RCB Manual

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3

Analysis & Design of Reinforced Concrete Buildings for Earthquake and Wind Forces

COPYRIGHT The computer program EngSolutions RCB and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with EngSolutions, Inc. Unlicensed use of the program or reproduction of the documentation in any form, without prior written authorization from EngSolutions, Inc., is explicitly prohibited. Further information and copies of this documentation may be obtained from:

EngSolutions, Inc. At: Dr. Ricardo E. Barbosa 8170 SW 29th Ct Ft. Lauderdale FL 33328 Tel: (954) 370-6603 Fax: (954) 370-0150 www.EngSolutionsRCB.com Email: [email protected]

© EngSolutions, Inc., 2000-2009 © Ricardo E. Barbosa, Ph.D. 1992-2000

Table of Contents

Chapter 1

Chapter 2

Chapter 3

Introduction

1

EngSolutions RCB .................................................................... Technical Overview ………......................................................... Organization of Manual ….......................................................... Program Versions ………........................................................... Technical Support.......................................................................

1 2 3 3 4

Installation

5

System Requirements ………..................................................... Software Installation ……............................................................ Software Initialization …….......................................................... Protection Key …….................................................................... Network License .....................................…...............................

5 6 6 7 8

EngSolutions RCB Interface

11

Running the Program …............................................................. EngSolutions RCB Main Window .............................................. Commands ................................................................................. Activating Commands …............................................................ Types of Commands .................................................................. User Interaction ………............................................................... Element Selection …….............................................................. Property Window ………….......................................................... Context Menu ............................................................................. Rotating the Structure …............................................................. Exiting EngSolutions RCB …...................................................... What to do Next ............................….........................................

11 12 15 15 15 16 16 16 17 17 17 17

Chapter 4

Chapter 5

EngSolutions RCB Concepts

19

The Structure .............................................................................. The Geometry..…………………………………………………….. The Elements ………….…………………………………………… Support Conditions ….…………………………………………….. Loads …….................................................................................. Self Weight ................................................................................. Vertical Floor Loads ……........................................................... Wind Forces ……....................................................................... Equivalent Static Earthquake Forces ……................................. Response Spectra …….............................................................. Dynamic Time-History Analysis …………….……….………….. Load Combinations ………......................................................... Analysis ..................................................................................... Modes / Frequency Analysis ……………………........................ Gravity and Lateral Load Analysis ................….......................... Linear Analysis ……………………………………………………… P-Delta Analysis …….................................................................. Gravity Load Analysis ................................................................ Incremental Analysis ………………………………………………. Seismic Analysis …………………………………………………… Time History Analysis ………..……………………………………. Stiffness of Elements ……………………………………………… Analysis Results …………......................................................... Design of Reinforced Concrete Elements ................................. Design of Beams ....................................................................... Column Design …….................................................................. Shear Wall Design ...................................................................... Design of Foundation Beams ………….…………………………. Design of Footings …………………………………………………. Design Results ..................……….............................................. Design of Structural Steel Elements ……….…………………….. Printing ...............................................................…….................

19 20 22 26 30 32 32 33 33 36 37 39 40 40 41 42 42 43 43 45 45 47 47 55 55 56 58 61 61 61 63 65

EngSolutions RCB Training Session

67

The Structure .............................................................................. Creating the Structure …............................................................ Assigning Supports ……............................................................... Applying Loads Manually ……...................................................... Generating Self Weight of Elements ............................................ Generating Floor Loads ……….................................................… Modes and Frequency Analysis …………………………….......… Displaying Mode Shapes …………………………………………… Generating Earthquake Forces ……………………………………. Analyzing the Structure …………………………………………….. Displaying Analysis Results ……………………………………….. Checking Story Drift Ratios ………………………………………… Defining Load Combinations ………………………………………. Designing of Structural Elements …………..…………………….. Displaying Design Results …………………………………………. Seismic Shear Resisted by Shear Walls …………………………. Design Check for Dual System …………………………………….

67 68 86 87 89 89 90 91 92 95 96 99 101 104 109 111 113

Chapter 6

Cost of the Structure ……………………………………………….. Modifying the Model ………………………………………………..

114 116

Reference

117

Earthquake Records ……............................................................ Differences in Use with RCBE ......…........................................... RCBE v5.2 Structures .....………................................................. Rotating the Structure ............….………………………………...... Wall Element Output …............………......................................... Load Scale ……………………..........…........................................ Estimate of Building Materials .....................................................

117 118 119 119 121 125 126

References

127

Appendix A

EngSolutions RCB Applications

Covert

Ocean Park Tower 1 & 2 Punta Pacifica, Panama, Rep. of Panama, Structural Engineer Gonzalo Sosa from Grupo G.S., S.A., Panama.

129

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Chapter 1 Introduction EngSolutions RCB EngSolutions RCB is a structural engineering program for tridimensional analysis and design of reinforced concrete buildings. EngSolutions RCB consists of several modules integrated into an exceptionally easy to use software package. Through its graphical interface it is possible to easily create, analyze and design complex building structures for earthquake and wind forces, according to different building codes. Creation of the structure, assignment of element properties, definition of supports and application of loads, are all performed interactively. Hence, there is no need for an input file. All operations including analysis and design are carried out within the program’s graphical interface. Generation of loads is fully automated releasing the engineer from lengthy manual calculations. Vertical floor loads can be automatically converted to span loads on adjoining beams and walls. Wind forces and earthquake forces can be generated automatically according to different international building codes. Once a building structure is created, it remains interactively displayed and all program commands remain available. The engineer can make changes at any time on the structure, such as change coordinates, add or remove elements, add or remove stories, modify element properties, change support conditions, change loading, etc., and see the influence of these changes on the analysis and design results. All these steps are accomplished with just a few mouse clicks. The program allows modeling the incremental construction of tall buildings, checking lateral story drifts, computing redundancy factors, and designing structural elements according to various seismic codes. It is possible to run simultaneously multiple instances of the program, which makes it easier to compare different structural solutions.

2

Technical Overview EngSolutions RCB is a mature and stable software system that has a proven track record of improving the profitability of engineering firms and enhancing the efficiency of regulatory building agencies. The main technical features of EngSolutions RCB are the following: • • • •

• •







• • • • • • •

• • • •

Native Windows 32 bit application that operates under Windows Vista\XP/2000/NT. No limit on number of nodes, elements or equations. Interactive procedure to create building models through typical floor framing plans. Automatic generation of seismic forces, static equivalent, spectral, and time-history, according to numerous international building codes, including: USA IBC-2003, ASCE 7-2005, UBC-97, UBC-94, ASCE7-93/95, NERPH-97, NERPH-85, Mexico RCDF2004, GUAD-97, CFE-93, Panama REP-04, REP-93, Colombia NSR-98 and CCCSR-84, Venezuela COVENIN-82, Peru E030-2000, Ecuador CEC-01 and CEC93, Chile NCH433.Of93, Dominican Republic DNRS/SEOPC-80, Costa Rica CSCR86. Complete library of earthquake records. Automatic generation of wind forces, according to various international codes, including: USA ASCE7-95, ASCE 7- 88, UBC- 94, Mexico RCDF-87, CFE-93, Dominican Republic DNRS/SEOPC-80. Accurate modeling of torsion effects: The engineer may specify different design eccentricities based on inherent and accidental eccentricities, and may choose from different methods of modal combination available, including SAV, SRSS, CQC, 1/2 SAV+SRSS, and 0.25 SAV + 0.75 SRSS. Automatic distribution of floor loads to span loads on adjoining beams and walls. Various floor systems can be considered, including one-way and two-way slab systems as well as one-way and two-way joist systems. Automated incremental analysis to model the construction sequence of high-rise buildings. Instead of applying gravity loads in a single step, the analysis can model the sequential addition of floors to the structure. Graphical display of lateral inter-story drifts that allows immediate check for compliance with building codes. New finite element formulations for accurate modeling of buildings with shear walls. Automated design of shear-walls, which includes dimensioning of boundary zones for special (ductile) seismic design. Boundary zones for shear walls can be design either according to the stress design method of the ACI-318-99 or to the strain method of UBC-97 and ACI-318-05. Automatic detailing of steel reinforcement for beams. Automatic generation of design load combinations according to different international building codes. Buildings can be modeled as supported on theoretical dimensionless nodal supports or on rigid footings, including spread footings for columns, continuous footings for walls, combined footings and mats. Automatic re-sizing of footings according to specified allowable soil pressure. Design of spread and continuous footings. Specification of member end-releases. Automatic generation of load combinations: according to several international codes.

3 •



Structural elements can be separated into elements that are part of the lateral force resisting system only, elements that are part of the gravity load resisting system and elements are part of both structural systems.

4

Technical Support Technical support is available to registered users only, therefore be sure to complete and return the registration card. Registered users are eligible for the following support services at no extra charge. Fax support. If you need assistance beyond what the EngSolutions RCB manual can provide, you may fax messages at (954) 370-0150. Please include the following information: • • • • •

Your name, company name, fax & phone numbers and Email address. EngSolutions RCB version number and License number. Your hardware and operating system configuration. A concise description of the problem. Selected information and/or printouts documenting the problem.

Email support. You may also send Email messages to [email protected] Please include the same information requested above. Telephone support. To help us provide a more efficient support service, we request that you send first a fax/Email message with the information requested above, before you call. Telephone support is used to discuss and solve cases already described in written form. Please contact us at (954) 370-6603. EngSolutions RCB technical support program is subject to change without notice. If you would like to share ideas with the creators of EngSolutions RCB, make comments about the software, or suggest improvements, please use any of the technical support options described above. Occasionally, we are unable to implement some requests for additions to the software as fast as we would like, and sometimes we cannot implement at all some of the suggested modifications, however, we do study and consider all the suggestions that we-receive.

5

Chapter 2 Installation This chapter deals with the installation of EngSolutions RCB on computers with Windows Vista/XP/2000. The complete EngSolutions RCB package includes a CD and a software protection key.

System Requirements To run EngSolutions RCB you must have certain hardware and software installed in your computer. The system requirements include: • • • • •

Personal computer with a Pentium processor. At least 518 MB of RAM. A color monitor with a minimum resolution 1024 x 768. A hard drive with at least 300 MB of free hard disk space. Operating system Windows Vista/XP/2000.

Software Installation To run EngSolutions RCB you need to install the software and then to initialize it. To install EngSolutions RCB follow the steps below: 1. If you are upgrading from a previous version of EngSolutions RCB uninstall such a version by opening the Control Panel, from the Windows Start button, and clicking the Add/Remove Programs icon. This command activates the EngSolutions RCB uninstall program. The uninstall program does not remove any folder; therefore, structure files previously saved remain untouched.

6 Next, delete manually the folder Bitmaps, located on the folder where the previous version of EngSolutions RCB was installed. Users of RCBE (our program predecessor to EngSolutions RCB) do not need to uninstall such a program, as EngSolutions RCB and RCBE are completely independent programs. 2. Insert the EngSolutions RCB CD in the CD drive. 3. Use Windows explorer to locate and activate the SetUp.exe program. Alternatively, you may activate the Windows RUN command and type the command line: D:\SETUP (assuming the CD drive is D) 4. Follow the screen instructions.

Note:

In the first window of the installation program (Welcome to the EngSolutions RCB installation program…) click on the OK button to continue. In the second window, where the installation folder is selected, click on the installation button ⎯not in the exit button (Exit Setup). The installation button is the one located under the message: Begin the installation procedure by clicking the button below. If your operating system is Windows Vista, do not install the program in the default folder (C:\Program Files\) but create a different folder such as C:\RCB\ If during the installation process a window pops up, warning that a more recent version of a given file is already present in your system, answer affirmatively to the question whether you want to keep the existing file. (A file being copied is older than the file currently in your system. It is recommended that you keep your existing file. Do you want to keep this file? ─Yes.)

Software Initialization Once the installation process is finished, initialize the program by running the initialization program from the Windows Start button (Start > Programs > Initialize EngSolutions RCB). The initialization program performs various tasks. First it displays the license agreement. Then, it asks user information (company name, user name, country). Next, the program installs the device driver for the protection key, which is required to run EngSolutions RCB. Finally, the program creates a shortcut in the Windows desktop, for an easier access to EngSolutions RCB.

Protection Key After the program has been initialized, connect the software protection key to your computer. Without the key EngSolutions RCB will not run. The key is transparent to the operation of your computer and connected peripherals. The only software that detects its presence is EngSolutions RCB. There are two types of protection keys available: (a) HASP USB keys which are connected to a USB port and (b) HASP parallel port keys which are connected to a parallel printer port. If your protection key is a HASP parallel port key and you have a printer connected to the parallel printer of your computer,

7 disconnect the printer, connect the key to the parallel port, and then connect the printer to the protection key.

Network License In the case of network licenses, a single protection key (HASP4 Net) is provided which is connected to one of the computers in the network. This HASP4 Net key is preprogrammed to allow a determined number of stations to run EngSolutions RCB at the same time. The computer to which the HASP4 Net key is connected does not have to be the network file server but any computer on the network, providing the HASP License Manager is installed on the same machine. The HASP License Manager is included in the EngSolutions RCB distribution CD. It is the application that communicates EngSolutions RCB and the protection Key (HASP4 Net key), functioning as a link between the two. When EngSolutions RCB is activated from a network station, it accesses the HASP License Manager and request permission to run. The HASP License Manager then checks that the correct protection key is connected and access the HASP4 Net key to verify that EngSolutions RCB is licensed to run and that the number of stations allowed to run EngSolutions RCB at the same time has not been exceeded. The following steps are necessary to run EngSolutions RCB in a network environment: The following steps are necessary to run EngSolutions RCB in a network environment: • • • •

Install and initialize EngSolutions RCB in each computer in the network where the program is going to be run, as indicated above. Connect the HASP4 Net key to a computer in the network. Install and start the HASP License Manager on the same computer the HASAP4Net key is connected to. If necessary, customize the HASP License Manager and EngSolutions RCB to adapt them to your network environment.

The HASP License Manager is available for the following environments: Windows NT/2000/XP/Vista, and Novell 3.12 and higher.

HASP License Manager for Windows The HASP License Manager is available as an executable for Windows NT/2000/XP and as a service for Windows NT/2000/XP/Vista. Both types of HASP License Managers can be installed with the setup file lmsetup.exe in the folder HASP4Net\Servers\Win32 in the EngSolutions RCB distribution CD. The HASP License Manager for Windows can communicate via TCP/IP, IPX and NetBIOS. The protocols can be loaded and unloaded using the HASP License Manager graphical user interface or command-line switches.

Installing HASP License Manager on a Windows NT/2000/XP/Vista Station

8 The HASP License Manager for Windows NT/2000/XP/Vista is nhsrvice.exe. Install it by running the setup file lmsetup.exe from the EngSolutions RCB distribution CD and following the instructions of the installation wizard. As installation type, select Service. The setup file lmsetup.exe is located in the folder HASP4Net\Servers\Win32. It is recommended that you install the HASP License Manager as an NT service, so there is no need to log in to the station to provide the functionality.

Nota:

If the HASP4 Net key is going to be connected to a Windows station in which EngSolutions RCB is not going to be used (and was not installed), before installing the HASP License Manager it is necessary to install the HASP device driver. To install the HASP device driver copy the file Hinstall.exe (from the HASP4Net folder in the EngSolutions RCB distribution CD). Then type hinstall –i from the command line.

Activating and Deactivating HASP License Manager To activate the HASP License Manager start it from the Start menu or the Windows Explorer. The HASP License Manager application is always active when any protocol is loaded and a HASP4 Net key is connected. To deactivate it, select Exit from the main menu. If the HASP License Manager is installed as a Windows NT service, you cannot exit using this menu option. Instead, use the standard Windows Service Administration in the Control Panel. Operating The HASP License Manager For information on how to operate the HASP License Manager including loading protocols, removing protocols, viewing the log for specific protocols, refer to NetLicenses.doc in the HASP4Net folder in the EngSolutions distribution CD.

HASP License Manager for Novell File Server The HASP License Manager for Novell Netware file servers is haspserv.nlm. It can communicate via IPX. Loading HASP License Manager To load the HASP License Manager: • • •

Connect the HASP key to a Novell server. Copy haspserv.nlm from the EngSolutions CD to the system directory of the file server. Load the HASP License Manager by entering: Load haspserv The HASP License Manager screen appears showing operation details.

Nota:

To load the HASP License Manager automatically, add the line load haspserv to the autoexec.ncf file in the system directory.

Removing HASP License Manager

9

To remove the HASP License Manager enter unload haspserv. Customizing the HASP License Manager When installing and operating the HASP License Manager you may want to adapt it to the network environment. You can use one of the following methods: • •

Operate the HASP License Manager with switches. Use the configuration file nhsrv.ini. A copy of nhsrv.ini is included in the HASP4Net\Servers folder in the EngSolutions RCB distribution CD. For information on customizing the HASP License Manager refer to NetLicenses.doc in the HASP4Net folder in the EngSolutions distribution CD.

Configuring EngSolutions RCB to the Network EngSolutions RCB can be configured to your network environment with a configuration file. If EngSolutions RCB finds the configuration file, it reads the file and uses the information. If not, default values are used. In the configuration file you can fine-tune how EngSolutions RCB searches for the HASP License Manager. The configuration file is nethasp.ini. A copy of nethasp.ini is included in the HASP4Net\Servers folder in the EngSolutions RCB distribution CD. For information on how to configure EngSolutions RCB refer to NetLicenses.doc in the HASP4Net folder in the EngSolutions RCB distribution CD.

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Chapter 3 EngSolutions RCB Interface This chapter describes the main elements of the EngSolutions RCB graphical interface and explains how the engineer interacts with them.

Runing the Program To run EngSolutions RCB double-click the shortcut to the program. After a few seconds, a splash window is shown, displaying copyright information, license number, and name of the engineer. The starting window, shown in Figure 3.1, follows the splash window. In this later window, the engineer chooses between creating a new structural model and opening a previously saved model.

Figure 3.1 EngSolutions RCB’s starting window

12

EngSolutions RCB Main Window The main window of EngSolutions RCB is shown in Figure 3.2. In this window, different views of the model can be shown, along with different diagrams displaying analysis and design results.

Figure 3.2 Main Window of EngSolutions RCB The main window of program EngSolutions RCB include the following elements:

13

1. Title Bar (at the top) includes buttons to minimize, maximize and exit EngSolutions RCB.

Figure 3.3 Menu Bar 2. Menu Bar (under title bar) provides access to menus and submenus to activate EngSolutions RCB commands. 3. Toolbars includes the most frequently used commands.

Standard Toolbar ⎯Located by default to the left under the menu bar.

View Toolbar ⎯Located by default to the left of the standard toolbar.

Element Toolbar ⎯Located by default vertically on the left border of the main window. Figure 3.4 Toolbars 4. Main View Window displays the structural model along with analysis and design results. Also in this area occasionally dialog windows and message windows are shown. 5. Status Bar presents messages along with pertinent information about the model. 6. Active Command Window This window is shown when an interactive command is activated. It shows subcommands available and options for multiple selection of

14 structural elements. By default, this window is shown in the right top corner of the main window. A typical active command window is shown in Figure 3.5.

Figure 3.5 Active command window 7. Property Window is a table containing properties of the selected element. The first line of this window shows the name of the selected element and is followed by a twocolumn table with the name and de value of each property. This window is shown simultaneously and below the Active command window.

Figure 3.6 Property window 8. Selected element window presents a solid 3D view of the selected element displaying its local axes. This window is displayed simultaneously and below the Property window.

15

Figure 3.7 Selected element window 9. Rotation window shows a reference system to rotate the model.

Figure 3.8 Rotation window

Commands EngSolutions RCB is a procedure-oriented program. At any stage, only one command or procedure can be active. Some examples of EngSolutions RCB commands that at a given instant may be active are: , Save current model

Create a new model a static analysis

, Edit properties of columns

, compute natural frequencies and modes of vibration

, Run

, etc.

Activating Commands A command is activated when the engineer selects it with the mouse in either a menu in the menu bar or in a toolbar. The name of the active command is shown in the Active command window. Types of Commands There are three types of commands in EngSolutions RCB, which require different degrees of user interaction. These are action commands, automated commands and interactive commands. Action commands require little or no user interaction. These commands are executed as soon as the user activates them. Some of these commands may require the user to

16 input additional information such as a file name o some parameter values. When the command is completed it is deactivated and the program remains idle waiting for the user to activate a new command. Examples of this type of command are: Save current structure

, run analysis

, etc.

Automated commands lead the engineer through a series of generation steps. There are usually available Next >> and Cancel buttons to go from one step to the following or to abort the command. At each step the program requires the input of pertinent parameters. The command is deactivated when it is completed or cancelled by the user. Examples of this type of command are the commands for generating new structures, automatic generation of wind loads, automatic generation of earthquake loads, etc. Interactive commands are executed numerous times and remain active until the user deactivates them or activates a new command. Examples of this type of command are: , beams , walls , definition of supports , manual Edition of columns , display of analysis results, etc. To execute these commands, the application of loads engineer interacts with the model selecting nodes or structural elements. Interaction takes place in the Main view window.

User Interaction Element Selection To select a member the user places the mouse cursor near the member and then presses and holds-down the left mouse button. The selected member is highlighted and displayed in the Selected element window. The command is executed when the mouse button is released. If the cursor is moved away from the selected member, the member is deselected and no command is executed upon mouse button release. A similar procedure is used to select nodes. To select a wall panel or a floor panel the user places the mouse cursor at about the center of the panel and then presses the left mouse button. The same holding-down-themouse-button applies to panels. By default nodes and structural elements are selected individually. The Selection options window includes options that allow selection of multiple elements. For example, options such as Beams up or Beams down, allow selecting in a single step, the beam pointed-at and all the beams above or below it. Property Window All elements have default properties that can be viewed by activating Edition commands and selecting elements. Properties are shown in the Property window. These properties can be edited entering new values for each property, pressing ENTER after each entry. The edited properties are assigned to the selected elements by clicking the Assign button in the property window. Context Menu A pop-up menu with display commands can be displayed in the Main working area using the right mouse button. This menu can be displayed only if there is a structure. The menu contains commands for zooming, moving selecting parts of the structure, and several display options.

17

Rotating the Structure In EngSolutions RCB structures can be viewed from any angle in a tridimensional space. To change the view angle the user interacts with the device-reference system in the Rotation Window. Refer to Rotating the Structure in Chapter 6 for an explanation on how to view the building structure from different angles.

Exiting EngSolutions RCB To exit EngSolutions RCB click the exit button in the main window Exit command in the File menu

–or activate the

What to do Next The EngSolutions RCB software package is so intuitive and easy to use, that many engineers have started using it productively in complex designs, before reading any documentation. As you learn to use EngSolutions RCB, its intuitive design will stand out more and more −indeed, you will be able to anticipate how features of EngSolutions RCB will work without having used them. This quality is what makes EngSolutions RCB attractive to so many structural engineers around the world. However, to understand the capabilities, assumptions and limitations of the program, it is highly recommended that the next chapter, EngSolutions RCB Concepts, be read before using the software. For a more through introduction to EngSolutions RCB it is recommended to follow Chapter 5, preferably at the computer, to understand the fundamentals of using the analysis and design interface.

