 psf ) + ¨ 2 ¸ (3 psf )» (0.080) = 8.4 lbs / ft ¹ © ¹ ¬© ¼

The resulting applied forces and internal forces for Design Building A Alternate are shown in Figure 2.3-8. 8.4 lb/ft 30 lb

30 lb BRACED 50 ft BAY

100 ft

BRACED BAY

720.0 lb TO WALL BRACING

75 ft

BRACED BAY

720.0 lb TO WALL BRACING

25 ft 720.0 lb TO WALL BRACING

APPLIED FORCES

570 lb

450 lb

480 lb

COMPRESSION

30 lb

30 lb

TENSION

150 lb

270 lb

240 lb

Figure 2.3-8 Eave Strut Applied and Internal Forces – Design Building A Alternate

The resulting seismic design forces for the eave struts are as follows: Eh = ρQE = (1.0) (570 lbs) = 570 lbs It should be noted that appropriate load factors need to be applied to the above loads when added to load combinations.

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An additional strut force is required to transfer the forces from the horizontal to the vertical bracing. Depending upon the positioning of the horizontal roof and vertical rod bracing, the eave strut might also act as a strut to transfer both the forces shown above, as well as the forces from the roof bracing to the wall bracing. Alternatively, a separate strut member could be provided at the bracing, similar to the situation shown in Figure 2.3-7. As a separate strut, the required seismic design force from the roof to the wall bracing would be as follows: Eh = ρ QE = (1.0) (3,661 lbs) = 3,661 lbs If only a single eave strut is provided to resist both forces, then the member seismic design force would be the following: Eh = 570 lbs + 3,661 lbs = 4,231 lbs Eave struts often serve as collectors or drag elements. ASCE 7 Section 12.10.2.1 requires collector elements, splices, and their connections in Seismic Design Categories C, D, E, and F to be designed using the special Em load combination forces in SDC C, D, E, and F. Eave struts become collectors when forces from the horizontal roof bracing systems are required to be transferred through a length of strut to the location of vertical braced frames. This becomes a particular design consideration when the location of roof bracing bays does not match the location of bays containing vertical braced frames. In this example, the bays align, therefore only a single span of strut at each braced frame acts as a collector element. Other tributary seismic forces carried by the eave strut are small in magnitude due to the typically small tributary width of roof and wall that attaches to the strut. Because the eave strut carries no more seismic forces in this regard than many other roof purlins, it was considered appropriate to design for this portion of the force in the same manner as other similar elements are designed. 2.3.13

Design of Side Wall

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. The member design follows similar procedures as shown for the roof bracing in Section 2.3.9. Member Forces

Seismic forces resisted by the side wall bracing can be calculated two ways.

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(1) As the sum of the forces from the roof bracing plus the eave struts: V = 3(3,661 lbs + 720 lbs ) = 13,143 lbs

(2) As the total calculated building seismic force (from Example 1, Section 1.4.2.2):

V = 13,140 lbs The difference is not significant and is primarily due to round-off of numbers in the analysis. For this example the total calculated building seismic forces from Example 1 will be used. Design forces for the horizontal beam at the braced bay were described in the preceding section. Forces in the bracing and adjacent columns are calculated in this section.

Figure 2.3-9 Longitudinal Side Wall Analysis Model

Horizontal Force per Longitudinal Braced Bay, QE: QE =

13,140 lbs = 4,380 lb/bay = 4.38 kips 3 bays

Brace Rod Length =

(25 ft )2 + (19 ft )2

Brace Rod Force: § 31.4 ft · ¸¸ (4.38 kips ) = 5.50 kips QE = ¨¨ © 25 ft ¹

Column Force: § 19 ft · ¸¸ (4.38 kips ) = 3.33 kips QE = ¨¨ © 25 ft ¹

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Seismic Design Guide for Metal Building Systems

2.3.13.1 Design of Side Wall Brace Rods Loads and Load Combinations (ρ = 1.0) Side Wall Brace Rod Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

P (kips) 0.00 0.00 5.50 Pa (kips) 3.85 −3.85 3.85 −3.85

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

2.3.13.2 Design of Side Wall Brace Columns

Side wall brace columns in this example need only meet the requirements of AISC 360. Note that these columns are elements of the building moment frames. Design of these columns may have to include the simultaneous orthogonal column forces caused by dead and collateral load conditions depending on the seismic design category. In metal building designs, orthogonal effects are typically found in columns and column bases which are elements of the seismic force resisting systems in each direction. For example, a column which serves as part of a transverse moment frame in one direction and as part of a concentrically braced frame in the other direction is subject to orthogonal effects. In accordance with ASCE 7 Section 12.5.2, orthogonal effects need not be investigated for buildings assigned to SDC B. For SDC C, the orthogonal effects are required only when Type 5 structural plan irregularity is present, i.e. nonparallel systems (see ASCE 7 Table 12.3-1). For high seismic applications (SDC D, E, or F) the orthogonal effects must be considered in all cases. ASCE 7 Section 12.5.3 lists two possible solutions 1. Apply 100 percent of the design force in one direction and 30% in the other, and 2. Simultaneous application of orthogonal ground motion.

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Seismic Design Guide for Metal Building Systems

While either option is sufficient to satisfy this code requirement, the first approach is commonly used for design of metal building systems because the other approach is tied with the more complex methods such as time-history analysis. Loads and Load Combinations (ρ = 1.0) Side Wall Brace Column Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

P (kips) −3.08 −1.18 −3.33 Pa (kips) −6.73 −2.07 −4.07 0.59

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. 2.3.13.3 Design of Side Wall Brace Beams

Side wall brace beams in this example need only meet the requirements of AISC 360. Loads and Load Combinations (ρ = 1.0) Side Wall Brace Beam Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

2-63

P (kips) 0.00 0.00 4.38 Pa (kips) 3.07 −3.07 3.07 −3.07

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) −0.09 −0.05 0.00 Va (kips) −0.14 −0.14 −0.05 −0.05

Seismic Design Guide for Metal Building Systems

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with the AISC 360-05 Sections D and E, using the ASD provisions. 2.3.14

Design of End Wall

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. The member design follows similar procedures as shown for the roof bracing in Section 2.3.9. Member Forces

A calculation, as shown below, can be made to obtain the brace rod and column forces. Alternatively, the forces from the frame analysis based on more accurate geometry can be used. From Example 1, Section 1.4.3.2, the total seismic design force for each end frame is: V = 1.79 kips

Figure 2.3-10 – Transverse End Wall Framing

Horizontal Force per End Wall Braced Bay, QE: QE =

1,790 lbs = 895 lb/bay = 0.90 kips 2 bays

Brace Rod Length =

(25 ft )2 + (21 ft )2

= 32.6 ft (using avg. ht. of 21 ft)

Brace Rod Force: § 32.6 ft · ¸¸ (0.90 kips ) = 1.17 kips QE = ¨¨ © 25 ft ¹

Column Force:

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Seismic Design Guide for Metal Building Systems

§ 21 ft · ¸¸ (0.90 kips ) = 0.76 kips QE = ¨¨ © 25 ft ¹ 2.3.14.1 Design of End Wall Brace Rods

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. The member design follows similar procedures as shown for the roof bracing in Section 2.3.9. Loads and Load Combinations (ρ = 1.0) End Wall Brace Rod Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

P (kips) 0.00 0.00 1.17 Pa (kips) 0.82 −0.82 0.82 −0.82

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

2.3.14.2 Design of End Wall Brace Columns

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. Loads and Load Combinations (ρ = 1.0) End Wall Brace Column Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

2-65

P (kips) −0.90 −0.47 −0.76 Pa (kips) −1.95 −0.88 −1.04 0.02

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with the AISC 360-05 Chapters D and E, using the ASD provisions. 2.3.14.3 Design of End Wall Beam

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. Loads and Load Combinations (ρ = 1.0) End Wall Brace Beam Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

P (kips) 0.00 0.00 0.90 Pa (kips) 0.63 −0.63 0.63 −0.63

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) −0.45 −0.24 0.00 Va (kips) −0.71 −0.71 −0.25 −0.25

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with the AISC360-05 Sections D and E, using the ASD provisions. 2.3.15

Design of Moment Frames

2.3.15.1 Design of Moment Frame Columns

As stated in Section 2.3, the provisions of AISC 341 are not applicable; therefore members are designed in accordance with AISC 360 only. Loads and Load Combinations (ρ = 1.0) Top of Interior Columns

P (kips) −5.98 −2.57 −0.84

Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE)

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M (ft-kips) 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

Pa (kips) −9.42 −8.25 −3.97 −2.80

Ma (ft-kips) 0.00 0.00 0.00 0.00

Va (kips) 0.00 0.00 0.00 0.00

P (kips) −6.20 −2.57 −0.84 Pa (kips) −9.65 −8.48 −4.10 −2.92

M (ft-kips) 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Bottom of Interior Columns Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

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Seismic Design Guide for Metal Building Systems

Top of Exterior Columns Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) ASD Load Combinations 1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE

P (kips) −2.73 −1.18 0.53 Pa (kips) −3.67 −4.41 −1.17 −1.92

M (ft-kips) −21.3 −9.15 −20.72 Ma (ft-kips) −16.97 −45.98 2.45 −26.56

V (kips) −1.45 −0.62 −1.26 Va (kips) −1.26 −3.02 0.06 −1.70

Allowable Strengths

The axial, shear, and flexural strength of the moment frame columns are calculated in accordance with AISC 360-05 Sections D, E, F, G and H, using the ASD provisions. Final Drift Check

The previously calculated drift checks were based on displacements using the initial trial member sizes. None of the trial member sizes changed as a result of the design of the moment frame beams and columns. As a result, the previously calculated drift checks are appropriate. Had the initial trial sizes for the moment frame beams and/or columns been changed, the drift calculations might need to be repeated. If the initial trial sizes for the moment frame beams and/or columns increased in flexural stiffness, the previously calculated drift checks would be conservative and not require recalculation. 2.3.15.2 Design of Moment Frame Beams

There are no additional requirements specific to beam members beyond AISC 360-05 requirements.

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2.4

DESIGN BUILDING B

The building configuration and initial trial moment frame and brace rod sizes is shown in the following figure. The brace rods for the end wall are initially assumed to be 0.625 inch diameter while the brace rods for the side wall are initially assumed to be 0.875 inch diameter.

O.F. WEB THK.

0.1489

I.F.

5X0.25

6X0.3125

6X0.5

6X0.375

6.596'

10'-0"

10'-0"

0.1489

0.125

0.125

5X0.25

5X0.25

20'-0"

16'-0"

10'-4 3/4"

0.25

0.1489

5X0.3125

5X0.25

6X0.3125

6X0.3125

6X0.3125

5X0.25

5X0.25

5X0.25

0.1489

0.125

5X0.3125

5X0.3125 8.108'

16'-0"

Symm. C L Frame

0.50 12

20' E.H.

11

21'-11 3/4"

L.F. 8 x 5/16 WEB THK 0.1489 R.F. 8 x 5/16

H

17'-0 1/2"

0.125

WEB THK.

1

5X0.25

O.F.

H

7.042' 10'-0"

0.1780

5X0.25 5X0.25

5X0.25

2

12

3

S

S

S

S

S

10 S

S

S

S

H

S

S

S

S

9

8

7

6 5

4

0.4170'

I.F.

65'

35'

CONNECTION DETAILS : 1

2

17.0

28.0

Location Web Dep.

BASE

3 N/A

5

6

7

8

9

10

11

12

17.5

17.5

17.5

28.0

17.0

17.0

17.5

17.5

2E/2E

CAP (EXT)

2E/1F

SPLICE

SPLICE

SPLICE

2E/2E

2E/2E

Plate Plate(DN)

8.0X0.375

2.25X0.25

5.0X0.25

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

6.0X0.5

8.0X1.25

Plate Plate(UP)

N/A

N/A

N/A

6.0X0.5

N/A

6.0X0.375

N/A

N/A

6.0X0.5

6.0X0.5

N/A

N/A

N/A

N/A

(8)-3/4

N/A

N/A

Type

HORZ STF

4 28.0

(4)-3/4

Bolts

(6)-3/4

(8)-3/4

(8)-3/4

BASE

CAP/STF 8.0X0.5 2.75X0.25

(8)-3/4

(4)-1

Figure 2.4-1 Design Building B – Trial Moment Frame Structural Analysis Models Transverse Moment Frame Model

Exterior Frame Columns: Fixed Top, Pinned Base Interior Frame Columns: Fixed Top, Fixed Base

Eh/2

7

6

5

OR

Emh/2

H

G

F

E

1

3 A

V/2

I

J

8

9

23 FT.

OR

B 70 FT.

Eh/2

10

OR

4

2

C

64 FT.

OR

K 19 FT.

V/2

19 FT.

2.4.1

D 64 FT.

Figure 2.4-2 Design Building B – Transverse Frame Analysis Model

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Emh/2

Seismic Design Guide for Metal Building Systems

Transverse End Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.4-3 Design Building B – Transverse End Wall Analysis Model Longitudinal Side Wall Model

Exterior Frame Columns: Pinned Top, Pinned Base Interior Frame Columns: Pinned Top, Pinned Base

Figure 2.4-4 Design Building B – Longitudinal Side Wall Analysis Model 2.4.2

Design Earthquake Forces

For this building example, where there are more than three moment resisting connections along the line of resistance, the redundancy factor ρ is taken as 1.0 (See discussion in Section 1.4.1.2 of this guide). The design earthquake forces on individual frame or brace lines based on Design Example 1 are as follows: Design Building B Site 3

Transverse Moment Frame Transverse End Wall Longitudinal Side Wall

V

Eh

Ev

Emh*

(kips) 9.01 6.90 50.57

(kips) 9.01 6.90 50.57

(kips) 0.200D 0.200D 0.200D

(kips) 22.53 13.80 101.14

The values of Emh in the table are based on Ωo = 2.5 for transverse moment frames and Ωo = 2.0 for the transverse end wall and longitudinal side wall. *

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Seismic Design Guide for Metal Building Systems

2.4.3

Member Forces

For Design Building B, the dead, collateral, and earthquake forces on individual frame or brace lines based on Design Example 1 using AISC 341-05, and the requirements of AISC 360-05 Section C2.1b (second order analysis by amplified first-order elastic analysis) are as follows:

Dead Load

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

Collateral Load

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

2-71

Axial (kips) −3.32 −2.98 −6.92 −6.40 −1.69 −1.45 −1.71 0 −0.90 0 0 −3.32 0

Moment (ft-kips) 0 −25.5 1.90 −0.70 −24.2 −40.8 12.4 0 0 0 0 0 0

Shear (kips) −1.58 −1.58 −0.13 −0.13 2.63 −3.17 −0.07 0 0 −0.45 0 0 −0.09

Axial (kips) −1.20 −1.20 −2.56 −2.56 −0.67 −0.58 −0.68 0 −0.47 0 0 −1.20 0

Moment (ft-kips) 0 −10.2 −0.76 −0.28 −9.67 −16.3 4.97 0 0 0 0 0 0

Shear (kips) −0.63 −0.63 −0.05 −0.05 1.05 −1.27 −0.03 0 0 −0.24 0 0 −0.05

Seismic Design Guide for Metal Building Systems

Earthquake Loads, Eh

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top Beam At Exterior Column Beam At Interior Column Beam At Center End Wall Brace Rod End Wall Brace Column End Wall Beam Side Wall Brace Rod Side Wall Brace Column Side Wall Beam

Maximum Earthquake Loads, Emh1

Moment Frame Ext. Columns - Bottom Moment Frame Ext. Columns - Top Moment Frame Int. Columns - Bottom Moment Frame Int. Columns - Top End Wall Brace Rod (Ωo = 2.0) End Wall Brace Column (Ωo = 2.0) End Wall Beam (Ωo = 2.0) Side Wall Brace Rod (Ωo = 2.0) Side Wall Brace Column (Ωo = 2.0) Side Wall Beam (Ωo = 2.0) 1

2.4.4

Axial (kips) 0.49 0.49 −0.09 −0.09 −0.88 −0.88 −0.63 5.86 −3.77 4.49 27.52 −16.65 21.91

Moment (ft-kips) 0 15.14 −45.78 26.65 20.12 −21.38 −19.68 0 0 0 0 0 0

Shear (kips) 0.90 0.90 3.60 3.60 −0.67 −0.67 −1.17 0 0 0 0 0 0

Axial (kips) 1.22 1.22 −0.23 −0.23 9.01 −5.80 6.90 42.34 −25.62 33.72

Moment (ft-kips) 0 37.85 −114.45 66.63 0 0 0 0 0 0

Shear (kips) 2.25 2.25 9.01 9.01 0 0 0 0 0 0

Ωo = 2.5, unless otherwise noted.

Seismic Analysis Results Summary for Horizontal Displacements

In this section, the horizontal displacement results are presented for Design Building B for each of the structural analysis models. The actual twodimensional linear elastic analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier. The seismic displacement results are based on the applied frame line base shear, V, using unfactored load values (i.e. E, not 0.7E).

