Seismic Design in Canada

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CANADIAN SEISMIC DESIGN OF STEEL STRUCTURES

Canadian Seismic Design of Steel Structures An Organized Overview By: Alfredo Bohl University of British Columbia Department of Civil Engineering March, 2005

Abstract In this report, an overall overview of the seismic design of steel structures in Canada will be given. The design philosophy, general requirements and modeling issues of the main steel seismic force resisting systems are presented; as well as physical testing and design procedures for moment-resisting connections. Special seismic steel framing systems will also be discussed.

Introduction Seismic design provisions established in the codes are constantly being changed and improved, for structures to have a better performance during earthquakes. A lot of research and development of new structural systems is continuously being carried out. However, there are still many aspects of steel seismic design that remain as a challenge.

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ALFREDO BOHL

The new upcoming 2005 Edition of the National Building Code of Canada, as well as the latest 8th. Edition of the Handbook of Steel Construction, contain significant changes compared to their previous editions regarding seismic design. The overview given in this report is based on the provisions contained in these documents. Since this is a very extensive topic, this report is intended to cover the main aspects of steel seismic design for the most common framing systems used in Canada. The first part of the report will be an overview of the seismic design requirements contained in the Handbook of Steel Construction. The clause 27 of the Handbook of Steel Construction covers the specific seismic design requirements for steel structures. In the last edition, new structural systems have been introduced, like the ductile plate walls. The force reduction factors for ductile systems have been increased, but detailing requirements for these systems are now more demanding. In this report, the steel seismic force resisting systems are classified in accordance to their ductility-related force modification factor, and each of these is explained separately. Also, the derivation of the new overstrength-related force modification factor for these systems, contained in the last edition of the National Building Code of Canada, will be presented. The second part of the report will cover the procedures to perform physical tests of beam-to-column moment-resisting connections for seismic applications, which are required when connections that are not prequalified are going to be used in a structure. Also, the design procedure for three types of prequalified connections, which are the most commonly used in Canada, will be presented. These procedures are contained in documents published by the Federal Emergency Management Agency.

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φR ≥ 1.0 D + γ (0.5 L + 1.0 E ) (S16-01, clause 7.2.6(b)(ii))

In the last part of the report, two special seismic steel framing systems are introduced, the special truss moment frame and the friction-damped steel frame.

Where:

Formatted spreadsheets have been developed to perform calculations related to some of the design procedures exposed in this report, including the design of links in eccentrically braced frames, and the design of moment-resisting connections.

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I recommend reading this term project to those who are interested in learning a little more about on how seismic design of steel structures is performed in Canada, and the structural systems that are available.

Load combinations including earthquakes The fundamental safety criteria that must be met in limit states design is the following (CISC 2004: 2-13): Factored resistance ≥ Effect of factored loads For load combinations that include earthquake, the effect of factored loads is the structural effect due to the factored load combinations taken as (CISC 2004: 1-20):

φ: Resistance factor. R: Resistance. D: Dead loads. L: Live loads. E: Live loads due to earthquake. γ: Importance factor, which should not be less than 1.00. However, for structures where it can be demonstrated that collapse will not cause injury or any other serious consequences, it should not be less than 0.80.

New force reduction factors in the 2005 NBCC With the introduction of the new 2005 Edition of the National Building Code of Canada (NBCC), the expression to determine the lateral seismic force at the base of the structure using the quasi-static analysis has been modified significantly. This expression in the upcoming code will be the following (Mitchell 2003: 309):

φR ≥ 1.0 D + γ (1.0 E ) (S16-01, clause 7.2.6(a))

V =

And either one of the following (the first expression is for storage and assembly, the second expression is for all other occupancies):

S (Ta )M v I EW Rd Ro

Where: -

φR ≥ 1.0 D + γ (1.0 L + 1.0 E ) (S16-01, clause 7.2.6(b)(i))

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V: Design shear force. S(Ta): Design spectral response acceleration. Mv: Factor for the higher mode effects on the shear base.