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Chapter 4 EngSolutions RCB Concepts The Structure In EngSolutions RCB, the structure of a building is idealized as an assemblage of column, beam, brace and wall elements, interconnected by horizontal floor diaphragm slabs, rigid in their own plane. The basic building geometry is defined with reference to a simple tridimensional grid system, formed by intersecting floor planes and vertical column axes. Column axes are defined through an architectural grid of either longitudinal and transverse axes, in the case of rectangular buildings, or radial and circumferential axes, in the case of cylindrical buildings. The program includes wizards that allow creating complex building models with minimum data entry. To generate the structure, the engineer enters story heights and spacing between frames. Based on this information the program presents a floor-framing plan that the engineer modifies interactively moving column axes, adding or removing slab panels, shear walls, columns and beams. This typical floor plan can be used to generate various stories of the model. It is possible to define various typical floor-framing plans. The ease in creating the model is the main reason why EngSolutions RCB has resulted so attractive to so many structural engineers around the world. It is possible to specify either rigid or deformable supports, elastic beams on elastic foundations or rigid footings on elastic foundations, which allows analyzing buildings founded on compressible soils. Rigid supports include the usual fixed, hinge, roller, and special supports for which the engineer specifies the degrees of freedom to be restricted. Deformable supports are defined as multiaxial springs. Deformable supports can also be used to model the lateral ground support on basement walls. For footings and beams on elastic foundations the program accepts different values of the subgrade reaction modulus for gravity load analyses and for lateral load analyses.

20 Once a building structure is created, the engineer may modify it, adding and removing elements, and changing the coordinates of the reference grid system of floors planes and column axes. The final building may be unsymmetrical and arbitrarily irregular in plan. Torsional behavior of the floors and interstory compatibility of the floors are properly modeled. The solution satisfies complete tridimensional force equilibrium and displacement compatibility at the nodes. Modeling of partial diaphragms, such as mezzanines and openings is possible. It is possible also to model cases with multiple diaphragms at each level, allowing to analyze buildings consisting of several towers, rising from a common base structure at the lower levels.

The Geometry The geometry of building models in EngSolutions RCB is based on a grid system defined by an architectural grid system of axes, which define the plan view of the model, and floor levels, which define the elevation of the model. This tridimensional grid is used to define the location of all structural elements.

Figure 4.1 Plan created from a rectangular architectural grid. Floor level 2 Most building models can be created from a rectangular grid system of longitudinal and transversal axes. First, an orthogonal grid system is created, by specifying separation between axes. Then the coordinates of the axis intersections are edited to accommodate the real geometry of the building. The command for editing axis intersections can be activated in the Elements Toolbar and in the Elements menu . EngSolutions RCB allows moving axes intersections arbitrarily as long as axes originally parallel do not intersect. That is, longitudinal axes (alphabetical axes in Figure 4.1) cannot intersect each other, neither transversal axes (numerical axes in Figure 4.1) can intersect each other

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Figure 4.2 (a) Floor level 6 The coordinates of nodes can be varied from floor to floor, allowing the creation of complex tridimensional building systems with a limited number of axes, as shown in Figure 4.2. The command to edit nodal coordinates can be activated in the Elements . toolbar and in the Elements menu

Figure 4.2 (b) 3D view (Faro del Saber Library, Structural Engineer A. Muns, Puerto Rico)

22 Before modeling the structure of a building, it is recommended to plan the model and idealize the structure minimizing the number of axes along each direction. It is preferable to have a model with a reduced number of architectural axes in a zigzag fashion than defining the model using an orthogonal grid consisting of a large number of axes. The edition and processing of the model as well as its visualization and interpretation of results is easier in models with a reduced number of axes, and when beams and shear walls are aligned along axes. Appendix A includes several actual models of real structures designed with EngSolutions RCB.

The Elements Members Columns, beams and braces are modeled as either prismatic elements or variable section elements, which may be subjected to axial and shear forces and torsion and bending moments. Shear and bending can act in any two perpendicular planes. Moment releases can be assigned near the ends of members. The effects of the finite dimensions of the beams and columns on the stiffness of the structure are automatically included in the analysis. In EngSolutions RCB the engineer may specify which frames or structural elements are part of the lateral force resisting system. Any element may be part of the lateral force resisting system only, part of the gravity load resisting system only, or part of both structural systems. Members are added and edited with the commands: columns , located in the Elements toolbar and in the Elements menu.

(a)

, beams

and braces

(b)

Figure 4.3 (a) Column Property Window (b) Table of column sections When any of the above commands is activated and an element is selected, the program shows the element’s Property window. Figure 4.3 (a) shows column properties. These include the structural system to which the element belongs (Gravity, Lateral, Gravity and Lateral), the name of the section, name of the material, the angle defining the element plan orientation, alignment of the member along each direction, type of conection at each end (rigid or pinned), reinforcement cover to centroid of steel (for reinforced concrete

23 columns) and in the case of structural steel members, spacing between intermediate supports (-1 if there are no intermediate supports, 0 for continuous support). When a new building model is created, by default all column elements are assigned a section named Column1, which have some particular cross section properties. If the name of the section in the Property Window is clicked, a window is displayed showing the table of column sections. This table, shown in Figure 4.3 b, includes a list of available column sections and the properties of the selected section. The cross section properties can be edited in this window. Furthermore, in this window, it is also possible to add new sections (Add), remove existing sections (Remove), import sections from existing files such as the AISC database (which is included in the EngSolutions RCB software package) or tables saved from previous projects (Import), and to save tables of sections (Save). Any change made to the properties of a particular section applies to all elements that have assigned such section. Similarly, the default material for all elements is Rconcrete1. If the name of the material in the Property window is clicked, a window is displayed showing the table of materials, as shown in Figure 4.7 b. This table includes a list of available materials, and the properties of the selected material. These properties include modulus of elasticity (E), shear modulus (G), unit weight, compressive strength of concrete (f’c), yield strength of longitudinal reinforcement (fy), yield strength of stirrups (fys), etc. In this window, it is possible to edit these properties, to add new materials (Add) such as reinforced concrete of a different quality or structural steel, to remove existing materials (Remove), to import materials previously saved (Import), and to save materials (Save) to be used in future projects. Any change made to the properties of a particular material apply to all elements which have been assigned such material

Global Axes Z Y

b

2

3

b

h

2

X h θ=0

3 θ = 90o

Figure 4.4 Local axes and orientation of columns – Plan view By default all column elements are created centered with respect to the nodes. That is, the centroid of a column coincides with the intersection between architectural axes. In the case of facades, it is possible to shift columns, fixing the distance between column faces and the node, using the alignment properties D2 and D3. In a Plan View of the model, the program draws column sections with their actual orientation, location and dimensions. Therefore, there is no ambiguity regarding the orientation and/or orientation of columns Properties of beam and brace elements are similar to those of column elements. By default all beam elements are assigned a section named Beam1. If the name of the section is clicked at, in the Property window, a new window is displayed showing the table of beam sections. In this table, it is possible to edit the properties of sections, to add new sections, to import sections from the AISC library, etc.

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The alignment property D3 of beam elements, shown in Figure 4.5, represents the distance between the top face of the beam and the centroid of the slab. Thus, in the case of a typical two-way slab with beams, the D3 property for all beams would be one half the thickness of the slab. In the case of spandrel beams, it is possible to locate vertically the location of each beam element using the D3 property.

Figure 4.5 Local axes and D3 alignment property of beam elements When any property is changed in the Property window such as the section, the material, alignment, etc., it is necessary to click the Assign button in that window to apply such change.

Shear walls In EngSolutions RCB walls can be modeled using three types of finite elements. Shell elements, membrane elements, and plate elements. Membrane elements are elements that only resist in-plane forces (i.e. they only have in-plane stiffness). Plate elements are elements that only resist out-of-plane forces (i.e. they only have out-of-plane stiffness). Shell elements are elements that resist both in-plane and out-of-plane forces. By default, shear walls in EngSolutions RCB are modeled as shell elements. Both shell elements and membrane elements include in-plane rotational stiffness (drilling-degrees of freedom). Therefore, any beam or column connected in the wall plane will have complete moment continuity, without any additional artificial elements such as rigid beams. Connecting individual panels makes easy to model general three-dimensional wall configurations, such as C-shaped core elevator walls, curved shear walls, discontinuous shear walls and shear walls with arbitrarily located openings. Various elements can be used to model a planar or three-dimensional wall. These modeling options along with the possibility to specify the structural system property allows an accurate modeling of buildings with shear walls, with the possibility of differentiating between structural walls and nonbearing walls. Walls are added and edited with the command Walls is located in the Elements toolbar . Shear walls are always added manually, preferably in a and in the Elements menu, plan view or in an elevation view, selecting two extreme nodes. The properties of each panel are: Structural system (Gravity, Lateral, Gravity & lateral), type of finite element (Shell, Membrane, Plate), name of material and element thickness. The wall length B and wall height H, are computed based on the coordinates of the nodes defining the element.

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Figure 4.6 EngSolutions RCB model of a bearing wall system (Project El Faro Fajardo, Structural Engineer A. Muns, Puerto Rico) The finite element used to model shear walls is a quadrilateral hybrid element developed for National Aeronautics and Space Administration, NASA (M. Aminpour, NASA Contractor Report 4282, Direct Formulation of a 4-Node Hybrid Shell Element With Rotational Degrees of Freedom, 1990).

(a)

(b)

Figure 4.7 (a) Wall Property Window (b) Table of materials

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Slabs Floors are in general idealized as rigid horizontal diaphragms. However, to distribute automatically floor loads to span loads on adjacent beams and walls, the engineer may assign load properties to individual slab elements. The default slab properties are selected by the engineer. When a new structural model is created, the engineer selects the predominant floor system. The program considers the following floor systems: one-way joist slabs, one-way slabs, two-way joist slabs, two-way slabs and one-way deck on secondary beams. Next, the engineer enters the properties of the predominant floor system, including slab thickness, geometry and spacing between joists (for joist systems), reinforcement direction, unit weight, superimposed dead load (partitions, equipment, etc.) and live load per unit area. With this data the program creates slab type Slab1, which is assigned to all existing floor panels. Once the model is created, the engineer may define other slab types and assign them to individual panels. Slabs are edited with the command Slabs located in the Elements Toolbar and in the Element menu . This command is also used to edit the slab geometry defining slab regions and slab holes.

Support Conditions Nodal supports The structure can be modeled as supported on theoretical nodal supports or on footings. Nodal supports can be rigid or deformable. Rigid supports include fixed supports, hinges, rollers, and special supports, for which the engineer specifies for each degree of freedom whether it is free or fixed. Deformable supports consist of elastic springs. In this case, the engineer specifies the spring constant for each degree of freedom, which can instead be fixed or free (0: free, -1: fixed, >0: spring constant). Figure 4.8 shows Support property windows for a rigid hinge support and for a deformable support. Nodal supports are added and edited with the command Supports located in the . Selection options in the Active Elements toolbar and in the Elements menu command window include the option: All ground nodes, which allow defining in a single step all the supports at the base of the model.

(a)

(b)

Figure 4.8 Nodal support properties: (a) rigid support (b) deformable support

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Footings In the early stages of building design it is preferably to model the structure as supported on theoretical nodal supports. Once the final section of elements have been defined, it is possible to include the footings considering their actual size. The program considers three types of footings. Spread footings for columns, continuous footings for walls and mats for combinations of columns and walls. Footings are idealized as rigid elements that can be fixed, pinned, or supported on vertical springs distributed on the area of the footing, representing the foundation soil. Footings are added and edited . with the command Footings in the Element toolbar and the Elements menu A spread footing is created by selecting with the mouse the corresponding column. The engineer must input the footing dimensions (B, L) and to indicate the relative position of the column within the footing. By default footings are concentric. At this stage of adding footings, the program does not check if the dimensions are appropriate. A spread footing is associated to a single column. Even if the user inputs large footing dimensions such that the program graphically shows several columns within the footing, in the mathematical model only the selected column is actually supported. The other columns within the footing are not supported. With the automatic resizing commands, which are available after analyzing the model, the program can compute the footing dimensions B and L so that the allowable soil pressure is not exceeded. A continuous footing is created by selecting the corresponding wall. The user must input the footing width B. The program computes the length of the footing as equal to the length of the wall. A continuous footing is associated to a single wall. The automatic resizing commands computes the required footing width such that he allowable soil pressure is not exceeded.

Figure 4.9 (a) Properties of spread footings (b) Table of foundation soil properties Combined footings and mat footings are created by drawing the footing contour. All elements (columns and walls) within are supported on the footing. Automatic resizing of mat footings shrinks or expands the footing geometry (keeping the original shape) such that the allowable soil pressure is not exceeded. Foundation Soil Properties

28 Foundation soil properties can be different for each footing. The properties the program requires are the allowable pressure, Pa, the increase in allowable pressure for combinations that include wind and earthquake, dPa (33% in most building codes) and the modulus of subgrade reaction. The user may input two values of the modulus of subgrade reaction. A subgrade reaction modulus for gravity load analysis, Kg, and a subgrade reaction modulus for lateral load analysis, Ks. For gravity load analysis, which is a permanent load condition, the subgrade reaction modulus Kg, can be estimated as the ratio between the allowable pressure and the expected long-term settlement under the footing. For earthquake and wind load analysis, which are rapid and transient loads under which the foundation soil has no time to consolidate, the soil stiffness is greater and the modulus of subgrade reaction Ks, can be estimated as the ratio between the allowable pressure and the expected short-term settlement. For pile caps an equivalent admissible pressure can be input, computed as the admissible load per pile divided by the square of the center-to-center spacing between piles. Similarly, an equivalent modulus of subgrade reaction can be computed as the ratio between the equivalent allowable pressure and the settlement of the pile group. Footing Support Conditions Footings may be considered fixed or may be allowed to rotate and/or undergo a vertical displacement. If footings are modeled as fixed elements, the subgrade reaction modulus is not used in the analysis; hence any arbitrary values can be input. If vertical displacements (settlements) are permitted, the program computes a vertical spring constant based on the subgrade reaction modulus and the footing area. If rotations are permitted, the program computes the rotational stiffness of the footing based on the subgrade reaction modulus and the moments of inertia of the footing. The analysis of building systems allowing rotation of footings is more realistic than analysis based on the usual assumption of fixed supports, particularly in combined frame-wall systems. In these systems, with the usual fixed support assumption, the analysis results show that the walls resist most of the lateral forces. In reality, just a small rotation at the wall footings is enough to produce a significant redistribution of lateral forces with columns resisting part of the loads initially resisted by walls. If these columns are not designed for these larger lateral loads, these overstressed elements may be end up suffering significant damage under lateral loading. The analysis of building systems allowing rotation of footings though more realistic has the disadvantage that produces larger computed story drifts and greater computed steel ratios. Considering that most building codes allow to model the building as completely fixed at its base and that the story drift limitations were established for that usual fixed base assumption, it turns out disadvantageous to use a model permitting footing rotations, as it leads to a more costly structural solution. For this reason, the program allows to model footings (spread, continuous and mats) as fixed. It should be kept in mind that if footings are modeled as fixed, it is not possible to model either tie beams or strap beams. If these elements are to be modeled as part of the structure, to obtain their real design it is necessary to allow rotation of the connected footings. When designing, eccentric footings, with strap beams, it is necessary to allow rotation of at least the eccentric footings. Foundation Beam Elements The foundation beam element is an element that resists flexure and shear, and is supported continually and elastically on subjacent soil. The element is based on a

29 Winkler model implemented as a displacement based finite element. The element can be used for analysis and design of cellular and two-way slab-and-beam mat foundations, analysis and design of combined footings, and for static and dynamic soil-structure interaction studies. located in the Foundation beams are added and edited with the command F-Beams Elements Toolbar and the Elements menu. In addition to the structural properties of conventional beam elements (including section and material), the foundation beam element has to additional properties. Soil type and tributary width B. Each soil type has in turn various properties buit from those only the subgrade reaction modulus is used in the analysis of foundation beams. The product of subgrade reaction modulus and tributary width represents the stiffness of the foundation soil, as a continuous spring uniformly distributed under the foundation beam element. Consistent with the Winkler model, the soil reaction at any point is equal to the product of such stiffness and the transversal displacement (settlement) of the element. The inertia of the structural element is defined by the section properties and is independent of the tributary width.

Figure 4.10 Models of beam on elastic foundation. (a) Using multiple beam elements (30 elements) and springs in auxiliary nodes (b) using 3 foundation beam elements. The program allows considering two different values of the modulus of subgrade reaction. A value Kg, which represents the long-term soil stiffness or stiffness under permanent loading, and a value Ks, which represents the short-term soil stiffness or stiffness for transitory loads. The Kg value is used in the gravity load analysis and the Ks value is used in the lateral load analysis. The soils engineer based on his evaluation of settlements can estimate values of the sugrade reaction moduli Kg and Ks. The Kg value represents the ratio between the contact pressure of a continuous footing of width B, and its long-term settlement. The Ks value represents the ratio between the contact pressure of a continuous footing of width B, and its immediate settlement. The Ks value can also be estimated from K1 values corresponding a a rapid plate load test (B= 1ft) either measured or estimated from published typical values for different foundation soils, corrected to the actual footing width B. Although it is possible to model foundation beams using conventional beam elements, segmenting them by introducing numerous auxiliary nodes, and adding elastic springs at those nodes, as shown in Figure 4.10 (a), applying this procedure to complete models of mat foundations, or in interaction-studies to models that include the superstructure, would result in unnecessarily complex models. The main advantage of using the

30 foundation beam element is that it is not necessary to introduce auxiliary nodes to model the soil reaction. The element formulation considers the presence of a continuous elastic support under the element.

Figure 4.11 Model to study soil-structure interaction using foundation beams. The foundation beam element may be used in models of individual beams or in complete models of one-way or two-way cellular mats foundations. Cellular mats are those in which the stiffer elements are beams or joists and the slab is made up of a grillage of these elements in contact with foundation soil, working under flexure and shear, having a thin slab at the plane in contact with the subsoil. The element can also be used in soil-structure interaction studies in which both the superstructure and the complete slab are modeled. Alternatively a simpler idealized slab may be modeled in this kind of studies, assigning to each beam element equivalent tributary widths and equivalent sections.

Loads Loads in EngSolutions RCB are grouped into load cases. Load cases are independent loadings for which the structure is analyzed internally, such as dead load (DL), live load (LL), snow load (SL), wind load (WL), earthquake load (EQ), etc. There can be up to 12 independent load cases. Load cases should not be confused with load combinations, which are defined later.

31 Loads for any load case can be applied manually to the nodes, members and walls, through graphical mouse interaction. Nodal loads are composed of concentrated forces and moments. Member loads include concentrated loads and moments, and trapezoidal distributed loads. Wall loads include concentrated and distributed loads at the top and sides of the wall. Loads and moments can be applied at any location along the member or wall, and can be referred either to the local axes of the element (1,2,3), or to the global coordinate system of the structure (x,y,z).

Figure 4.11 Property window with member load data. The commands to apply loads manually are located in the Load menu. When any of those commands is activated, the program presents a property window where the engineer enters the load data. The load assignment is carried out by selecting with the mouse the elements to be loaded. Figure 4.11 shows an example of member load data.

Figure 4.12 Command for automatic generation of loads. EngSolutions RCB can also generate automatically the loads of complete load cases, representing significant savings in tedious manual calculations. Figure 4.5 shows the

32 automatic loading submenu. The load cases that can be generated automatically are: self weight (D0), vertical floor loads (DL, LL1, LL2), wind loads (WLx, WLy), and earthquake loads (EQx, EQy), which can be static equivalent, spectral, o may correspond to a time history analysis. Self weight The self-weight of elements can be generated automatically with the command Self Weight. The program uses the cross sectional area of each element defined in the Sections table and the unit weight defined in the Materials table. Weight of beams and braces is applied as a uniformly distributed load along the length of the member. The weight of columns is applied as a concentrated load in the upper node of the element. The weight of walls is represented as a uniformly distributed load at the top of the element. Self-weight loads are grouped in a load case named Self Weight, D0.

Vertical Floor Loads Vertical floor panel loads can be automatically converted to span loads on adjoining beams and walls using the properties assigned to slabs: Thickness, reinforcement direction, superimposed dead load and live load.

Figure 4.13. Distribution of floor loads to beams and walls (Sky Loft Tower, Structural Engineer J. Robert & Associates, Puerto Rico) The program reports the total floor dead load (self weight of the slab plus superimposed dead load) (DL) and live load (LL) for each floor and the total for the whole building, and displays for each beam and wall the corresponding tributary slab load, as shown in

33 Figure 4.13. This way, the engineer can visualize how the floor loads are being distributed in her model. Wind Forces Wind forces can be generated according to various building codes, including American codes: ASCE 7-95, ASCE 7-88, UBC-94; Mexican codes: RCDF-87, CFE-93 and Dominican code: DNRS/SEOPC. EngSolutions RCB load generator guides the user throughout the generation process. First, the program asks for wind load parameters such as basic wind speed, importance factor, exposure category, topographic factor and wall pressure coefficients. Then the program classifies the structure, according to its response to wind loading, as either rigid or flexible, and computes the gust effects factor, using the rational analysis of the selected code. The velocity pressure at each floor level is reported. The program automatically identifies exterior nodes, determines nodal tributary areas, and computes wind forces on the roof and windward, leeward, and side walls. Load cases for two orthogonal directions (x & y) are generated in a single step. The program reports total wind forces at each floor level as well as all the values needed for the overturning and sliding check. (i.e. total base wind shear, overturning moments due to lateral forces and to roof uplift forces, total building weight and stabilizing gravity moment). The program generates two wind load cases: WX and WY Equivalent Static Earthquake Loads Static equivalent earthquake loads can be generated automatically according to numerous international building codes, including, American codes: IBC-2003, UBC-97, ASCE 7-05, ASCE 7-95; Mexican codes: RCDF-04, RCDF-93, CFE-93, GUAD-97; Colombian codes: NSR-98 (includding seismic microzoning of Bogota, Armenia and Medellin) and CCCSR-84; Venezuela COVENIN-82, Peru E030 2003, Ecuador CEC-01, Chile NCh433-93, Panama REP-2004 and REP-94, Costa Rica CSCR-86 and Dominican Republic DNRS/SEOPC-80. New building codes are continually added to EngSolutions RCB. The load generation process is guided by the program. The engineer selects a building code from a list of available codes, enters the number of basements, and then inputs seismic parameters. Seismic parameters include parameters such as effective peak acceleration (or seismic zone factor, or spectral response accelerations), importance factor, site profile coefficient, response modification factor (ductility factor). The appropriate parameters with the proper terminology for the selected building code are requested by the program. Figure 4.14 shows this stage of the generation for IBC-2003. Next, the program computes and reports the seismic base shear. The engineer may change the value of the computed base shear. The engineer may also specify an accidental eccentricity and a definition of the design eccentricity, in terms of both the actual static (inherent) eccentricity (es, distance from center of mass to center of rigidity), and the accidental eccentricity (δε). The program proposes the definition, appropriate for the selected code, however, the user makes the final selection. In most building codes the design eccentricity is simply: ε = es ±δε. Next, the program reports for each story the center of mass, center of rigidity, static (inherent) eccentricity, accidental eccentricity, and design eccentricity. Then the program computes inertial forces shifting the center of mass according to the accidental eccentricities. Then, the program reports seismic forces for each story for two orthogonal directions (x & y). Then, the program produces a report with the results of the seismic forces.