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Horizontal Displacements at the Eave Height Resulting from Applying the Frame Line Base Shear, V

2.4.5

Transverse Moment Frame

0.588 in

Transverse End Wall Braced Frames

0.278 in

Longitudinal Side Wall Braced Frames

0.708 in

Basic Load Case Analysis Results Summary for Member Forces

In this example, the member forces are presented for each of the basic load cases. Two seismic load cases are included. One seismic load case is for Eh and the other is for Emh. For the examples presented here, Eh and V are identical but since this is not always the case, separate basic load cases have been identified for the purposes of this document. The actual two-dimensional analysis was done by others and is not presented here, but is based on the structural models and applied loadings presented earlier. 2.4.6

Story Drift Checks

Story drift is evaluated based on ASCE 7-05 Section 12.8.6. Typically for metal buildings, three story drifts are calculated corresponding to the three structural models. The story drifts are calculated using ASCE 7 Equation 12.815. They are increased by an incremental factor to account for P-delta effects. For this example, three sets of drift checks will be made for each design. Note that footnote a of ASCE 7 Table 12.12-1 states “there shall be no drift limit for single-story structures with interiors walls, partitions, ceilings, and exterior walls that have been designed to accommodate the story drifts.” If this exception is utilized, it would be prudent to communicate this on the contract documents (i.e. the interior walls, partitions and ceilings should be detailed to accommodate drift). For illustrative purposes, this Guide provides drift calculations, even though it could be argued that they are unnecessary. 2.4.6.1 Determine Story Drift without P-Delta Effects

δx =

C d δ xe I

(ASCE Eq. 12.8-15)

Where: Cd = the deflection amplification factor from Design Example 1, i.e.: Cd = 3, for the transverse moment frame Cd = 3.25, for the transverse end wall

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Seismic Design Guide for Metal Building Systems

Cd = 3.25, for the longitudinal side wall I = the occupancy importance factor from Design Example 1 = 1.0

δxe = the elastic horizontal deflections resulting from applying the base shear V to an elastic structural analysis model of the building seismic-force-resisting system. For this example, these analyses were performed by others and the results provided in Section 2.1.4 of this example. Note that the base shear V of this example and Design Example 1 were determined using the simplified code period formulas. Alternatively, if a dynamic analysis (or Rayleigh equation) is performed and used for both design and analysis, as discussed in Section 1.3.1, the upper bound period limits of ASCE 7 Section 12.8.2 are not used when calculating drift. Substituting the above values and the previous displacement into ASCE 7 Equation 12.8-15: Story Drift w/o P-Delta Effects, δx Transverse Moment Frame

3(0.588 in ) = 1.76 in 1.0

Transverse End Wall

3.25(0.278 in ) = 0.91 in 1.0

Longitudinal Side Wall

3.25(0.71 in ) = 2.31 in 1.0

2.4.6.2 Determine P-Delta Incremental Factor in Accordance With ASCE 7 Section 12.8.7

For each seismic load combination, ASCE 7 Section 12.8.7 requires that the story drift, δx, be increased by a factor relating to the P-delta effects. This Pdelta incremental factor is defined as: Incremental Factor =

1.0 1−θ

Where the stability coefficient,θ , is determined in accordance with ASCE 7 Section 12.8.7. It should be noted that in ASCE Section 12.8.7, it states that if θ ≤ 0.10 , the P-delta effects can be ignored, which is the same as stating that the incremental factor may be taken as 1.0.

θ=

Px Δ V x hsx C d

(ASCE 7 Eq. 12.8-16)

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Seismic Design Guide for Metal Building Systems

Where: Px = the total unfactored vertical load at and above Level x; where computing Px, tributary to the frame line under consideration

Δ = the design story drift occurring simultaneously with Vx, inches (Note that for a single story building that Δ is equal to δx) Vx = the seismic shear force acting between level x and level x-1 hsx = the story height below level x (for buildings with pitched roof, the story height is taken as the eave height), inches Cd = deflection amplification factor in ASCE 7 Table 12.2-1 In addition, per ASCE 7 Section 12.8.7, θ shall not exceed θmax.

θ max =

0.5 ≤ 0.25 βC d

(ASCE 7 Eq. 12.8-17)

β = the ratio of the shear demand to capacity between level x and level x-1. Where the ratio is not calculated, β = 1.0 can conservatively be used. Note that ASCE 7 permits that where the P-delta effect is included in an automated (second order) analysis, Eq. 12.8-17 shall still be satisfied. However, the value of θ computed from Eq. 12.8-16, using the results of the P-delta analysis, is permitted to be divided by (1 + θ) before checking Eq. 12.8-17. For initial design calculations, it is typical to assume β = 1.0 and determine θmax based on that assumption, since member capacities have yet to be calculated. Once a design has been established, if the drift is greater than allowable, the β factor along with the P-delta incremental factor should be reevaluated based on actual shear demand to actual capacity and the drift rechecked. For this example, separate values of θ, θmax and the P-delta incremental factor are determined for each of the seismic-force-resisting systems (along each brace/frame line). The value of Px is the total vertical load obtained previously in this design example and is the sum of all unfactored column axial loads (including gravity only columns with axial loads taken at the top of the columns) resulting from dead load, floor live load and collateral load tributary to the frame line under consideration. Note that if the flat roof snow load is greater than 30 psf, Px would also include 20 percent of the snow load, unless otherwise required by the authority having jurisdiction. However it should also be noted that Px need not include the roof live load. For the example, the end wall Px is taken as the end wall brace column load multiplied times 8, while the side wall Px is taken as half of the total of all moment frame and end wall column loads. The following calculations illustrate the determination of Px for two example building designs.

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Seismic Design Guide for Metal Building Systems

2.4.6.3 Determination of Px

In the following calculations, the negative sign indicating compression has been ignored for simplicity in presentation. Transverse Moment Frame

Px = 2(2.98 + 6.40 + 1.20 + 2.56 ) = 26.28 kips Transverse End Wall

Px = 8(0.90 + 0.47 ) = 10.96 kips Longitudinal Side Wall

Px = 0.5[9(26.28) + 2(10.96 )] = 129.2 kips 2.4.6.4 Determine the P-Delta Incremental Factors

Vx is taken from the problem statement for this design example and hx is taken as the eave height of 240 inches. Cd and δx are indicated previously in this design example. β is not calculated and is therefore taken as 1.0. Substituting the above data into the P-delta equations, one obtains:

Px

Story Drift Parameters θ θmax Incremental factor

Transverse Moment Frame

26.28

0.0071

0.17

1.0

Transverse End Wall

10.96

0.0018

0.15

1.0

Longitudinal Side Wall

129.2

0.0076

0.15

1.0

Note, if θ > θmax in any of the above cases, either the seismic-forceresisting system would need to be redesigned or β would need to be calculated in order to determine if adequate shear capacity was present in the design. It should be noted that in this example P-delta effects could be ignored in all frame lines. 2.4.6.5 Determine the Design Story Drift with P-Delta Effects and Compare with IBC Drift Allowables of ASCE 7 Section 12.12

The design story drift with P-delta effects, Δ, is determined by simply multiplying the story drift without P-delta effects by the P-delta incremental factor. The design story drift is compared with the allowable story drift, Δa, specified in ASCE 7 Table 12.12-1. The allowable story drift is a function of occupancy category and building types.

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Seismic Design Guide for Metal Building Systems

In Design Example 1, it was determined that the occupancy category was II. From ASCE 7 Table 12.12-1, the allowable drift for this example is 0.025hsx provided the interior walls, partitions, ceilings, and exterior wall systems have been designed to accommodate the story drift and the building is four stories or less in height. Note that the allowable drift would be 0.020hsx, if the aforementioned conditions are not met. hsx is taken as the eave height, equal to 20 feet for this example. It is recommended that the building first be checked for the value of 0.020hsx. If it is acceptable, then no special detailing of architectural components will be required beyond that already specified. For this design example, separate drift check calculations are made for each of the seismic forces resisting systems for each design.

Design Story Drifts

Δ

0.020hsx

0.025hsx

Transverse Moment Frame

1.76 in

4.8 in

6.0 in

Transverse End Wall

0.91 in

4.8 in

6.0 in

Longitudinal Side Wall

2.31 in

4.8 in

6.0 in

In the example, all the design story drifts are less than the 0.020hsx design allowables; therefore, no special detailing of architectural components is required beyond that already specified. 2.4.7

Basic Load Combinations

The basic load combinations are discussed in Section 2.1.8.1. From the problem statement and Design Example 1, Ev = 0.200D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0 . Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable basic load combinations are: (1.0 + 0.14 S DS ) ( D + C ) ± 0.7 ρQ E

Eq. 5

(0.6 − 0.14S DS ) D ± 0.7 ρQE

Eq. 8

Substituting SDS = 1.00 yields the following: 1.14( D + C ) ± 0.7 ρQE

Eq. 5

0.46 D ± 0.7 ρQE

Eq. 8

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Seismic Design Guide for Metal Building Systems

2.4.8

Allowable Strength Seismic Load Combinations with Overstrength Factor

The load combinations with overstrength factor are discussed in Section 2.1.8.2. From the problem statement and Design Example 1, Ev = 0.20D, S ≤ 30 (so S = 0), C is considered as D if it results in an adverse loading, and L = 0. Therefore, Equation 6 will not govern and will not be considered further in this example. The applicable load combinations with overstrength factors are: (1.0 + 0.14 S DS ) ( D + C ) ± 0.7Ω oQ E

Eq. 5

(0.6 − 0.14S DS ) D ± 0.7Ω o QE

Eq. 8

Substituting SDS = 1.00 yields the following:

2.4.9

1.14( D + C ) ± 0.7Ω o QE

Eq. 5

0.46 D ± 0.7Ω o QE

Eq. 8

Design of Diaphragm Systems Including Horizontal Roof Bracing

The example buildings contain three sets of horizontal roof bracing that transfer wind and seismic forces from the end walls and roof to the sets of vertical bracing that are provided along the longitudinal walls of the buildings. These horizontal roof bracing systems are acting as diaphragms in transferring horizontally applied loads to the seismic force resisting elements, consistent with the definition of a diaphragm in 2006 IBC Section 1602.1. Each set of horizontal bracing is laid out between adjacent transverse moment frames that are spaced 25 feet apart, with bracing work points spaced at 25 foot centers across the building width, so as to align with the vertical columns that are spaced along each end wall of the building. Thus, wind against the end walls and seismic forces are transferred from the end wall columns at the roof, through roof purlins that act as struts, to the work points of the horizontal roof bracing. In the transverse direction (assuming flexible diaphragm behavior), each frame resists a tributary portion of the roof seismic force. Typically, the roof spans the short distance between each frame without bracing; however, experience has shown that horizontal bending of purlins and girts in conjunction with the stiffness of roof panels are adequate to resist the marginal forces that develop over this short distance. Horizontal seismic load effects, Eh, and component forces, Fp, shown in subsequent sections are unfactored. Note that in allowable strength design load combinations used in conjunction with AISC 341-05, these seismic loads are factored by either 0.7 or 0.525.

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Seismic Design Guide for Metal Building Systems

2.4.9.1 Determination of Diaphragm Design Force Coefficients Including Horizontal Bracing

Diaphragms, including horizontal bracing requirements, are specified in ASCE Section 12.10. Design forces are calculated by the following: n

Fpx =

¦F

i

i=x n

¦w

wpx

ASCE Eq. 12.10-1

i

i= x

where Fpx

= diaphragm design force

Fi

= design force at level i (determined by ASCE 7 Eq. 12.8-11)

wi

= weight tributary to level i

wpx

= weight tributary to diaphragm at level x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx Note that for a one-story building, the equation for Fpx simplifies to the following: Fpx = V but is still subject to the maximum and minimum limitations above. Per ASCE 7 Section 12.3.4.1, the redundancy factor, ρ, that is applied to diaphragms (including horizontal bracing systems) is 1.0 for all Seismic Design Categories, when the loads are determined in accordance with ASCE 7, Eq. 12.10.1. The load combinations to be used for the design of members and connections in the horizontal bracing system need not consider special seismic load combinations with the overstrength factor except where the members also serve as collectors or are common to the vertical seismic force resisting system (See Section 1.4.3 for further discussion). Design Building B is required to be designed using SDC D requirements. Roof bracing/diaphragm design forces in the longitudinal axis of the building are based on the design forces used for the bracing of the longitudinal side walls. Substituting in the values calculated in Section 1.3.4.4: wpx = wi = W = 164.2 kips Fi = V = 50.57 kips yields, using ASCE 7 Eq. 12.10-1

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Seismic Design Guide for Metal Building Systems

n

¦F

i

Fpx = Froof ,longitudinal =

i= x n

¦w

50.57kips wroof = 0.308wroof,longitudinal 164.2kips

w px =

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (1.225) (1.00)wpx ≤ Fpx ≤ (0.4) (1.225) (1.00)wpx 0.245wpx ≤ Fpx ≤ 0.490wpx Therefore, use Fpx = 0.308wroof,longitudinal Diaphragm design forces for the metal roof deck that spans the short 25-foot dimension between transverse frames is based on the design forces used for the transverse frames. For a typical interior bay, substituting in the values from Section 1.3.4.4, wpx = wi = W = 31.5 kips Fi = V = 9.01 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i= x n

¦w

w px =

9.01kips wroof = 0.286wroof,transverse 31.5kips

i

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (1.225) (1.00)wpx ≤ Fpx ≤ (0.4) (1.225) (1.00)wpx 0.245wpx ≤ Fpx ≤ 0.490wpx Therefore, use Fpx = 0.286wroof, transverse For the two end bays, the average of the two adjacent frame design forces is used. Substituting in the values from Section 1.3.4.4:

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Seismic Design Guide for Metal Building Systems

wpx = wi = W = 31.5 kips + 22.4 kips = 53.9 kips Fi = V = 9.01 kips + 6.90 kips = 15.91 kips yields, using ASCE 7 Eq. 12.10-1 n

¦F

i

Fpx = Froof ,transverse =

i= x n

¦w

w px =

i

(9.01kips + 6.90kips ) w (31.5kips + 22.4kips ) roof

= 0.295wroof,transverse

i= x

with the limitation that 0.2SDSIwpx ≤ Fpx ≤ 0.4SDSIwpx (0.2) (1.225) (1.00)wpx ≤ Fpx ≤ (0.4) (1.225) (1.00)wpx 0.245wpx ≤ Fpx ≤ 0.490wpx Therefore, use Fpx = 0.295wroof, transverse The controlling diaphragm design force in the longitudinal direction, is the largest of the three forces calculated above, resulting in: Fpx = 0.308wroof,longitudinal 2.4.10

Determination of Diaphragm Seismic Weights Including Horizontal Bracing

Seismic forces resulting from the roof and wall weight are resisted in the longitudinal direction by three bays of horizontal roof bracing that collect and transfer these forces to the vertical side wall bracing. The following calculations consider only diaphragm forces in the longitudinal building axis. In the longitudinal direction, the horizontal roof bracing resists forces resulting from both the roof and frame weights: Roof panel and insulation Roof purlin Frame Collateral Load Total

= = = = =

1.5 psf 1.0 psf 2.0 psf 1.5 psf 6.0 psf × roof area

In the longitudinal direction, the diaphragm also resists tributary forces for the end walls, at a weight of 3.0 psf times the tributary wall area. The resulting seismic weights are equal to:

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Seismic Design Guide for Metal Building Systems

Roof Weight = (200 ft ) (250 ft ) (6 psf ) = 300,000 lbs = 300 kips

End Wall Weight = 2 ×

(200 ft ) (22.09 ft ) × 3.0 psf 2

= 13,254 lbs = 13.3 kips

Where, 22.09 feet is the average height of the end walls. Total Seismic Weight roof ,longit = 300.0 + 13.3 = 313.3 kips 2.4.11

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

For Design Building B, the diaphragm design force in the longitudinal direction becomes: Froof = 0.308wroof (from Section 2.4.9.1) Froof, longitudinal = 0.308(313.3 kips) = 96.50 kips Froof ,longitudinal = 2.4.12

(96.50kips) (1000 lbs / kip ) = 200 ft

482.5 lb/ft

Determination of Diaphragm Element Design Forces Including Horizontal Bracing

Each building has three sets of horizontal roof bracing which combine to resist the longitudinal forces. Distribution of the total applied forces to each set of bracing may be subject to differing opinions. For simplicity’s sake and to promote a more uniform roof bracing design, it is preferred to assume that forces are distributed equally between each set of bracing. 2.4.12.1 Horizontal Bracing Systems

For Design Building B, the seismic design force applied at each work point of the roof bracing is:

(482.5 lb/ft ) (25 ft ) = 4,021 lbs 3 sets of bracing

The reaction force at each end of the truss is equal to:

(200 ft − 25 ft ) (482.5 lb/ft ) = 14,073 lbs 2 × 3 sets of bracing

The 25 feet is deducted because the last 12.5 feet at each end of the span is assumed to load the eave strut and vertical bracing directly.

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Seismic Design Guide for Metal Building Systems

4,021 lb

1

4,021 lb

2 A

4,021 lb

3 B

4,021 lb

4

4,021 lb

5 D

C

4,021 lb

6 E

4,021 lb

7 F

8 G

8 @ 25 ft = 200 ft

14,073 lb

14,073 lb

Figure 2.4-5 Plan View of Typical Roof Bracing – Design Building B

The actual design forces in each brace element must reflect the member orientation and the tension-only nature of the rod bracing used. For this example, the lateral spacing of bracing points (25 ft) is equal to the longitudinal column spacing; thus, each rod is oriented at 45 degrees. Design Load Combination

IBC and AISC 341-05 are nonspecific but imply an inherent difference between vertical braced frames and horizontal bracing systems that are used as diaphragms. Although vertical tension-only bracing is permitted, connections are designed using the load combination with overstrength, Em = ΩoQE (see Section 2.3.1), horizontal tension-only bracing systems are permitted to be designed using the normal Eh = ρQE load combinations. From Figure 2.4-5, the rod tension and connection seismic design force in Rod (1) is: QE =

14,073 lbs 14,073 lbs = = 19,902 lbs = 19.90 kips cos(45°) 0.707

The maximum seismic design force in the horizontal bracing rods is: E h = ρQE = (1.0) (19.90 kips ) = 19.90 kips where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 Note that the required design force is computed for Rod 1 in Figure 2.4-5, while the design forces for Rods 2, 3, and 4 are smaller. The analysis to determine these smaller forces is not included in this example. Brace rods are designed using the AISC 360-05.

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Seismic Design Guide for Metal Building Systems

The compression members of the horizontal truss system (at the most heavily loaded strut that is not a collector, shown as Member “A” in Figure 2.4-6) must be designed for a seismic design force equal to: Eh = ρQE = (1.0) (14,073 lbs ) = 14,073 lbs where ρ = 1.0 for diaphragms per ASCE 7-05, Section 12.3.4.1 AISC 360-05 is also used for the design of the compression struts. The design of these struts should consider applicable vertical loads plus any bending moment that may result from eccentricity between the location of horizontal bracing forces and the center of the compression member. Special strut members as shown in Figure 2.4-7 may be needed when cold-formed purlin section cannot be shown to be adequate to resist the resulting stresses. In addition, the tension/compression chord seismic design force must be resisted by the roof beams and splices of the main building frames at braced bays as shown in Figure 2.4-6 and is equal to: Chord Force =

(14,073 lbs ) (100 ft ) − 4,021 lbs(25 + 50 + 75 ft ) = 32,166 lbs = 32.17 kips 25 ft

4,021 lb

4,021 lb

2010 lb

4,021 lb

32,166 lb 2 A

4

3 B

C

RIDGE

EAVE

1

32,166 lb

14,073 lb

Figure 2.4-6 Design Building B, Free Body Diagram Showing Bracing Chord Seismic Design Force at Mid-Span

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Seismic Design Guide for Metal Building Systems

purlin

P strut

2.4-7. Positioning the Roof Bracing and Struts to Minimize Eccentricity 2.4.12.2 Eave Struts

The eave struts are the members at each eave of the roof that form the intersection of roof and wall. The eave struts often serve as collector elements for earthquake forces along the building length and transfer them to the vertical bracing systems. The applied eave strut seismic design forces, for Design Building B, are calculated as follows: From end wall: ( 20 ft )( 25 ft ) (3 psf ) (0.308) = 116 lbs 4 From tributary roof and side wall: ª§ 25 ft · º § 20 ft · «¨ 2 ¸ (6 psf ) + ¨ 2 ¸ (3 psf )» (0.308) = 32.5 lbs / ft ¹ © ¹ ¬© ¼

The resulting applied forces and internal forces for Design Building B are shown in Figure 2.4-8.