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Comparing this expression with the one in previous codes, the 2005 NBCC recognizes two force modification factors, Rd and Ro. The factor Rd reflects the capability of the structure to dissipate energy through inelastic behavior, this factor corresponds to the R factor used in the previous 1995 edition. The factor Ro accounts for the dependable portion of reserve strength in a structure designed according to the NBCC provisions, it is related to the calibration factor U used in the previous code (Mitchell 2003: 309). The main modification in the determination of the base shear in the new code is that the account of overstrength is considered explicitly. In the previous code, the factor U considered implicitly all the sources of overstrength in the structure, like the actual strength of the material. Instead, the factor Ro takes into account the various sources of overstrength, through the following expression (Mitchell 2003: 310 – 311):

Ro = Rsize Rφ R yield Rsh Rmech Where: -

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IE: Earthquake importance factor of the structure. W: Expected weight of the structure. Rd: Ductility-related force modification factor. Ro: Overstrength-related force modification factor.

Rsize: Factor accounting for overstrength arising from restricted choices of sizes of elements and rounding up of dimensions. Rφ: Factor accounting for overstrength due to the difference between the nominal and factored resistances, equal to 1/φ, where φ is the material resistance factor defined in the CSA standards.

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Ryield: Ratio of the “actual” yield strength to the minimum specified yield strength. Rsh: Factor accounting for overstrength due to development of strain hardening, has larger values for more ductile systems. Rmech: Factor accounting for overstrength arising from for the additional resistance that can be developed before a collapse mechanism forms in the structure. This additional resistance in the structure can only be displayed if it is redundant and if yielding takes place in a sequence instead in all the elements at the same time.

Due to the experience gained in past earthquakes, the Rd factors in steel structures have been increased for ductile and moderately ductile systems in the new 2005 NBCC to 3.5 and 5.0, compared to 3.0 and 4.0 in the previous code. So, the design forces for these systems are now lower; however, the detail requirements to ensure adequate ductility according to these factors are more demanding (Mitchell 2003: 312). The clause 27 of the CISC 8th. Edition of the Handbook of Steel Construction (HSC), developed by the Canadian Institute of Steel Construction (CISC), provides the seismic design requirements for steel structures in Canada. It provides the force reduction factor for several structural systems, corresponding with the provisions in the 2005 NBCC, and gives design and detail requirements to provide ductility consistent with the factors used, in accordance to the Canadian Standards Association (CSA) standard. These minimum requirements have been introduced in this last edition in order to avoid brittle failure and to mobilize energy dissipation properties through the structure (CISC 2004: 2105).

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Steel seismic force resisting systems

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The 2005 NBCC recognizes different types of steel seismic force resisting systems (SFRS), their corresponding Rd and Ro factors, and the design and detail requirements for each of them according to the CSA standard CSA-S16-01 (Mitchell 2003: 313 – 314). In each of these SFRS, there are certain structural elements which are designed to dissipate energy by inelastic deformation; these must be able to sustain various cycles of inelastic loading with a minimum reduction of strength and stiffness. The other elements and connections must respond elastically to loads induced by yielding elements.

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⎛ ∑ C f Rd ∆ f U2 = 1+ ⎜ ⎜ ∑V h f ⎝ Where:

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⎞ ⎟ (S16-01, clause 27.1.8) ⎟ ⎠

U2: Amplification factor that takes into account secondorder effects due to gravity loads, it must not exceed 1.4. Cf: Factored axial force. ∆f: First-order lateral displacement. Vf: Factored shear force. h: Storey height.