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Figure 4.14 Seismic parameters for generating seismic forces according to IBC-2003 Next, the program reports for each story the center of mass, center of rigidity, static (inherent) eccentricity, accidental eccentricity, and design eccentricity. Then the program computes inertial forces shifting the center of mass according to the accidental eccentricities. Then, the program reports seismic forces for each story for two orthogonal directions (x & y). Then, the program produces a report with the results of the seismic forces. It is noticed that the nodal forces applied by the program are simply inertial forces proportional to nodal masses and do not represent the seismic response of the structure. These forces are not proportional to the stiffness of elements and do not show the distribution of shear forces in the structure, The way these seismic inertial forces are

35 resisted by the different structural elements is determined in the analysis, based on the stiffness characteristics of the different elements conforming the lateral load resisting system and their connection with the floor diaphragms.

Figure 4.15 Report with summary of seismic forces Nota:

Accidental Torsion Starting with version 6.1, in the automatic generation of seismic forces only two load cases are generated: EQUAKE X (EQX) and EQUAKE Y (EQY). In previous versions, two load cases were generated for each direction according to the two possible signs of accidental torsion, for a total of 4 load cases: (EQX1, EQX2 y EQY1, EQY2.) Starting with version 6.1, each one of the load cases generated represents an envelope for the two definitions of accidental torsion. For each load case (for instance EQX) the program generates a set of seismic forces without accidental torsion and computes two sets of accidental torsion. During the analysis, the structure is subjected first to the set of seismic forces with no accidental torsion. In this analysis, the program computes nodal displacements, story drifts along each column and wall boundary, and internal forces in all structural elements (moments, shears, axial loads, wall stresses, etc.). Next, the program applies the first set of accidental torsion. In those locations (or elements) where the result of

36 displacement, drift or internal force increase, such result is updated. On the contrary, on those locations where the displacement, drift or internal force decreases, the result is not modified. Then, the program applies the second set of accidental torsion and updates the results according to the same criterion, to obtain this way an envelope of seismic results.

Response Spectra EngSolutions RCB can also perform response spectra analysis according to various international building codes. Figure 4.16 shows the seismic building codes implemented in the program. The analysis can be performed in a single step for two orthogonal directions or for a specified attack angle. Before doing the seismic analysis however, the engineer must perform a dynamic analysis, using the EngSolutions RCB analysis commands that will be discussed in a later section, to compute the tridimensional modes of vibration, natural frequencies, modal participation factors, and percentages of participating mass. The load generation process is guided by the program. The engineer selects a building code and enters the number of basements. In computing the approximate empirical period of vibration Ta, based on the building height, the program considers only those stories above ground. That is, the program assumes that during earthquake loading, buried stories move along with the surrounding soil. Next, the program asks the engineer to input the seismic parameters corresponding to the selected building code. The program computes the spectral acceleration for each mode, according to the selected code. The engineer can edit the values of spectral acceleration, which allows considering any other design response spectra, such as that corresponding to a specific earthquake record. Various methods of modal combination are available in EngSolutions RCB, including summation of absolute values (SAV), square roof of summation of squares (SRSS), complete quadratic combination (CQC), and a combination of the first two: ½(SAV+SRSS) and 0.25(SAV)+0.75(SRSS). Next, The program computes the base shear for each mode and the combined base shear. The program also evaluates the equivalent static base shear, that the selected codes requires as a minimum design base shear. This minimum static shear is usually computed based on an empirical fundamental period defined by the code. The program suggests a design base shear, based on the combined value and the minimum static shear. The engineer may change the proposed value. If the design base shear is different from the combined base shear, the program automatically scales the combined shears for all story levels. A set of inertial forces is obtained by combining the modal nodal forces, scaling them to obtain the appropriate floor shear. The treatment of accidental torsion is the same as that in the equivalent static analysis, specifying a design eccentricity and shifting the center of mass, a set of static forces is computed which is later combined with the spectral analysis results to obtain an envelope of analysis results. Once again is noticed that the set of combined nodal forces that the program presents are just inertial forces rather than the seismic response, which is later determined during the analysis stage.

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Figure 4.16 Building codes for seismic spectral and time history analyses. Dynamic Time-History Analysis The dynamic time history analysis is guided by the program and consists of various steps. First, the engineer selects the building code that will gobern the analysis, form the list shown in Figure 4.16. Next she enters the damping ratio (default is 5% for all modes) and enters the corresponding seismic parameters. The program computes the spectral accelerations according to the code, and determines the static base shear. Next the engineer selects the earthquake records to be applied to the model. The program includes an extensive database of earthquake records. In a later section it is shwon how to add new accelergrams to this database. Figure 4.16 shows the window in which earthquake records are selected and scaled. For each record, the engineer must input first the acceleration scaling factor, then, add it to the list of selected records by clicking the Add button. The engineer can add up to 5 different records. By default, only the horizontal component with maximum peak acceleration is considered. However, the engineer can include the two horizontal components and the vertical component, marking the corresponding checkmark in this window. When the vertical component is included, it is necessary to include computation of vertical mode shapes during the modes-frequency analysis. By default the vertical modes are inhibited in the modes-frequency analysis.

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After selecting the earthquake records, the program presents a table comparing the response spectra of the selected records and the code-specified design response spectrum, and applies the scaling required by the selected code. Next, the program reports the dynamic base shears for the scaled selected records and the static base shear, and performs again any scaling required by the selected code. The procedure to comply with accidental torsion requirements is the same used in the equivalent static force and spectral procedures. Accidental torsion is applied statically shifting the center of mass.

Figure 4.17 Selection and scaling of earthquake records In this stage of seismic force generation all the information required to perform the analysis is assembled. However, the actual dynamic analysis is conducted when the engineer activates the Run analysis command in the Analysis menu. At this later stage, the program applies, at the base of the structure, each one of the selected earthquake records along each direction (X y Y), obtaining the response of the structure at every time instant and saving the maximum values of drifts, displacements and internal forces in each one of the resisting elements.

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Load Combinations Load combinations are the loading conditions for which the building is designed. Load combinations are assembled as combinations of the load cases. An example of a load combination is: 1.4DL + 1.7LL, where DL is the dead load and LL is the live load. In EngSolutions RCB there can be up to 150 load combinations. To generate load combinations the engineer selects in the menu shown in Figure 4.18, the building code according to which the load combinations are to be generated. The program generates all the combinations considering all sign combinations (sense) for seismic and wind forces.

Figure 4.18 Command for automatic generation of load combinations The engineer may specify to consider bidirectional effects in earthquake loading (e.g. 100% of earthquake in one direction acting simultaneously with 30% in the other direction), to generate the load combinations accordingly. Depending on the building code used to generate seismic forces the program determines whether seismic forces are strength level or service level loads, to select the appropriate seismic load coefficients. The engineer may alter this determination. When seismic forces have been design according to ASCE 7-05, IBC-2003, or UBC-97, the program includes in the load combinations the redundancy factors, which are determined during the analysis. For these codes, the program also considers through load combinations the effects of the vertical component of the ground motion, creating additional combinations increasing and decreasing factors for gravity loads. The generated load combinations are displayed in a table, as shown in Figure 4.19. In this table the engineer may edit load coefficients for any combination, add manually new combinations by entering individual load case coefficients, and may remove any combination specified by the selected code. Load combinations can only be generated after load cases have been created.

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Figure 4.19 Table of load combinations

Analysis EngSolutions RCB performs two types of analysis. Modes/frequency analysis in which the program determines the free vibration characteristics of the structure, and load analysis in which the program determines the response of the structure, in terms of displacements and internal forces, to each one of the load cases. The engineer may base both types of analyses on cracked sections by specifying inertia modification factors, torsion-constant modification factors, and area modification factors for beams, columns and braces. For walls, the user may specify independent modification factors for in-plane and out-of-plane flexural and shear stiffness. Modes/Frequency Analysis EngSolutions RCB provides the solution for the free vibration response of the building in terms of its three-dimensional mode shapes and natural frequencies. Mode shapes, frequencies and modal participation factors are obtained using the Lanczos method with selective orthogonalization described by Golub et al, 1985, which is an improved version of the subspace iteration method used in most commercial software. For large buildings, the program improves computational speed using the iterative procedure for large sparced matrices described by Underwood, 1975.

41 The implementation of the Lanczos procedure is general allowing analyses of complex buildings. The building may be unsymmetrical and arbitrarily irregular in plan. Torsional behavior of the floors and interstory compatibility of the floors are properly modeled. Instead of the usual 3 degree-of-freedom-per-floor-level simplified analysis, EngSolutions RCB considers the full stiffness matrix of the structure, allowing modeling partial diaphragms, such as mezzanines and openings, as well as cases with multiple independent diaphragms at each level, allowing to analyze buildings consisting of several towers, rising from a common base structure at the lower levels. The mass matrix is created automatically, based on the gravity loads acting on the structure. The program asks for the coefficients of each load case to be used in the evaluation of the lumped mass matrix. The load combination for the mass matrix could be for instance: M = (1.0 DL + 0.25 LL)/g. The program asks the engineer for the number of modes to be computed and performs the analysis. Obviously, the modes/frequency analysis can only be conducted after gravity loads have been created. The dynamic analysis can be linear (first order) or P-Delta (second order) allowing to consider the effects of initial stresses on the natural frequencies and modes of vibration of the structural model. It is pointed out that approximated methods for computing periods, such as the RayleightRitz procedure, presented in most building codes (T = 2 π ((Σ wi δi) / (g Σ fi δi))1/2), would produce accurate results only in the case of regular buildings of simple geometry consisting of a single diaphragm per floor level. On the other hand, approximated fundamental periods evaluated with empirical equations such as Ta = 0.1N and Ta = Ct(hn)3/4, which are based on field measurements on real buildings (mostly during the San Fernando Earthquake), will typically predict shorter periods as these real buildings, with their partitions, stairs, facades, and other non-structural elements, are stiffer than the ‘naked’ structural model analyzed. It is a good practice (not a requirement) to do the modes/frequency analysis before the generation of wind loads. The natural frequency is needed to classify the main wind force resisting system, in terms of its response to wind loading, and to evaluate the gust effects factor of flexible buildings. If it is not available, it is estimated based on the overall features of the building, using the approximated equations of the selected code. It is also advisable (not a requirement) to do the modes/frequency analysis before the generation of seismic loads, even if the design is based on static equivalent seismic loads. The fundamental period of the structure is needed to compute the base shear force. Furthermore, the fundamental mode shapes in each direction, which contain all the information of stiffness and mass distribution in the building, allow an accurate evaluation of the center of rigidity of the structure.

Gravity and Lateral Load Analysis EngSolutions RCB performs a tridimensional finite element analysis to determine nodal displacements, story drifts, internal forces and moments on members, and internal stresses on walls, for each load case that has been defined. Prior to the actual analysis, the program determines the rigid length at the end of each member, based on the element sections and a specified rigid zone factor, to consider the finite dimensions of elements. Next, the program computes buckling loads for columns. Then, the program initiates the actual solution procedure. Figure 4.20 shows the different analysis options.

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Linear Analysis The linear analysis is a first order elastic analysis in which the equilibrium equations are formulated in the original undeformed configuration. The program assembles the stiffness matrix of the whole structure adding the contribution of individual elements. Then the program triangularizes the stiffness matriz using the Gauss elimination procedure. Then, the program computes by backsubstitution nodal displacements and determines internal forces and stresses on the elements.

Figure 4.20 Analysis Options P-Delta Analysis The P-Delta analysis is a second order elastic analysis in which the equilibrium equations are formulated in the deformed configuration. It is considered that as the structure undergoes deformation, it carries the applied loads with it. The changes in position of applied forces are cumulative in nature and cause additional second-order forces, moments and displacements, which are not included in the first-order analysis. The analysis is carried out in exact form, incorporating directly in the stiffness matrix of each element a geometric component. This way, secondary effects are represented exactly in all aspects of the structural analysis without any additional computational effort or iterative approximations, such as those required in the Direct Method used in some commercial programs. When the P-Delta analysis option is selected, the program requests the engineer to input the gravity load combination to perform the P-Delta analysis. This combination represents the permanent gravity load, or better yet, the gravity load acting when the earthquake loading occurs. The default gravity load combination is: 1.0DL+ 0.25 LL. This is the vertical load that is going to be carried by the structure laterally when it deforms under lateral loading. The change in position of this gravity load is what will cause the additional second-order forces, moments and displacements. The P-Delta analysis involves two analyses. First, the program performs a preliminary linear elastic analysis and determines the solution (displacements and internal forces for all elements). From this preliminary analysis the program determines the internal

43 forces/stresses in each element, corresponding to the above gravity load combination. Next, the program performs the actual P-Delta analysis. In this stage, when assembling the stiffness matrix for each element, instead of using the conventional stiffness matrix for stress-free elements, the program assembles the nonlinear stiffness matrix for elements carrying the stresses corresponding to the gravity load combination. The additional terms in this stiffness matrix resulting from the existing stresses correspond to the so-called geometric matrix. Triangularizing the assembled stiffness matrix, using Gauss elimination, and backsubstituting the load vectors for each case, the program computes nodal displacements, and determines internal forces and stresses on the elements. Gravity Load Analysis The program performs the gravity load analysis and the lateral load analysis separately. In the gravity load analysis only those elements that are part of the gravity load resisting system are considered to contribute stiffness, and the program solves for vertical load cases including self weight of elements (D0), floor dead loads (DL), live loads (LL), and snow loads (SL). Incremental Analysis Building design is usually based on the analysis of an idealized structure, whose geometry corresponds to the final configuration of the building. Dead loads are applied to this idealized structure in a single step. In the real structure, on the other hand, the geometry changes continually during construction, and loading is incremental as new floors are added. In cases of tall buildings (more than 15 stories), this basic difference between the real structure and the system analyzed can result in important errors due to the fact that the final state of stresses and deformations depends on the construction and load history, even if the material behaves elastically. The application of vertical loads to the whole structure in a single step may result in unrealistic moment diagrams on the upper beams and columns, due to excessive axial deformations of the interior columns. The difference between the axial deformation of interior and exterior columns, which in the analysis accumulates from one floor to the next, is not real. Each floor is built as a horizontal surface. Any difference in axial deformation that may exist between the columns directly under a particular floor is deleted when the concrete of that floor is placed. Not only the displacement pattern in a given level, obtained from a conventional analysis, is wrong, but also, for any particular column, the variation of vertical displacements throughout the height of the building is completely different from the real one. In the conventional analysis the vertical deformation increases with the height, reaching a maximum at the top roof. In reality, floors are built at project elevations and the displacements at the roof are minimal. The column displacement at the top level is produced only the weight of the floor slab, rather than the accumulated from lower floors. The errors in displacements that occur in conventional analyses have naturally an effect on the internal forces and moments, calculated from those deflections. Figure 6.10 shows the moment diagrams and the variation with height of the negative moments in the floor beams, from (a) a conventional analysis and (b) an incremental analysis. While in the incremental analysis the negative moments in the floor beams tend to be constant with height, in the conventional analysis, the negative moments at the central columnsupport decrease with height, due to excessive axial deformations of the central column, while at the end supports the negative moment increase.

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Figure 4.21 Displacements, (a) conventional analysis, applying dead load in a single step, (b) incremental analysis, modeling the construction process The differences in the distribution of internal forces and moments that exist between the structure loaded in a single step and that build incrementally, are clearly reflected in the design of elements, specially in that of beams and columns of the upper levels. The conventional analysis, underestimates the negative reinforcement of beams at the interior supports and overestimates it at the ends. With regard to the exterior columns of the upper levels, the conventional analysis leads to steel ratios greater than actually required, due to the excessive moments that are obtained for these low-axial-load elements.

Figure 4.22 Moment diagrams (a) conventional analysis (b) incremental analysis The incremental analysis method implemented in EngSolutions RCB, takes into account the story-by-story construction process, eliminating the limitations present in the conventional linear analysis, used in most structural analysis programs. The method is described in detail in Barbosa (1994).

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The incremental construction analysis, implemented in EngSolutions RCB, consists substantially of a series of stages, each one corresponding to the addition of a new floor (or some new floors). In each stage, columns, girders and walls of new floors are added to the structure (i.e. to the finite element mesh representing the structure). The updated structure is subjected only to the dead load associated to the new elements. The displacements and internal forces and moments, obtained in each stage, are added to the previous values. The process is automated to perform all the incremental analysis in a single run. Obviously, the live load and lateral load analyses are performed on the final configuration, in single step. In the automated incremental analysis, the engineer specifies how many floors are to be added in each stage of the analysis. The user controlled incremental analysis is more general as it can consider any arbitrary construction sequence. The engineer assigns to each element in the model (beams, columns, braces, walls, slabs, supports, footings), in the Property window of the element, a property named Step. This property represents the construction stage at which the element is added to the structure. This way, in addition to conventional story-by-story construction sequence any arbitrary construction sequence can be modeled. Seismic Analysis In the lateral load analysis only those elements that are part of the lateral load resisting system are considered. Elements that are purely gravitatory are cracked during the analysis so that any small seismic contribution they might otherwise offer gets distributed to the elements that are part of the lateral load resisting system. If seismic loads were applied manually or automatically with the equivalent static force procedure, the seismic analysis is performed using a static linear or P-Delta analysis described above right after the gravity load analysis. If spectral seismic forces were generated, the program performs a static analysis for the combined nodal forces establishing this way a sign for deformations and internal forces in elements. Then, the program establishes an envelope between this static solution and the spectral combination. Time History Analysis In the time history analysis, after determining the gravity load solution the program applies to the model each one of the scaled earthquake records selected during the seismic load definition. The program determines at each time step the dynamic response using a modal combination procedure, saving maximum values for lateral displacement, intersory drift, axial load, shear and moments on columns, beams, wall and brace elements and stress resultants and resultant forces and moments on shear walls. Throughout the time history analysis, as shown in Figure 4.23, the program shows the deformed configuration during the seismic event. The program applies first the first record in X-direction and then in Y-direction. Next the program follows with the other selected records. Whenever for a given earthquake record the intense phase of the ground motion has passed, and it becomes clear that the remaining vibration will not modify the envelope of results obtained so far, the engineer may terminate the computation for that particular record to pass to the next analysis, by closing the window showing the scaled accelerogram. Using the time history analysis it is possible to design a building structure for a series of real seismic events, establishing the elastic response, without the approximate combination procedures required in the spectral analysis. The program provides an elastic solution, which as in the other seismic procedures, is modified using the response modification factor R, and the displacement amplification factor Cd.

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Figure 4.23 Seismic time history analysis (Sky Loft Tower Structural Engineer J. Robert & Associates, Puerto Rico)

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Stiffness of Elements

Nota:

Activating the command Options in the View menu, the engineer may specify inertia reduction factors, torsion-constant reduction factor and area reduction factor for beams, columns, and brace elements. The engineer may also specify stiffness modification factors for shear walls (in plane axial, flexure and shear, and out-of-plane bending, torsion and shear). These factors allow analysis to be based on cracked sections. It is noticed that the ACI-318 building code and most international building codes derived from it, state that when elastic analysis are used to determine deformations at either service level or strength level, it is recommended to the the stiffness values EI represent the stiffness of the elements in the appropriate state, and propose tables of stiffness modification factors for each case. However, most seismic codes (ASCE 7, IBC, UBC, ATC, RCDF, NSR, REP, etc.) use the concept of Response modification factor (R or Q) and Displacement amplification factor (Cd o Q) to account for the nonlinear behavior of elements (cracking of concrete and yielding of reinforcement). Therefore, applying both procedures simultaneously -cracked sections and displacement amplification factorswould imply considering the same effects twice. Nevertheless, some regulatory building agencies often require analyses based on cracked sections. In these cases, in order to comply with drift limits without penalizing unnecessarily the design, it is recommended to consider the following: a. Some building codes (e.g. NSR-98) explicitly state that when the analysis is based on cracked sections, the computed interstory drifts can be reduced by a factor equal to 0.7. b. Most building codes (e.g. ASCE7, IBC, REP, etc.) allow considering a separate set of seismic forces for the purpose of drift analysis, different from that used for designing structural elements. In determining these forces, it is recommended to compute the fundamental periods from a modes/frequency analysis considering cracked sections (which results in longer periods), and to keep in mind the following provisions of the above codes: •

In determining the base shear for drift analysis, there is no upper-bound limit on the fundamental period (e.g. 1.4 Ta).



In determining the seismic coefficient Cs for drift analysis, there is no required minimum value for long periods.



For drift analysis the redundancy factor is equal to 1.0

The program default settings for stiffness reduction factors is 1.0, corresponding to gross sections, except for torsion. The default value of the reduction factor for torsion is 0.1, which is consistent with ACI-318 Sec R.11.6.2.1y R.11.6.2.2 and the common practice in seismic areas of minimizing torsional stiffness of reinforced concrete members so that any torsional moments in these elements can be re-distributed as flexure by orthogonal members. Beam design in EngSolutions RCB includes design for torsion, therefore, reinforcement is provided for equilibrium torsion (torsion that cannot be redistributed).

Analysis Results EngSolutions RCB provides interactive graphic display of analytical results including the static deformed shape of the building, bending moment diagram, shear force diagram, axial force diagram, torsion moment diagram, wall internal forces, wall stresses (resultants, mid-plane, front face, back face), support reactions, shear ratio stress, story drifts, and mode shapes. All these results can also be printed in tabular form in a report.

48 Analysis results can be displayed for the whole structure or for a selected group of elements. The EngSolutions RCB graphic interface includes commands to view selected groups of elements. Numerical analysis results for any node, wall, or along any member can be visualized in the main graphic window simply by selecting the element with the mouse.

Figure 4.24 Moment diagram for a frame in a 3D model Analysis results can be presented for any load case or for any load combination. The displayed results correspond to the load case or load combination currently active, which is always printed in the EngSolutions RCB main graphic window. The engineer may

49 quickly change the active load case or load combination by clicking its label with the mouse.