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Seismic Design Guide for Metal Building Systems

32.5 lb/ft 116 lb

116 lb BRACED 50 ft BAY

BRACED BAY

100 ft 2,785.7 lb TO WALL BRACING

75 ft

BRACED BAY

25 ft

2,785.7 lb TO WALL BRACING

2,785.7 lb TO WALL BRACING

APPLIED FORCES

1,741 lb

2,205.3 lb

1,857.1 lb

COMPRESSION

116 lb

116 lb

TENSION

1,044.7 lb

580.4 lb

928.6 lb

Figure 2.4-8 Eave Strut Applied and Internal Forces – Design Building B

The resulting seismic design forces for the eave struts are as follows: Eh = ρQE = (1.0) (2,205.3 lbs) = 2,205.3 lbs It should be noted that appropriate load factors need to be applied to the above loads when added to load combinations. An additional strut force is required to transfer the forces from the horizontal to the vertical bracing. Depending upon the positioning of the horizontal roof and vertical rod bracing, the eave strut might also act as a strut to transfer both the forces shown above, as well as the forces from the roof bracing to the wall bracing. Alternatively, a separate strut member could be provided at the bracing, similar to the situation shown in Figure 2.4-7. As a separate strut, the required seismic design force from the roof to the wall bracing would be as follows: Emh = Ωo QE = (2.0) (14,073 lbs) = 28,146 lbs If only a single eave strut is provided to resist both forces, then the member seismic design force would be the following: Emh = 2,867 lbs + 28,146 lbs = 31,013 lbs

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Seismic Design Guide for Metal Building Systems

Eave struts often serve as collectors or drag elements. ASCE 7 Section 12.10.2.1 requires collector elements, splices, and their connections in Seismic Design Categories C, D, E, and F to be designed using the special Em load combination forces. Eave struts become collectors when forces from the horizontal roof bracing systems are required to be transferred through a length of strut to the location of vertical braced frames. This becomes a particular design consideration when the location of roof bracing bays does not match the location of bays containing vertical braced frames. In this example, the bays align, therefore only a single span of strut at each braced frame acts as a collector element. Other tributary seismic forces carried by the eave strut are small in magnitude due to the typically small tributary width of roof and wall that attaches to the strut. Because the eave strut carries no more seismic forces in this regard than many other roof purlins, it was considered appropriate to design for this portion of the force in the same manner as other similar elements are designed. 2.4.13

Design of Side Wall OCBF

Ordinary concentrically braced frame member design is covered in AISC 34105, Section 14. Brace members are designed using Eh, while the required strength of brace connections need not exceed either the maximum force that can be developed by the system or a load effect based upon using the amplified seismic load, Emh (i.e. the load combination using overstrength factors). Note that the redundancy factor, ρ, is equal to 1.3 as discussed in Section 1.4.1.3. The member design follows similar procedures as shown for the roof bracing in Section 2.4.9. Member Forces

Seismic forces resisted by the side wall bracing can be calculated two ways. (1) As the sum of the forces from the roof bracing plus the eave struts: V = 3(14,073 lbs + 2,786 lbs ) = 50,577 lbs

(2) As the total calculated building seismic force (from Example 1, Section 1.4.2.4):

V = 50,570 lbs The difference is not significant and is primarily due to round-off of numbers in the analysis. For this example the total calculated building seismic forces from Example 1 will be used.

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Seismic Design Guide for Metal Building Systems

Design forces for the horizontal beam at the braced bay were described in the preceding section. Forces in for bracing and adjacent columns are calculated in this section.

Figure 2.4-9 Longitudinal Side Wall Analysis Model

Horizontal Force per Longitudinal Braced Bay, QE: QE =

50,570 lbs = 16,860 lb/bay = 16.9 kips 3 bays

Brace Rod Length =

(25 ft )2 + (19 ft )2

= 31.4 ft

Brace Rod Force: § 31.4 ft · ¸¸ (16.9 kips ) = 21.2 kips QE = ¨¨ © 25 ft ¹

Column Force: § 19 ft · ¸¸ (16.9 kips ) = 12.84 kips QE = ¨¨ 25 ft © ¹ 2.4.13.1 Design of Side Wall Brace Rods Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P M Side Wall Brace Rod Design Forces (kips) (ft-kips) Dead (D) 0.00 0.00 Collateral (C) 0.00 0.00 27.5 0.00 Earthquake (Eh = ρQE) 42.4 0.00 Earthquake w/overstrength (Emh = ΩoQE) Ma Pa ASD Load Combinations (kips) (ft-kips) 1.0336( D + C ) + 0.7 ρQE 19.3 0.00 1.0336( D + C ) − 0.7 ρQE 0.00 −19.3 0.566 D + 0.7 ρQE 19.3 0.00 0.566 D − 0.7 ρQE 0.00 −19.3

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V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

1

ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) 29.7

Ma (ft-kips) 0.00

Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−29.7

0.00

0.00

0.566 D + 0.7Ω o QE

29.7

0.00

0.00

0.566 D − 0.7Ω o QE 0.00 0.00 −29.7 Note that the ASD Load Combinations w/overstrength are only used for the brace rod connection design.

2.4.13.2 Design of Side Wall Brace Columns

Side wall brace columns must meet the requirements of Section 8.3 of AISC 341-05. Note that these columns are elements of the building moment frames. Design of these columns may have to include the simultaneous orthogonal column forces caused by dead and collateral load conditions depending on the seismic design category. In metal building designs, orthogonal effects are typically found in columns and column bases which are elements of the seismic force resisting systems in each direction. For example, a column which serves as part of a transverse moment frame in one direction and as part of a concentrically braced frame in the other direction is subject to orthogonal effects. In accordance with ASCE 7 Section 12.5.2, orthogonal effects need not be investigated for buildings assigned to SDC B. For SDC C, the orthogonal effects are required only when Type 5 structural plan irregularity is present, i.e. nonparallel systems (see ASCE 7 Table 12.3-1). For high seismic applications (SDC D, E, or F) the orthogonal effects must be considered in all cases. ASCE 7 Section 12.5.3 lists two possible solutions (1) Apply 100 percent of the design force in one direction and 30% in the other, and (2) Simultaneous application of orthogonal ground motion. While either option is sufficient to satisfy this code requirement, the first approach is commonly used for design of metal building systems because the other approach is tied with the more complex methods such as time-history analysis. Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P Side Wall Brace Column Design Forces (kips) Dead (D) −3.32 Collateral (C) −1.20 Earthquake (Eh = ρQE) −16.7 Earthquake w/overstrength (Emh = ΩoQE) −25.6

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M (ft-kips) 0.00 0.00 0.00 0.00

V (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) −16.4 −7.02 −13.6 9.81 Pa (kips) −22.6

Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

13.2

0.00

0.00

0.566 D + 0.7Ω o QE

−19.8

0.00

0.00

0.566 D − 0.7Ω o QE

16.0

0.00

0.00

ASD Load Combinations

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with the AISC 360-05 Sections D and E, using the ASD provisions. 2.4.13.3 Design of Side Wall Brace Beams

Side wall brace beams must meet the requirements of Section 8.3 of AISC 34105. Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P M Side Wall Brace Beam Design Forces (kips) (ft-kips) Dead (D) 0.00 0.00 Collateral (C) 0.00 0.00 21.9 0.00 Earthquake (Eh = ρQE) 33.7 0.00 Earthquake w/overstrength (Emh = ΩoQE) Ma Pa ASD Load Combinations (kips) (ft-kips) 1.0336( D + C ) + 0.7 ρQE 15.3 0.00 1.0336( D + C ) − 0.7 ρQE 0.00 −15.3 0.566 D + 0.7 ρQE 15.3 0.00 0.566 D − 0.7 ρQE 0.00 −15.3

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V (kips) −0.09 −0.05 0.00 0.00 Va (kips) −0.14 −0.14 −0.05 −0.05

Seismic Design Guide for Metal Building Systems

ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) 23.6

Ma (ft-kips) 0.00

Va (kips) −0.14

1.0336( D + C ) − 0.7Ω o QE

−23.6

0.00

−0.14

0.566 D + 0.7Ω o QE

23.6

0.00

−0.05

0.566 D − 0.7Ω o QE

−23.6

0.00

−0.05

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. 2.4.14

Design of End Wall OCBF

Ordinary concentrically braced frame member design is covered in AISC 34105, Section 14. Brace members are designed using Eh, while the required strength of brace connections need not exceed either the maximum force that can be developed by the system or a load effect based upon using the amplified seismic load, Emh (i.e. the load combination using overstrength factors). Note that the redundancy factor, ρ, is equal to 1.3 as discussed in Section 1.4.1.3. The member design follows similar procedures as shown for the roof bracing in Section 2.4. Member Forces

A calculation, as shown below, can be made to obtain the brace rod and column forces. Alternatively, the forces from the frame analysis based on more accurate geometry can be used. From Example 1, Section 1.4.3.4, the total seismic design force for each end frame is: V = 6.90 kips

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Seismic Design Guide for Metal Building Systems

Figure 2.4-10 – Transverse End Wall Framing

Horizontal Force per End Wall Braced Bay, QE: QE =

6,900 lbs = 3,450 lb/bay = 3.45 kips 2 bays

Brace Rod Length =

(25 ft )2 + (21 ft )2

= 32.6 ft (using avg. ht. of 21 ft)

Brace Rod Force: § 32.6 ft · ¸¸ (3.45 kips ) = 4.50 kips QE = ¨¨ © 25 ft ¹

Column Force: § 21 ft · ¸¸ (3.45 kips ) = 2.90 kips QE = ¨¨ © 25 ft ¹ 2.4.14.1 Design of End Wall Brace Rods Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P M End Wall Brace Rod Design Forces (kips) (ft-kips) Dead (D) 0.00 0.00 Collateral (C) 0.00 0.00 5.86 0.00 Earthquake (Eh = ρQE) 0.00 Earthquake w/overstrength (Emh = ΩoQE) 9.01

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V (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems

1.0336( D + C ) + 0.7 ρQE 1.0336( D + C ) − 0.7 ρQE 0.566 D + 0.7 ρQE 0.566 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.0336( D + C ) + 0.7Ω o QE

Pa (kips) 4.10 −4.10 4.10 −4.10 Pa (kips) 6.31

Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00

1.0336( D + C ) − 0.7Ω o QE

−6.31

0.00

0.00

0.566 D + 0.7Ω o QE

6.31

0.00

0.00

0.566 D − 0.7Ω o QE

−6.31

0.00

0.00

ASD Load Combinations

1

Note that the ASD Load Combinations w/overstrength are only used for the brace rod connection design.

2.4.14.2 Design of End Wall Brace Columns

End wall brace columns must meet the requirements of Section 8.3 of AISC 341-05. Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P M Column Design Forces (kips) (ft-kips) Dead (D) 0.00 −0.90 Collateral (C) 0.00 −0.47 0.00 Earthquake (Eh = ρQE ) −3.77 0.00 Earthquake w/overstrength (Emh = ΩoQE) −5.80 Ma Pa ASD Load Combinations (kips) (ft-kips) 1.14 D + C ) + 0.7 ρQE 0.00 −4.20 1.14( D + C ) − 0.7 ρQE 1.08 0.00 0.46 D + 0.7 ρQE 0.00 −3.05 0.46 D − 0.7 ρQE 2.23 0.00 Pa Ma ASD Load Combinations (kips) (ft-kips) w/overstrength1 1.14( D + C ) + 0.7Ω o QE 0.00 −5.62 1.14( D + C ) − 0.7Ω o QE 2.50 0.00 0.46 D + 0.7Ω o QE 0.00 −4.47

0.46 D − 0.7Ω o QE

3.65

2-93

0.00

V (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00 Va (kips) 0.00 0.00 0.00 0.00

Seismic Design Guide for Metal Building Systems 1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame columns are calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. For allowable strength design, if

Ω c Pa Pn

> 0.4 , the requirements of AISC 341-

05, Section 8.3 must be satisfied. There are no additional requirements specific to column members in Section 14 of Part I, AISC 341-05 for OCBF. 2.4.14.3 Design of End Wall Beam

End wall brace beams must meet the requirements of Section 8.3 of AISC 34105. Loads and Load Combinations (ρ = 1.3, Ωo = 2.0) P End Wall Brace Beam Design Forces (kips) Dead (D) 0.00 Collateral (C) 0.00 4.49 Earthquake (Eh = ρQE) 6.90 Earthquake w/overstrength (Emh = ΩoQE) Pa ASD Load Combinations (kips) 1.0336( D + C ) + 0.7 ρQE 3.14 1.0336( D + C ) − 0.7 ρQE −3.14 0.566 D + 0.7 ρQE 3.14 0.566 D − 0.7 ρQE −3.14 Pa ASD Load Combinations 1 (kips) w/overstrength 1.0336( D + C ) + 0.7Ω o QE 4.83

M (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00 0.00 0.00 0.00 Ma (ft-kips) 0.00

V (kips) −0.45 −0.24 0.00 0.00 Va (kips) −0.71 −0.71 −0.25 −0.25 Va (kips) −0.71

1.0336( D + C ) − 0.7Ω o QE

−4.83

0.00

−0.71

0.566 D + 0.7Ω o QE

4.83

0.00

−0.25

0.566 D − 0.7Ω o QE

−4.83

0.00

−0.25

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Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial strength of the brace frame beams is calculated in accordance with AISC 360-05 Sections D and E, using the ASD provisions. 2.4.15

Design of Ordinary Moment Frames

2.4.15.1 OMF Columns

Moment frame columns must meet the requirements of AISC 341-05. Loads and Load Combinations (ρ = 1.3, Ωo = 2.5) Top of Interior Columns

V (kips) −0.13 −0.05 3.60 9.01 Va (kips) 2.31

0.46 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.14( D + C ) + 0.7Ω o QE

P M (kips) (ft-kips) −6.40 −0.70 −2.56 −0.28 26.65 −0.09 66.63 −0.23 Ma Pa (kips) (ft-kips) −10.28 17.54 −10.15 −19.77 18.33 −3.01 −2.88 −18.98 Pa Ma (kips) (ft-kips) −10.38 45.52

1.14( D + C ) − 0.7Ω o QE

−10.05

−47.76

−6.51

0.46 D + 0.7Ω o QE

−3.11

46.32

6.25

0.46 D − 0.7Ω o QE

−2.78

−46.96

−6.37

Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.14( D + C ) + 0.7 ρQE 1.14( D + C ) − 0.7 ρQE 0.46 D + 0.7 ρQE

2-95

−2.73 2.46 −2.58 Va (kips) 6.10

Seismic Design Guide for Metal Building Systems

Bottom of Interior Columns

M (ft-kips) 1.90 −0.76 −45.78 −114.45 Ma (ft-kips) −30.75 33.35

0.46 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.14( D + C ) + 0.7Ω o QE

P (kips) −6.92 −2.56 −0.09 −0.23 Pa (kips) −10.87 −10.74 −3.25 −3.12 Pa (kips) −10.97

1.14( D + C ) − 0.7Ω o QE

−10.65

81.41

−6.51

0.46 D + 0.7Ω o QE

−3.34

−79.24

6.25

0.46 D − 0.7Ω o QE

−3.02

80.99

−6.37

Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.14( D + C ) + 0.7 ρQE 1.14( D + C ) − 0.7 ρQE 0.46 D + 0.7 ρQE

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−31.17 32.92 Ma (ft-kips) −78.82

V (kips) −0.13 −0.05 3.60 9.01 Va (kips) 2.31 −2.73 2.46 −2.58 Va (kips) 6.10

Seismic Design Guide for Metal Building Systems

Top of Exterior Columns

0.46 D − 0.7 ρQE ASD Load Combinations w/overstrength1 1.14( D + C ) + 0.7Ω o QE

P (kips) −2.98 −1.20 0.49 1.22 Pa (kips) −4.42 −5.11 −1.03 −1.71 Pa (kips) −3.91

M (ft-kips) −25.5 −10.2 15.14 37.85 Ma (ft-kips) −30.10 −51.30 −1.13 −22.33 Ma (ft-kips) −14.20

V (kips) −1.58 −0.63 0.90 2.25 Va (kips) −1.89 −3.15 −0.10 −1.36 Va (kips) −0.94

1.14( D + C ) − 0.7Ω o QE

−5.61

−67.19

−4.09

0.46 D + 0.7Ω o QE

−0.52

14.77

0.85

0.46 D − 0.7Ω o QE

−2.22

−38.23

−2.30

Design Forces

Dead (D) Collateral (C) Earthquake (Eh = ρQE) Earthquake w/overstrength (Emh = ΩoQE) ASD Load Combinations 1.14( D + C ) + 0.7 ρQE 1.14( D + C ) − 0.7 ρQE 0.46 D + 0.7 ρQE

1

Note that the ASD Load Combinations w/overstrength are only used for Ω P column base design and for column axial check where c a > 0.4 , as Pn specified in AISC 341-05, Section 8.3.

Allowable Strengths

The axial, shear, and flexural strength of the moment frame columns are calculated in accordance with AISC 360-05 Sections D, E, F, G and H, using the ASD provisions.

Ω c Pa

> 0.4 , the requirements of AISC 341Pn 05, Section 8.3 must be satisfied. Flexure need not be combined with axial forces when considering this provision.

For allowable strength design, if

There are no additional requirements specific to column members of ordinary moment frames in Section 11, Part I of AISC 341-05 beyond AISC 360-05 requirements. Final Drift Check

The previously calculated drift checks were based on displacements using the initial trial member sizes. None of the trial member sizes changed as a result of

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the design of the moment frame beams and columns. As a result, the previously calculated drift checks are appropriate. Had the initial trial sizes for the moment frame beams and/or columns been changed, the drift calculations might need to be repeated. If the initial trial sizes for the moment frame beams and/or columns increased in flexural stiffness, the previously calculated drift checks would be conservative and not require recalculation. 2.4.15.2 Design of OMF Beams

There are no additional requirements specific to beam members beyond the AISC Specification (360-05) requirements.