Ductile behavior of steel frames Steel frames are classified in three types, depending on their ductility. The more ductile systems have the highest force reduction factors (CISC 2004: 2-105):

In order to ensure that yielding in some elements will occur before others, relative strengths between the dissipating and nondissipating elements must be known, so we must know the probable yield stress. For non-dissipating elements, the minimum yield stress given in the material standard and specifications must be used. In energy dissipating elements, the probable yield stress should be used, being taken as RyFy, where Ry = 1.1. The product RyFy must be at least 385 MPa, and the yield strength Fy should not be less than 350 MPa. Width-thickness limits are calculated using this Fy value (CISC 2004: 2-107). The amplification factor that takes into account the P-delta effects for structural elements in SFRS is calculated differently compared to conventional design:

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Ductile or Type D: These frames are designed so that they can have severe inelastic deformations. They have a force reduction factor between 4.0 and 5.0. Moderately ductile or Type MD: Inelastic deformations are more limited than in type D frames, members are designed to resist greater loads. They have a force reduction factor between 3.0 and 3.5. Limited ductile or Type LD: These are new types of frames introduced in the 8th. Edition of HSC. Inelastic deformations are even more limited and design loads are greater than in type MD frames. They have a force reduction factor of 2.0.

The connections in type D and MD frames must be tested physically to ensure that they satisfy certain deformation criteria under cyclic loads. In type LD frames, physical test are not necessary, and can be detailed as traditional connections. In the following part of this report, we will expose the design and detail requirements for the different types of SFRS

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defined in the CAN/CSA S16-01, classified according to their Rd factors.

SFRS with Rd = 5.0 Ductile SFRS defined in CAN/CSA S16-01 with a force reduction factor of 5.0 are the ductile moment-resisting frames and the ductile plate walls. We will expose the design philosophy and general requirements of these systems according to the CAN/CSA S16-01.

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weakening the beam at the point where the plastic hinges are expected to form. Plastic hinges can also be formed in columns only at the base of the structure for multi-storey buildings, since if they develop at different locations, a storey may have very large inelastic deformations compared to the ones expected in the design. For single storey buildings, this is not a problem and plastic hinges can be formed at the top of the column. In these cases, columns must be class 1 sections.

Ductile moment-resisting frames In ductile moment-resisting frames, the energy dissipating elements are the beams, so they must be able to undergo inelastic response without stability failures. The columns must be stronger than the beams. So, beams must be class 1 sections and columns must be class 2. The failure mode of the different types of class sections are shown in the following table: Class 1 2 3 4

Failure mode Plastic design, permits attainment of the plastic moment and subsequent redistribution of the bending moment (plastic deformation). Compact, permits attainment of the plastic moment but need not allow for subsequent moment redistribution (plastic-elastic deformation). Non-compact, permits attainment of the elastic yield moment (elastic deformation). Slender section, strength of section is governed by local buckling of elements in compression. Table No.1: Failure modes for different class sections Source: Chu 2003: 5.

Figure No.1: Failure mechanisms: (a) desired (b) undesired Source: CISC 2004: 2-108.

The main advantages of this type of system is that they absorb less shear forces due to their flexibility and have high energy dissipation capacity. However, they are subjected to large inter-storey drifts (Schubak 2005: 6-2). At plastic hinge locations, beams must be braced to resist lateral and torsional displacement. It is not necessary to brace the last hinge to be formed which will lead to a failure mechanism. The maximum unbraced length between plastic hinges is: Lcr 17250 + 15500κ = (S16-01, clause 13.7(b)) ry Fy

Beams are designed so that plastic hinges form at a short distance from the columns, without failure of the connections. This is done by strengthening the beams near the columns or by alfredo_bohl_report.doc

Where:

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Lcr: Unbraced length. ry: Radius of gyration about the weak axis. κ: Ratio of the smaller factored moment to larger factored moment at opposite ends of the unbraced length, positive for double curvature and negative for single curvature. Fy: Yield strength.

For plastic analysis, the distribution of moments due to seismic loads may be taken as varying linearly with zero at one end and the plastic moment at the other, in order to determine κ. Formation of plastic hinges in beams induces forces in elements and connections adjacent to them. This force is calculated as 1.1Ry times the nominal resistance of the beam, ZFy, where Z is the plastic modulus of the steel section.