Figure 4.25 Relative story drifts EngSolutions RCB also includes a command for the graphical display of story drifts (lateral displacement of one level relative to the level below), which allows immediate check of compliance with local building codes. The user may specify a displacement amplification factor to magnify drifts, along with a limit story-drift ratio (story-drift divided by story-height). The program shows column axes and wall boundaries in different colors, depending on whether or not the amplified relative story drift ratio exceeds the

50 specified limit value. The engineer may select any column or wall boundary to view Drift values. Members The analysis member results displayed by the program and output in the printed report are the internal forces including: axial force, shear forces, torsion moments and bending moments. These internal forces are referred to the member’s local axes. In the graphic display, it is possible to see the variation of these forces along the element by selecting it. The Active command window of bending and shear diagrams, include the option: Member results, which presents these results in tabular form.

Figure 4.26 Contours of vertical stress resultants in shear walls

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Shear Walls For shear walls the program present various types of results as contours including: stresses in the wall midplane, on front face, in the back face, and stress resultants (stresses integrated on the wall thickness), which correspond to internal forces per unit length of wall. The program also presents for each wall segment total internal forces at the top and bottom ends of the wall, including axial force, in-plane shear force, and moment, which are the forces needed to design the element. The program presents results for individual wall segments and for the multiple segments of a particular plane wall. Stresses and internal forces in shear walls are referred to the element local axes. A detailed description and sign conventions of analysis output for shear walls id presented in Chapter 6. Nodal Supports EngSolutions RCB reports nodal support reactions referred to the global model axes X,Y, and Z. Foundation Beams The analysis results that the program shows for this type of element include deflexions, shear forces, and bending moments along the element. The program also presents the soil reaction under foundation beams, drawn at the same scale as distributed forces. The engineer may change the scale factor activating the command Load scale in the Loads menu. When the analysis results command for reactions on foundation beams is active, the engineer may select any of the beams and the program shows in tabular form, in the Property window, an equivalent linear reaction defined by the reaction values at the two ends of the element (wi y wj). This reaction is an equivalent linear reaction that produce at the ends of the element the same fixed-end moments and shears as the real cubic soil reaction. Results for Footings Footing pressures The program includes various analysis and design results associated to footings. One of these is the Footing pressures command in the Results Analysis menu. When this command is activated the program presents contours of contact pressures under the footing. The command has two options: “Selected load combination” y “Envelope all load combinations”. Footing pressures for the active load combination With the option “Selected load combination”, which is the default option, the Footing pressures command shows the pressures at the base of the footings for the active load case or active load combination. It is pointed out that the color scale bar simply covers the range of maximum and minimum stresses with no comparison to the allowable soil pressures. As in most analysis results commands, if the active load combination/ load case title is clicked at, the next load combination is activated and the pressure diagram is updated. If any footing is marked with the left mouse button, the program selects the whole footing group and presents in a window the results in tabular form. The footing group corresponds to all footings connected to the selected footing. As an example, in the case of a wall with columns at its ends, representing boundary elements, if a continuous footing has been defined for the wall and spread footings for the columns, the program identifies the three footings as a group, both during the analysis and the presentation of results. Similarly, for a “C” shaped shear wall composed of three segments, each supported in a continuous footing, when marking one of these segments with the mouse, the program selects the three segments and displays the total results ―for the active load combinations― for the whole group.

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Figure 4.27 Contact pressures in a model with variable foundation depth (Agromonte House, Structural Engineer A. Muns, Puerto Rico) The results presented by the program are the total reaction forces at the center of gravity of the footing group, which includes the forces Rx, Ry, Rz, and the moments Mx, My y Mz; and the maximum and minimum footing pressure under the footing group Pmax and Pmin. Forces and moments are referred to the global coordinate system and the sign convention used is the same used for nodal supports, shown in Figure 4.24. Compressive pressures are positive and tensile pressures are negative.

Figure 4.24 Positive direction for footing reactions

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Pressure envelope The option “Envelope all load combinations”, of the Footing pressures command allows to verify graphically if the size of footings is appropriate, by comparing contact pressures with the allowable soil pressure. With this option, the program presents the envelope from all load cases of the ratio between the maximum contact pressure and the allowable pressure Pcmax/Pa. The program draws in red shades those footings for which the ratio Pcmax/Pa is greater than 1.0. When the command is activated the program displays a window in which the following parameters are to be defined. •

Type of load combinations. The pressure envelope can be determined for service load combinations or for the existing ultimate load combinations. If the service load combination option is selected, which is the default option, the program saves temporarily the existing ultimate load combinations and generates the set of service load combinations. The user may edit these combinations, changing coefficients, and adding or removing load combinations. After accepting the generated service load combinations, the program computes for each footing the maximum contact pressure under the footing Pcmax, the allowable pressure Pa and the ratio Pcmax /Pa, for each load combination, taking into account the increment in allowable pressure permitted for combinations including lateral loads, dPa. The program draws the footing according to the maximum value of the ratio Pcmax /Pa from all load cases considered. Once all footings have been drawn, the program re-establishes the existing ultimate load combinations.



Type of contact pressure. By default, the contact pressure that the program uses is the maximum pressure Pmax, computed from the vertical reaction Rz, the moments Mx, My, and the properties of area and moment of inertia of the footing group, assuming a lineal distribution of contact pressures. The program includes the option of considering the average footing pressure under the footing Pavg, computed simply as the vertical reaction force divided by the area of the footing group. The program also includes the option of using an equivalent uniform pressure Peqv, acting in a reduced area whose centroid coincides with the point of application of the vertical reaction.



Self-weight of footing. The program allows to add the weight of the footing to the computed contact pressures. The weight of footings is estimated as a fraction of the vertical reaction Rz corresponding to service gravity loading (D0+DL+LL). The default value of such a fraction is 0.10 and can be edited by the program user.

Once the above parameters are selected, the program draws each footing, selecting its color according to the maximum value of the ratio between the contact pressure and the allowable pressure. When a footing is selected with the left mouse button, the program selects the footing group and presents the following results considering the selected set of load combinations: maximum and minimum values of the vertical reaction for the selected set of load combinations, Rzmax y Rzmin , maximum and minimum values of contact pressure under the footing (the footing pressure is evaluated for each load combination in each corner of the footing) Pcmax , Pcmin (where Pc is Pmax, Peqv, or Pavg), and the maximum and minimum values of the ratio between the contact pressure and the allowable pressure Pc max /Pa and Pc mix /Pa. It is noted that because the allowable pressure is different for load combinations that include lateral loads, the load combination for which the contact pressure is maximum may be different from the load combination for which the ratio Pc max /Pa is maximum.

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Automatic resizing of footings The command window for the command Footing pressures includes the button Autoresize all which allows to automatically resize all footings so that the maximum value of the ratio between the maximum contact pressure and the allowable pressure, Pcmax/Pa, becomes equal to 1.0. Footings can also be automatically resized individually with the button Auto resize which becomes available when a footing is selected with the mouse, being active the option Envelope all load cases. The procedure used to resize footings is the same with both buttons. The program presents the same window described for presenting envelopes, in which the user selects the type of load combinations to be used for resizing footings, the type of contact pressure which will be compared to the allowable pressure and whether or not a fraction of the vertical service load is to be included to represent the self weight of the footing. Once these parameters are selected, the program determines the minimum dimensions that the footing should have so that for no load combination the maximum contact pressure Pcmax, exceeds the allowable pressure, Pa. In the case of spread footings for columns, the program determines the dimensions B and L taking into account the size of the column and the alignment of the footing (whether the footing is eccentric or concentric), so that the cantilever in both directions are equal. In the case of continuous footings, the program determines the width of the footing B. In the case of combined footings or mats of arbitrary geometry, the program reduces uniformly the footing plan dimensions keeping its shape and trying to equate the maximum contact pressure and the allowable pressure, without allowing neither any overlap with other footings, nor changes on which elements ―columns and walls― are supported by the footing.

Other Results EngSolutions RCB includes graphic commands that allow a better understanding of the seismic behavior of the structure. The program computes and draws for each earthquake loading direction, the shear ratio r for each resisting element. For a given direction, the shear ratio is the ratio between the shear force that the element resists and the total story shear. The element-story shear ratio ri is the ratio of the design story shear in the most heavily loaded single element divided by the total design story shear. The program reports also, for each loading direction, rmax, which is defined as the maximum elementstory shear ratio occurring in any of the story levels at or below the two-thirds height level of the building (UBC-97). The display of the element-shear ratio allows the engineer to visualize the path of earthquake forces from the top to the base of the structure. Additionally, EngSolutions RCB computes for each seismic loading direction the redundancy factor of the structure, ρ. The redundancy factor es computed as ρ = 2 – 20/ [ rmax Ab½] (where Ab is the ground floor area of the structure in square feet). The redundancy factor is an index of the redundancy of the structure that varies between 1.0 and 1.5. The lower value corresponds to structures with numerous elements resisting the seismic loading so that if any of them behaves unsatisfactorily during the earthquake, its load can be resisted by the other elements. On the other hand, the larger value correspond to structures with a limited number of few elements resisting the earthquake loading, thus, as these elements are critical, they are designed for amplified seismic loads.

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Design of Reinforced Concrete Elements Structural elements can be designed in accordance to the Strength Design Method of ACI 318-05, ACI-318-99, RCDF-04, RCDF-93, NSR-98 and other international building codes. EngSolutions RCB computes the required steel reinforcement for any concrete section considering all design load combinations. Although each norm has some particular details, the design procedures are similar and are described below in general terms. In the seismic design of elements the engineer may specify different ductility levels for columns, walls, beams, and braces. Therefore, it is possible to have for instance a dual system consisting of special shear walls and intermediate moment resisting frames. Elements that are not part of the seismic force resisting system are design with no ductility provisions. In EngSolutions RCB, the engineer can specify which frames or structural elements will resist the lateral loading. Each element has a property named System that defines to which structural system the element belongs. A particular element may be part of the gravity system only, or the lateral system only, or both gravity and lateral load resisting systems. The above functionality allows conducting more efficient designs. For instance, if for a given structuration, it is obtained in a preliminary analysis that several elements, —due to their location and/or size— contribute little to resist seismic forces, it would be inefficient and expensive to design them for special ductility provisions. It would be better to to declare those elements as purely gravitatory. This way, during the lateral load analysis the program will automatically crack these elements so that the small seismic force they were carrying gets distributed to the lateral load resisting elements. During the design, these elements that are not part of the lateral load resisting system are design without any seismic provisions, making sure they can resist their gravity lateral load even under the lateral displacements occurring during the design earthquake loading.

Design of Beams In the design of beams, EngSolutions RCB calculates and reports the required areas of steel for flexure, shear and torsion, based upon the beam moments and shears from all the design load combinations. The reinforcing requirements are calculated at eleven, equally spaced sections, along the clear span of the beam.. All beams are designed for major direction flexure and shear. Any effects due to axial forces and minor direction bending that may exist in the beam, must be investigated independently by the user. EngSolutions RCB first establishes the envelopes of negative moment and positive moment, from all design load combinations, at the eleven design sections. If appropriate, these envelopes are modified to account for the provisions for seismic design (ductile design). Thus, for beams in special design (special frames/ ductile frames), the moment envelopes are modified so that: 1) at any end support of the beam, the beam positive moment is not less than ½ of the beam negative moment at that end; 2) the negative moment at any design section is not less than ¼ of the negative moment at any end section; 3) the positive moment at any design section is not less than ¼ of the positive moment at any end section. Similar provisions are enforced for intermediate design (intermediate frames), with factors of 1/3, 1/5 and 1/5 for conditions 1, 2, and 3 respectively.

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Flexural reinforcement for negative and positive moments are calculated on the basis of the modified design envelopes and the section properties and design parameters provided by the user. EngSolutions RCB enforces the minimum steel ratio, specified by the code, including the provisions for seismic design. The program also checks for the number of bar layers to fit the tension reinforcement and automatically adjust the value of the effective depth, d, if necessary. For design according to ACI-318-99 and previous, When the required reinforcement ratio ρ is greater than 75% of the balanced reinforcement ratio ρb, compression reinforcement is added, up to the limit allowed by seismic requirements (e.g. ρmax = 0.025, for special moment resisting frames), but never exceeding and additional amount corresponding to 0.75ρb. Wen designing according to ACI-318-05 the tensile unit deformation in the reinforcement is limited to εt = 0.004. Shear reinforcement calculation is based on the envelope of absolute value of shear force, from all the design load combinations, which is also established at the eleven design sections. In cases of special and intermediate moment resisting frames, the shear envelope is modified so that the design shear at any design section is not smaller than the seismic shear, computed from the moment capacities of each end of the beam and the gravity shear forces. The end moment capacities are estimated with no strength reduction factors, and in the case of special moment resisting frames, using a stress of 1.25 fy in the longitudinal reinforcement. EngSolutions RCB computes and reports the size of stirrups and their required spacing along the length of the beam, taking into account the limits for seismic design, in concrete shear capacity and the shear that can be resisted by the steel, specified by the design code. The results for stirrups and longitudinal reinforcement (positive and negative) reported by the program include reinforcement required for torsion. Column Design In the design of columns, EngSolutions RCB calculates the required areas of longitudinal steel, at each clear end of the element (top and bottom), based upon the acting axial load and biaxial bending moments, for each design load combination. The program reports the largest computed area of steel along with the load combination that requires it (critical load combination). The program also reports the required shear reinforcement, considering all design load combinations. EngSolutions RCB uses the moment magnifier concept to account for slenderness effects. The design axial load and biaxial design moments, at any end of the column, for any load combination are P = Pu M2 = δb2 Mub2 + δs2 Mus2 M3 = δb3 Mub3 + δs3 Mus3 where is Pu is the axial load Mub2 and Mub3 are moments in the minor and major direction caused by gravity loads, Mus2 and Mus3 are moments in minor and major direction caused by lateral loads, δb2, δb3, δs2, and δs3 are the moment magnification factors. EngSolutions RCB obtains the magnified moments δs2 Mus2 and δs3 Mus3 directly from the P-Delta results. The program assumes a P-Delta analysis has been carried out. The moment magnification factor δb for each local direction, 2 and 3, is computed as

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δb = Cm /[1 - Pu / φPc] where Pc = π2 EI /(KLu)2 and Cm = 0.6 + 0.4(Mib / Mjb) but not less than 0.4 Mib and Mjb are the moments at the ends of the column and Mjb is numerically larger than Mib. The magnification factor must be a positive number greater than one. Therefore Pu must be less than φPc. If Pu is found to be greater than φPc an insufficient section condition is reported. The stiffness EI for each local column direction is computed as EI = 0.4 Ec Ig/ (1 + βd) where βd is the ratio of the maximum factored axial dead load to the total factored axial load. In the design of special moment resisting frames, before magnifying moments, the ultimate end-column moments are increased by a code specified factor, usually equal to 1.2 (6/5), to satisfy the strong column-weak beam requirements of the design code. EngSolutions RCB determines the required longitudinal reinforcement at each end of the column for each load combination, based on the design axial load and biaxial design moments (P, M2, M3). The reinforcement is assumed to be uniformly distributed around the section of the column, with a constant clear cover d’. The computation of the required steel reinforcement is based on an iterative procedure that involves the generation of selected portions of load-biaxial moment interaction surfaces for varying steel ratios. The load-biaxial moment interaction surfaces are computed using the method proposed by Gouwens (1975). The shear reinforcement is designed for each load combination in the two local directions of the column. In designing the shear reinforcement for a particular load combination in a particular direction, the factored forces Pu and Vu are determined first. Then, the shear force Vc that can be resisted by the concrete, which depends on Pu, is computed. Next, the reinforcing steel to carry the balance Vu - φVc is determined. Vu is determined as the maximum factored shear force along the column length, in the direction considered, for the load combination considered. In the design of intermediate and special moment resisting frames (intermediate and high seismic risk), a shear force Vu is also determined from the end moment capacity of the member. The end moment capacities are estimated with no strength reduction factors, and in the case of special moment resisting frames, using a stress of 1.25 fy in the longitudinal reinforcement. EngSolutions RCB computes and reports the size of stirrups, cross-ties or legs and their required spacing along the length of the column, taking into account the limits for seismic design, in concrete shear capacity, balance shear that can be resisted by the steel, and spacing of stirrups, specified by the design code.

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Shear Wall Design In the design of walls, EngSolutions RCB computes the required vertical and horizontal reinforcement, at each end section of the wall (top and bottom), based upon the acting shear force, axial load and in-plane bending moment, for each design load combination. The program reports the largest computed reinforcement and the critical load combinations. The calculation procedure consists in designing the wall for shear first, and then checking adequacy under combined axial load and bending moment in the plane of the wall. The vertical and horizontal reinforcement, required by shear, are determined according to the design code, including the special provisions for seismic design. EngSolutions RCB enforces the code requirements for minimum steel ratio, reinforcement spacing and number of layers of reinforcement. For low rise buildings, the uniformly distributed vertical reinforcement required for shear, usually provides adequate resistance for combined axial loads and bending moment in the plane of the wall. If additional reinforcement is required, EngSolutions RCB concentrates it at the ends of the wall. For high rise buildings in high seismic risk regions, boundary elements are usually required. Design of boundary elements can be conducted according to the stress design method (ACI-318-99 and previous) or the strain design method (UBC-97, ACI-318-05, RCDF-04). In the stress method the need of boundary elements is established by computing the maximum extreme-fiber compressive stress. If such stress value exceeds 0.2f’c, boundary elements are required. If the engineer modeled the boundary elements as columns, the program determines the required reinforcement. If boundary elements were not modeled but are required, the program determines their required size and reinforcement. In this design method, boundary elements are design as short columns, capable of supporting the total factored gravity loads acting on the wall plus the vertical force required to resist the overturning moment produced by earthquake loading. That is, boundary elements are design as if the wall itself did not exist. The contribution of concrete and reinforcement on the wall web is ignored. The stress design method being so conservative in flexure, results in expensive designs as it leads to large boundary elements with large steel ratios, producing also structures that most likely would behave poorly under severe earthquake loading. Ignoring the contribution of the wall’s web results in rigid massive elements (wall plus boundary elements) with a large flexo-compression capacity, much larger that computed in the design, but with no additional shear capacity. Under earthquake loading, these massive elements would attract more seismic force, making it more feasible a fragile shear failure. Special reinforcement provisions for boundary elements, aimed at increasing flexocompression ductility would not increase the actual ductility of the element, as these elements with their large flexocompression capacity are inherently fragile in shear. For the above reason the stress design method is no longer allowed in some building codes (e.g. UBC-97, SEAOC-99, RCDF-04). In the strain design method (UBC-97, ACI-318-05, RCDF-04) the contribution of concrete and reinforcement along the web of the shear wall to axial load and in-plane

59 bending is taken into account, which results in significantly lower reinforcement quantities and smaller boundary elements. UBC-97 considers two alternative procedures to determine if boundary zones are required: a simplified procedure and a procedure based on computation of unit compressive strains. According to the simplified procedure boundary zones are not required on shear walls or portions of shear walls when: Pu ≤ 0.10 Ag f’c for symmetrical wall sections Pu ≤ 0.05 Ag f’c for unsymmetrical wall sections And either Vu ≤ 3 Acv f’c½ and Mu/(Vu Lw) ≤ 3 or Mu/(Vu Lw) ≤ 1 For shear walls and portions of shear walls meeting the conditions above and having a factored axial load Pu < 0.35 Po (where Po is the nominal axial strength for no eccentricity) shear zones must be provided at each end of the wall in a distance varying linearly from 0.25 Lw to 0.15 Lw for Pu varying from 0.35 Po to 0.15 Po. The boundary zone should have a minimum length of 0.15 Lw. Alternatively the requirements for boundary zones of shear walls or portions of shear wall may be based on the determination of the compressive strain levels at edges when the wall or portion of wall is subjected to displacement levels corresponding to the design earthquake loading. Boundary zone shall be extended over those portions of the wall where compressive strains exceed 0.003. The boundary zone should have a minimum length of 18 in at each end of the shear wall or portion of shear wall. In no instance designs are permitted in which compressive strains exceed εmax = 0.015. The maximum axial load in this method is limited to 0.35 Po. Shear walls or portions of shear wall in which Pu > 0.35 Po should not be considered to contribute to earthquake induced loading. In both, the stress design method and the strain design method, stirrups must be provided in the boundary zones. The purpose of these stirrups is to provide confinement to the vertical reinforcement and concrete, to increase the capability of the element to deform inelastically. These stirrups are required because compression reinforced concrete elements would otherwise fail explosively if not properly confined. However unlike stirrups in columns, these stirrups are not intended to resist shear forces, hence spacing requirements such as d/4, included in some buildings codes, are not really required. The spacing and area of stirrups (Ash) should instead be based solely on confinement requirements, as done in UBC-97. In the shear wall design implementation in EngSolutions RCB, the engineer must select if boundary elements are to be designed by the stress design method (ACI-318, NSR-98, RCDEF-93, etc) or by the strain design method (UBC-97, ACI-318-05, RCDF-04). If the engineer selects the strain design method, the program uses first the simplified procedure to establish if boundary zones are required. If according the this procedure boundary zones are required for a particular shear wall or portion of a shear, and if such shear wall originates from the base of the structure and extends upward several stories, the program confirms the need to provide boundary zones by computing compressive strains. If the program detects that boundary zones are required and the engineer did not

60 previously define them, the program dimension them automatically and determines their required reinforcement. If boundary zones were defined as columns at the ends of the shear wall, the program uses those dimensions and computes the required reinforcement without verifying dimension requirements. In the strain design method, it is preferred to let EngSolutions RCB dimension automatically boundary zones, if they are required. That is, it is better no to introduce in the model prefixed-columns at the wall ends to represent boundary zones.

Figure 4.28 Steel ratio in shear walls (Picasso Tower, Structural Engineer Postensa S.A. de C.V., Mexico)

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Design of Foundation Beams Foundation beams are designed using the same procedures used for aerial beams. The command for designing foundation beams is the same used for aerial beams. Design of Footings EngSolutions RCB performs structural design of spread footings for columns and continuous footings for walls. The program does not design combined footings or mat footings. The footing design command assumes that the plan dimensions of footings are adequate, that is, the contact pressure does not exceed the allowable soil pressure. The command also assumes that the existing load combinations are ultimate design load combinations. When the footing design is activated, the program computes the required footing thickness and the required reinforcement in each direction. The assumptions and design computation sequence is as follows. In determining the thickness, the program starts with a thickness equal to 0.8 times the minimum dimension of the column (or wall thickness in the case of continuous footings). The program modifies the computed thickness, if necessary, so that the thickness is not smaller than a minimum thickness equal to 10 inches. Next, based on the modified thickness and a value of reinforcement cover (assumed to be equal to 4 inches, to the centroid of reinforcement), the program computes an effective depth for flexion as d = h – 4 in. Next the program computes the ultimate moment along each direction (envelope from all design load combinations) considering a lineal (non uniform) distribution of net pressure under the footing. Based on the ultimate moment along each direction, the program computes the required effective depth d, required for the steel ratio not to exceed 1.2 the minimum steel ratio. The program takes as effective depth, the larger between the determined above from minimum dimensions and that calculated to ensure a low steel ratio. Based on the computed effective depth d, the program starts an iterative procedure, sweeping all load combinations, comparing ultimate shear forces, including one-way shear Vu1 and two-way shear Vu2 with the shear resisted by concrete in each case, φVc1 and φVc2 respectively. If for any load combination, the ultimate shear force is greater that the corresponding one resisted by concrete, the effective depth is increased and the check is repeated until a final effective depth d, is reached for which the ultimate shear for all load combinations are smaller that the shear resisted by concrete. The program determines then for this effective depth the corresponding footing thickness, the required steel ratio along each direction and verifies that the amount of reinforcement is not smaller than that required for temperature.