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2.5

BEAM-TO-COLUMN CONNECTION DESIGN

As previously discussed in Section 1.3.3.1, the R = 1 approach is used throughout this Guide for the beam-to-column connection design. Design Building A (R > 3)

1.0336( D + C ) + 0.7 Emax

P (kips) −1.55 −0.66 0.07 Pa (kips) −2.24

M (ft-kips) −19.8 −8.48 64.8 Ma (ft-kips) 16.1

V (kips) 2.39 1.02 −1.58 Va (kips) 2.42

1.0336( D + C ) − 0.7 Emax

−2.33

−74.6

4.63

0.566 D + 0.7 Emax

−0.83

34.1

0.25

0.566 D − 0.7 Emax

−0.93

−56.6

2.46

Design Forces

Dead (D) Collateral (C) Earthquake (Emax = 3.5QE )1 ASD Load Combinations

1

Emax = 3.5QE , which gives equivalent seismic forces to R = 1

Design Building B

1.14( D + C ) + 0.7 Emax

P (kips) −1.69 −0.67 −3.08 Pa (kips) −4.85

M (ft-kips) −24.2 −9.67 70.4 Ma (ft-kips) 10.7

V (kips) 2.63 1.05 −2.35 Va (kips) 2.55

1.14( D + C ) − 0.7 Emax

−0.53

−87.9

5.84

0.46 D + 0.7 Emax

−2.93

38.1

−0.44

0.46 D − 0.7 Emax

1.38

−60.4

2.85

Design Forces

Dead (D) Collateral (C) Earthquake (Emax = 3.5QE )1 ASD Load Combinations

1

Emax = 3.5QE , which gives equivalent seismic forces to R = 1

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AISC 341-05 does not require qualifying cyclic testing for the moment connections of ordinary moment frames, provided the prescriptive requirements of Section 11.2a are followed. This section prohibits using single-sided partial-joint penetration groove welds and single-sided fillet welds to resist tensile forces in the connection. However, double-sided partial-joint-penetration groove welds and double-sided fillet welds are permitted if the connections are designed to resist a required force of 1.1R y Fy Ag of the tension portion of the connection part. AISC 341-05, Section 7.2, stipulates that all faying surfaces shall be prepared as required for slip-critical joints with a Class A surface. However, an exception is provided for end-plate moment connections, whereby the faying surfaces of these connections are permitted to be coated with coatings not tested for slip resistance, or with coatings with a slip coefficient less than that of a Class A surface. In this example, the end-plate connection design procedure in the AISC/MBMA Design Guide 16, Flush and Extended Multiple-Row Moment End-Plate Connections, is used for the design of this connection. 2.5.1

Design Building A

2.5.1.1 Beam-to-Column End-Plate Connection Design

AISC/MBMA Design Guide 16 is based on LRFD design; however it stipulates that ASD design forces should be multiplied by 1.5. Therefore, from the above table, the controlling moment at the connection is −74.6 × 1.5 = −111.9 ft-kips. The maximum positive moment (34.1 × 1.5 = 51.2 ft-kips) will not control the design. However, since the connection is not symmetrical, the end plate and bottom bolts should be checked for the maximum positive moment and axial force. AISC/MBMA Design Guide 16 has a procedure for modifying the connection moment due to the effects of axial load. The procedure is to convert the factored axial load into an equivalent moment that is added to the factored connection moment for axial tension, or subtracted from the factored connection moment for axial compression. For this example the axial load is compression, 2.33 × 1.5 = 3.50 kips. The equivalent moment, Maxial, is §P · § 3.50 kips · (30.5 in − 0.25 in ) = 4.4 ft - kips M axial = ¨ u ¸ (d − t f ) = ¨ ¸ 2 12 in/ft ¹ © © 2¹

The connection design negative moment is then M c = 111.9 − 4.4 = 107.5 ft - kips The shear force that accompanies this design moment is equal to 4.63 × 1.5 = 6.95 kips. The end-plate width is 6 in to match the column flange width. The beam flange width is 5 in, ASTM A572 Gr 50 steel and 0.75 in diameter A325-N bolts ( Fnt = 90 ksi, Fnv = 48 ksi) are used.

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Seismic Design Guide for Metal Building Systems

Geometric design data 1 2

b f = 5 in tf =

1 4

p f ,i = 1 in p f ,o = 1

in

b p = 6 in tp =

1 2

3 16

in

pb = 3 in pext = 2

in

g = 3 in

1 2

d = 30

in 1 2

in

t w = 0.1780 in

Figure 2.10-1 Geometric Design Data

Calculate:

γ r = 1.0 for extended connections § 0.25 · d 0 = 30.5 + 1.1875 − ¨ ¸ = 31.5625 in © 2 ¹

h0 = 31.6875 in

§ 0.25 · d1 = 30.5 − 0.25 − 1.5 − ¨ ¸ = 28.625 in © 2 ¹

h1 = 28.75 in

§ 0.25 · d 2 = 30.5 − 0.25 − 1.5 − 3.0 − ¨ ¸ = 25.625 in © 2 ¹

h2 = 25.75 in

Using the AISC/MBMA Design Guide 16 analysis procedure (Appendix B), the end-plate yield-line strength is: 2-101

Seismic Design Guide for Metal Building Systems

φ b M pl = φ b F py t 2p Y where:

Y=

bp ª§ h1 · § h2 · § h0 · 1º 2 ¸ +¨ ¸ +¨ ¸ − » + h1 p f ,i + 0.75pb + h2 (s + 0.25pb ) + g «¨ ¸ ¨ ¨ 2 2 «¬© p f ,i ¹ © s ¹ © p f ,o ¸¹ 2»¼ g

[(

s=

)

]

1 1 bp g = (6.0 in)(3.0 in) = 2.12 in 2 2

p f ,i = 1.5 in ≤ s ∴use p f ,i = 1.5 in

Y=

6.0 ª § 28.75 in · § 25.75 in · ¸+ ¸ +¨ «¨ 2 ¬ ¨© 1.5 in ¸¹ ¨© 2.12 in ¸¹

+

§ 31.6875 in · 1 º ¸¸ − » ¨¨ © 1.1875 in ¹ 2 ¼

2 {(28.75 in) [1.5 in + 0.75 (3.0 in )] + (25.75 in) [2.12 in + 0.25 (3.0 in )]} 3.0 +

3.0 in = 295.1 in 2

φb M pl = 0.9(50.0 ksi ) (0.5 in ) 2 ( 295.1 in ) = 3320 in − kips For 0.75-inch diameter A325 bolts:

Pt = π d b2 Fnt / 4 = π (0.75 in) 2 (90 ksi) / 4 = 39.76 kips

φ M np = φ [2 Pt ( ¦ d n )] = 0.75[2(39.76 kips ) (31.5625 in + 28.625 in + 25.625 in )] = 5117 in − kips Since:

φ M np >

φb M pl 1.11

=

3320 in − kips = 2991 in − kips , 1.11

there is thin plate behavior with prying action forces. Bolt prying force for outer bolts: Qmax,o = w′ =

w′t 2p 4 ao

§ F′ F py2 − 3¨ o ¨ w′t p ©

· ¸ ¸ ¹

2

1 · 6.0 in § 3 1 · § − ¨ db + ¸ = − ¨ in + in ¸ = 2.1875 in 2 © 16 ¹ 2 16 ¹ ©4

bp

3

3

§t · § 0.5 in · ¸¸ − 0.085 = 1.006 in ao = 3.682¨¨ p ¸¸ − 0.085 = 3.682¨¨ © 0.75 in ¹ © db ¹ 2-102

Seismic Design Guide for Metal Building Systems

ao < pext − p f , o = 2.50 in − 1.1875 in = 1.3125 in

ª 2 § 0.85b p · § π d b3 Fnt ¨ ′ ′ = + Fo «t p F py ¨ 0.80w ¸¸ + ¨¨ 2 «¬ ¹ © 8 ©

·º 1 ¸» ¸ 4p f ,o ¹»¼

ª § 0.85(6.0 in ) · º 2 + 0.80( 2.1875 in ) ¸ + » «(0.50 in ) (50.0 ksi ) ¨ 2 1 © ¹ » =« 3 «§¨ π (0.75 in ) (90.0 ksi ) ·¸ » 4(1.1875 in ) ¸ «¨© » 8 ¹ ¬ ¼ = 14.45 kips (2.1875 in)(0.50 in) Q max,o = (4)(1.006 in)

2

§ · 14.45 kips ¸¸ = 6.04 kips (50.0 ksi ) − 3¨¨ © (2.1875 in)(0.50 in) ¹

2

2

Bolt prying force for inner bolts:

Qmax,i =

w′t 2p 4ai

§ F′ F − 3¨ i ¨ w ′t p © 2 py

· ¸ ¸ ¹

2

ai = 1.006 in (same for outer bolts) ª § 0.85b p · § π d 3F Fi′ = «t 2 F py ¨¨ + 0.80 w′ ¸¸ + ¨¨ b nt «¬ p © 2 ¹ © 8

·º 1 ¸¸» ¹»¼ 4 p f ,i

ª § 0.85(6.0 in ) · º 2 + 0.80( 2.1875 in ) ¸ + » «(0.50 in ) (50.0 ksi ) ¨ 2 1 © ¹ » =« 3 § · in ksi π ( 0 . 75 ) ( 90 . 0 ) «¨ » 4(1.50 in ) ¸¸ «¨© » 8 ¹ ¬ ¼

= 11.44 kips Qmax,i = 6.33 kips

Connection strength for bolt rupture with prying action Tb = specified bolt pretension load = 28 kips [2( Pt − Qmax,o )d 0 + 2( Pt − Qmax,i )d1 + 2Tb d 2 ] M q = max

[2( Pt − Qmax,o )d 0 + 2Tb (d1 + d 2 )] [2( Pt − Qmax,i )d1 + 2Tb (d 0 + d 2 )] [2Tb (d 0 + d1 + d 2 )]

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Seismic Design Guide for Metal Building Systems

[2(39.76 − 6.04 kips ) (31.5625 in ) + 2(39.76 − 6.33 kips ) ( 28.625 in ) + 2( 28 kips ) ( 25.625 in )] = 5477 in − kips

= max

[2(39.76 − 6.04 kips ) (31.5625 in ) + 2( 28 kips ) ( 28.625 + 25.625 in )] = 5167 in − kips [2(39.76 − 6.33 kips ) ( 28.625 in ) + 2( 28 kips ) (31.5625 + 25.625 in )] = 5116 in − kips [2( 28 kips ) (31.5625 + 28.625 + 25.625 in )] = 4805 in − kips

= 5477 in − kips Since φM pl = 3320 in − kips < φM q = 0.75(5477 in − kips) = 4108 in − kips

φM n = φM pl = 3320 in − kips = 276.7 ft − kips > M c = 107.5 ft − kips ok It is accepted practice to assume that the compression side bolts resist the shear force at the connection. For 0.75-inch diameter A325-N bolts, Fnv Ab = 48 kips(0.4418 in 2 ) = 21.2 kips

The design shear strength of the four compression side bolts is then

φVn = 4(0.75) ( 21.2 kips ) = 63.6 kips > 6.95 kips ok The compression bolts are satisfactory. For this example, CJP welds are used for the beam flange to end-plate welds. From AISC 341-05 Table J2.4, the minimum weld size at the beam web and the end-plate is 1/8-in. If E70 electrodes are used, 3/16-in fillet welds on both sides of the web are sufficient to develop the web in tension. Welds on both sides of the web are required only from the inside of the tension flange to three bolt diameters below the innermost bolt. If the 2002 AISC Seismic Provisions are used, fillet welds are acceptable for the beam flange to end-plate weld. Also, it is noted that the maximum fillet weld size specified in AISC 360-05 Section J2.2.b is not applicable to the beam flange and web to end-plate fillet welds, if used.

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2.5.1.2 Panel Zone Design

According to the AISC/MBMA Design Guide 16, panel zone plates in gable frames can be designed using the AISC 360-05 rules for beam webs. When using these equations, the variable h is the depth of the panel zone plate at the rafter side. The required shear force is Vu =

M u Pu − 2 h

where Mu = required flexural strength Pu = required thrust at the rafter face of the panel zone Because of seismic load reversal, tension field action cannot be used for the seismic design. To the authors’ knowledge, no test data is available that shows that full tension field action can be developed for positive moment (that is, moment that causes compression in the outside flanges) at the panel zone region of gable frames. The nominal strength, Vn, is determined using the provisions in the AISC 360-05 Section G, as follows: Vn = (0.6 Fy )( Aw )(C v ) where For h / t w ≤ 1.10 k v E / Fy

C v = 1.0 For 1.10 k v E / Fy < h / t w ≤ 1.37 k v E / Fy Cv =

1.10 k v E / Fy h / tw

For h / t w > 1.37 k v E / Fy Cv =

1.51Ek v ( h / t w ) 2 Fy

where Aw = av t w kv = 5 +

5 (a v / h) 2

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Seismic Design Guide for Metal Building Systems

av = width of the panel zone at the column top tw = panel zone plate thickness The panel zone dimensions for this example are shown in Figure 2.10-2. A 0.1489-inch thick plate is to be checked for Mu = 111.9 ft-kips and Pu = 3.50 kips. w

Figure 2.10-2 Panel Zone Dimensions

The applied shear force, Vu, is Vu =

M u Pu − 2 h

=

(111.9 ft − kips ) (12 in ) 3.5 kips − = 43.02 kips 29.99 in 2

The allowable shear stress, Fv, is h = 29.99 in t w = 0.1489 in 29.99 in h = = 201.4 t w 0.1489 in a v = 33.75 in a v 33.75 in = = 1.125 h 29.99 in

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Seismic Design Guide for Metal Building Systems

kv = 5 +

5 = 8.951 (1.125) 2

Since

h / t w > 1.37 k v E / Fy = 1.37 8.951( 29000 ksi ) / (50 ksi ) = 98.71 Cv =

1.51Ek v 1.51( 29000 ksi ) (8.951) = = 0.1933 ok 2 ( h / t w ) Fy ( 201.4) 2 (50 ksi )

And,

φVn = φ (0.6 Fy ) ( Aw ) (Cv ) = 0.9(0.6) (50 ksi ) (33.75 in ) (0.1489 in ) (0.1933) = 26.23 kips < 43.02 kips Since Vu = 43.02 kips > φVn = 26.23 kips , the 0.1489-inch thick panel zone plate is not quite adequate. An increase to 0.1780-inch thick panel zone plate is required. Alternatively, a diagonal stiffener could be used. 2.5.2

Design Building B

The design forces for Design Buildings A and B are very similar with regard to the beam-to-column moment connection. It is not necessary to show repetitive calculations for Design Building B. Design Building B does have fixed interior column bases that would need to be designed for the strength-based load combinations and follows the same procedure as used in the knee area connections.

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2.6

COLUMN BASE AND ANCHOR BOLT DESIGN

AISC 341-05 defines “column base” as an “Assemblage of plates, connectors, bolts, and rods at the base of a column used to transmit forces between the steel superstructure and the foundation.” Section 1912 of the 2006 IBC, as well as AISC 341-05 note that the available strength of the concrete elements of the column base such as the anchor bolt embedment length and any reinforcing steel shall be designed in accordance with ACI 318, Appendix D, provided they are within the scope of Appendix D. The strength of anchors that fall outside the scope of ACI 318, Appendix D, as amended by IBC 2006, Section 1908.1.16, shall be in accordance with an approved procedure. AISC 341-05 also stipulates that the available strength of anchor rods is to be determined in accordance with Section J3 of AISC 360-05. Furthermore, Section 8.5 of AISC 341-05 gives column base requirements for axial, shear, and flexural strength, as summarized below. • The required axial strength of the column bases shall be the summation of the vertical components of the required strengths of all steel elements that are connected at the column base. This shall include the analysis of the column base attachment to the foundation. • The required shear strength of the column base shall be the summation of the horizontal components of the required strengths of all steel elements connected to the column base, including the column base attachment to the foundation. For diagonal bracing utilized as part of the seismic load resisting system (SLRS), the horizontal force component shall be determined from the required strength of the bracing connections. For columns, the horizontal component shall be equal to or greater than the smaller of 1) § 2 · 2( R y Fy Z x / H ) using LRFD, or ¨ ¸ ( R y Fy Z x / H ) using ASD, for © 1.5 ¹ the column, or 2) the shear calculated using the load combinations of the applicable building code, including the amplified seismic load. • The required flexural strength of the column base shall be the summation of the required strengths of all steel elements connected to the column base, including the column base attachment to the foundation. For diagonal bracing utilized as part of the seismic load resisting system (SLRS), the required flexural strength shall be equal to or greater than the required strength of the bracing connections. For columns, the required flexural strength shall be equal to or greater than § 1.1 · the smaller of 1) 1.1( R y Fy Z ) using LRFD, or ¨ ¸ ( R y Fy Z ) using © 1.5 ¹ 2-108

Seismic Design Guide for Metal Building Systems

ASD, for the column, or 2) the moment calculated using the load combinations of the applicable building code, including the amplified seismic load. •

Section 8.5 includes an exception to the 0.75 factor on the nominal strength for anchor bolts in SDC C, D, E, or F. After a joint AISC/ACI committee discussed the 0.75 factor, ACI 318-08 Appendix was revised to prescribe that 0.75 applies only to the concrete elements of the interface. The exception will be removed from AISC 341-10.

AISC 341-05 includes an extensive commentary to the column base section, which provides additional discussion and guidance on this topic. Specifically, it states that column bases are required to be designed for the same axial forces for the connections framing into them. Also, if the system connections are required to be designed for either amplified seismic loads or loads based on member strengths, then the column base connection must be designed for the same loads.