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Columns must be able to resist the accumulated forces due to yielding of elements and gravity loads. In order to assure that the plastic hinges will form in the beams before the columns (except in single-storey buildings), the following equation must be satisfied at each beam-column intersection:

∑M

rc

⎛ d ⎞⎞ ⎛ ' ≥ ∑ ⎜⎜1.1R y M pb + Vh ⎜ x + c ⎟ ⎟⎟ (S16-01, clause 27.2.3.2) 2 ⎠⎠ ⎝ ⎝

Where:

∑M

Non-dissipating elements adjacent to columns must be able to resist forces induce by formation of plastic hinges. This force is calculated as 1.1Ry times the nominal resistance of the column, which is given by:

rc

⎛ Cf ' = 1.18φM pc ⎜1 − ⎜ φC y ⎝

⎞ ⎟ ≤ φM pc (S16-01, clause 27.2.3.2) ⎟ ⎠

Where: -

⎞ ⎟ ≤ M pc (S16-01, clause 27.2.3.1) ⎟ ⎠

-

Where:

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Mpc: Nominal plastic moment resistance of the column. Cf: Axial force resulting from summing Vh acting at the level considered and above. Vh: Shear force acting at the plastic hinge location when 1.1RyMpb is reached at beam hinge location. Mpb: Nominal plastic moment resistance of the beam. φ: Resistance factor, equal to 0.9 for this case. Cy: Axial compression force at yield stress.

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In the case of columns, the maximum unbraced length between plastic hinges is determined the same way as in beams, taking κ = 0. In high seismic areas, the maximum axial load shall be 0.3AFy for all load combinations, because the flexural resistance of the column deteriorates fast when high axial loads are applied, limiting the ductility.

⎛ Cf 1.18M pc ⎜1 − ⎜ φC y ⎝

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ΣMrc’: Sum of column factored flexural resistances at the intersection of beam and column centrelines. x: Distance from the plastic hinge location to the column face, it is determined by physical testing of the joints. Procedures on how to determine this distance for prequalified connections will be exposed later. dc: Depth of column. PAGE 6 OF 50

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The following free-body diagrams help to understand how these calculations are performed:

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elements. If the plastic hinges are expected to form in the beams, the panel zone must resist forces arising from beam moments of: ⎛

∑ ⎜⎜1.1R M ⎝

y

pb

d ⎞⎞ ⎛ + Vh ⎜ x + c ⎟ ⎟⎟ (S16-01, clause 27.2.4.1) 2 ⎠⎠ ⎝

For single-storey buildings, if plastic hinges are expected to form near the top of the columns, the panel zone shall resist forces due to the plastic hinge moments of as 1.1Ry times the nominal resistance of the column. For high seismic areas, the sum of the panel zone depth and width, divided by the thickness, must be less than 90. In this case, the shear resistance of the panel zone is given by: 2 ⎛ 3bc t c ⎞ ⎜ ⎟ (S16-01, clause 27.2.4.2(a)) Vr = 0.55φd c w' Fyc ⎜1 + ⎟ ' d d w c b ⎝ ⎠

Where: Figure No.2: Free-body diagram showing forces necessary for beam and column design Source: CISC 2004: 2-110.

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Special consideration must be taken in column splices having partial-joint-penetration-groove welds if the axial force in the column is tensile, since they are not ductile under tension loads. In this case, splices are designed more conservatively, they must resist twice this tensile force. In relation to the column joint panel zone, limited inelastic deformations are permitted if they are properly detailed. The entire perimeter of doubler plates must be welded to the contiguous

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Vr: Shear resistance. w’: Sum of thickness of column web plus the doubler plates. Fyc: Yield strength of the column. bc: Width of column flange. tc: Thickness of column flange. db: Depth of beam.