Design Results The design process is graphically displayed in EngSolutions RCB. Elements are drawn as they are designed in different colors, depending on the required amount of steel. Elements with insufficient cross section are marked in red. This way, the designer can clearly see which elements need to be resized. In addition, EngSolutions RCB

62 computes for all the designed elements, the volume of concrete and weight of steel required, which allows making cost analyses for various structural solutions. After the design process is finished, the user can display detailed design results for any element just by selecting it with the mouse, after activating the Design Results command. Beams In the case of beams, EngSolutions RCB displays the envelopes of negative moment, positive moment, and shear force, from all design load combinations, as well as the required area of steel reinforcement and size and spacing of stirrups at various sections of the member. EngSolutions RCB can also propose detailing of reinforcement for beams, displaying bar cutoffs and splicing, based on the design results, code provisions for development, anchorage and splicing, and detailing options and bar data specified by the engineer. Columns In the case of columns, EngSolutions RCB displays the load-biaxial bending moment interaction surface for the required longitudinal reinforcement, reports the size of stirrups, cross-ties or legs and their required spacing along the length of the column, the area of longitudinal reinforcement and the design load and bending moments for the most critical load combination.

Figure 4.29 Design Results for Columns Shear Walls

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For shear walls EngSolutions RCB reports the required vertical reinforcement on the wall and on the boundary elements and displays the load-moment integration diagram for the required reinforcement. In addition, EngSolutions RCB reports the required size and spacing of horizontal reinforcement. Footings The design results menu includes a command for footings. The design results for footings are not actually stored but the footings are simply redesigned each time the command is activated. For this reason, it is possible to display design results for footings that have not been previously designed. When the command is activated, the program displays the required steel ratio along each direction for each footing. If a footing is selected with the mouse, the program presents the design results in tabular form. The design results presented by the program are the following. The require footing thickness h, proposed reinforcement along each direction (including number of rebars, rebar diameter and rebar spacing), area of reinforcement, ultimate moment (envelope) along each direction and the ratio between the ultimate shear and that resisted by concrete for shear action in one and two directions.

General Design Sequence The general suggested sequence to use the new features of this version is the following: 1. Create the building model (columns, beams, wall, slabs). 2. Add manually spread footings for columns and continuous footings for walls, entering approximate footing dimensions (B and L for spread footings and B for wall footings). If there are eccentric footings their alignment properties can be set. In this stage it is also possible to define combined footings and mat footings. 3. Generate loads: self-weight, dead load and live load on slabs. 4. Generate earthquake and wind forces. For preliminary analysis, equivalent static seismic forces can be considered. For more detailed analysis mode shapes should be computed first to allow generation of inertial forces according to spectral or time history analyses. 5. Run analysis. 6. Verify story drifts. 7. Modify dimensions of structural elements recreating in (3) self-weight and carrying out 4 and 5 until requirements for (6) are met. 8. Resize footings. 9. If some footings overlap, redefine them as combined or mat footings. 10. Re-analyze. 11. Generate ultimate load combinations. 12. Design structural elements.

Design of Structural Steel Elements EngSolutions RCB includes the command: Results: Steel design that allows to check and design steel members, according to the Load and Resístanse Factor Design (LRFD) of AISC and RCDF. This command applies only to elements whose material property is structural steel. The section property of the element can be any shape (W, M, S, T, C, L, 2L, P, etc.) created manually or imported from a library of steel sections. The program includes the AISC library.

64 The procedure for design check steel members is as follows. Once element properties have been assigned and the ananalysis has been carried out, the command Results: Steel Design is activated. In response, the program draws each steel member in color depending on the value of its capacity ratio. The capacity ratio is essentially the ratio between the ultimate load and the nominal strength reduced by a strength reduction factor. When the capacity ratio is > 1.0 the section is insufficient. When the capacity ratio is < 1.0 the section is larger than required. Theoretically, for an optimum design the capacity ratio of all elements should be about 1.0. When the Steel design command is active, selecting any member produces a report with a detailed calculation of its capacity ratio. The Steel design command includes command buttons for automatically resizing columns, beams, and braces. When any of these buttons, for instance the Autosize columns command button, is clicked, the program displays the list of the column sections. The user may remove some sections, add or import additional sections. The modified list of sections is the one used for automatically resizing elements. The program selects from this list, for each column the lightest section that produces a capacity ratio near to 1.0. This command only applies to columns visible in the screen. That is, if a determined elevation view has been selected, only the columns in the visible frame are automatically resized. The program does not perform a re-analysis. It simply uses existing analysis results to compute capacity ratios and required sections. The command buttons for auto-sizing beams and braces operate similarly.

Beams In the design check of beams, the program divides the clear length of the member in 11 stations, and computes at each one the capacity ratio for negative moment, positive moment and shear force. In computing nominal bending strength the program considers the following limit states: (a) flange local buckling, (b) web local buckling and (c) lateral torsional buckling. In beam properties, it is possible to indicate the spacing of lateral supports for the upper flange and for the bottom flange. These properties have a strong effect on the computed bending strength of the element. If the upper flange is continually connected to the floor slab, the spacing between lateral stiffeners equal to zero can be specified. If there are not intermediate supports, a spacing equal to –1 should be specified. The program does not perform composite design.

Columns The design check for columns is carried out for each end of the element. The limit states considered are tension yielding (tension members), flexural buckling (compression members), flange local buckling, web local buckling and lateral torsional buckling. The program does not check flexural-torsional buckling. Thus columns with one or none axes of symmetry, or elements with very low torsional stiffness for which flexo-torsion might be critical should be check for such a limit state, independently of the program. In column properties the user may indicate the spacing of intermediate lateral supports for instability around each local axis of the member.

Braces The design check for diagonals is carried out for each end of the element, considering tension yielding (tension members), flexural buckling (compression members), flange local buckling, web local buckling and lateral torsional buckling. In brace properties the

65 user may indicate the spacing of intermediate lateral supports for instability around each local axis of the member.

Printing All structural data including coordinates of axis intersections and nodes, element properties, applied loads, etc., along with analysis and design results, can be printed as an organized report or saved in file for later printing. Reports can be saved as text files (*.txt) or as Eprint files (*.epr) Printing commands apply only to elements that are currently visible. EngSolutions RCB includes different options to make visible selected parts of the structure. In an Elevation view, only one frame is visible. In a Plan view only one floor plan is visible. In a 3D View, either the whole structure is visible or selected floors, frames or regions. Therefore, the engineer has complete control on the amount of printing. She can print design results for a single element, or all project data, analysis and design results for the whole structure. Results from automatic generation of earthquake and wind forces can be printed at the end of the generation process or they can be saved in a file for later printing. Reports can be saved as text files (*.txt) or as Eprint files (*.epr) EngSolutions RCB includes program Eprint which allows to preview and print reports saved in format *.epr. Wen a report is saved as a text file, the text formatting of the document is lost. If the report is saved as an *.epr file, it is possible to print the report at a later time using program Eprint, without loosing the document formatting. Any graphical image on the EngSolutions RCB main view area can be printed with the Print command in the File menu. EngSolutions RCB saves a copy of the image in its main window in Windows Paint program. Before printing from Paint de page must be configured (File >Page Setup) to scale to fit the image in a single page.

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Chapter 5

Training Session In this section you will create, analyze and design your first EngSolutions RCB building structure. You will be guided step by step through a simple example. The basic steps you take in processing the example building will show you principles that you will use with every other building that you design.

The Structure The example structure is a 10-story building located in a high seismic risk zone. The structural system is a dual system, consisting of special reinforced concrete moment resisting frames and special reinforced concrete shear walls. The floor system is a twoway slab with beams. The columns and shear walls have constant cross-sections throughout the height of the building. The floor beams and slabs also have the same dimensions at all floor levels. Although the dimensions of the structural elements in this example are within practical range, the structure itself is hypothetical and has been chosen mainly for illustrative purposes. Structural elements are designed according to ACI-318-05. Seismic forces, in this example, are defined according to ASCE 7-2005. However, the procedure for generating seismic forces according to other seismic codes such as UBC-97, NSR-98, RCDF-04, CFE-93, GUAD-97, REP-04, E030-03, and CEC-01, is similar. Story drift ratio amplified for the deflection amplification factor Cd, is limited to 0.02. Other pertinent design data are as follows: Load data: Slab self-weight: 87.5 psf (7” two-way slab) Superimpossed DL*: 50 psf Live load: 50 psf Roof live load: 30 psf * Partitions, ceiling and mechanical

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Elements: Interior columns: Exterior columns: Beams: Walls: Slab: Materials: Concrete: Reinforcement:

20” x 20” 16” x 28” 16” x 20” 12” 7” two-way f’c = 4.0 ksi w = 150 pcf fy = 60 ksi

Occupancy category:

II (Importance factor. I =1)

Foundation soil: Site class

S = C (Very dense soil, ASCE 7, IBC)

Mapped Spectral Accelerations* Ss = 1.0, S1 = 0.4 (Equivalent to UBC-97 Z= 0.3) * Maximum considered earthquake

Figure 5.1. Building considered in training example: Roof plan, typical floor framing plan (Floor levels 3-10), floor plan floor level 2 and a longitudinal elevation

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Creating the Structure • • • • •

Run EngSolutions RCB and in the Starting window select the option 3D Frame/Wall in the group Create New Structure, to create a new three-dimensional model. In the story information window input 10 stories and press ENTER. Input the first story height equal to 15 ft and press ENTER: In the second entry, type 10 and press ENTER. Press the ENTER key several times to repeat the previous value, until reaching the story height for the upper story.

The Building Wizard window should look as follows:

• •

Press ENTER or click the Next> button. Accept the proposed grid type (default), corresponding to an orthogonal system of architectural axes.

• • •

Press ENTER or click the Next> button. For number of longitudinal axes type 4 and press ENTER. Enter the spacing between frames A and B equal to 20 ft and press ENTER.

70 •

Press ENTER twice to repeat the previous value. The Building Wizard window should look as follows:

• • •

Press ENTER or click Next>. For Number of transversal frames type 7 and press ENTER. For spacing between transversal axes. Enter 25, 12.5, 12.5, 12.5, 12.5, and 25, pressing ENTER after each entry. The Building Wizard window should look as shown below:

71 • •

• • • •

Press ENTER or click Next>. In the Reentrant corners window do not do any editing. In the case of buildings with re-entrant corners, such as buildings with floor plans shaped as “L”, “T”, “U”, etc., in this step of the creation process the engineer may permanently remove slab panels that do not exist. However, this can be done more conveniently later, after the 1st story has been created. Click the Next> button In the Local Axes Coordinates is possible to edit coordinates of axis intersections, in cases the architectural axes are not rectangular. The edition of axis intersections can also be done after the model has been created. Click the Create button to create the first floor plan of the model. A window is shown, asking for the type of floor system. Select 4, which correspond to a 2-way slab.



Change the slab thickness to 7” and click OK

Based on the previous data, EngSolutions RCB creates a first story, which we can edit and use as basis for defining the rest of the model. Change the current 3D view to a plan view by clicking the Plan View button (View ), in the View toolbar. If necessary, use the Zoom buttons or the Move Buttons:

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button , to enlarge, reduce or move the floor plan to the center of your screen. The floor plan should look as shown in Figure 5.2.

Figure 5.2 Preliminary Floor Plan In order to define the wall boundaries it is necessary to insert an axis between axes B and C, which for demonstration purposes we did not include when entering the axis information. To insert an Axis • • • • •

Activate the Axes edition command , in the Elements toolbar In the Edit frames window (active command window) select the option Insert a frame. Along transversal axis 7, click with the left mouse button a point, intermediate between axes B and C. A window is displayed asking for the relative distance, from B to the new Axis. Type a relative distance equal to 0.5 to insert an axis in the middle of axes B and C. The dialog window looks as shown below:

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• •

Click the OK button. The program creates a new axis B’.

The next step is to create the shear walls of the elevator core. To add shear walls • •

Activate the Wall edition command in the Elements toolbar In the Edit walls window (active command window) select option Add wall

• •

In the Wall property window enter a wall thickness equal to 12 in. Point the mouse cursor and click with the left mouse button to the intersection defining the first end of the shear wall (for instance C-2) Move the mouse cursor to the other end of the wall and click the left mouse button (for instance B-2). The program automatically connects the interior axis B’ creating two wall segments Using the same procedure add all shear walls of the elevators core.

• •

The configuration after adding the walls should look as shown in Figure 5.3. Note:

To remove a wall segment activate the Wall edition command (if it is not active), select the wall segment and click the Remove button in the Property window.

In the next step, we will edit beams. We can remove the beams embedded within the walls and inexistent beams along transversal axes 3 and 5, add the longitudinal beam along axis B’, and assign beam properties. To remove beams • • •

Activate the Beam edition command , in the Elements toolbar. In the Edit beams window (active command window) select option Existing beams. This is the default option when the command is activated. Select a beam by pointing at it with the mouse cursor and clicking the left mouse button. For instance, mark the longitudinal beam C(2-3)

74 • • • •

In the window properties click the Remove button. To remove various beams in a single step, press and maintain down the SHIFT key and select the following beams: 2(B-B’), 2(B’-C), A(2-3), A(5-6), C(5-6) Click the Remove button. Use the same procedure to remove transversal beams 3(A-B), 3(C-D), 5(A-B) y 5(C-D)

Figure 5.3 Configuration after adding structural walls To add beams • • •

In the Edit beams window (active command window) select the option Add beams Point and click the intersection that defines the first end of the beam (e.g. B’-3) Move the mouse cursor to the other end of the beam and click the left mouse button (e.g. B-5). The program automatically connects the intermediate axis 4 creating two beam segments.

The configuration after adding and removing beams should look as shown in Figure 5.4

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Figure 5.4 Configuration after adding beams To edit beam properties • •

• • • • • • • •

In the Edit beams window (active command window) select the option Existing beams In the Edit beams window, in the selection options group, click the mini-button All beams. With this button, all beams are selected in a single step. The property window shows the properties that are common to all selected beams. All have section property: Beam1. Click in the Property window the name Beam1 A table is displayed showing the properties of section Beam1. Click the beam width (b), type 16 in and press ENTER. Click the depth of the beam (h), type 20 in and press ENTER. The program automatically computes area and inertia properties of the section. Click OK so that Beam1 become a rectangular beam section 16” x 20”. In this example all beams will have this section. In a real project, we need to add various beam sections to this table. Click in the Property window the name of the material Rconcrete1 (reinforced concrete 1) Edit the compressive strength of concrete (f’c = 4 ksi) and enter modulus of elasticity E and shear modulus G (~0.4 E) corresponding to the specified concrete quality

76 •

Click OK

In the following step we will remove the slab panels in the elevator area. To remove slab panels • • • •

in the Elements toolbar. Activate the Slab edition command Point the mouse cursor to the center of the panel to be removed and click the left mouse button Click the Remove button in the property window To remove various panels in a single step, press and keep down the SHIFT key, mark all panels to be removed and click the Remove button. Use this procedure to remove all panels in the elevator area.

The configuration after removing slab panels should look as shown in Figure 5.5

Figure 5.5 Configuration after removing slab panels

Note:

To re –add slab panels previously removed, select option Add slab panel in the Edit slabs Window. Then select the panels to be added and click the Add button in the Property window.

77 In the next step we will edit columns. We will remove the inexistent columns in axes 3 and 5. We will also remove columns at the ends of shear walls. If due to seismic considerations boundary zones are required at the ends of shear walls, the program will automatically detect that condition and add them. To remove columns • • • • • •

Activate the Column edition command en the Elements toolbar In the Edit columns window (active command window) select the option Existing columns Point at the column to be removed and select it by clicking the left mouse button. For instance select column A-3 Click the Remove button in the Property window (or press the Del key) To remove various columns in a single step press and hold down the SHIFT key, mark the columns and click the Remove button. Use this procedure to remove columns from axes 3 and 5, and columns B-2, C-2, B-6, C-6 in the View toolbar to redraw the floor plan. Click the Refresh button

To edit column properties • • • • • • •

In the Edit column window, in the Selection options group, click the mini-button All columns to select all columns In the Column properties window click property Column1 In the Table of sections, change the section dimensions to b=20 in, h = 20 in. In the property Name, in the Table of sections, click at Column1 and change this name to 20x20 Click OK Click the Assign button to assign these changes Click at any point in the screen without pointing at any column

To change properties of exterior columns • • • • •

In the selection options of the Edit columns window, select the option Story L-Frame cols. Select column D-1. All columns along axis D are selected Press and hold down the SHIFT key Select column A-1. All columns along axis A are selected Change the selection option to Single column and release the SHIFT key

To add a new section • • • • • • • •

In the Column properties window click at the name of the section C20x20 In the table of sections, click the Add button to add a new section. Select a rectangular section and click the Next> button. Edit the size of the new section to b = 16 in, h = 28 in Click OK. In the table of sections, change the name of the new section to C16x28. Click OK. Click Assign to apply these changes.

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Figure 5.6 Column sections To modify column properties • • • • • •

Select column B-1. Pressing and holding down the SHIFT key, select also columns C-1, B-7 y C-7. In the Column property window click the name of the section C20x20. In the sections list (left side of the table of sections) select section C16x28 and click OK. In the Column properties window, in the property corresponding to orientation edit the property value entering 90 degrees (to rotate the selected columns) and press ENTER. Click the Assign to apply these changes.

The configuration to edit columns should look as shown in Figure 5.7. As an additional exercise, it is suggested to change the section of column A-4, for a new circular section 24 in diameter (Oval: 24 in x 24 in) When the intermediate Axis B’ was inserted new nodes were created in axes 1 and 7. Node B’-1 segments beam 1(B-C) into segments 1(B-B’) and 1(B’-C). These fictitious nodes have no effect on the final analysis and design results. In designing beams, the

79 program recognizes that the above two segments correspond to beam 1(B-C) and designs it as a single element. However, these fictitious nodes increase unnecessarily the size of the model, increasing the number of degrees of freedom and the solution time. For this reason and other reasons, it is convenient to remove any fictitious nodes so that beams and walls are not segmented unnecessarily.

Figure 5.7 Final configuration of first aerial slab.

To remove fictitious nodes • • • •

in the Elements toolbar. Activate the Nodes edition command In the Edit nodes window (active command window) select the option Existing nodes Pressing and holding down the SHIFT key, mark nodes B’-1, B’7, A-3, A-5, D-3 y D-5 Click the Remove button.

Note:

To add previously removed nodes, select the option Add node in the Edit node window. Then select the nodes to be added and click the Add button in the Node properties window.

The final configuration of the first floor plan should look as shown in Figure 5.7. It is recommended to save periodically the model to avoid loosing information.

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To Save the model •

In the File menu or in the Standard toolbar activate the command Save and save the model assigning a file name.

We will use the first story created as basis to created the additional floor levels. To create next level • • •



Change the current plan view to a 3D View clicking the 3D View button in the View toolbar. Click the Next Floors button in the main 2 12500iwhA In the displayed 00iwhA, indicate that you just want to create up to floor level 3 (the default is 11, which is the upper level)

Click OK

The program creates a n125story. If there are plan changes we can edit the n125floor plan, preferably in a plan view To edit the typical floor plan • • • • • • • •

Change again to a plan view clicking the Plan 2 125button . The program shows the current Floor level in the selection box n1ar the V 12 5buttons5(in this5case5floor level 3) Activate the Slab edition command. Select the lower left panel pointing at its center and clicking the left mouse5button. Remove the slab panel clicking the Remove5button in the Slab properties window. Activate the Column edition command. Select column A-7 and remove it by clicking the Remove button. Activate the Beam edition command Select an remove beams A(6-7) y 7(A-B)

The final configuration of the typical floor plan should look as shown in Figure 5.8 To create the additional floors • • •

Click the Next Floors5button. In the Create additional stories windows accept the defaults by clicking OK Change the current view for a 3D view to see the complete model

81 •

If necessary, enlarge, reduce or move the model to see the whole model in the main view window, using the commands Zoom(+), Zoom(-) and Move

.

Figure 5.8 Typical floor framing plan

To edit the roof (roof of elevators and machine room) • • • • • • • • • • • •

Change the current 3D View for a plan view (Floor level 11) Activate the Slab edition command In the Selection options group of the Edit slabs window (active command window) select the option Floor panels Select any slab panel. All slab panels in the active floor are selected. Click the Remove button to remove all slab panels of the upper floor level In the Edit slabs window select the option Add slab panel In the Slab properties window click at the slab name: Slab type 1. In the Table of slab sections click at the Add button to add a new slab type. Select a two-way slab and click OK. Enter a slab thickness of 6 in and live load 30 psf. Then click OK. Press and hold down the SHIFT key and mark the slab panels corresponding to the elevators and the central machine room Click the Add button to add these panels

The roof floor plan should look as shown in Figure 5.9

82 The beams and columns of the exterior axes could be removed individually. However, it is much easier to remove the nodes, which will automatically remove the framing elements.

Figure 5.9 Roof plan after re-addition of slabs •

• • • • • • • • •

in the Elements toolbar. Note that the Node Activate the Node edition command edition command should not be confused with the Axis Intersection edition command . In the Edit nodes window (active command window) select the option Floor L-Frame. Mark any on axis D. All nodes along D are selected. Click the Remove button. Nodes, beams and columns along D axis are removed. Select any node on axis A. Click the Remove button. All nodes and elements along Axis A are removed. In the Edit nodes window select the Single node selection option. Press and hold down the SHIFT key and mark the exterior nodes B-1, C1, B-7, C-7. Click the Remove button. Close the Edit nodes window to deactivate the command.

The final roof configuration should look as shown in Figure 5.10. • •

Change the actual view for a 3D view using the 3D View button in the View toolbar. Save the model.

83 The final configuration of the 3D model should look as shown in Figure 5.11.

Figure 5.10 Roof floor framing plan

Making visible selected parts of the structure To make visible a particular floor framing plan • •

Click the Plan View button in the View toolbar In the selection box located near the View buttons, select the desired floor level. For instance select floor level 10.

To make visible a particular frame of the model • •

in the View toolbar. Click the Elevation view button In the selection box located near the View buttons, select the desired frame. For instance select frame B.