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2.7

FOUNDATION FORCES FOR FOUNDATION DESIGN

Typically the metal building manufacturer is not responsible for the foundation design. However, the metal building manufacturer specifies the loads imposed upon the foundation. It is very important that the foundation loads are clearly identified. Current practice is to proportion footings using allowable bearing pressures although strength design is permitted. In IBC Section 1605.3, two sets of load combinations which use allowable stress are specified. Either set may be used for design. The first set called the Basic Load Combinations are based on the load combinations found in ASCE 7. This set does not permit increases in allowable values to be used with wind or seismic load. The second set called the alternate basic load combinations is based on load combinations found in the Uniform Building Code prior to 1997 and permit an increase in allowable values to be used with wind or seismic loads. It is expected that for foundation designs, the alternate basic load combinations will be used in most cases. IBC Section 1801.2.1 states that where the foundation is proportioned using the strength design combinations of IBC Section 1605.2 and the computation of the seismic overturning moment is by the equivalent lateral-force method or the modal analysis method; the proportioning shall be in accordance with Section 12.3.4 of ASCE 7. Section 12.13.4 of ASCE 7 permits a 25 percent reduction in the foundation overturning moment if equivalent static procedures are used (provided the structure is not an inverted pendulum or cantilever column) and a 10 percent reduction if modal analysis procedures are used. However, Section 1605.3.2 states that when the alternate basic load combinations are used to evaluate sliding, overturning and soil bearing at the soil-structure interface, the reduction for foundation overturning provided in Section 12.3.4 of ASCE 7 shall not be used. The vertical seismic load effect, Ev ( 0.2S DS D ), is required to be combined with other loads. The way this effect is be included with other loads is clearly illustrated in Section 12.4 of ASCE 7. It is important to note that Exception 2 of Section 12.4.2.2 of ASCE 7 states that Ev is permitted to be taken equal to zero where determining demands on the soil-structure interface of foundations when used in ASCE 7 Equation 12-4.2. The net effect of the all the changes in the IBC and ASCE 7 in the areas associated with the soil-structure foundation interface and load combinations is expected to be negligible from prior codes. Because there are so many options for designing the foundations, it is recommended that the unfactored basic loads be provided to the foundation designer to allow the opportunity to develop the load combinations depending on the approach he or she would prefer to take. It is also recommended that the design values of ρ and Ω that were used

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be included with the load information. The values in the following sections have been taken from the analysis results and base shear values previously determined in this design example. 2.7.1

End Wall Columns with Bracing Connected to the Top and Bottom

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Ev = 0.048(D + C)

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Ev = 0.048(D + C)

Design Building A (R > 3) P M Vframe (kips) (kips) (ft-kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 ±0.70 ±0.83 0.00 ±0.07 ±0.00 Design Building A (R = 3) P M Vframe (kips) (kips) (ft-kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 ±0.76 ±0.90 0.00 ±0.07 ±0.00 Design Building B P M Vframe (kips) (ft-kips) (kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 ±3.77 ±4.49 0.00 ±0.27 ±0.00

Design Forces

Dead (D) Collateral (C) Earthquake (Eh), Frame Earthquake Ev = 0.2(D + C)

Note that if ASD is used for foundation design, Eh should be divided by 1.4 and Ev can be taken as zero when used ASCE 7 Equation 12.4-2. 2.7.2

End Wall Columns without Bracing Connected to the Top and Bottom

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Ev = 0.048(D + C)

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Design Building A (R > 3) P M Vframe (kips) (kips) (ft-kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 0.00 0.00 0.00 0.00 −0.08

Seismic Design Guide for Metal Building Systems

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Ev = 0.048(D + C)

Design Forces

Dead (D) Collateral (C) Earthquake (Eh), Frame Earthquake Ev = 0.2(D + C)

Design Building A (R = 3) P M Vframe (kips) (kips) (ft-kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 0.00 0.00 0.00 0.00 −0.08 Design Building B P M Vframe (kips) (kips) (ft-kips) 0.00 0.00 −0.90 0.00 0.00 −0.47 0.00 0.00 0.00 0.00 0.00 −0.27

Note that the corner columns have half the tributary load as interior end wall columns and both D and C should be divided by two. 2.7.3

Exterior Rigid Frame Columns with Bracing Connected to the Top and Bottom Design Building A (R > 3) Vlong P Vframe (kips) (kips) (kips)

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.048(D + C)

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.048(D + C)

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−3.08 −1.18 ±0.45 ±3.08 ±0.20

−1.45 −0.62 ±1.09 0.00 ±0.10

0.00 0.00 0.00 ±3.12 0.00

Design Building A (R = 3) Vlong P Vframe (kips) (kips) (kips) 0.00 −3.08 −1.45 0.00 −1.18 −0.62 0.00 ±0.53 ±1.26 ±3.33 0.00 ±3.12 0.00 ±0.20 ±0.10

Seismic Design Guide for Metal Building Systems

Design Building B Vlong P Vframe (kips) (kips) (kips) 0.00 −3.32 −1.58 0.00 −1.20 −0.63 0.00 ±0.49 ±0.90 ±16.65 0.00 ±20.0 0.00 ±0.90 ±0.44

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.2(D + C)

Note that the columns are pinned at the base and transmit no moment to the foundations. 2.7.4

Exterior Rigid Frame Columns without Bracing Connected to the Top and Bottom Design Building A (R > 3) Vlong P Vframe Design Forces (kips) (kips) (kips) Dead (D) 0.00 −3.08 −1.45 Collateral (C) 0.00 −1.18 −0.62 Earthquake Eh, Frame 0.00 ±0.45 ±1.09 Earthquake Eh, Long. 0.00 0.00 0.00 Earthquake Ev = 0.048(D + C) ±0.20 ±0.10 0.00

Design Loads

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.048(D + C)

Design Building A (R = 3) Vlong P Vframe (kips) (kips) (kips) 0.00 −3.08 −1.45 0.00 −1.18 −0.62 0.00 ±0.53 ±1.26 0.00 0.00 0.00 0.00 ±0.20 ±0.10 Design Building B Vlong P Vframe (kips) (kips) (kips) 0.00 −3.32 −1.58 0.00 −1.20 −0.63 0.00 ±0.49 ±0.90 0.00 0.00 0.00 0.00 ±0.90 ±0.44

Unfactored Loads

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.2(D + C)

Note that the columns are pinned at the base and transmit no moment to the foundations.

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2.7.5

Interior Rigid Frame Columns Design Building A (R > 3) Vlong P Vframe (kips) (kips) (kips) 0.00 0.00 −6.20 0.00 0.00 −2.57 0.00 0.00 ±0.72 0.00 0.00 0.00 0.00 0.00 ±0.42

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.048(D + C)

Design Building A (R = 3) Vlong P Vframe (kips) (kips) (kips) 0.00 0.00 −6.20 0.00 0.00 −2.57 0.00 0.00 ±0.84 0.00 0.00 0.00 0.00 0.00 ±0.42

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.048(D + C)

Design Forces

Dead (D) Collateral (C) Earthquake Eh, Frame Earthquake Eh, Long. Earthquake Ev = 0.2(D + C)

P (kips) −6.92 −2.56 ±0.09 0.00 ±1.90

Design Building B Vlong Mframe Vframe (kips) (kips) (ft-kips) 0.00 1.90 −0.13 0.00 −0.05 −0.76 0.00 ±3.60 ±45.78 0.00 0.00 0.0 0.00 0.00 ±0.23

Note that the columns are pinned at the base and transmit no moment to the foundations for Design Building A. Also, for Design Building B, the columns are pinned at the base in the longitudinal direction but are fixed at the base in the transverse direction.

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2.8

WELDING ISSUES AND QUALITY ASSURANCE REQUIREMENTS

2.8.1

Welding Issues

For seismic applications, AISC 341-05 references the 2004 version of AWS D1.1. Section 7.3 and Appendix W of the Seismic Provisions give an expanded list of welding requirements over those in previous editions. First, all member and connection welds within the Seismic Load Resisting System (SLRS) are required to be made with filler metals with a Charpy VNotch (CVN) toughness of 20 ft-lb at a temperature of 0° F (- 18° C). Welds designated as demand critical have additional requirements, including: 1. Charpy V-Notch toughness of 20 ft-lb at a temperature of -20° F, as well as 40 ft-lb at a temperature of 70° F as determined by an appropriate AWS classification test methods. 2. Charpy V-Notch toughness of 40 ft-lb at a temperature of 70° F as determined by Appendix X, or other approved method when the steel frame is normally enclosed and maintained at a temperature of 50° F or higher. If the structure is maintained at a temperature lower than 50° F, the qualification temperature for Appendix X is to be a maximum temperature of 20° F higher than the anticipated service temperature. 3. The following electrodes are exempt from the production lot testing requirement when the CVN toughness of the electrode is  20 ft-lb at a temperature not exceeding -20° F as determined by AWS classification test methods. a. SMAW electrodes classified in AWS 5.1 as E7018 or E7018-X b. SMAW electrodes classified in AWS 5.5 as E7018-C3L or E8018-C3 c. GMAW solid electrodes It should be noted that the manufacturer’s certificate of compliance shall be considered sufficient evidence of meeting this requirement. Specific examples given for demand critical welds include: 1. Complete-joint-penetration (CJP) welds between the column and base plate when CJP groove welds used for column splices in the designated SLRS have been designated as demand critical. 2. Typical examples of demand critical welds in special moment frames (SMF) and intermediate moment frames (IMF) include beam flange to column welds, welds of single plate shear connections to columns, beam web to column welds, column splice welds, and base plate to

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column base welds. These requirements would also apply for beam to end-plate moment connection welds. 3. Typical examples of demand critical welds in ordinary moment frames (OMF) include beam flange to column welds (also beam to endplate welds), welds of single plate shear connections to columns, and beam web to column welds. These requirements would also apply for beam to end-plate moment connection welds. 4. Typical examples of demand critical welds in eccentrically braced frames (EBF) include CJP groove welds between link beams and columns. Other welds such as those joining the web plate to flange plates in built-up EBF link beams, as well as column splice welds made with CJP groove welds, should also be considered as demand critical welds. All welding is to be performed in accordance with a welding procedure specification (WPS) as required in AWS D1.1 and approved by the engineer of record. All WPS should be verified to ensure that the essential variables of the WPS are within the operating parameters provided by the filler metal manufacturer. Secondly, it should be verified that the selected filler metal is classified by the filler metal manufacturer with the appropriate level of CVN toughness. The 2006 IBC requires the submittal of filler metal manufacturer’s certifications of compliance for their filler metals in IBC Table 1704.3. 2.8.2

Quality Assurance

Quality assurance inspection performed by an independent inspection agency, is not a requirement of AWS D1.1. Inspection is required by AWS D1.1, but is addressed generically in a form that includes both the fabricator’s or erector’s inspection and the outside inspection that is provided by, but at the prerogative of, the owner. AWS D1.1 does include visual quality criteria, nondestructive testing (NDT) methodology and NDT quality criteria, but does not specify the location or types of welds that require NDT. This task is left to the engineer. AWS D1.1 does not contain specific quality criteria applicable for seismic loading, low cycle fatigue or plastic hinging regions, addressing only static (elastic) and high-cycle fatigue applications. Any special quality requirements for seismic applications are left to the engineer. AISC 341-05 contains the provision for and requirements of a quality assurance plan in Section 18 and Appendix Q. The plan must meet any building code requirement such as those in the 2006 IBC, in addition to any requirements of the engineer. The emphasis is placed upon visual inspection. Nondestructive Testing (NDT), however, is required for CJP and PJP groove welds along with other items as detailed in Appendix Q. The form of NDT is specified within Appendix Q, based on the tested item. The 2006 IBC requires special inspection for steel construction, with a few exceptions as noted in Section 1705.3. Special inspection is performed by independent, qualified individuals or agencies approved to perform such

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inspections by the building official. Special inspection includes an inspection of the fabricator’s operations and quality control procedures, unless the fabricator is otherwise approved by the building official. Structural steel welding operations must receive continuous special inspection, except for single-pass fillet welds 5/16" or less, for which periodic special inspection is permitted. Section 1705 of IBC 2006 requires a quality assurance plan for seismic-forceresisting systems in Seismic Design Categories C, D, E or F. The quality assurance plan must be prepared by a registered design professional and specify the special inspection requirements and testing requirements, including the type of testing and frequency of testing. Structural observation by the engineer or his or her designated representative is also a requirement. The exact extent of additional special inspection, testing and structural observation for seismic applications is not defined within the IBC, but is rather left to the determination of the registered design professional. AISC 341-05 gives appropriate guidance in this area. The fabricator and erector must complete a statement of responsibility acknowledging their awareness of the quality assurance plan, their plans and procedures for providing quality control to achieve the contract requirements, and identification of those individuals responsible for performing such functions. The 2006 IBC Section 1704.2.2 allows in-shop quality assurance activities to be waived if welding is performed on the premises of an approved fabricator.

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2.9

APPROVED STEEL AND WELDING MATERIAL

The use of materials for members and connections in metal building systems is governed by provisions of the pertinent material specifications (see IBC, Chapter 22) which lists the approved materials or ASTM Specifications, and in some cases the procedure for dealing with non-listed materials. Although AISC 360-05 covers a large portion of metal building elements and connections, as described in the AISC Code of Standard Practice, it is not the only relevant specification. Other steel construction, such as cold-formed steel, steel joists or steel cables (wire strand) are covered elsewhere. International Building Code (Section 2205.2) stipulates how the structural steel shall be used in seismic applications: 1. Metal buildings assigned to a low Seismic Design Category (A, B or C) are not restricted with regard to material selection for seismic-force resisting systems (SFRS). In other words, all materials listed in AISC 360-05 are appropriate as long as the system modification factor, R, is not greater than 3 or the SFRS is not a cantilevered column system. 2. When a building is assigned to a high Seismic Design Category (D, E or F), the use of AISC 341-05 becomes mandatory (IBC Section 2205.2.2). In turn, AISC 341-05, Section 6.1, contains the approved list of materials validated for ductile behavior. The same section of AISC 341-05 also prescribes an upper limit on the specified yield strength, Fy, in elements subject to inelastic behavior, which is 55 ksi for ordinary frames (OMF and OCBF) and 50 ksi for all higher ductility systems. Since metal building systems almost exclusively use ordinary moment and braced frames this is not a practical limit. However, when a ductile SFR system is selected, the specified yield strength of Fy = 50 ksi becomes an upper limit, even when the actual tensile strength is higher. Use of steel materials other than structural steel for seismic applications is only partially covered by the standards. In low seismic applications, if R factor is not greater than 3.0 (“structure not detailed for seismic”) or the SFRS is not a cantilevered column system, any material is permitted; however, designers must make their own judgment for buildings assigned to high seismic design categories. At this time, several widely used seismic-force resisting systems are not listed in the IBC or ASCE 7 due to lack of test data and research. On the other hand, these standards cover nearly eighty systems, and the list is growing. Each system assures a certain level of ductility, overstrength and redundancy, expressed by factors R and Ωo. The higher the R-factor, the higher is the ductility and/or overstrength of the system. Conversely, if the R-factor is taken as unity (R = 1), the system will have no assumed ductility and the only behavior

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that can be theoretically achieved is elastic. This rational approach is suitable for most seismic force resisting systems where traditional design was based on the elastic behavior of materials and systems and there is long history of satisfactory performance. Ignoring system ductility and overstrength is equivalent to using a system modification factor, R = 1, which is conservative for many design cases. Cable bracing and low buildings with through-fastened metal wall panels used as shear walls are the examples where the above approach is utilized in this manual. It should be noted that when the R = 1 option is used, the quality assurance and control procedures discussed in Sections 2.8 and 2.9 of this guide should still be performed even though the R value is less than 3.

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DESIGN EXAMPLE 3 Evaluation of Design Options for a Metal Building System with a Concrete Deck Mezzanine (Rigid Diaphragm) These examples illustrate how metal building systems can be used for the lateral-forceresisting system when a mezzanine with a concrete deck is added. Three different cases will be evaluated with the mezzanine being an increasing percentage of the total floor area. In particular, the code limitations on single story construction are examined when a mezzanine is present. 3

Background........................................................................................................................................ 3-2 3.1 Case 1 – Small Interior Mezzanine........................................................................................... 3-4 3.1.1 Problem Statement:.............................................................................................................. 3-4 3.1.2 Design Example Objective: ................................................................................................. 3-5 3.1.3 Solution: .............................................................................................................................. 3-5 3.1.4 Vertical Distribution of Forces: ........................................................................................... 3-6 3.1.5 Torsional Analysis Check.................................................................................................... 3-7 3.2 Case 2 – Small Mezzanine Full Length of Building................................................................. 3-8 3.2.1 Problem Statement:.............................................................................................................. 3-8 3.2.2 Design Example Objective: ................................................................................................. 3-9 3.2.3 Solution: .............................................................................................................................. 3-9 3.2.4 Vertical Distribution of Forces: ........................................................................................... 3-9 3.2.5 Torsional Analysis Check.................................................................................................. 3-10 3.3 Case 3 – Large Mezzanine as Separate Story......................................................................... 3-12 3.3.1 Problem Statement:............................................................................................................ 3-12 3.3.2 Design Example Objective: ............................................................................................... 3-13 3.3.3 Solution: ............................................................................................................................ 3-13 3.3.4 Torsional Analysis Check.................................................................................................. 3-16

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Seismic Design Guide for Metal Building Systems

3

BACKGROUND A. General Ordinary moment frames (OMF) have no height or weight limitations for Seismic Design Categories (SDC) A, B, or C. Section 12.2.5.6 of ASCE 7 provides limitations on OMF and intermediate moment frame (IMF) usage in SDC D and E. Section 12.2.5.7 has further restrictions for SDC F. B. Permitted Conditions for OMF and IMF (all other conditions are NOT permitted) 1. SDC D (ASCE 7 Sections 12.2.5.6 and 12.2.5.7) (a) Single-story, up to 65 feet in height provided that: • Tributary dead load to the roof ≤ 20 psf (all OMF and IMF higher than 35 feet), and • Wall weight above 35 feet ≤ 20 psf (all OMF and IMF higher than 35 feet). (b) Multi-story IMF less than or equal to 35 feet in height. Note that there are no roof, floor or wall weight limits for this option. 2. SDC E (ASCE 7 Sections 12.2.5.6 and 12.2.5.7) (a) Single-story, up to 65 feet in height provided that: • Tributary dead load to the roof ≤ 20 psf (all OMF and IMF higher than 35 feet), and • Wall weight above 35 feet ≤ 20 psf (all OMF and IMF higher than 35 feet). (b) Multi-story IMF less than or equal to 35 feet in height provided that: • Tributary dead load to the roof and floor ≤ 35 psf, and • Wall weight ≤ 20 psf. 3. SDC F (ASCE 7 Section 12.2.5.8 and 12.2.5.9) (a) Single-story, up to 65 feet in height provided that: • Tributary dead load to the roof ≤ 20 psf, and • Wall weight ≤ 20 psf. (b) Multi-story up to 35 feet in height (IMF only), provided that: • Tributary dead load to the roof and floor ≤ 35 psf, and • Wall weight ≤ 20 psf. C. Definition of a story versus a mezzanine IBC Section 505.2 indicates that “the aggregate area of a mezzanine or mezzanines within a room shall not exceed one-third of the area of that room or

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Seismic Design Guide for Metal Building Systems

space in which they are located. … In determining the allowable mezzanine area, the area of the mezzanine shall not be included in the area of the room.” IBC Section 505.1 indicates that “a mezzanine or mezzanines in compliance with this section shall be considered a part of the floor below.” Neither IBC, nor ASCE 7 defines a mezzanine, with respect to structural provisions. In the absence of clear definition, the authors of this guide opted for the only definition available within either standard, which is associated with IBC fire and occupancy provisions of Chapter 5. It is the opinion of the authors that a better measure of whether a mezzanine should be treated as a floor from a seismic perspective would be weight rather than floor area. However, no such requirements currently exist in the seismic requirements. The closest to this requirement is provided in Section 12.2.3.1 of ASCE 7-05, which deals with structures associated with other structures in which case the weight limit is 10% of the total weight. In Chapter 15 of ASCE 7, nonbuilding structures supported by other structures need to be included in a combined analysis when the weight of the nonbuilding structure exceeds 25% of the total weight. One should check with the local building official for any possible restrictions on the use of mezzanines; however, it is not uncommon for local building codes to allow explicitly for mezzanines larger than the 33% limitation of IBC Section 505.2. For purposes of determining member seismic design forces, it is the opinion of the authors that as a rule of thumb, torsional analysis should not be ignored on any mezzanine building system where the mezzanine weight is greater than 25% of the deadweight of the tributary portion of the building to which it is attached.