To make visible part of a model in 3D • • •

Change the current view to a 3D view clicking the 3D View button in the View toolbar. In the View menu, select the command: View > Visible > Floor. The Visible window is displayed. To make visible floors 1 to 3, floor 3, and floor 9, select the option Floors and input the following text: 1-3, 7, 9

84



Click OK. After examining the result, make visible the complete structure, activating the command: View > Visible > All.

Figure 5.11 3D configuration Interactive commands, such as printing command and design commands, operate only on the elements that are visible. Therefore, when a certain region of the structure, such

85 as a particular frame, and a design command is activated, the program only designs the elements of that frame. In this example the geometry is perfectly regular. If in the real structure, the axes do not conform an orthogonal grid, we can edit the individual axes intersections to model the actual geometry. To Edit Axis intersections • • • •

in the Elements toolbar. Activate the Axis intersection edition command Change the current view to a plan view corresponding to floor level 10. Edition of axis intersections can be done in any view. However, it is much easier to perform such editing in a plan view. Select the intersection to be edited. For example select intersection D-7. The Axis properties window shows the coordinates of the intersection. Edit the C coordinate. Click the current zero value (0 ft), type –6.0 m, press ENTER to complete the entry, and press ENTER again or click the Assign button to assign the new property.

Figure 5.12 Configuration after editing axis intersection D-7

86 The floor plan configuration should look as shown in Figure 5.12. The change in coordinates applies to all floor plans even though only floor plan 10 was visible, as the Axis intersection object referts to the complete collection of nodes form floor level 1 to the upper floor, associated to the same intersection of architectural axes. The command to modify the coordinates of the particular node corresponding to the selected floor plan is the Nodes edition command nodes.

, which operates on individual

To return to the original example geometry, re-edit the X coordinate of axis intersection D-7, entering 0 ft and pressing ENTER twice to complete the entry and to assign the new value. In this element all elements were defined in plan view, generating individual stories, which usually is the most convenient way for modeling a building structure. Alternatively, in cases of regular geometries, is feasible to create first a 3D basic model, generating all floors at once and then remove/add beams, columns, walls, and slabs, working with the complete 3D view, or alternating floor plans with elevations. In EngSolutions RCB, is possible to add and remove elements at any time.

Assigning Nodal Supports In this example the structure is idealized as supported on nodal supports. Nodal supports in EngSolutions RCB can be rigid or deformable. Rigid supports include the conventional: fixed, hinges, rollers, and special supports in which the engineer decides which degrees of freedom are restrained. Deformable supports consists of multiaxial elastic springs. In this example the structure is modeled as supported on fixed supports. To assign supports • • • •

in the Elements toolbar. Activate the Nodal supports edition command Change the current view to a 3D view of the complete model. Select in the Support properties window the type of support. By default, the selected type of support is fixed, which is the one to be used in the present example. To assign a support a particular node, select the node pointing it with the mouse cursor and pressing the left mouse button. For instance, select the lower node of column A-7. A fixed support is generated in that point.

By default, the active selection option in the Edit supports window is Single node. To assign all nodal supports in a single step, click the mini-button All ground nodes in the Selection. The command to assign supports as all interactive commands in the Elements toolbar, is an interactive command that remains active even after all nodal supports have beenn assigned. The engineer may reassign other support types to some particular nodes. The command remains active until the engineer deactivates the command or activates a new command. To deactivate the Nodal supports edition command close the Edit supports window (Active command window )

87

Applying Loads Manually Loads can be applied manually or automatically. Manual loads can be applied to nodes, members and walls. In most cases, loads are applied automatically. However, the manual procedure to apply loads will be illustrated first. To apply loads to members •

Activate the command Load > Member in the menu bar. The menu that must be opened to activate the command is shown below.



A window is shown asking for a tile for the load case that will be created. Type DEAD and press ENTER. Click the OK button. In the load properties window the engineer defines the type of load. The types of load are: Class: force or moment, Type: distributed or concentrated, System: global o local, Direction: X, Y, or Z (or local axes 1, 2, or 3) etc. The default load is a distributed load defined with reference to the global axes of the structure, acting along the Z direction.

• • •

Accept the default type of load. Click at the A/L value (0), which defines the starting point of the load. Type 0.2 and press ENTER. Click at the B/L value (1), which defines the loaded length. Type 0.6 and press ENTER. Click at the initial value of the load Wiz. Type 3 and press ENTER. The program automatically makes the final value of the load Wjz equal to the initial value. With the above, a distributed load of 3 kip/ft, starting at 0.2 L and ending at 0.8 L (loaded length is 0.6L), where L is the length of the loaded member. The Load properties window should look as shown in Figure 5.13.



• •

In the window Edit member loads (active command window), select the option Members down in the Selection group. This multiple-selection-option means that when an element is marked, that element and those elements directly below it are selected. Point at beam D(6-7) on floor level 10, press and hold down the left mouse button to see the selected elements and then release the mouse button. Repeat the previous step, selecting the same elements. Note:

When loads are re-applied to members, loads get added. Hence, in our example, the distributed load acted on the elements is now 6 kip/ft.

88 •

Point as beam 7(C-D) on floor level 10, press and hold down the left mouse button to see the selected members. Keeping the mouse button down move the mouse cursor away from the marked element and the release the button. Note:

If an element is marked and then the mouse cursor is moved away, when the mouse button is released, the element is not selected and the command is not executed. This feature of marking elements and see them before they get selected is useful in complex model where the wrong element may be marked.

Figure 5.13 (a) Member loads window and (b) Load properties window

To see the value of an existing load • • •

In the Edit member loads window (active command window) select the option Existing loads. Select any loaded member. The properties will be displayed in the Load properties window. Note:

If an element has various type of loads (distributed forces, concentrated forces, moments, etc.) it is possible to select each one of these loads by repeatedly selecting the element.

To edit an existing load • • •

With the Load Edition command being active, select any loaded element. Edit the load value in the Load property window. For instance change the initial value of the load to 4 kip/ft and press ENTER to complete the entry. Press ENTER again or click the Assign button to assign the new value. The uniformly distributed loads is replaced by a trapezoidal load.

To remove an existing load • •

Winth the Load Edition command being active, select any loaded element. Click the Remove button to remove the load.

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Generating Self Weight of Elements •

Activate the command Load > Automatic > Self Weight in the menu bar.

To compute the self-weight of each element, the program uses the section of the element and the unit weight of the assigned material. Alternatively, the user may input modified unit weights for columns, beams and walls. •

Click OK.

Note:

The Weight of beams and braces is applied as a uniformly distributed load along the length of the member. The weight of columns is applied as a concentrated load in the upper node of the element. The weight of walls is represented as a uniformly distributed load at the top of the element. Selfweight loads are grouped in a load case named Self-Weight, D0. This load case does not include the self-weight of slabs.

Generating Floor Loads Previously to generating floor loads, change the current view to a Plan view. Select for instance the floor-framing plan of floor level 10. This is in order to visualize the floor load distribution performed by EngSolutions RCB. • Activate the command Load > Automatic > Floor Load in the menu bar. • A window is displayed; asking if the existing load case DEAD should be deleted. Load case DEAD groups the member loads applied manually in a previou section of this example. Click the YES button to remove these loads. EngSolutions RCB makes the distribution of floor loads for each floor level using the properties assigned to slabs, and show total values of dead load and live load for each floor level and for the complete model. For our example structure the total values are: DL = 6381 kip and LL = 2325 kip. Dead load includes the self-weight of the slab and the superimposed dead load. The computed loads are grouped into load cases DEAD and LIVE, which are abbreviated as DL and LL. To see the floor load distribution move the Automatic distribution of floor loads window (point at the window title bar, press the left mouse button and move the window while holding down the mouse button) The floor load distribution should look as shown in Figure 5.14. Each element and its tributary area are drawn in the same color. The method for load distribution is general and works well even in the case of irregular geometries, floor panels supported along 3 or 2 sides only, panels with different reinforcement direction, floor with ‘diagonal’ walls or beams, etc. •

Click OK to close the Automatic distribution of floor loads window.

To see the load distribution on a different floor, it is necessary to run the command again allowing the program to delete the previous loads. Floor loads are generated for all the floor levels in the model. Once floor loads have been generated automatically, it is possible to add manually any missing loads corresponding to non-structural models not present in the model (e.g.

90 stairs, cantilevers, etc) These manual loads can be grouped in a separated load case (DEAD 2, etc.) or can be included in the same load case generated automatically by the program.

Figure 5.14 Distribution of floor loads to adjoining beams and walls.

Modes and Frequency Analysis To compute the natural frequencies of the building model and its mode shapes: •

Activate the command Analysis > Modes/freq in the menu bar.



A window is displayed asking to input the number of modes to be computed. Type 12 and click OK.



A window is displayed to specify the load combination for computing masses. Accept the proposed values, that is, press ENTER for each factor.

Note:



In EngSolutions RCB the mass matrix is computed automatically based on the loads acting on the structure. In this example the mass matrix is computed as M = (D0 + DL + .25 LL) / g.

The program shows a record of all analysis steps. When the dynamic analysis is completed, the program shows in a table the accumulated percentage of the participating mass. In this example, with 12 modes, in the X-direction participates

91 99.9% of the mass, and in the Y-direction participates 98.3%. If any of those values was smaller than that prescribed in the building code (80% to 90%) and earthquake forces were to be determined from an spectral analysis or a time history analysis, it would be required to repeat the analysis computing a larger number of modes. •

Press OK.

Displaying Mode Shapes To visualize the mode shapes it is convenient to change the current view to a 3D view.

Figure 5.15 Display of mode shapes •

Activate the command Results > Analysis > Mode Shapes in the menu bar.



The first mode shape is shown. Click the mini-button Next Mode in the Mode Shapes window (active command window) to see other mode shapes and their respective natural frequencies and periods. The fourth mode shape is shown in Figure 5.15.



Click the mini-button Animate in the Mode Shapes window to se an animation of the active mode shape. Click anywhere in the main window to stop the animation.

92

Generating Earthquake Forces EngSolutions RCB can generate automatically static equivalent earthquake forces, or perform response spectrum analysis, or perform a time-history analysis, according to numerous seismic codes. In this example a spectral analysis will be carried out according to ASCE 7-05. The loading procedure for other seismic codes such as UBC-97, NSR-98, RCDF-04, CFE-93, GUAD-97, REP-04, E030-03, CEC-01 is similar to that of ASCE7-05. To perform a spectral analysis •

Activate the command Load > Automatic > EQ Spectral in the menu bar.

Figure 5.16 Seismic parameters •

A window is displayed, showing several seismic codes available. Select ASCE 7-05.



A window asking for the number of stories below ground is displayed. Press ENTER to accept the default zero value (i.e. no basements).

93 •

A window is displayed asking if the analysis would be carried out for a specified angle of attack or for two orthogonal directions X and Y. Click OK to perform two spectral analyses in the X and Y directions.



The program asks for the number of modes to be considered in the modal analyses. By default, the program suggests the same number of modes that were computed. Press ENTER to accept the default value of 12.



Input values of the Response modification coefficient R equal to 7 for the two directions (X and Y), which according to ASCE 7-05, correspond to dual structural systems of shear walls and special moment resisting frames (SMRF) resisting at least 25% of the prescribed seismic forces. Click Next>.



Input the seismic parameters as shown in Figure 5.16.



Accept the computed design response acceleration parameters computed by the program, which correspond to the entered mapped spectral accelerations and site class. Sds = 0.67 (spectral acceleration at the plateu of the design response spectrum), Sd1 = 0.37 (spectral acceleration in the descending branch of the design response spectrum for T=1 sec). Click Next>>. Accept the proposed Seismic Design Category SDC = D. Click Next>>.

• • •

Figure 5.17 Static base shear

94 The total weight of the building, computed from the load combination that was used to determine the mass matrix (W = D0 + DL + 0.25 LL), is reported along with the static base shear Vo in each direction. Press ENTER to accept the computed values. The combined dynamic base shear cannot be smaller than Vo. The corresponding table is shown in Figure 5.17.



EngSolutions RCB reports in a table the Period T, for each mode of vibration and the corresponding spectral acceleration Sa. In this table, the user may edit the values of Sa. Hence, any response spectrum different from the code specified design spectrum, includding the spectrum of a specific earthquake record, could be considered in the spectral analysis. For our example we accept the spectral acceleration obtained from the selected code. Click Next>>.



A window is displayed, showing various methods of modal combination available, including SAV, SRSS, CQC, ½(SAV+SRSS) and 0.25 SAV + 0.75 SRSS. For this example select SRSS (square root of sum of squares) and click OK.

Figure 5.18. Design Base Shear •

EngSolutions RCB displays a table with the modal inelastic spectral acceleration Sa/R, modal effective weight W’, and modal base shear Vm, for each mode and in

95 each direction of earthquake loading. This table also shows, for each direction, the Dynamic (combined) base shear, the Static base shear and the Design base shear, which is the larger from of the previous values. The engineer may edit the value of the design base shear. If the design base shear is different from the dynamic base shear, EngSolutions RCB automatically scales the combined shears for all stories. The design base shear for the example structure are: Vx = 731 kip and Vy = 590 kip. •

Click Next >>. Click Next >> again to accept the default values of accidental eccentricity, which are the values specified in the selected seismic code (For ASCE 7-05, accidental torsion is 5% of the corresponding building dimension).



A window is displayed asking which method to use to compute the center of rigidity of each floor level. Select the option based on the fundamental mode shapes, and click OK.



Click OK to accept the default definitions of design eccentricity, which is the appropriate for the selected seismic code. The design eccentricity is defined in terms of the static (inherent) eccentricity (es distance from the center of mass to the center of torsion), and the accidental eccentricity (δε). For ASCE 7-05 the design eccentricities are: es + δε and es - δε.



A table is displayed showing for the first definition of design eccentricity (es + δε), the following data for each story and for each direction of earthquake loading: center of mass, static (inherent) eccentricity, accidental eccentricity, and design eccentricity.



Click Next >> to display the above data for the second definition of design eccentricity (es - δε).



Click Next >> to generate load case EQX. The program draws combined nodal forces and displays a table showing for each story the resultant dynamic force, accumulated shear, and accidental torsion. When the actual analysis is conducted, the program solves the model for these combined forces, and based on the results, establishes initial values and signs for displacements and element internal forces. Then the program establishes the actual result envelopes from the spectral analysis.



Click Next >> to generate load case EQY. The program draws combined nodal forces and displays a table showing for each story the resultant dynamic force, accumulated shear, and accidental torsion. When the actual analysis is conducted, the program solves the model for these combined forces, and based on the results, establishes initial values and signs for displacements and element internal forces. Then the program establishes the actual result envelopes from the spectral analysis.



The program produces a report with a summary of the earthquake loading definition. This report can be printed with its own Print command, or it can be Saved as either a text file (*.txt) or as an Eprint file (*.epr), which can latter be printed with program Eprint. Users of Adobe Acrobat can print the report selecting as printer Adobe PDF, to create a pdf file.



Close the Report.



Save the model.

Analyzing the Structure To run the analysis •

Activate the Run Analysis command menu.

in the Standard toolbar or in the Analysis

96 •

Do the following in the Analysis options window: (a) select the P-Delta option for order of analysis (b) select option Incremental for type of gravity load analysis, (c) mark the checkmark indicating to compute the redundancy factor. The type of lateral load analysis is Spectral, which was the procedure used to define earthquake loading.

In cases of buildings of moderate height, a conventional analysis may be used for the gravity load analysis. For tall buildings however, an incremental analysis modeling the construction process is more accurate. For this example an incremental analysis is selected for demonstration purposes. • • •

• •

Click OK to perform the analysis. The program asks how many stories are to be added in each incremental construction step of the analysis. Click OK to accept the default value equal to 1. A table is shown with the gravity load coefficients during each construction step. The default values are 1 for self weight, 0.8 for the additional dead load during the intermediate steps and 1 at the end of construction (the loading from finishing elements is applied at the end of construction). For live load the proposed factor is 0 for the intermediate steps and 1 at the end of construction. Alternatively, a live load during construction can be specified as a factor of the final live load. Click OK to accept the proposed values. Click OK to accept the proposed gravity load coefficients for the P-Delta (it is suggested to use the same combinations used to define masses in the lateral load analysis)

The program performs the analysis simulating the story-by-story construction process. AT the end of the analysis, the program reports the computation time along with a record of the analysis steps.

Displaying Analysis Results Deformed Shape • • •



Activate the command Results > Analysis > Deformed shape in the menu bar. The original configuration and the deformed shape of the model, for the active load case EQY, are displayed. Click the active load case title (EQY) to change to the next load case (D0). Click the load case title again several times to see the deformed shape for each load cases until the load case EQY becomes active again Point at any member in the original configuration (no the deformed one). Press and hold down the left mouse button to view graphically and numerically the deflectons at any point, as shown in Figure 5.23. Drag the cursor (while holding down the mouse button) along the length of the selected member to display deflectons along the member.

Bending Moment Diagram • •

Activate the command Results> Analysis > Moment diagram in the menu bar. Click the load case title a few times to see moment diagrams for different load cases. If necessary, use the mini-buttons Double scale and Half scale in the Bending moment window to enlarge or reduce the scale of the diagram.

97 • • •

In order to see the results for a specific frame instead of the complete model, change the current 3D View for an elevation view using the View buttons. Select longitudinal frame A. The moment diagrams for load case DL should look as shown in Figure 5.24. Point-and-hold-down the left mouse button at any member to display graphically and numerically the moment at any point. Drag the mouse cursor along the member to display local information.

Note:

The sign convention for shear and moment diagrams can be changed activating the command View > Options. In this example, diagrams are being drawn in the direction of tensions (negative moments upward and positive moments downward).

Figure 5.23 Displaying deformed shape • •



Select the option Member results in the Bending Moment window. Select column A-7 in the first story. With this option, the program shows values of the six internal forces (axial force, flexural moments, torsion moment and shear forces) along the element, for the active load case, as shown in Figure 5.25. Close the window with internal force results.

98

Shear Force Diagram • • •



Change the view to a 3D View using the View buttons. Activate the command Results> Analysis > Shear diagram in the menu bar. Click the load case title a few times to change the load case, observing the shear diagrams for each case. If necessary, use the mini-buttons Double scale and Half scale in the Bending moment window to enlarge or reduce the scale of the diagram. Point-and-hold-down the left mouse button at any member to display graphically and numerically the shear at any point. Drag the mouse cursor along the member to display local information.

Figure 5.24 Moment diagram fro frame A Support Reactions • •

Activate the command Results > Analysis > Support reactions in the menu bar. Select any support. The Support reaction property window shows the six reaction components for the selected load case.

99

Figure 5.25 Internal forces along an element

Checking Story Drift Ratios EngSolutions RCB displays an envelope of relative lateral displacements between consecutive floors (drifts) divided by the story height (story drift ratio), for all lateral load cases. This allows a quick check for compliance with local building codes. To display lateral story drift ratios: •

Activate the command Results > Analysis > Story drift in the menu bar.



A window is displayed asking for the displacement amplification factor D, and the limit (allowable) story drift ratio. Enter for the two directions of seismic loading a displacement amplification factor equal to 5.5 and a limit story drift ratio equal to

100 0.020, which are the appropriate values for the selected code, for the dual structural system selected in the example. Click the OK button. Note:

For ASCE7-05 D = Cd/I, where Cd = deflection amplification factor and I = Importance factor. For RCDF-04 and CFE-93, D = Q, where E = seismic behavior factor. For NSR-98 D = 1.0 as for that norm, seismic forces are not divided by R, but computed internal forces due to earthquake loading, determined during the analysis, are divided by R.





EngSolutions RCB computes for each column and for the boundary of each shear wall portion, the relative lateral displacement between consecutive floors divided by the corresponding story height, for each lateral load case, and draws column axes in different colors according to the maximum computed value. The program uses red colors when the limit value is exceeded, yellow when the maximum computed value is close to the limit value, and green colors when the computed drift ratio is smaller than the limit value. The program also presents the maximum story ratio computed for the whole building (considering all column axes, all stories, all load cases), and the maximum value computed for the center of mass of all stories.

101

Figure 5.26 Envelope of lateral story drift ratio •

The Story drift window (active command window) includes options for presenting results for the two components (X and Y) of story drift ratio and for the resultant drift ratio.



Select any column or wall boundary. The program shows in the Property window the values of lateral drift ratio for the selected element.

Defining Load Combinations Load combinations are the loading conditions for which the structure is designed. Load combinations are assembled as combinations of load cases. EngSolutions RCB generates automatically the design load combinations required by various building codes. To define load combinations: • •

Activate the command LoadComb > ACI-318-05 in the menu bar. A window is displayed asking for parameters needed to define load combinations. The program propose appropriate values according to the selected code but allows the engineer to change these defaults. These values include the following: (a) Level at which seismic forces are defined (service or strength) (b) Bidirectional effects factor (e.g. 30%, means considering 100% earthquake in one direction acting simultaneously with 30% earthquake in the other direction) (c) Redundancy factor (when seismic forces were defined according to ASCE 7-05, IBC-03, or UBC-97). (d) Coefficient for the vertical component of earthquake loading (when seismic forces were defined according to ASCE 7-05, IBC-03, or UBC-97).

102

Figure 5.27 Design load combinations • •

Click OK to accept the proposed values for the above parameters. The program generates a total of 22 load combinations (34 if wind loads cases had been generated), which are the ones required by the selected code. The second of those combinations becomes the active load combination. Analysis results can now be displayed for the active load combination. The active load combination can be selected by clicking the load combination number (left column) in the load combination table. The engineer may edit the load coefficients in the table

To display analysis results for load combinations • • • .

Activate the command Results > Analysis > Deformed shape in the menu bar. The program shows the deformed structure for the active load combination. Click the load combination title to change the active load combination.

Figure 5.28 Analysis results for active load combination To display shear wall results:

103

Activate the command Results > Analysis > Wall Stresses >Stress resultants. The program displays contours of vertical stress resultant for the active load combination. For this combination, seismic loads are EQX directed in the -X direction and 0.3 EQY directed in –Y direction. As shown in Figure 5.29, wall on axis C are in compression while walls on axis B are resisting a small traction. Compression is larger on walls near axis 2 than in walls near axis 6.

Figure 5.29 Vertical stress resultants in walls Activate the command Results > Analysis > Wall Internal forces. Select the wall segment 6(B’-C’). The program presents in the Property window values of axial load P, shear force V, and moments M, at the top and at the bottom ends of the wall segment. Select in the Wall internal forces window (active command window) the selection option Plane wall. The program shows now the total forces for the complete plane wall 6(B-C), combining results for the wall portions 6(B-B’) and 6(B’-C). The above internal forces are the ones used to design walls.

104 Sign conventions and detailed information about the wall element output is presented in Chapter 6.

Designing Structural Elements EngSolutions RCB designs structural elements according to various building codes. In the structural design, the program determines the required steel reinforcement for any section, considering all load combinations.

To design beams • • •

Activate the command Design> Beams in the menu bar. Select as building code ACI-318-05. Select special seismic design.

EngSolutions RCB starts the design process, determining for each beam element, the required areas of steel for flexure, shear and torsion at eleven, equally spaced sections, along the clear span of the element.

105

Figure 5.30 Beam design All beams are designed only for mayor bending. Any effect due to axial loads and minor bending must be investigated by the engineer, independently from the program. EngSolutions RCB first establishes the envelopes of negative moment and positive moment, from all load combinations, at the eleven design sections. These envelopes are modified to account for the special provisions for seismic design. Thus, for high seismic risk cases (special moment resisting frames), the moment envelopes are modified so that: 1) at any end support of the beam, the beam positive moment is not less than ½ of the beam negative moment at that end; 2) the negative moment at any design section is not less than ¼ of the negative moment at any end section; 3) the positive moment at any design section is not less than ¼ of the positive moment at any end section. Flexural reinforcement for negative and positive moments is calculated on the basis of the modified design envelopes, the section properties and the material properties (f’c y fy). EngSolutions RCB enforces the minimum steel ratio specified in the design code, including provisions for seismic design. The program checks for the number of bar layers to fit the tension reinforcement and automatically adjusts the value of the effective depth, d, if necessary. Shear reinforcement calculation is based on the envelope of absolute value of shear force, from all the design load combinations, which is also established at the eleven design sections. In cases of special seismic design, the shear envelope is modified so that the design shear at any design section is not smaller than the seismic shear, computed from the moment capacities of each end of the beam and the gravity shear forces. The end moment capacities are estimated with no strength reduction factors, and using a stress of 1.25 fy in the longitudinal reinforcement. EngSolutions RCB computes the size of stirrups and their required spacing along the length of the beam, taking into account the limits for seismic design, in concrete shear capacity and the shear that can be resisted by the steel reinforcement, as specified in the selected design code. The top and bottom fibers of each member are drawn in different colors according to the steel ratio required at each section, which allows the user to see which members need to be resized. Estimate of building materials After all beam elements have been designed, the program reports the required amount of materials, including volume of concrete, weight of flexural reinforcement and weight of stirrups. The computation of volume of concrete is based on the dimensions of the cross section of the elements and their total length (node-to-node). Thus, there is a small error in the computation, as the volume of the nodes (intersections between longitudinal and transverse beams) is counted twice. The computed weight of stirrups is based on actual bars and includes the weight of hooks. The computed weight of flexural steel is on the other hand theoretical, as it is based on the values of steel ratio computed at eleven design sections. The actual weight of flexural reinforcement is larger because of splices, hooks and the conversion to actual bar sizes.

106

To design columns • • •

Activate the command Design > Columns in the menu bar. Select as design building code ACI-318-05. Select special seismic design.

EngSolutions RCB starts the design process, determining for each column, the required areas of longitudinal steel, at each clear end of the element (top and bottom), based upon the acting axial load and biaxial bending moments, for each design load combination. The program determines the largest computed area of steel along with the load combination that requires it (critical load combination). The program also determines the required shear reinforcement, considering all design load combinations.

Figure 5.31 Column design EngSolutions RCB uses the moment magnifier concept to account for slenderness effects. The computation of the required steel reinforcement is based on an iterative procedure that involves the partial generation of load-biaxial moment interaction surfaces, for varying steel ratios. The reinforcement is assumed to be uniformly distributed around the section of the column, with a constant concrete cover d’. The

107 program enforces the requirements of strong column-weak beam for special moment resisting frames. The shear reinforcement is designed for each load combination in the two local directions of the column. In cases of special seismic design, the reinforcement is also designed for a shear force determined from the end moment capacity of the member. The end moment capacities are estimated with no strength reduction factors, using a stress of 1.25 fy in the longitudinal reinforcement. EngSolutions RCB computes the size of stirrups, cross-ties or legs and their required spacing along the length of the column, taking into account the limits for seismic design, in concrete shear capacity, balance shear that can be resisted by the steel, and spacing of stirrups. During the design process, each column is drawn in different colors according to the required steel ratio, which allows the user to see which members need to be resized. Estimate of building materials After all column elements have been designed, the program reports the required amount of materials, including volume of concrete, weight of longitudinal reinforcement and weight of ties. The computation of volume of concrete is based on the dimensions of the cross section of the columns and their clear length. The computed weight of ties is based on actual bars and includes any cross-ties required as well as the weight of hooks. The computed weight of longitudinal steel is theoretical, as it is based on the required steel ratio rather than on actual bars.

To design shear walls • • • •

Activate the command Design > Walls in the menu bar. Select as building code ACI-318-05. Select special seismic design. Select designing boundary zones using the strain method (UBC, SEAOC)

EngSolutions RCB starts the design process, determining for each wall, the required vertical and horizontal reinforcement, at each end section of the wall (top and bottom), based upon the acting shear force, axial load and in-plane bending moment, for each design load combination. The program determines the largest computed reinforcement and the critical load combinations. The calculation procedure consists in designing the wall for shear first, and then checking adequacy under combined axial load and bending moment in the plane of the wall. The vertical and horizontal reinforcement, required by shear, are determined according to the design code, including the special provisions for seismic design. The program enforces code requirements for minimum steel ratio, reinforcement spacing and number of reinforcement layers. For low-rise buildings, the uniformly distributed vertical reinforcement required for shear, usually provides adequate resistance for combined axial loads and bending moment in the plane of the wall. If additional reinforcement is required, the program concentrates it at the ends of the wall.

108 For high-rise buildings in seismic risk regions, boundary elements are usually required. EngSolutions RCB determines if boundary elements are required using either the stress method or the strain method. If the engineer defined boundary zones as columns, the program computes the required steel reinforcement. One column may act as boundary zone of various wall portions (for example a column at a corner of a “C” shaped shear wall). The amount of steel reinforcement that should be provided is that larger (not the addition) from those reported by the program in column design results and those reported in wall design results.

Figure 5.32 Shear wall design If the engineer did not create the boundary zones but they are required, the program automatically sizes them and determines the required steel reinforcement. The width of the boundary zones is initially taken as the wall thickness, and their length along the wall is taken as a fraction of the wall length. If the computed steel ratio is excessive, the two dimensions of the boundary zone is increased simultaneously. The complete wall section included boundary zones is also checked for adequacy under combined axial load and bending in the plane of the wall.

109 During the design process, each wall is drawn in different colors according to the required vertical steel ratio, which allows the user to see which elements need to be resized. Estimate of building materials After all wall elements have been designed, the program reports the required amount of materials, including volume of concrete, weight of longitudinal reinforcement and weight of horizontal reinforcement. The computation of volume of concrete is based on the thickness of the walls, and the dimensions of the panel as well as the size of any boundary element. The computed weight of horizontal reinforcement is based on actual bars but does not include the weight of hooks. The computed weight of vertical reinforcement is based on the required steel ratio rather than on actual bars. It is noticed that in walls with boundary elements the amount of materials may get overestimated. However, the user can make manually the necessary adjustments. If the user generates boundary elements as columns, they are included in the estimate of materials for columns. In the design of walls, these boundary elements are again included in the estimate of materials. In fact, some of theses elements might be included twice: as boundary elements for longitudinal wall portions and as boundary elements for transversal wall portions.

Displaying Design Results The user can display detailed design results for any element just by selecting it with the mouse, after activating the appropriate command. To display beam design results •

Activate the command Results > Design > Beams

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Figure 5.33 Beam design results •

Point-and-click with the left mouse any beam, such as beam A(1-2) floor 2, to display graphically and numerically its design results..

EngSolutions RCB displays the envelopes of negative moment, positive moment, shear force, and torsion from all design load combinations, and prints the required area of steel reinforcement and size and spacing of stirrups at various sections of the member. The program also proposes a distribution of stirrups along the member. (e.g. 13 #3 @ 3” + 27 #3 @ 7” + 13 #3 @ 3”) •

In the Beam design window select the option Reinforcement detail. The program presents a suggested reinforcement detailing for the complete beam

Figure 5.34 Suggested reinforcement detailing

To display column design results • •

Activate the command Results > Design > Columns. Point-and-click with the left mouse button any column such as column A-1 story 1, to display its design results.

EngSolutions RCB displays the load biaxial-bending moments interaction surface for the required longitudinal reinforcement, size of ties and cross-ties, and their required spacing along the length of the member, the area of longitudinal reinforcement, the design load and bending moments for the most critical load combination and the buckling load (smaller buckling load from the two local directions).

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Note:

If for all load combinations the required vertical reinforcement is the minimum steel ratio (0.01), the program reports as the critical load combination the first load combination.

Figure 5.35 Column design results To display shear wall design results • •

Activate the command Results > Design > Walls. Point-and-click with the left mouse button any shear wall, such as wall 6(B-C) story 1, to display graphically and numerically its design results.

EngSolutions RCB prints the required vertical reinforcement on the wall and on the boundary elements, the design load and moment for the most critical load combination, the size and spacing of the horizontal reinforcement which is always distributed in two layers, the design shear force, the concrete shear contribution, the critical load combination for shear, and displays the load-bending moment interaction diagram for the required vertical reinforcement. Note:

1. If for all load cases the required vertical reinforcement in the wall and boundary elements is the minimum steel ratio, EngSolutions RCB reports as the critical load combination the first load combination. 2. The ultimate load Pu and ultimate moment Mu presented in the design results are the corresponding to the complete wall group (wall and boundary elements), i.e. the total axial load Pu = Pb1 + Pub2 + Pw and the total moment Mu = Mw + (Pb1 – Pb2) * L/2. The interaction diagram displayed also corresponds to the group wall and boundary elements. 3. The load combination reported as critical for flexo-compression for the group (wall and boundary elements) might be different from the one that governs the design of boundary elements.

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Seismic Shear Resisted by Shear Walls To determine the fraction of seismic shear resisted by shear walls follow the steps below:

Figure 5.38 Shear wall design results

Activate the command Load > View> Load cases The program shows a lis of load cases. Click at load case EQUAKE X (EQX) to select it. Activate the command Results > Analysis > Wall internal forces In the selection options group, select the Plane wall option. Change the current view for a plan view of floor level 2. Select a shear wall oriented in the direction of the selected earthquake loading. In this case, the active load case is EQX, thus select a transversal shear wall, such as 2(B-C). The Property window shows the shear resisted by the element (V = 455 kip). Repeat the above for shear wall 6(B-C) (V=333) Select load case EQY by clicking the load case title, and repeat the steps above. The values obtained for our example structure, following the above steps, are shown in Table 5.1. Since analysis results in terms of internal forces for earthquake loading are ENVELOPES, which include accidental torsion, the summation of the maximum shears resisted by individual walls is greater than the total applied shear (design base shear). During the analysis, the program applied the seismic load case (for example EQX) without accidental torsion and obtained internal forces for each element. Then the program applied statically the accidental torsion in one direction (shifting the center of mass in +Y), and in those elements where the internal force increased the value of the internal force was updated. In those elements where torsion resulted favorable, the value

113 of the internal force was not updated. Next the program applied accidental torsion in the other direction (i.e. shifting the center of mass in –Y) and followed the same procedure described above to update internal forces in elements.

TABLE 5.1 Base shear wal resisted by shear walls. Total base shears: Vy = 579 kip, Vx = 731 kip Earthquake in Y, EQY Wall Shear Force (kip)

Earthquake in X, EQX Wall Shear Force (kip)

B(2-3) B(5-6) B’(2-3) B’(5-6) C(2-3) C(5-6)

2(B-C) 6(B-C)

99.4 99.7 90.2 90.2 108.0 108.4

455 333

Σ 788 kip

Σ 596 kip

Despite the effect of accidental torsion, it is clear that most of the base shear is resisted by the shear walls. This behavior is typical of frame/shear wall models in which shear walls are assumed perfectly fixed at the base. The above is the most common support hypothesis (and it is the one implied on most building codes). If the structure had been modeled as supported on footings on elastic foundations, the distribution of the base shear would have been different. In fact, a very small wall rotation (wall rocking) is usually enough to release the walls and make the frames increase their share of the seismic load.

Design Check for Dual System In the earthquake loading definition, the structural system was considered to be a dual system and appropriate values of the Response modification coefficient and Deflection amplification factor were used. Accordingly, shear walls and moment resisting frames were designed to resist earthquake loading lateral forces in proportion to their rigidities considering interaction between shear walls and frames on all levels. Now to comply with the requirements for dual systems, the capability of the frames to resist 25% of the prescribed seismic forces must be verified, and if necessary, their design must be adjusted to guaranty this requirement. Such verification can be accomplished easily as follows: Save the current model. in the Elements toolbar. Activate the Wall edition command Change the current view for a 3D view with all elements visible. In the selection options group, in the Edit walls window, click the mini-button All walls to select all shear walls in the model.

114 In the Property window change the structural system for all walls to Gravity only. Click the Assign button to apply the new property. Save the model with a different name using the command File > Save As. With the above steps, shear walls are no longer part of the seismic force resisting system. Activate the command LoadComb > Individual load cases. The program creates a set of load combinations corresponding to individual load cases. Starting from those combinations, edit the load coefficients, creating load combinations that include 0.25 EQ, consistent with the design code. If necessary, add new load combinations. For instance, for ACI-318-05 the load combinations are the ones shown in Figure 5.39.

Figure 5.39 Design load combinations for checking frames in dual systems Run the analysis. Design columns and walls. Designing beams and columns for the above (0.25EQ) load combinations, results in minimum steel ratios for practically all elements, proving that without any additional reinforcement, frames are capable of resisting 25% of the prescribed seismic forces. In the case that for any element the required steel ratio at any section was larger than that determined from the original interactive wall-frame design, a manual record should be made so that final specified reinforcement is not smaller than that computed in this design check.

Cost of the Structure The cost of structural elements —beams, columns and shear walls— can be estimated from the estimate of building materials made by the program as follows.

115 Let: Cc = Cost of 1 yd3 of concrete + cost of labor and formwork for its placement. For instance: US$ 140.00 (4000 psi) + US$ 120.00 = US$ 260.00 Cs =

Cost of 1Lb of steel reinforcement. For instance US$ 0.50 (60,000 psi)

The cost of beams can be estimated as follows: Cbeams = 1.1 Vc Cc + 1.05 Wstirrups Cs + 1.2 Wlongitudinal Cs The equation above includes the following factors: a 1.1 factor for volume of concrete Vc, to account for losses (10%); a 1.05 factor for weight of stirrups Westribos to account for losses (5%); and a 1.2 factor for longitudinal reinforcement Wlongitudinal to account for hooks and splices (15%) and losses (5%). EngSolutions RCB includes the weight of hooks in Wstirrups. The cost of columns can be estimated as follows: Ccolumns = 1.1 Vc Cc + 1.05 Wstirrups Cs + 1.1 Wlongitudinal Cs The equation above includes the following factors: a 1.1 factor for volume of concrete Vc, to account for losses (10%); a 1.05 factor for weight of stirrups Wstirrups, to account for losses (5%); and a 1.1 factor for weight of longitudinal reinforcement Wlongitudinal, to account for losses (5%), hooks and splices (5%). EngSolutions RCB includes the weight of hooks and cross-ties in Wstirrups. The cost of shear walls can be estimated as: Cwalls = 1.1 Vc Cc + 1.1 (Wvertical + Whorizontal) Cs A factor equal to 1.1 for volume of concrete is included to account for loses and a 1.1 factor for weight of reinforcement to account for splices, hooks and losses. The cost of structural elements per ff2 of construction is computed as follows: C = (Cvigas + Ccolumnas + Cmuros) / Aconstruccion

TABLE 5.2. Estimate of building materials obtained with EngSolutions RCB

Vigas Columnas Muros

Concrete Volume (Yd3) 433 143 447

Weight Longitudinal Reinforcement (Lb) 41079 21933 13375

Weight Transversal Reinforcement (Lb) 32484 25016 14515

Using the above equations and unit costs: Cc = US $260 / yd3, Cs = US$ 0.50 / Lb; construction area Aconstrution = 51000 ft2, and the amounts of concrete and steel reinforcement computed by the program, the cost of the structure (beams + columns + walls):

116 C = US$ 7.35 /ft2

Modifying the Model In EngSolutions RCB, the engineer can make changes at any time on the structure, such as change element properties, add or remove elements (beams, columns, diagonals, walls, floors), change the coordinates of column axes, change story heights, change loading, etc. The user can also see the influence of each change that he makes, on the analysis and design, with just a few clicks of the mouse. Furthermore, the user can get a good idea of the cost implications of each change, based on the estimate of building materials performed by the program. The engineer may run multiple instances of the program simultaneously to compare alternative solutions. All this flexibility is what makes EngSolutions RCB so attractive to many engineers around the world.

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Chapter 6 Reference Earthquake Records In the time history analysis, EngSolutions RCB can read earthquake records in different formats. The program includes an extensive library of earthquake records. The engineer may add new earthquake to the library in several formats. The first step for adding new records is to edit the text file EQLIst.txt, which is a listing of all the earthquake records, adding the information for the new record. This file is located in folder EQUAKES. Second, a copy of the files containing the actual records is placed in this folder. The data to be added to the EQList.txt text file include: name and date of the earthquake, station identification, Magnitude, epicentral distance, soil type, orientation for each of the three components of ground motion (major horizontal, minor horizontal, vertical), peak ground accelerations for each component and file name. This data can be obtained from the heading of each file. The fields for each of the above data in file EQList.txt, is easily deduced, based on the data already included in the file. The records can be inserted in any location or can be added to the end of the list. The formats accepted buy the program are the following:

1. California Institute of Technology, Caltech Caltech records, such as those included in the SMARTS library, are constant interval records. Each file includes a 25-line text heading, followed by 100 integer data and 100 decimal data, containing general record information. After the above data, the file contains acceleration data, in integer format, in mm/sec2 units. In this format, an independent file for each component is required. File extensions for Caltech format is

118 *.CT1, *.CT2 and *.CT3 for horizontal component with major acceleration, horizontal component with minor acceleration and vertical component respectively. 2. California Strong Motion Instrumentation Program, CSMIP CSMI earthquake records, such as those in the COSMOS library, have a similar structure as those of Caltech, except there is an additional line separating the heading from the acceleration data and that acceleration data is in decimal format, in cm/seg2 units. In this format, an independent file for each component is required. File extensions for CSMIP format is *.CM1, *.CM2 and *.CM3 for horizontal component with major acceleration, horizontal component with minor acceleration and vertical component respectively. 3. Ingeominas – Colombia Ingeominas Earthquake records are constant interval records and include a 12- line heading followed by acceleration data in decimal format, in cm/seg2 units. File extensions for Ingeominas is *.AC1, *.AC2 and *.AC3 for horizontal component with major acceleration, horizontal component with minor acceleration and vertical component respectively. 4. Mexican Strong Motion Database (BMDSF) Records from the Mexican Strong Motion Database are constant interval records and include after the heading acceleration data for the three components. Any record from the database BMDSF Vol 2 Mexican Society for Earthquake Engineering can be added following the procedure below: (a) Using BMDSF Vol 2, search and select the desired records. (b) Change the file extension of the generated files to *.MEX (c) Copy the files to Folder EQUAKES as indicated above (d) Since BMDSF records include data for the tree components on the same file, when editing file EQList.txt, the file name should be repeated three times. In the EngSolutions RCB library the following records from the Michoacan Earthquake of September 19,85, hace already been added (1) Ciudad Universitaria, Mesa Vibratoria, (2) Central Abastos, (3) SCT B-1 Office. Using the above records as a guide, it the engineer may add easily other records from BMDSF. 5. Normalized Format The normalized format is a simple format that only includes acceleration data. The structure of the file is as follows. A one-line heading identifying the record. A second line with the following data: Peak acceleration as a fraction of gravity, time step and earthquake duration. This line is followed by acceleration data (as a fraction of gravity). Each line may include up to 5 acceleration data in decimal format. In this format, a separate file is required for each component. File extensions for normalized format is *.NR1, *.NR2 and *.NR3 for horizontal component with major acceleration, horizontal component with minor acceleration and vertical component respectively.

Differences in Use with RCBE EngSolutions RCB includes numerous features and commands not available in RCBE, its predecessor program. Still, EngSolutions RCB is much easier to use. Users of RCBE can start using EngSolutions RCB without much additional training as the interface of both software packages are similar. The main difference in use between the two programs, is in the edition of elements. While in RCBE different procedures are used to assign properties to members, walls, supports, frames, etc., EngSolutions RCB is more consistent and uses the same

119 procedures for all types of objects that define the building model (columns, walls, slabs, braces, nodes, frames, floors, etc). Additionally, whereas in RCBE there are different commands for properties (such as View properties, Assign properties, Erase properties, etc) and commands to add and remove elements, in EngSolutions RCB all these editing operations are performed within the same command. The procedures for editing elements are described in detail in the Help utility. It is strongly recommended that before using EngSolutions RCB, both new users and RCBE users become familiar with these procedures. As a minimum, it is recommended to review the section on edition of properties of any type of elements ⎯for instance columns⎯as once this section is understood, given the consistency of EngSolutions RCB, the user may easily infer the procedures for other types of objects. It is therefore recommended to activate the Help command, select the topic The Structure, then Edition, and then click the Columns icon

RCBE V5.2 Structures To open structures created with RCBE: • • •



Run RCBE and open the structure. Exit RCBE creating a re-start file of the structure Run EngSolutions RCB. In the first window that pops up there is a list of previously saved structures, and the re-start file of the RCBE structure (C:\RCBE\WORK\RCBUILD.E). To activate this list, select the option Open Existing Structure and in the list select the file corresponding to the RCBE file. If for some reason the re-start file of the RCBE structure is not shown in the list, use the Open command in the File menu of EngSolutions RCB. In the Open file window, change the default file type to (*.e). Then locate the RCBUILD.E file in the working folder of RCBE (C:\RCBE\WORK) and open it. Structures processed with RCBE must be re-analyzed and designed with EngSolutions RCB as the RCBE results are not compatible with EngSolutions RCB.

Rotating the Structure In EngSolutions RCB, 3D can be viewed from any angle in a tridimensional space. The rotation window includes three mouse-selectable points, shown in Figure 6.6, that allow to rotate the structure, modifying the location of the view point or viewingeye. The location of the view point with respect to the center of the structure can be defined in polar coordinates by two angles and a relative distance. The angles are a horizontal angle in the X-Y plane, and a vertical angle defining the inclination, with the horizontal, of the viewing vector. • The red point represents the view point and enables to get closer or farther from the structure. • The yellow point enables to change the inclination or vertical angle with the horizontal. • The gray point enables to change the horizontal angle around the vertical axis.

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Figure 6.1 Elements in rotation window

To rotate the building structure • Point-and-click at the point whose action is going to be activated, using the left mouse button. The point, viewing vector and its projection on a horizontal plane, are highlighted in red. • Move the mouse to drag the selected point in the direction desired. If the red point is activated, move the mouse along the viewing vector to increase or decrease the relative distance between the view point and the center of the structure. If the yellow point is activated, move the mouse vertically, up or down, to change the selected inclination of the viewing vector. If the gray button is activated, move the mouse in a circular pattern to change the horizontal angle. • Click again the mouse button to complete the rotation operation.