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Seismic Design Guide for Metal Building Systems

3.1 3.1.1

CASE 1 – SMALL INTERIOR MEZZANINE Problem Statement: Building Design Example at Site 2 (SDC D) Given: Roof Dead Load = 5 psf Roof Collateral Load = 5 psf Eave Height = 20 ft Wall Dead Load = 3 psf (metal walls including girts) Mezzanine Dead Load = 60 psf Mezzanine Height = 10 ft Note that weight limits for classification of steel moment frames given in ASCE 7 Sections 12.2.5.6 through 12.2.5.9 refer to dead loads tributary to the frame under consideration (dead loads are clearly defined and listed in ASCE 7 Section 3.1.1). Therefore, roof live, floor live, snow load, or other non-permanent loads are not required by ASCE 7 to be part of this evaluation. These provisions are written specifically for the classification of steel moment frames, which differs from the calculation of effective seismic weights in ASCE 7 Section 12.7.2. The latter requires the inclusion of all dead loads and a portion of other loads, as applicable.

3-4

10 Bays @ 25' = 250'

Seismic Design Guide for Metal Building Systems

25'

Full height columns typical all four corners

200' Metal Building With Mezzanine – Case 1 3.1.2

Design Example Objective: Determine vertical distribution of earthquake forces for the given building to lateral-force-resisting system elements.

3.1.3

Solution: 1. Determine if the mezzanine qualifies as a story. Amezz = 25 ft × 25 ft = 625 ft2 Aroom = 200 ft × 250 ft – 625 ft2 = 49,375 ft2 Amezz 625 ft 2 = × 100 = 1.3 % < 33% Aroom 49,375 ft 2 ∴Mezzanine is considered small enough not to be treated as a separate story and building can be classed as single story.

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Seismic Design Guide for Metal Building Systems

2. Tributary dead load check. wroof (allowable) = 20 psf wroof (actual) = 5 psf + 5 psf = 10 psf

wmezz ( estimated )

§ 25 ft · 60 psf × ¨ × 25 ft ¸ © 2 ¹ = 3.75 psf = (25 ft × 200 ft )

wtotal = 10 psf + 3.75 psf = 13.75 psf ≤ 20 psf ∴OMF can be used for lateral and vertical stability of the mezzanine. 3. Wall weight check (above 35 feet). Not applicable since building height is less than 35 feet. Ordinary moment frame meets all three criteria, therefore is an acceptable framing system. Note that the three checks in this section were to verify that the system qualifies as a means to resist the seismic forces. Some seismic forces were estimated. The actual seismic forces are calculated in Section 3.1.4. It is the designer’s responsibility to ensure that a load path exists for these loads and to properly account for them. 3.1.4

Vertical Distribution of Forces:

The weight of the roof and the weight of the mezzanine, tributary to one frame, are calculated as follows. Note that the weight of the roof includes the weight of the walls above 10 feet.

wx ( roof ) = ( 25 ft ) ( 200 ft ) (10 psf ) + 2( 25 ft ) (10 ft ) (3 psf ) = 51,500 lb = 51.5 kips

wx ( mezzanine) = (12.5 ft ) ( 25 ft ) (60 psf ) = 18,750 lb = 18.75 kips

Therefore,

C vx ( roof ) =

wx hx n

¦w h

=

(51.5 kips ) ( 20 ft ) = 0.846 (51.5 kips ) ( 20 ft ) + (18.75 kips ) (10 ft )

i i

i =1

C vx ( mezzanine ) =

wx hx n

¦w h

=

(18.75 kips ) (10 ft ) = 0.154 (51.5 kips ) ( 20 ft ) + (18.75 kips ) (10 ft )

i i

i =1

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Seismic Design Guide for Metal Building Systems

W( oneframe ) = wx( roof ) + wx( mezzanine ) = 51.5 kips + 18.75 kips = 70.25 kips C s = 0.216 (from Section 1.3.4.3 of this Guide) V( oneframe ) = C sW( oneframe ) = 0.216(70.25kips ) = 15.17 kips Fx ( roof ) = Cvx ( roof )V = 0.846(15.17 kips ) = 12.84 kips Fx ( mezzanine ) = Cvx ( mezzanine )V = 0.154(15.17kips ) = 2.34 kips The frames should also be checked for the following vertical distribution which may produce more bending in the interior columns of the frames. Fx ( roof ) = C s wx ( roof ) = 0.216(51.5 kips ) = 11.12 kips Fx ( mezzanine) = C s wx ( mezzanine) = 0.216(18.75 kips ) = 4.05 kips 3.1.5

Torsional Analysis Check

If the weight of the mezzanine divided by the tributary weight of the frames associated with the mezzanine is greater than 25%, then a torsional rigidity analysis should be performed. This would include all parts of the structural systems that would seismically resist lateral seismic and torsional forces. wx( mezzanine ) wx( mezzanine ) + wx( roof )

=

18.75 kips = 0.27 > 0.25 18.75 + 51.5 kips

Therefore, a torsional rigidity analysis should be performed.

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Seismic Design Guide for Metal Building Systems

3.2.1

CASE 2 – SMALL MEZZANINE FULL LENGTH OF BUILDING Problem Statement:

Building Design Example at Site 2 (SDC D) Given: Roof Dead Load = 5 psf Roof Collateral Load = 5 psf Eave Height = 20 ft Wall Dead Load = 3 psf (metal walls including girts) Mezzanine Dead Load = 50 psf Mezzanine Partition Load = 10 psf (see ASCE 7-05 Section 3.1.1 which includes partition loads as dead loads) Mezzanine Height = 10 ft Mezzanine

25'

10 Bays @ 25' = 250'

3.2

200'

Metal Building With Mezzanine – Case 2

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Seismic Design Guide for Metal Building Systems

3.2.2

Design Example Objective:

Determine vertical distribution of earthquake forces for the given building to lateral-force-resisting system elements. 3.2.3

Solution:

1. Determine if the mezzanine qualifies as a story. Amezz = 25 ft × 250 ft = 6,250 ft2 Aroom = 200 ft × 250 ft – 6,250 ft2 = 43,750 ft2 A mezz 6,250 ft 2 = × 100 = 14.3 % < 33% A room 43,750 ft 2 ∴Mezzanine is considered small enough not to be treated as a separate story and building can be classed as single story. 2. Tributary dead load check. wroof (allowable) = 20 psf wroof (actual) = 5 psf + 5 psf = 10 psf

wmezz ( estimated ) =

60 psf × (25 ft × 25 ft ) = 7.5 psf (25 ft × 200 ft )

wtotal = 10 psf + 7.5 psf = 17.5 psf ≤ 20 psf ∴OMF can be used for lateral and vertical stability of the mezzanine. 3. Wall weight check (above 35 feet). Not applicable since building height is less than 35 feet. Ordinary moment frame meets all three criteria, therefore is an acceptable framing system. Note that the three checks in this section were to verify that the system qualifies as a means to resist the seismic forces. Some seismic forces were estimated. The actual seismic forces are calculated in Section 3.2.4. The assumption was that the column inside the structure that supports the mezzanine was only partial height and didn’t extend to the roof. 3.2.4

Vertical Distribution of Forces:

The weight of the roof and the weight of the mezzanine, tributary to one frame, are calculated as follows. Note that the weight of the roof includes the weight of 10 feet of the left wall and 5 feet of the right wall (adjacent to the mezzanine). The weight of the mezzanine includes the weight of 10 feet of the wall adjacent to the mezzanine. wx ( roof ) = ( 25 ft ) ( 200 ft ) (10 psf ) + ( 25 ft ) (10 ft + 5 ft ) (3 psf ) = 51,125 lb = 51.13 kips

3-9

Seismic Design Guide for Metal Building Systems

wx ( mezzanine ) = ( 25 ft ) ( 25 ft ) (60 psf ) + ( 25 ft ) (10 ft ) (3 psf ) = 38,250 lb = 38.25 kips Therefore, C vx ( roof ) =

wx hx n

¦w h

=

(51.13 kips ) ( 20 ft ) = 0.728 (51.13 kips ) ( 20 ft ) + (38.25 kips ) (10 ft )

i i

i =1

C vx ( mezzanine ) =

w x hx n

¦w h

=

(38.25 kips ) (10 ft ) = 0.272 (51.13 kips ) ( 20 ft ) + (38.25 kips ) (10 ft )

i i

i =1

W( oneframe ) = wx( roof ) + wx( mezzanine ) = 51.13 kips + 38.25 kips = 89.38 kips C s = 0.216 (from Section 1.3.4.3 of this Guide) V( oneframe ) = C sW( oneframe ) = 0.216(89.38 kips ) = 19.31 kips Fx ( roof ) = Cvx ( roof )V = 0.728(19.31 kips ) = 14.06 kips Fx ( mezzanine ) = C vx ( mezzanine )V = 0.272(19.31 kips ) = 5.25 kips The frames should also be checked for the following vertical distribution which may produce more bending in the interior columns of the frames. Fx ( roof ) = C s wx ( roof ) = 0.216(51.13 kips ) = 11.04 kips Fx ( mezzanine) = C s wx ( mezzanine) = 0.216(38.25 kips ) = 8.26 kips The above forces should be increased for torsional effects where they may be significant. Note that since the main frames were all assumed to be the same, that the stiffness and therefore the distribution would be based on tributary areas. Stiffness of the end bay frames must be maintained for this to be a valid assumption. That is, expandable endwall frames would be desired, since beam and post frames with rods or shear walls would likely be stiffer than the interior moment frames. 3.2.5

Torsional Analysis Check

If the weight of the mezzanine divided by the tributary weight of the frames associated with the mezzanine is greater than 25%, then a torsional rigidity analysis should be performed. This would include all parts of the structural systems that would seismically resist lateral seismic and torsional forces.

3-10

Seismic Design Guide for Metal Building Systems

wx( mezzanine ) wx( mezzanine ) + wx( roof )

=

38.25 kips = 0.43 > 0.25 38.25 + 51.13 kips

Therefore, a torsional rigidity analysis should be performed.

3-11

Seismic Design Guide for Metal Building Systems

3.3

CASE 3 – LARGE MEZZANINE AS SEPARATE STORY

3.3.1 Problem Statement:

Building Design Example at Site 2 (SDC D) Given: Roof Dead Load = 5 psf Roof Collateral Load = 5 psf Eave Height = 20 ft Wall Dead Load = 3 psf (metal walls including girts) Mezzanine Dead Load = 50 psf Mezzanine Partition Load = 10 psf (see ASCE 7-05 Section 3.1.1 which includes partition loads as dead loads) Mezzanine Height = 10 ft A

M

H

O 65'

65'

70'

11 10

10 Bays @ 25' = 250'

9 8 7 6 5 4 3 2 1 A

B

C

E

F

G

J

K

M

8 @ 25' = 200'

Metal Building With Mezzanine – Case 3

3-12

Seismic Design Guide for Metal Building Systems

3.3.2

Design Example Objective:

Determine vertical distribution of earthquake forces for the given building to lateral-force-resisting system elements. 3.3.3

Solution:

1. Determine if the mezzanine qualifies as a story. Amezz = 135 ft × 150 ft = 20,250 ft2 Aroom = 200 ft × 250 ft – 20,250 ft2 = 29,750 ft2 A mezz 20,250 ft 2 = × 100 = 68 % < 33% A room 29,750 ft 2 ∴ Mezzanine needs to be treated as a separate story. Once the building (or frame) is classified as multi-story, it may be necessary to reevaluate the diaphragm condition and some other criteria, such as building vertical irregularities. With tapered frames (columns) the soft story or stiffness requirements should be investigated. 2. Since an ordinary moment frame cannot be used for lateral stability for more than a single story, the following are possible options to consider: a. Intermediate moment frames (IMF) – IMF’s do not have the story limitation of either ASCE 7 Sections 12.2.5.6 or 12.2.5.7 that ordinary moment frames have, therefore they are permitted for the lateral stability system for this example. The complete lateral force resisting system associated with the column lines identified in the figure above is as follows: Transverse Lines 1 and 11

OMF or OCBF

Lines 2 thru 8

IMF

Lines 9 and 10

OMF

Longitudinal Lines A and M

OCBF

Lines D and H

IMF

Note that AISC 341-05 contains some changes to the IMF system, so the latest version (2005) of that framing system comes with more stringent requirements when compared to earlier editions. The requirements for IMF’s in AISC 341-05 must be followed, including: i. Beam to column connections need to meet the general requirements of AISC 341-05, Section 10.2a, or be prequalified in accordance with AISC 358, as stipulated in Section 10.2b. The publication of AISC 358 covers three common configurations of bolted end-plate moment 3-13

Seismic Design Guide for Metal Building Systems

connections; however, the range of tested parameters imposes severe restrictions on the beam depth and flange sizes (AISC 358, Chapter 6, Table 6.1). Note that test parameters will be expanded in the next version of AISC 358 to be published in the near future. ii. The width-to-thickness limitations of compression members shall meet the compactness requirements, λp of Table B4.1 of AISC360-05, in accordance with AISC 341-05 Sections 10.4 and 8.2a. When prequalified connections from AISC 358 are used, column elements must meet more stringent limits for seismically compact elements of AISC 341-05, Section 8.2b. iii. The specified minimum yield stress of the steel to be used for members in an IMF is limited to 50 ksi, unless the suitability of the material is determined by testing or other rational criteria (AISC 341-05, Section 6.1). Structural steel materials with a pronounced yield plateau, good weldability, and elongation of at least 20 percent (on 2 inch specimen) are generally acceptable (AISC 341, Commentary, Section C6.1). iv. Demand critical welds are required near connection end-plates, when prequalified moment connections of AISC 358 are used. The more stringent notch toughness criteria for filler metal must conform to AISC 341-05, Section 7.3b. v. Protected zones are designated areas in the frame rafter near plastic hinge locations where any discontinuities made with holes or welds must be avoided, as described in AISC 341-05, Section 7.4. For the size and location of protected zones near prequalified moment connections refer to AISC 358 Section 6.4(8). b. Two-stage equivalent lateral force procedure – Another solution is to make the break at the top of the slab of the mezzanine. The complete lateral force resisting system associated with the column lines identified in the figure above is as follows: Transverse Lines 1 and 11

OMF or OCBF

Lines 2 thru 10

OMF

Note that the base of columns in the mezzanine area is at the top of the mezzanine. Also, the mezzanine framing and bracing scheme is not specified. As long as the columns of the upper floor rest on the mezzanine as a foundation, a two-stage equivalent system is allowed with the following restrictions: i. The stiffness of the lower portion must be at least 10 times the stiffness of the upper portion.

3-14

Seismic Design Guide for Metal Building Systems

ii. The period of the entire structure shall not be greater than 1.1 times the period of the upper portion considered as a separate structure fixed at the base. iii. The flexible upper portion shall be designed as a separate structure using the appropriate values of R and ρ. iv. The rigid lower portion shall be designed as a separate structure using the appropriate values of R and ρ. The reactions from the upper portion shall be those determined from the analysis of the upper portion amplified by the ratio of the R/ρ of the upper portion over R/ρ of the lower portion. This ratio shall not be less than 1.0. c. OCBF (typically tension-only rods or angle bracing) has height limitations similar to OMF; however, no weight limits apply to OCBF with height below 35 feet. In many cases OCBF is not a suitable alternative to moment frames, since brace diagonals would interfere with the open space requirements inside a building. The complete lateral force resisting system associated with the column lines identified in the figure above is as follows: Transverse Lines 1 and 11

OMF or OCBF

Lines 2 thru 8

OCBF

Lines 9 and 10

OMF or OCBF

Longitudinal Lines A and M

OCBF

Lines D and H

OCBF

d. Depending on the size of the building and loads, the whole building can be configured not to rely on the lateral resistance of interior frames. In other words, roof and floor diaphragms can be used to collect and transfer interior loads towards the endwalls and sidewalls, so resistance to lateral forces is provided by systems within four exterior walls. If the building height does not exceed 35 feet, the SFRS in four walls can be OCBF. When the height or weight limits are exceeded, the special concentrically braced frame (SCBF) is a workable solution. SCBF requires detailing in accordance with AISC 341-05, Section 13, where brace connections are sized to match the expected tension yielding strength of the braces. The complete lateral force resisting system associated with the column lines identified in the figure above is as follows: Transverse Lines 1 and 11 OMF or OCBF Lines 2 thru 8

Core building (Lines A thru H) stabilizes Lines H thru M

3-15

Seismic Design Guide for Metal Building Systems

Lines 9 and 10 OMF Longitudinal Lines A thru H Stabilized by core building Lines H and M Treated as a width extension and braced by OCBF 3.3.4

Torsional Analysis Check

By inspection, the mezzanine weight exceeds 25% of the total weight and therefore, a torsional analysis should be performed.

3-16

Seismic Design Guide for Metal Building Systems

DESIGN EXAMPLE 4 Determination of Seismic Design Forces and Detailing Requirements for a Metal Building with Concrete or Masonry Walls (Hardwalls) The purpose of this example is to illustrate the seismic design of a metal building with hardwalls (i.e. concrete or masonry outer walls). Problem Statement: ..................................................................................................................................... 4-2 Design Example Objective:......................................................................................................................... 4-2 4

Distribution of Seismic Design Loads ............................................................................................... 4-3 4.1 Determine Earthquake Design Forces ...................................................................................... 4-3 4.1.1 Determine Latitude and Longitude for the Site ................................................................... 4-3 4.1.2 Determine Site Profile Class................................................................................................ 4-3 4.1.3 Determine Maximum Considered Earthquake (MCE) Site Ground Motion Values ........... 4-3 4.1.4 Determine Site Design Spectral Response Acceleration Parameters................................... 4-3 4.1.5 Determine the Occupancy Importance Factor and Seismic Design Category ..................... 4-3 4.1.6 Determine the Seismic Base Shear, V ................................................................................. 4-4 4.1.7 Determine the Seismic Load Effect, E, for the Building in each Direction ....................... 4-11 4.2 Wall Design and Wall to Metal Connection........................................................................... 4-12 4.2.1 Wall Design Loads ............................................................................................................ 4-12 4.2.2 Connection to Longitudinal Walls..................................................................................... 4-16 4.2.3 Wall Anchors at Front and Rear Walls .............................................................................. 4-20 4.2.4 Transfer of Seismic Forces to Shear Walls........................................................................ 4-22 4.3

Side Wall Girts ....................................................................................................................... 4-23

4-1

Seismic Design Guide for Metal Building Systems

Problem Statement: NON-LOAD BEARING “ TILT-UP NON-LOAD BEARING7-¼ 7-1/4" TILT-UP PANEL PANEL CONCRETE SHEAR WALL. SHEAR WALL) (INTERMEDIATE PRECAST ROOF PURLINS SUPPORTEDBY BY BEAMS BEAMS AND ROOF PURLINS SUPPORTED COLUMNS. AND COLUMNS

4@

25 F

NON-LOAD BEARING 7-¼ “ TILT-UP PANEL NON-LOAD BEARING 7-1/4"SHEAR TILT-UP PANEL (INTERMEDIATE PRECAST WALL)

T. =

100 FT.

24 FT.

TRANSVERSE MOMENT FRAMES EXTERIOR COLUMNS: FIXED TOP, PINNED BASE INTERIOR COLUMNS: PINNED TOP, PINNED BASE

FRAME

CONCRETE SHEAR WALLS.

27 FT.

WALL

ROOF SLOPE 1/2 : 12

8@

. FT 25

=

T. 0F 20

LOAD BEARING 7-¼ “ TILT-UP LOAD BEARING 7-1/4" TILT-UPPANEL PANEL CONCRETE SHEARSHEAR WALL. (INTERMEDIATE PRECAST ROOF PURLINS SUPPORTED BY A BY WALL) ROOF PURLINS SUPPORTED LEDGER ANGLE ANGLE. A LEDGER

Metal Building Framing – Design Example 4 Building Use: Manufacturing Loads: Roof Live Load: 20 psf Ground Snow Load: 15 psf Design Wind Velocity: 85 mph, 3-second gust, Wind Exposure B Collateral Load: 3 psf (sprinkler system) Location: 522 S. Main St. Alturas, CA 96101-4115 Soils Properties: IBC/ASCE 7 Site Class D Design Example Objective: Provide seismic design forces and recommended connection design details for a metal building with concrete or masonry walls. Also, provide seismic design forces for the moment frames and the concrete and masonry walls.

4-2

Seismic Design Guide for Metal Building Systems

4

DISTRIBUTION OF SEISMIC DESIGN LOADS

4.1

DETERMINE EARTHQUAKE DESIGN FORCES See Design Example 1 for procedure.

4.1.1

Determine Latitude and Longitude for the Site Latitude = 41.480 Longitude = −120.542

4.1.2

Determine Site Profile Class Site Class D (given)

4.1.3

Determine Maximum Considered Earthquake (MCE) Site Ground Motion Values S S = 70.1% g

Fa = 1.239

S MS = 86.9% g

S1 = 27.1% g

Fv = 1.857

S M 1 = 50.3% g

TL = 16 sec.

(Long-period transition period, from ASCE 7 Figure 22-16)

Long period may affect design of buildings that have the fundamental period longer than 4 seconds. As the period of typical metal building systems is shorter than 1 second, this parameter can be disregarded. 4.1.4

4.1.5

Determine Site Design Spectral Response Acceleration Parameters

S DS =

2 § 86.9 % g · S MS = 0.67¨ ¸ = 0.579 g 3 © 100 ¹

S D1 =

2 § 50.3 % g · S M 1 = 0.67¨ ¸ = 0.335 g 3 © 100 ¹

Determine the Occupancy Importance Factor and Seismic Design Category

See Design Example 1 for procedure. 4.1.5.1 Determine the Building Occupancy Category per IBC 2006 Table 1604.5, and Importance Factor, based on ASCE 7 Section 11.5-1

Based on the problem description, the building use is manufacturing with “normal occupancy”. Therefore, the category is “II” and the corresponding seismic importance factor I = 1.0 .

4-3

Seismic Design Guide for Metal Building Systems

4.1.5.2 Determine the Seismic Design Category (SDC) Based on IBC Tables 1613.5.6(1) and 1613.5.6(2), with Occupancy Category II and the SDS and SD1 Site Values

From Table 1613.5.6(1): SDC = D From Table 1613.5.6(2): SDC = D Therefore the SDC is D 4.1.6

Determine the Seismic Base Shear, V

See Design Example 1 for procedure. 4.1.6.1 Determine the Approximate Fundamental Period, Ta, for the Example Building in Accordance with ASCE 7 Section 12.8.2 Ta = Ct hn

x

(ASCE 7 Eq. 12.8-7)

Where: CT = 0.028 in the transverse direction because the structural system is steel moment frame CT = 0.020 in the longitudinal direction and the transverse end walls because the structural systems are neither ordinary braced frames nor moment frames or steel eccentric braced frames. The concrete shear walls are therefore classified as “other”. hn = 24 feet, eave height for all frames x = 0.8 for steel moment frame x = 0.75 for “all other structural systems”. Transverse direction moment frames:

Ta = 0.028(24 feet )

0.8

= 0.356 seconds

Transverse direction end walls:

Ta = 0.020(24 feet )0.75 = 0.217 seconds

Longitudinal direction sidewalls:

Ta = 0.020(24 feet )0.75 = 0.217 seconds

4.1.6.2 Determine the Initial Effective Seismic Weight, W, of the Building per ASCE 7 Section 12.7.2

Assumed Weights for Initial Seismic Loads Roof panel and insulation = 1.5 psf Roof purlin

= 1.0 psf

Frame

= 2.0 psf

Wall Girts

= 1.0 psf

Collateral Load

= 3.0 psf

4-4

Seismic Design Guide for Metal Building Systems

= 90.6 psf

Tilt-Up Wall

Transverse Moment Frame (One Frame) Roof Area = (100 ft ) (25 ft ) = 2,500 ft 2 Wall Area = 2(24 ft ) (25 ft ) = 1,200 ft 2 Parapet Area = 2(3 ft ) (25 ft ) = 150 ft 2 Roof Weight = (2,500 ft 2 ) (1.5 + 1.0 + 2.0 + 3.0 psf ) = 18,750 lbs = 18.75 kips

Longitudinal Wall Weight at Roof Level =

(1,200 ft ) (1.0 + 90.6 psf ) + (150 ft ) (90.6 psf ) 2 2

2

= 68,550 lbs = 68.55 kips Total Effective Seismic Weight = 18.75 + 68.55 = 87.3 kips Front Transverse End Wall (One End Wall)

§ 25 ft · 2 Roof Area = (100 ft ) ¨ ¸ = 1,250 ft 2 © ¹ § 25 ft · 2 Longitudinal Wall Area = 2(24 ft ) ¨ ¸ = 600 ft 2 © ¹ § 25 ft · 2 Longitudinal Wall Parapet Area = 2(3 ft ) ¨ ¸ = 75 ft 2 © ¹ End Wall Area = (100 ft ) (27 ft ) = 2,700 ft Roof Weight

= (1,250 ft 2 ) (1.5 + 1.0 + 2.0 + 3.0 psf ) = 9,375 lbs = 9.38 kips

Longitudinal Wall Weight at Roof Level =

(600 ft )(1.0 + 90.6 psf ) + (75 ft ) (90.6 psf ) 2 2

2

= 34,275 lbs = 34.28 kips End Wall Weight = (2,700 ft 2 ) (90.6 psf ) = 244,620 lbs = 244.6 kips Total Effective Seismic Weight = 6.88 + 34.28 + 244.6 = 285.8 kips Rear Transverse End Wall (One End Wall) § 25 ft · 2 Roof Area = (100 ft ) ¨ ¸ = 1,250 ft 2 © ¹ 4-5

Seismic Design Guide for Metal Building Systems

§ 25 ft · 2 Longitudinal Wall Area = 2(24 ft ) ¨ ¸ = 600 ft © 2 ¹ § 25 ft · 2 Longitudinal Wall Parapet Area = 2(3 ft ) ¨ ¸ = 75 ft © 2 ¹ End Wall Area = (100 ft ) (27 ft ) = 2,700 ft 2 Roof Weight = (1,250 ft 2 ) (1.5 + 1.0 + 2.0 + 3.0 psf ) = 9,375 lb = 9.38 kips Longitudinal Wall Weight at Roof Level

(600 ft ) (1.0 + 90.6 psf ) + (75 ft ) (90.6 psf ) = 2 2

2

= 34,275 lbs = 34.28 kips End Wall Weight = (2,700 ft 2 ) (90.6 psf ) = 244,620 lb = 244.6 kips Total Effective Seismic Weight = 9.38 + 34.28 + 244.6 = 288.3 kips Longitudinal Side Wall (One Side Wall) Roof Area = (100 ft ) (200 ft ) = 20,000 ft 2 Longitudinal Wall Area = (27 ft ) (200 ft ) = 5,400 ft 2 End Wall Area = (100 ft ) (24 ft ) = 2,400 ft End Wall Parapet Area = (100 ft ) (3 ft ) = 300 ft 2 Roof Weight

(20,000 ft ) (1.5 + 1.0 + 2.0 + 3.0 psf ) = 75,000 lb = 75.0 kips = 2

2

Longitudinal Wall Weight = (5,400 ft 2 ) (1.0 + 90.6 psf ) = 494,640 lb = 494.6 kips End Wall Weight at Roof Level (Two End Walls) =

2(2,400 ft 2 ) (1.0 + 90.6 psf ) § 300 ft 2 · ¸¸ (90.6 psf ) + 2¨¨ 2(2 ) © 2 ¹

= 137,100 lbs = 137.1 kips Total Effective Seismic Weight = 75.0 + 494.6 + 137.1 = 706.7 kips

4-6

Seismic Design Guide for Metal Building Systems

4.1.6.3 Select Design Coefficients and Factors and System Limitations for Basic Seismic Force Resisting Systems from ASCE Table 12.2-1

Transverse Moment Frames For ordinary steel moment frames, select from ASCE 7 Table 12.2-1 the following: R = 3.5

o = 3

C d = 3.0

Per definition in ASCE 7-05 Section 12.3.1.1, roof diaphragm condition is flexible for both directions, since building has metal roof and concrete shear walls parallel to the direction of loading, along both principal axes. Note g of ASCE 7 Table 12.2-1 allows for a reduction of Ωo for moment frames when the roof diaphragm is flexible. R = 3.5

o = 2.5

C d = 3.0

Note that design of FR beam-to-column moment connections of ordinary moment frames uses seismic load effects where R=1.0 (see Design Example 1 for explanation). Transverse Front End Wall For intermediate precast shear wall, select from ASCE 7 Table 12.2-1 the following: R = 4.0

o = 2.5

Cd = 4

Note: As of 2005 edition, ASCE 7 lists the intermediate precast shear walls which is more practical alternative to special concrete shear walls, yet it allows adequate building height for buildings assigned to Seismic Design Categories D and E. Transverse Rear End Wall For intermediate precast shear wall, select from ASCE 7 Table 12.2-1 the following: R=5

o = 2.5

C d = 4.5

Despite its name, this intermediate precast shear wall is not identical to the wall used at the front end wall. The SFRS selected for that end wall is a “bearing wall system”; hence, the R and Cd factors are lower. The SFRS chosen for the rear and longitudinal walls is a non-bearing type shear wall, i.e., “building frame system”. Longitudinal Walls For intermediate precast shear wall, select from ASCE 7 Table 12.2-1 the following: R=5

Ω o = 2.5

C d = 4.5 4-7

Seismic Design Guide for Metal Building Systems

Footnote g of ASCE 7 Table 12.2-1 also applies to concrete/masonry walls listed above with flexible diaphragms. The final overstrength factor, after ½ reduction, for SFR systems used in this example is shown in the following table. Summary R 3.5* 4 5 5

Transverse Moment Frames Transverse Front End Wall Transverse Rear End Wall Longitudinal Walls

Ωo 2.5 2.0 2.0 2.0

Cd 3 4 4.5 4.5

* For design of FR beam-to-column moment connections of ordinary moment frames, R=1.0 ASCE 7 Section 12.2.3.2 states “where a combination of different structural systems is utilized to resist lateral forces in the same direction, the value of R used for design in that direction shall not be greater than the least value for any of the systems utilized in the same direction.” However, the same provision allows that R-factor is determined independently for each line of resistance, if three listed conditions are met. This building satisfies all three, i.e., (1) the building occupancy is I or II, (2) the building has no more than two stories in height, and (3) the roof diaphragm is flexible. Roof diaphragm design still requires the least R-factor for each direction of loading. Same section of ASCE 7 also states that “the deflection amplification factor, Cd, and the system overstrength factor, Ωo, in the direction under consideration at any story shall not be less than the largest value of this factor for the R-factor used in the same direction being considered.” Therefore, determining R, Ωo and Cd from the tabulated values and stated limitations yields:

R*** 3.5** 4 5 5

Transverse Moment Frames Transverse Front End Wall* Transverse Rear End Wall* Longitudinal Walls*

Ωo 2.5 2.0 2.0 2.0

Cd 4.5 4.5 4.5 4.5

* Intermediate precast shear walls ** For design of FR beam-to-column moment connections of ordinary moment frames R=1.0 *** Transverse direction diaphragm design uses R=3.5

4-8

Seismic Design Guide for Metal Building Systems

4.1.6.4 Determine the Seismic Base Shear, V, for Two-Dimensional Models

V = C sW

ASCE 7 Eq. 12.8-1)

Where: Cs =

S DS §R· ¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-2)

Except Cs need not exceed: Cs =

S D1 §R· T¨ ¸ ©I¹

T ≤ TL

for

(ASCE 7 Eq. 12.8-3)

and Cs shall not be taken less than: C s = 0.01

(ASCE 7 Eq. 12.8-5)

and in addition, if S1 ≥ 0.6g, then Cs shall not be taken as less than: Cs =

0.5S1 §R· ¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-6)

Summarize Design Parameters S DS = 0.579 S D1 = 0.335

TL = 16 sec. I = 1.0

R-factor is 3.5, 4.0 or 4.5, depending on the SFRS under consideration. Transverse Direction (Moment Frames) T = Ta = 0.356 seconds

(T < TL=16 sec)

W = 87.3 kips Cs =

S DS 0.579 = = 0.165 § R · § 3.5 · ¨ ¸ ¨ ¸ ©I¹ © 1 ¹

C s (max ) =

S D1 § 1 · ¨ ¸= § R · ©T ¹ ¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-2)

0.335 § 1 ¨¨ § 3.5 · © 0.356 sec ¸ ¨ © 1 ¹ 4-9

· ¸¸ = 0.269 ¹

(ASCE 7 Eq. 12.8-3)

Seismic Design Guide for Metal Building Systems

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for this example because S1 < 0.60 g . Therefore, C s = 0.165

V = CsW = (0.165)(87.3 kips ) = 14.40 kips

(ASCE 7 Eq. 12.8-1)

Front End Walls

T = Ta = 0.217 seconds

(T < TL=16 sec)

W = 285.8 kips Cs =

S DS 0.579 = = 0.145 § R · § 4.0 · ¨ ¸ ¨ ¸ ©I¹ © 1 ¹

Cs (max ) =

S D1 § 1 · ¨ ¸= § R·©T ¹ ¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-2)

· 0.335 § 1 ¨¨ ¸ = 0.386 § 4.0 · © 0.217sec ¸¹ ¨ ¸ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8.-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for this example because S1 < 0.60 g . Therefore, C s = 0.145 V = CsW = (0.145) (285.8 kips ) = 41.44 kips

(ASCE 7 Eq. 12.8-1)

Rear End Walls T = Ta = 0.217 seconds

(T < TL=16 sec)

W = 288.3 kips Cs =

S DS 0.579 = = 0.116 § R · § 5.0 · ¨ ¸ ¨ ¸ ©I¹ © 1 ¹

C s (max ) =

(ASCE 7 Eq. 12.8-2)

· S D1 § 1 · 0.335 § 1 ¨¨ ¸ = 0.309 ¨ ¸= § R · © T ¹ (5.0) © 0.217 sec ¸¹ ¨ ¸ ©I¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for this example because S1 < 0.60 g . Therefore, C s = 0.116

4-10

Seismic Design Guide for Metal Building Systems

V = CsW = (0.116) (288.3 kips ) = 33.44 kips

(ASCE 7 Eq. 12.8-1)

Longitudinal Direction Side Walls T = Ta = 0.217 seconds

(T < TL=16 sec)

W = 706.7 kips Cs =

S DS 0.579 = = 0.116 § R · § 5.0 · ¨ ¸ ¨ ¸ ©I¹ © 1 ¹

C s (max ) =

S D1 § 1 · ¨ ¸= § R · ©T ¹ ¨ ¸ ©I¹

(ASCE 7 Eq. 12.8-2)

· 0.335 § 1 ¨¨ ¸ = 0.309 § 5.0 · © 0.217 sec ¸¹ ¨ ¸ © 1 ¹

C s (min ) = 0.01

(ASCE 7 Eq. 12.8-3)

(ASCE 7 Eq. 12.8-5)

Equation 12.8-6 is not applicable for this example because S1 < 0.60 g . Therefore, C s = 0.116 V = CsW = (0.116) (706.74 kips ) = 81.98 kips 4.1.7

(ASCE 7 Eq. 12.8-1)

Determine the Seismic Load Effect, E, for the Building in each Direction

See Design Example 1 for procedure. 4.1.7.1 Determine the Redundancy Factor, ρ, in each Direction based on ASCE 7 Section 12.3.4.2

Because the building design utilizes a flexible diaphragm assumption, the redundancy factor is calculated separately for each line of resistance. The ASCE 7 redundancy factor rule utilizes the number of shear wall bays, determined as the length of the wall divided by the wall height as follows: (100 ft ÷ 27 ft) = 3.7 for transverse walls (200 ft ÷ 27 ft) = 7.4 for longitudinal wall Any shear wall having length equal to or longer than three times its height will satisfy the redundancy requirement of ASCE 7 section 12.3.4.2.a), so the redundancy factor can be taken as unity (ρ = 1). Longitudinal Walls (Shear Walls) Redundancy factor is ρ = 1

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Seismic Design Guide for Metal Building Systems