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Wall Element Output General This section describes the types of analysis output for wall elements and the sign conventions used to report output in EngSolutions RCB. The output is referred to the local element coordinate system. Graphical output is reported as wall stresses, stress resultants, and total wall internal forces. Local Coordinate System The output stresses, stress resultants and total internal forces of wall elements (as well as stiffness matrix and load vectors) are all referred to an orthogonal local coordinate system. This local coordinate system is determined by the four nodes i, j, k, l, that define the element, as shown in Figure 1. The local axis 1 goes from node i to node j. The local axis 2 goes from node i to node l. The local axis 3 is defined by the cross product of local axes 1 and 2. The above definition applies to the particular case of rectangular wall elements.

Figure 1. Local coordinate system For a general non-rectangular wall element, the local axes are defined similarly as follows. The local axis 1 goes from node i to node j. The local axis 3 is formed as the cross product between the local 1-axis already defined and a vector that goes from node i to node k. The local axis 2 is defined by the cross product of axis 3 by axis 1. EngSolutions RCB requires that the four nodes i, j, k , l defining any wall element be coplanar. Faces of Wall Element The six faces of a wall element are defined as the positive 1 face, negative 1 face, positive 2 face, negative 2 face, positive 3 face and negative 3 face, as shown in Figure 2. The positive 1 face of the element is the face that is perpendicular to the 1-axis of the element and whose outward normal (pointing away from the element) is in the positive 1- axis direction. The negative 1 face of the element is the face that is perpendicular to the 1-axis of the element and whose outward normal (pointing away from the element) is in the negative 1-axis direction. The other faces have similar definitions.

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Figure 2. Wall faces Wall Stresses The basic wall element stresses are identified as normal stresses S11 and S22, shear stress S12, and transverse shear stresses S13 and S23. One might expect that there would also be a S21, but it is always equal to S12, so it is not actually necessary to report S21. Sij stresses (where i can be equal to 1 or 2 and j can be equal to 1, 2, 3) are stresses that occur on face i of an element in direction j. Direction j refers to the local axis direction of the wall element. Thus, normal S11 stresses occur on face 1 of the element (perpendicular to the local 1 axis) and are acting in the direction parallel to the local 1 axis (that is, the stresses act normal to face 1). As another example, shear stresses S12 occur on face 1 of the element (perpendicular to the local 1 axis) and are acting in the direction parallel to the local 2-axis.

Figure 3. Wall stresses on a point in a wall element The sign convention used for stresses in EngSolutions RCB is shown in Figure 3. Positive stresses Sij are those that acting on the positive face i are directed in the negative direction of axis j. Thus, compressive normal stresses are positive and tensile normal stresses are negative. EngSolutions RCB includes different commands to graphically display contours of stresses on walls. The command Result→:Wall stresses→ Mid-plane stresses show contours of stresses on the mid-surface of each wall. The command Result→:Wall stresses→Front face stresses show contours of stresses on the positive 3 face of each wall, and the command Result→:Wall stresses→Back face stresses show contours of stresses on the negative 3 face of each wall. When any of these commands is activated, the program by default shows contours of vertical stresses (S22). However, the command includes a list of options to display all types of stresses (S11, S22, S12, S13, S23). If a wall element is selected when any of these commands is active, the program displays the local coordinates of the element and the values of stresses at the four nodes of the selected element.

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Stress Resultants In theory of plates stresses are not used as unit of force because stresses vary through the thickness of the plate. Instead, it is preferred to employ a quantity that integrates the effect of the variation through the thickness. Such quantities are known as stress resultants and are defined for the mid-surface of the elements. Stress resultants, like stresses, act throughout the element. They are present on any point on the mid-surface of the element and are reported as forces and moments per unit of in-plane length. The stress resultants are defined as follows. In the equations below, t is the thickness of the element and x3 is the thickness coordinate measured from the mid-surface of the element.

t 2

F11 =



S11 dx3 ≡ In-plane force in direction 1



S22 dx3 ≡ In-plane force in direction 2



S12 dx3 ≡ In-plane shear force



S11 x3 dx3 ≡ Out-of-plane bending moment in 1 (about axis 2)



S22 x3 dx3 ≡ Out-of-plane bending moment in 2 (about axis 1)

t − 2 t 2

F22 =

t − 2 t 2

F12 =

t − 2 t 2

M11 =

t − 2 t 2

M22 =

t − 2 t 2

M12 =



S12 x3 dx3 ≡ Out-of-plane twisting moment



S13 dx3 ≡ Transverse shear force en 1



S23 dx3 ≡ Transverse shear force en 2

t − 2 t 2

V13 =

t − 2 t 2

V23 =

t − 2

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Figure 4. Positive directions for stress resultants. (a) Internal distributed forces: F11, F22, F12, V23, V23. (b) Internal distributed moments M11, M22 and M12. The command Result→:Wall stresses→ Stress Resultants shows contours of stresses resultants on the mid-surface of each wall. When the command is activated, the program by default shows contours of vertical internal force (F22). However, the command includes a list of options to display all types of stress resultants (F11, F22, F12, M11, M22, M12, V13, V23). If a wall element is selected when the command is active, the program displays the local coordinates of the element and the values of stress resultants at the four nodes of the selected element.

Total Internal Forces EngSolutions RCB outputs ⎯for each wall segment⎯ the resultant internal forces at the top and bottom ends of the element, as would be reported for an equivalent column. These total internal forces are referred to the centroidal axis of the segment and include in-plane axial force P, in-plane Moment M, in-plane shear force V, out-of-plane shear Vo, out-of-plane moment Mo, and out-of-plane torque To.

125 Figure 5. Positive directions for total internal forces. (a) In-plane internal forces, P, V, M. (b) Out-of-plane internal forces Vo, Mo, To. When the command Result→:Wall Internal Forces is activated, the default command option is in-plane end force and the default selection option is single segment. If a wall segment is selected, the program shows the resultant in-plane forces P, M, V at the top and at the bottom of the wall segment. If the selection option is changed to Plane Wall, the program outputs the values for the whole plane wall rather than the individual wall segment selected. These are the values reported in the Print command and are also the values used for designing shear walls.

LOAD SCALE EngSolutions RCB provides independent graphic load scales for each and all load types: concentrated load, distributed load, surface load, concentrated moment, and distributed moment. Any of these graphics scales may be changed by the user at any time. To change graphic load scales: •

Click at the Load Scale command window is displayed.



Click and/or hold down the left mouse button at the upward or downward arrow ⎯at the load scale of interest⎯ to increase or decrease the graphic load scale, respectively. The graphic load scale can be also changed by clicking at its numerical value and pressing ENTER after the new entry.

in the Load menu. The Load Scales

Since the numerical value in each load scale box is graphically represented by the unaltered load displayed above ⎯respectively⎯ the numerical values decrease as the graphic load scale increases, and vice-versa. •

Click at the OK button to accept the graphic scales changes made ⎯if any. To avoid any graphic scale changes made and/or exit the Load Scale command click at the Cancel button.

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Estimate of Building Materials Beam elements When beam elements are designed, the program reports, at the end of the design process, the required amount of materials, including volume of concrete, weight of flexural reinforcement and weight of stirrups. The computation of volume of concrete is based on the dimensions of the cross section of the elements and their total length (node-to-node). Thus, there is a small error in the computation, as the volume of the nodes (intersections between longitudinal and transverse beams) is counted twice. The computed weight of stirrups is based on actual bars and includes the weight of hooks. The computed weight of flexural steel is on the other hand theoretical, as it is based on the values of steel ratio computed at eleven design sections. The actual weight of flexural reinforcement is larger because of splices, hooks and the conversion to actual bar sizes. Users of EngSolutions RCB can find a ‘personal corrective factor’ on the first few projects in which the program is used, by comparing the actual weight of flexural reinforcement and the theoretical values. This factor can be used in future projects to make quick approximate estimates of materials. Column elements When column elements are designed, the program reports at the end of the design process, the required amount of materials, including volume of concrete, weight of longitudinal reinforcement and weight of ties and crossties. The computation of volume of concrete is based on the dimensions of the cross section of the columns and their clear length. The computed weight of ties is based on actual bars and includes any cross ties required as well as the weight of hooks. The computed weight of longitudinal steel is theoretical, as it is based on the required steel ratio rather than on actual bars. Wall elements When wall elements are designed, at the end of the design process, the program reports the required amount of materials, including volume of concrete, weight of longitudinal reinforcement and weight of horizontal reinforcement. The computation of volume of concrete is based on the thickness of the walls, and the dimensions of the panel, as well as the size of any boundary element. The computed weight of horizontal reinforcement is based on actual bars but does not include the weight of hooks. The computed weight of vertical reinforcement is based on the required steel ratio rather than on actual bars. It is noticed that in walls with boundary elements the amount of materials is overestimated. However, the user can make the necessary adjustments manually. If the user generates boundary elements as columns, they are included in the estimate of materials for columns. In the design of walls these boundary elements are included again in the estimate of materials. In fact, some of these elements may be include twice. For example, in cases of C-shaped core elevator walls, the corner boundary elements are included twice in the estimate of materials. First, in the design of the ‘web’ wall segment, and second, in the design of the ‘flange’ wall segment. Therefore, the volume of concrete of these boundary elements might be included three times. The actual steel reinforcement that needs to be placed in these boundary elements is the largest of the three computed values (as a column, as a boundary element of the ‘web’ wall segment and as boundary element of the ‘flange’ wall segment).

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References 1. American Concrete Institute, Building Code Requirements for Reinforced Concrete ACI 318-89, Detroit, Michigan, 1989, 1995, 1999, 2002, 2005. 2. American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures, ASCE 7-88, ASCE 7-93, ASCE 7-95, ASCE 7-98, ASCE 7-05, New York, 1990, 1994, 1996, 1999, 2005. 3. Aminpour M., NASA Contractor Report 4282, Direct Formulation of a 4-Node Hybrid Shell Element With Rotational Degrees of Freedom, 1990. 4. Applied Technology Council, Guidelines for Seismic Rehabilitation of Buildings ATC33.03, Redwood City, CA, 1995. 5. Barbosa, R., Structural Analysis of Construction and Alteration of Concrete Buildings, IX Structural Engineering Congress, Mexican Society of Structural Engineers, A.C., Zacatecas, Mexico, 1994. 6. Barbosa, R., Structural Program RCBE For Analysis and Seismic Design of Buildings, IX Latin-American Earthquake Engineering Conference, Santo Domingo, Dominican Republic, 1996. 7. Colombian Earthquake Resistant Building Code, Bogota, Colombia, 1984. 8. Federal Power Commission, Civil Design Handbook – Seismic Design, Mexico D.F., Mexico, 1993. 9. Department of Standards, Codes and Systems, Secretary of Public Construction and Communications, Tentative Provisions for Wind Analysis of Structures, Dominican Republic, 1979. 10.Department of Standards, Codes and Systems, Secretary of Public Construction and Communications, Tentative Provisions for Seismic Analysis of Structures, Dominican Republic, 1979.

128 11. Golub, H. And C. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, Maryland, 1985. 12.Gowens, A.J. Biaxial Bending Simplified, Reinforced Concrete Columns, ACI Publication SP-50, American Concrete Institute, Detroit, Michigan, 1975. 13.International Code Council, International Building Code, 2000, 2003, 2006 14.International Conference of Building Officials, Uniform Building Code, Whittier, California, 1994, 1997. 15.National Standards Institute, Official Chilean Norm 433.Of93 Seismic Design of Buildings, Chile 1993. 16. Ministry of Housing and Construction, Technical Norm E030 Earthquake Resistant Design, Lima, Peru, 2003. 17. Ecuadorian Normalization Institute, Ecuadorian Construction Code – Earthquake Hazard and Minimum Requirements for Earthquake Resistant Design, Ecuador, 2001. 18. Naeim, F., The Seismic Design Handbook, 2nd Edition, Kluwer Academic Publishers, New York, 2001.

19.NEHRP Recommended Provisions for Seismic Regulations for New Buildings, FEMA, Washington, DC, 1995, 1997, 2003.

20.Colombian Norms for Earthquake Resistant Design, NSR-98, AIS, Bogotá, Colombia, 1998. 21. Federal District Construction Code, Mexico D.F., Mexico, 1987, 1993, 2004. 22. Structural Design Requirements – Republic of Panama, Panama 2005. 23.SEAOC Blue Book, Recommended Lateral Force Requirements and Commentary, Structural Engineers Association of California, 1999. 24. Underwood R., “An Iterative Block Lanczos Method for the Solution of Large Sparse Symmetric Eigenproblems,” Report STAN-CS-75-496, Department of Computer Science, Stanford University, Stanfort, California, 1975.

129

Appendix A EngSolutions RCB Applications This section includes selected models from projects in different countries that have been analyzed and designed with the structural software EngSolutions RCB.

1

Ocean Park Towers 1 and 2, Punta Pacifica, Panama, Rep. of Panama – Structural Engineer G.S. Group, Panama, Gonzalo Sosa N. – RC shear walls – postensioned slabs

2

Sky-Loft Tower, San Juan, Puerto Rico - Structural Engineer Jorge Robert & Associates, Puerto Rico Special RC shear walls and Special RC MRF

3

Puentemadero Tower, Medellín, Colombia – Structural Engineer PSI, S.A., Colombia Special RC shear walls and Intermediate RC MRF

4

City Santafe Tower 1, Mexico – Structural Engineer PESA, S.A., Mexico Special RC shear walls and RC MRF

5

Puentepiedra Tower, Medellín, Colombia – Structural Engineer, PSI, S.A., Colombia Special RC shear walls and Intermediate RC MRF

6

Victoria Tower, Obarrio, Panama, Rep. of Panama – Structural Engineer Alan Pinzon, Panama RC shear walls – postensioned slabs

7

Courtyard View Building, Punta Pacifica, Panama, Rep. de Panama – Structural Engineer, MAVEANG, S.A., Panama, Ernesto Ng

8

Kings Landing Parking, San Luis, Missouri – Structural Engineer The Consulting Engineers Group, San Antonio, Texas - Precast concrete building

9

Mercy Hospital Parking Garage – Structural Engineer The Consulting Engineers Group, San Antonio, Texas - Precast concrete building

10

Metropolitan at MidTown Parking, Charlotte, North Carolina – Structural Engineer Carl Walker, Tampa, Florida - Precast concrete building

11

Vitri Tower, Panama, Rep. of Panama – Structural Engineer, Axel Chang, Ph.D., Estructuras Nacionales, S.A., Panama - RC shear walls – postensioned slabs

12

Saint Moritz – Tower 2, Medellin, Colombia – Structural Engineer Carlos Blodek, C.E.B. S.A., Colombia Special RC shear walls and Intermediate RC MRF

13

Montevechio Building, Cali, Colombia – Structural Engineer Solarte & Cia., Ltda., Colombia Special RC shear walls and Special RC MRF

14

Bella Vista Park, Panama, Rep. of Panama – Structural Engineer, Axel Chang, Ph.D., Estructuras Nacionales, S.A., Panama - RC shear walls – postensioned slabs

15

Sabaneta Tower (Hotel), Sabaneta, Ant., Colombia – Structural Engineer Cesar Espinal Consultoria Estructural, Colombia - Special RC shear walls and Intermediate RC MRF

16

17 Fenicia Tower, Cali, Colombia – Structural Engineer Solarte & Cia. S.A., Colombia Special RC shear walls and Special RC MRF

San Marino Tower, Panama, Rep. of Panama – Structural Engineer Alan Pinzón, Panama

18 RC shear walls – postensioned slabs

Reforma & Constituyentes Tower (RJ32), México, DF - Structural Engineer DYS S.C. and Postensa S.A. de C.V., México - Hybrid RC/ SS structure

19

Bahia Obarrio Building, Panama City, Rep. of Panama – Structural Engineer Alan Pinzon

20 RC shear walls – postensioned slabs

21

Bosques del Oeste Building, Cali, Colombia – Structural Engineer Solarte & Cia, S.A., Colombia Special RC shear walls

22

North Point Building – Tower 2, Bogota, Colombia – Structural Engineer England & Duran Ltda, Colombia - Special RC shear walls and Intermediate RC MRF

23

Marquis Building, Cartagena, Colombia – Structural Engineer England & Duran Ltda, Colombia Intermediate RC shear walls and Intermediate RC MRF

24

Cristimar Building, Rodadero, Santa Marta, Colombia – Structural Engineer Manuel Alarcon-Badillo Ordinary RC shear walls and RC MRF

25

Bridge Boca del Rio, Mexico – Structural Engineer, Hector Margain & Assoc., Mexico

26

Montecanelo Tower 1, Medellín, Colombia – Structural Engineer Carlos Blodek, C.E.B. S.A., Colombia Special RC shear walls and Intermediate RC MRF

27

Mirador de Avalon Building, Cali, Colombia – Structural Engineer Solarte & Cia S.A., Colombia Special RC shear walls

28

Colibri Tower, Sabaneta, Ant., Colombia – Structural Engineer Cesar Espinal Consultoria Estructural, Colombia - Special RC shear walls and Intermediate RC MRF

29

Portovita Condominium, Panama, Rep. of Panama – Structural Engineer Fernando Romero & Assoc., Panama - RC shear walls – postensioned slabs

30

Faro Sabaneta, Sabaneta, Ant., Colombia – Structural Engineer Cesar Espinal Consultoria Estructural, Colombia - Special RC shear walls

31

Arena Building, Guayaquil, Ecuador – Structural Engineer Solarte & Cia. S.A., Colombia Special RC shear walls

32

Picasso Tower, México, D.F. – Structural Engineer Postensa, S.A. de C.V., México Special RC shear walls, RC MRF, postensioned two-way joist slabs

33

Tijuana Nueva Tower, Mexico – Structural Engineer Hector Margain & Assoc., Mexico Special RC shear walls and RC MRF

34

Santa Maria Tower 3, Medellin, Colombia - Structural Engineer Carlos Blodek, C.E.B. S.A., Colombia Special RC shear walls and Intermediate RC MRF

35

Vela Tower 10, Mexico – Structural Engineer Hector Margain & Assoc., México RC MRF

36

San Nicolas Towers (3 Twers), Bogotá, Colombia – Structural Engineer Santana Estupiñan, Ltda., Colombia - Special RC shear walls and Intermediate RC MRF

37

Proyecto Lomas, México, D.F., Postensa S.A. de C.V., México Special RC shear walls, RC MRF, postensioned two-way joist slabs

38

Turpial Tower and Sinsonte Tower, Sabaneta, Ant., Colombia - Structural Engineer StructuraCesar Espinal Consultoria Estructural, Colombia - Special RC shear walls and Intermediate RC MRF

39

El Faro del Saber, Cayey, Puerto Rico – Structural Engineer Armando Muns, P.E., Puerto Rico Special RC shear walls and Special RC MRF

40

Rhin 45 Building, México, DF – Structural Engineer Postensa S.A. de C.V. México

41 RC MRF, postensioned two-way joist slabs

Tesa Tower, Bogota, Colombia – Structural Engineer England & Duran Ltda, Colombia

42 Special RC shear walls and Intermediate RC MRF

Balcones de Patio Bonito, Medellitn, Colombia – Structural Engineer Mario Leon Jaramillo, Colombia Special RC shear walls and Intermediate RC MRF

43

Porttower, Cancun, Mexico – Structural Engineer Ingeniería Estructural Burela & Ortiz S.A. de C.V. And Postensa S.A. de C.V. - Special RC shear walls, RC MRF, postensioned two-way joist slabs

44

Gaudi Building, Medellín, Colombia – Structural Engineer Mario León Jaramillo, Colombia Intermediate RC shear walls and Intermediate RC MRF

45

Segovia Plaza Building, Bogota, Colombia – Structural Engineer Guillermo Alonzo Villate & Cia. Ltda Special RC shear walls and Intermediate RC MRF

46

Galilea Tower, Medellin, Colombia – Structural Engineer JAR Ingenieria Diseño Estructural Intermediate RC MRF (7 cross shaped columns - spans 16m x 10 m)

47

Cabo San Lucas, Medellin – Structural Engineer JAR Ingenieria Diseño Estructural Special RC shear walls and Intermediate RC MRF

48

El Rosario Clinic, Medellin, Colombia – Structural Engineer Mario Leon Jaramillo, Colombia Intermediate RC MRF

49

Premium Plaza Shoping Center, Medellin – Structural Engineer Mario Leon Jaramillo, Colombia Intermediate RC shear walls and Intermediate RC MRF

50

Immigration Station Acayucan, Veracruz – Structural Engineer Burela & Ortíz S.A. de C.V., México

51

Textiles KN, Puebla, Mexico – Structural Engineer Burela & Ortíz S.A. de C.V.

52

Arboleda Country 1 and 2, Bogota, Colombia – Structural Engineer Santana Estupiñan, Ltda, Colombia Special RC shear walls and Intermediate RC MRF

53

Chico Virrey Building, Bogota, Colombia – Structural Engineer Santana Estupiñan, Ltda, Colombia Special RC shear walls and Intermediate RC MRF

54

Portal del Prado Shopping Center, Barranquilla, Colombia – Structural Engineer Puccini Theran, Ltda, Colombia - Intermediate RC MRF

55

Bosque Cordoba Building, Bogota, Colombia – Structural Engineer Guillermo Gamboa Special RC shear walls and Intermediate RC MRF

56

Main Library, University CES, Medellin, Colombia – Structural Engineer Mario Leon Jaramillo, Colombia - Intermediate RC MRF

57

Sotara Building, Cali, Colombia – Structural Engineer Solarte & Cia. S.A., Colombia Special RC shear walls and and special steel braces

58

Sport Center Aguila Brewing Co., Barranquilla, Colombia – Structural Engineer Manuel Alarcon-Badillo

59

Auditariom, El Tintal High School, Bogotá, Colombia – Structural Engineer Guillermo Alonzo Villate & Cia. Ltda. Special RC shear walls and Intermediate RC MRF

60

Sabina Park Stadium, Kingston, Jamaica - Stewart Engineering, North Carolina

61

Suba Arena, Bogota – Structural Engineer England & Duran, Ltda, Colombia

62

Lafrancol (French-Colombian Phramaceutical Laboratory) Building B, Cali, Colombia – Structural Engineer Posso Asociados Ltda, Colombia - Special RC MRF

63

Bosques de Quitumbe, Quito, Ecuador – Structural Engineer Solarte & Cia. S.A., Colombia Special RC shear walls

64

Guayanita Building, Caracas, Venezuela – Structural Engineer Solarte & Cia. S.A., Colombia Special RC shear walls

65

Orthodox Chapel, Bosque Real, Huixquilucan, Mexico – Structural Engineer Burela & Ortíz S.A. de C.V. Special moment-resisting-steel-frame system

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