Transverse End Walls (Shear Walls) Redundancy factor is ρ = 1 Transverse Direction (Moment Frames) Moment frames in the building interior do not satisfy ASCE 7 exception in Table 12.3-3, for moment frames; therefore, the redundancy factor for transverse direction is ρ = 1.3. 4.2

WALL DESIGN AND WALL TO METAL CONNECTION

Non-load bearing concrete shear walls on the longitudinal sides and at the rear of the building are subjected to wind and seismic forces that occur in directions both parallel and against the walls. The load-bearing wall at the building front is subjected to these forces plus tributary roof dead and live loads. 4.2.1

Wall Design Loads

4.2.1.1 Shear Wall Forces

Shear walls are designed to resist seismic forces resulting from the self-weight of the wall, plus the seismic force that is transferred to the wall from the building. The connection from the building to the wall only needs to be designed for the portion of seismic force that is transferred from the building to the wall (not the portion due to the shear wall’s self-weight). In this example, the force transferred from the building to the walls results from the sum of the tributary weights of the roof and the concrete walls not parallel to the direction of the seismic force. The seismic force transferred from the metal building to the concrete walls would be a set of uniform loads, as follows: Longitudinal Walls V = 0.116W = (0.116) (75.0 kips + 137.1 kips ) = 24.56 kips

For a wall length of 200 feet the resulting force per foot is

(24.56 kips ) (1000 lbs/kip) = 123 lb/ft 200 ft

Front Wall V = 0.145W = (0.145) (6.88 kips + 34.28 kips ) = 5.96 kips

For a wall length of 100 feet the resulting force per foot is

(5.96 kips ) (1000 lbs/kip) = 60 100 ft

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Seismic Design Guide for Metal Building Systems

Rear Wall V = 0.116W = (0.116) (9.38 kips + 34.28 kips ) = 5.05 kips

For a wall length of 100 feet the resulting force per foot is

(5.05 kips ) (1000 lbs/kip) = 51 lb/ft 100 ft

However, different building configurations can result in significantly different strength requirements for the connection between building and wall. This is discussed more completely in Section 4.2.4. ASCE 7-05, Section 12.5 lists the requirements for direction of loading, i.e., orthogonal effects. Unless Type 5 horizontal irregularity (nonparallel systems) is present, for typical metal building systems with flexible diaphragms, the code requirements apply only to columns common to two intersecting systems, when the building is assigned to SDC D, E, or F. Therefore, other elements of the seismic force resisting system, such as roof diaphragm, collectors or beams are not subject to design requirements of this section. 4.2.1.2 Code Out-of-Plane Wall Forces

All of the perimeter walls in this example are supported by the building against out-of-plane wind and seismic forces. This requires anchoring the wall to the building at intervals of 4 to 8 feet. Anchor spacing at greater than 8-foot intervals is not recommended for normal wall construction. Note that ASCE 7 Section 12.11.2 specifies that wall bending must be considered if the spacing of anchors exceeds 4 feet. ASCE 7 Section 12.11.2 specifies that wall anchors must be designed to resist the force Fp′ , per unit length of wall, using the greater of the following: 1. A force of 0.4 SDS I ww ≥ 0.1 times weight of the structural wall 2. A force of 400 SDS I (lbs/linear foot) of wall 3. 280 lbs/linear foot of wall where: Fp = the design force in the individual anchors I

= occupancy importance factor (from Section 4.1.2.1, I = 1.0 )

SDS = the design earthquake short-period response acceleration (from Section 4.1.1, S DS = 0.579 g ) ww = the weight of the wall tributary to the anchor

§ 22.5 ft · + 4.5 ft ¸ (90.6 psf ) = 1,427 lb/ft =¨ © 2 ¹ 4-13

Seismic Design Guide for Metal Building Systems

Structural walls (longitudinal shear walls) of this example are not anchored to the roof diaphragm (See Figure 4.2-2). The wall is connected to transverse frames via spandrel beam bolted connections. Also, the roof diaphragm is connected to the eave perimeter members, which are bolted at the top of the transverse moment frames. Therefore, there is no direct connection between the roof diaphragm and longitudinal walls; hence, the ASCE 7-05 provisions of 12.11.2.1 do not apply for the transverse direction of loading. Since wall forces (in the transverse direction) are transferred to resisting frames via beam action, the forces in the roof diaphragms include only seismic loads related to seismic weight of the roof (plus portion of snow, if any), which is typically small. The required strength for wall anchors is based on the largest of: 1.

Fp′ = 0.4 S DS Iww = 0.4(0.579) (1.0) (1,427 lb/ft ) = 330 lb/ft ≥ 0.1ww = 0.1(1,427 lb/ft ) = 143 lb/ft

2. Fp′ = 400S DS I = 400(0.579) (1.0) = 232 lb/ft 3. Fp′ = 280 lb/ft

For this example, the weight of the concrete walls is 90.6 psf and all walls are 24 feet tall with a 3-foot parapet. Note that these heights are adjusted for the actual location of the spandrel beam, which is at 22.5 feet. Therefore, the required anchorage force per foot of wall length is equal to Fp′ = 330 lb/ft The spandrel beam connection to frame columns should use this force. The beam reaction based on anchorage forces at the longitudinal walls is: § 25 ft · Fp = 330 lb/ft ¨ ¸ = 4,125 lbs © 2 ¹

In the longitudinal direction, roof diaphragm is anchored directly to the concrete wall, at the front end wall (See Figure 4.2-4). Since this roof diaphragm is flexible, additional provisions of ASCE 7 Section 12.11.2.1 apply. The required strength for wall anchors is calculated from ASCE 7 Equation 12.11-1: Fp′ = 0.8S DS Iww = 0.8(0.579) (1.0) ww = 0.463ww lb/ft Using purlin spacing of 5 feet, and the unit wall weight calculated earlier, the anchorage force becomes: Fp′ = 0.463(1,427 lb/ft ) = 661 lb/ft Fp′ = 662 lb/ft (5 ft ) / 1000 = 3.31 kips

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Seismic Design Guide for Metal Building Systems

Additional requirements of ASCE 7 Section 12.11.2.2.2 require that the force Fp in selected steel elements is further increased by 1.4, so the final seismic anchorage force for each purlin at the front end wall is: Fp = 1.4 (3.31 kips) = 4.63 kips This force applies to the following purlin anchorage strength checks: • Bolt strength, shear, tension, or combined (as applicable) • Connection bearing at the purlin connection bolt • Purlin support member (angle, channel, etc.) • Purlin support member connection to wall embedded plate (welded or bolted connection) Note that Code treats the component force Fp essentially the same way as the base shear V: they are both covered under the common term QE which represents the effect of horizontal seismic forces. All applicable ASD or LRFD load combinations, and load factors apply (0.7 for ASD, and 1.0 for LRFD). The exception is that the redundancy factor for non-structural components can be taken as ρ = 1.0. 4.2.1.3 Wall-Supported Gravity Loads from Building

In this example, the front wall is the only load-bearing wall present. From Section 4.1.6.2, the tributary area of roof supported by this wall is 1,250 sq. ft. The total dead load supported by the wall is 6,875 lbs, or 68.8 lb/ft of the 100foot wall length. The code-specified basic roof live load for this example is 20 psf, which is reducible for large tributary areas. Because the actual tributary area that is supported by each roof connection is relatively small (i.e., one purlin, 5 ft × 25 ft ÷ 2) = 62.5 ft2), no reduction is permitted for this connection. The total unreduced live load supported by the front wall is:

(20 psf ) (1250 ft 2 ) = 25,000 lbs or 250 lb/ft for the 100-foot wall length. Assuming typical 5-foot purlin spacing, each purlin connection to the front wall requires (5 ft) (250 psf) ÷ 1000 = 1.25 kips This represents the roof live load reaction plus tributary portion of the dead loads. Because the site is subjected to a ground snow load requirement of 15 psf, the wall is also required to support tributary roof snow loads (including drift loads against the 3-foot parapet), but because snow loading is not required to be considered together with seismic loads in areas where the flat roof snow load is 30 psf or less, the roof snow load is not calculated here.

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Seismic Design Guide for Metal Building Systems

4.2.2

Connection to Longitudinal Walls

In this example, the two longitudinal walls are nonload-bearing shear walls. As defined in the ASCE 7 Section 11.2, a nonload-bearing wall is limited to supporting no more than 200 lb/ft of applied vertical loads. Although dead loads alone might fall within this limit, combined dead plus live or dead plus snow load conditions would exceed this limit. Therefore, vertical loads from the roof need to be prevented from transfer to the wall by providing separate framing, slotted-hole connections, or other means in order to have the wall classified as a nonload-bearing wall. Note that AISC 341-05, Section 7.2 requires that bolts be installed in standard holes or in short-slotted holes perpendicular to the applied load (see Figure 4.2-1). It is the wall designer’s responsibility to determine and provide the required details, not the metal building manufacturer. However, it would be prudent to alert the wall designer that these provisions have not been made in the metal building manufacturers’ design and need to be provided by the wall designer when such conditions are present.

STANDARD HOLE

;

SHORT SLOT ⊥ FORCE

;

SLOT || FORCE

Figure 4.2-1 Use of Bolt Holes in High Seismic Applications

The geometry of the connection used between the roof and wall also needs to consider several other factors. First, the means of drainage from the roof needs to be considered. One approach is to provide concrete or masonry walls that are shorter than the roof so that the metal roofing can extend over the top of the wall. But in this example, the walls extend above the roof, with a 3-foot parapet. For this example, drainage will be assumed to be provided via a gutter system that will be provided along the continuous length of the longitudinal walls between the metal roof and concrete walls, as shown in Figure 4.2-2. Because this detail separates the roof framing from the concrete wall, the nonload-bearing conditions of the ASCE 7 are satisfied.

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Figure 4.2-2 Section Showing Continuous Gutter System

Another factor that needs to be considered in the connection between the building and wall are the code requirements for maximum lateral spacing of anchorage against out-of-plane wall forces. Transverse moment frames that brace the walls are spaced at 25 feet apart, whereas normal wall anchor spacing for a 7.25-inch wall thickness are typically spaced about 4 to 6 feet apart. Therefore, either a spandrel beam or eave trusses need to be provided to collect the forces from the walls and transfer them to the moment frames. 4.2.2.1 Spandrel Beam used as a Connecting Element

If a spandrel beam is used, as shown in Figure 4.2-2, the following factors should be considered in the design: 1. The horizontal deflection of the beam should be limited based on the acceptable maximum deflection allowances. There are no Code prescribed serviceability limits for seismic loads; however, AISC Design Guide No. 3 recommends a deflection limit of L/240 for wind loading, assuming 10 year-wind and elastic behavior. Therefore, it is recommended that a similar serviceability limit (L/240) be used assuming a seismic load (Fp) as described below. 2. The beam must be designed to transfer the longitudinal wind or seismic forces from the building roof horizontal bracing system into the shear wall. Horizontal roof bracing rods, if used, can be sloped down from the plane of bracing to connect directly to the support beam or column web adjacent to the support beam.

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Seismic Design Guide for Metal Building Systems

3. The true, cantilevered height of the wall parapet should be measured from the height of the spandrel beam, not from the point of intersection of the roof line and wall. 4. The spandrel beam must be designed to resist the out-of-plane seismic wall forces.

Maxim um Lateral Beam Deflection

Figure 4.2-3 Spandrel Beam Used as Connecting Element

The spandrel beam is the main load-carrying element in the structural wall (shear wall); therefore, it should be designed for the out-of-plane forces per ASCE 7 Section 12.11.1. Fp′ = 0.4 S DS I ww  0.1 ww

(ASCE 7 Eq. 12.11-1)

Where: SDS = design spectral response acceleration = 0.579g for this design example ww = (22.5 ft/2 + 4.5 ft) (90.6 psf / 1000) = 1.427 kip/ft = the weight of the concrete wall tributary to the spandrel I

= importance factor = 1.0 for this design example

Fp′ = 0.4 (0.579 g ) 1.0 ww = 0.232 ww > 0.1 ww The weight of the wall tributary to the spandrel beam based on a 25-foot spacing of the transverse frames and a wall weight given by: W p = (25 ft ) ww = 25 (1.427 kips/ft ) = 35.68 kips The total horizontal wall force is given by: Fp = 0.232W p = 0.232(35.68 kips ) = 8.28 kips

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Seismic Design Guide for Metal Building Systems

The spandrel beam should be designed for the following member forces: End Reaction, Rhoriz =

Fp 2

=

8.28 kips = 4.14 kips 2

Applied uniform load, whoriz =

Fp L

=

8.28 kips 1000 = 331 lb/ft 25 ft

Max. bending moment, M max (horiz ) = =

whoriz L2 8

(331 lb/ft ) (25 ft )2 8(1000 lbs/kip )

= 25.86 ft - kips

For member design, all component forces and moments calculated above will be further multiplied by the applicable load factor: 0.7 for ASD and 1.0 for LRFD. Both, the redundancy and the overstrength factors used with component forces are unity (1.0). Assuming that the building details permit a maximum deflection of 1 inch, the required minimum moment of inertia, Imin, would be, 1.0 inch =

5wL4 384 EI

5(330 lb/ft ) (25 ft ) (12 in/ft ) = = 100 in 4 (384) (29,000,000 psi ) (1.0 in ) 4

I min (horiz )

3

Note that the building code does not require the primary resisting systems, which in this case are the transverse moment-resisting frames and the building end walls, to be designed to resist the forces resulting from application of the Fp component forces. Note: ASCE 7-05 Section 12.5 lists the requirements for direction of loading, i.e., orthogonal effects. Unless Type 5 horizontal irregularity (non-parallel systems) is present, for typical metal building system the Code requirements apply only to columns common to two intersecting systems, when building is assigned to Seismic Design Category D through F. Therefore, other elements of the seismic-force resisting system, such as roof diaphragm, collectors or beams are not subject to design requirements of this section. 4.2.2.2 Eave Trusses Used as Connecting Element

An alternative means to resist the Fp wall anchorage forces is to provide continuous lines of eave trusses along the longitudinal sides of the building, as shown in Figure 4.2-3. Eave trusses are lighter than horizontal beams and have less deflection concerns, but are more complex to erect. 4-19

Seismic Design Guide for Metal Building Systems

Figure 4.2-3 Eave Trusses Used as Connecting Elements 4.2.3

Wall Anchors at Front and Rear Walls

At the two end walls, a simple wall anchor connection can be provided by connecting the roof purlins to the walls with a connection designed for the required out-of-plane anchorage force, and by designing the purlins for the resulting tension/compression forces. These purlins are capable of providing a strong and continuous cross-tie across the length of the building, although the purlins alone do not necessarily provide a clearly defined load path into the horizontal roof bracing system that takes the forces to the longitudinal shear walls. Assuming a uniform purlin spacing of 5 feet, the required design out-of-plane anchorage force between the wall and purlin would be: Fp = (331 lb/ft ) (5 ft ) = 1,655 lbs At the bearing wall, the resulting connections might resemble one of those shown in Figures 4.2-4. Connections at the nonbearing wall might be similar, except with vertically slotted holes in the connections so that the purlin weight is supported entirely on the adjacent roof beam. Forces are transferred from the purlins to the horizontal bracing by one of the following mechanisms: • Where metal roof systems with documented shear strength and stiffness values are used, the metal roofing can act as a subdiaphragm to transfer forces from the purlins to the main horizontal bracing cross ties. Documentation of shear strength and stiffness could be in the form of

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Seismic Design Guide for Metal Building Systems

calculations per the appropriate analytical method or test results based on a recognized test procedure. The level of documentation required may depend on the engineer of record. Due to the generally large depth of diaphragm versus the relatively short span between main horizontal bracing cross ties, the shear forces associated with this transfer tend to be trivial. • An alternative load path is to provide a spandrel member along the rake at the end walls, similar to that shown in Figure 4.2-4(a), which can transfer forces to the main horizontal bracing cross ties. Additionally, the transverse shear forces at the end frames and the gravity forces at the front wall must be accounted for in the design.

(a)

(b) Figure 4.2-4 Example of Wall Anchor Connection

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4.2.4

Transfer of Seismic Forces to Shear Walls

In Section 4.2.1.1, the total seismic design force from the metal building to the concrete walls was determined. The design of the load path and connections that transmit this force needs to consider a number of factors. • Building walls are generally not continuous, but instead often contain many openings that reduce the total effective shear wall length, as shown in Figure 4.2-5. Location of Horizontal Roof Bracing

Effective Shear Wall Length

Figure 4.2-5 Hypothetical Wall Elevation

When the location of the resisting shear walls does not align with the locations of the applied forces (in this case, the roof horizontal bracing and the forces from the individual wall panels), then a collector element needs to be provided to transfer these forces to the resisting elements. ASCE 7 Section 12.10.2.1 requires that these collector elements in SDC C or higher be designed using the special load combination with overstrength of ASCE 7 Section 12.4.3.2 • If the concrete wall sections are not interconnected at each end, the attached metal building will transfer seismic forces to the shear wall caused by the metal building weight, as well as the self-weight of concrete wall sections that are too flexible to resist seismic forces due to wall openings. In this instance, a substantial steel collector element may be required. This design approach is generally not recommended, since (1) a greater weight of steel would be needed to provide a separate steel collector element than if it were included in the wall design, and (2) the designer of the walls would need to provide an extensive amount of information (the detailed distribution of shear forces between the walls and collector system). • If the concrete wall system is interconnected along the wall length, then seismic forces from the roof horizontal bracing can be directly connected to the wall, provided that the continuous wall reinforcing is designed as a collector element to transfer the combined forces of metal building and walls to the resisting shear wall sections. This is generally the preferred approach, although details relating to continuity of the wall reinforcing across the wall joints need to be able to accommodate expected thermal and shrinkage movements of the individual wall sections while also providing sufficient strength to meet code requirements. This is often accomplished by providing a sleeve or by 4-22

Seismic Design Guide for Metal Building Systems

wrapping the continuous reinforcing bars within the wall for a short distance on each side of the joint to provide a slight elasticity to permit small shrinkage movements to occur without inducing high tensile stresses in the bars. The real meaning of these factors is that clear communication and coordination needs to occur between the designer of the metal building and the designer of the perimeter walls, when any attachment or force transfer is planned. In the absence of communication and a clearly defined scope, it is all too easy for the designer of the metal building to assume that the wall designer will provide the needed elements, and the designer of the wall to assume that the metal building will do likewise, with the result that code-required elements may be missed. 4.3

SIDE WALL GIRTS

Intermediate side wall girts are generally not used with single-story structural concrete or masonry walls, since it is simpler and more economical to connect the wall along one line at the top.

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