If this does not apply, the width-to-thickness limit of the panel zone should satisfy:

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k h = 439 v w Fy

(S16-01, clause 13.4.1.1(a))

Where: -

h: Clear depth of the web between flanges. w: Width of plate. kv: Shear buckling coefficient. In this case, the shear resistance of the panel zone is given

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The beams, columns and joints must be braced. Lateral bracing at joints must be provided at least at one beam flange when the plastic hinges form in the beam, and at both beam flanges when they form near the top of the columns. In case no lateral support can be provided at a certain level, the slenderness ratio of the column shall not exceed 60. Most of the requirements described previously are summarized in the following figure. This figure also shows details for type MD and LD systems, which will be described later:

by: Vr = 0.55φd c w' Fyc (S16-01, clause 27.2.4.2(b))

The beam-to-column joints and connections must be capable to develop an inter-storey drift angle of 0.04 rad under cyclic loading, this has to be demonstrated by physical testing. The strength at the column face must be at least Mpb, or 0.8Mpb when reduced beam sections are used. The factored resistance of the connection must be at least enough to resist gravity loads and shears induced by moments of 1.1RyZFy at the plastic hinge location. As it is mentioned in clause 27, the appendix J of the CAN/CSA S16-01 contain references to documents which show the procedures to perform physical test of connections in momentresisting frames. Except the fact that joints must be capable to develop an inter-storey drift angle of 0.04 rad under cyclic loading, all other requirements described regarding panel zones, joints and connections do not need to be satisfied if these procedures are used. Design requirements for connections contained in some of these documents will be shown later in this report.

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Figure No.3: Summary of design requirements for moment-resisting frames Source: Mitchell 2003: 314.

Modeling moment-resisting frames to perform structural analysis is usually a simple task, using beam elements to represent the longitudinal axis of the beams and columns, while joints are represented as simple points (nodes) where these elements intersect. However, when we have very deep beams and columns, the joints will be very large, and cannot be accurately modeled using nodes. If we have large joints, the deformations in these are smaller than in adjacent beams and columns, and the frame stiffness is increased. Therefore, we need to model the joint in

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these cases (Schubak 2005: 6-4). This can be done by overlapping segments of the beams and columns with rigid elements, as shown in the following figure:

Figure No.5: Failure mechanism of ductile plate walls Source: Mitchell 2003: 311.

Figure No.4: Model of a joint in moment-resisting frames for deep beam and column sections Source: Schubak 2005: 6-4.

Ductile plate walls Plate walls are transversely stiffened vertical plate girders constituting web plates designed to resist lateral loads. Ductile plate walls are framed by columns and beams connected with moment-resisting connections. In this system, the main energy dissipating element is the web plate; framing elements also dissipate energy once the plate has yielded. Plate walls can develop large inelastic deformations by yielding of the web and formation of plastic hinges in the framing elements. The main advantage of this SFRS compared to other systems is their large stiffness, which reduces the displacements and, therefore, the amount of nonstructural damage during an earthquake.

The web plate carries the shear forces by tension fields that develop in the web plates parallel to the direction of the stress principal axis. This tension field and the shear force and bending moment of the storey produce axial forces and moments to the beams and columns. The overall behavior of the plate wall can be modeled by equivalent diagonal braces:

Figure No.6: Plate diagonal tension brace model Source: CISC 2004: 2-91.

When using this model, the area of the equivalent diagonal brace can be estimated by the following expression:

The general requirements for beams, columns, panel zones, joints and connections are the same as in moment-resisting frames; except that columns must always be class 1. Columns splices must develop full flexural resistance of the smaller column section.

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A=

wLSin 2 (2α ) (S16-01, clause 20.2) 2SinθSin 2θ

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1+ Tan 4α =

wL 2 Ac

⎛ 1 h3 ⎞ ⎟⎟ + 1 + wh⎜⎜ ⎝ Ab 360 I c L ⎠

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(S16-01, clause 20.3.1)

Where: -

A: Area of the equivalent diagonal brace. w: Web plate thickness. L: Distance between column centerlines. α: Angle of inclination of the principal stresses measured from the vertical axis, it must be between 38º and 45º. θ: Angle of inclination of the equivalent diagonal brace measured from the vertical axis. Ac: Cross-sectional area of the column. h: Storey height. Ab: Cross-sectional area of the beam. Ic: Moment of inertia of the column.

This model allows to find moments in beams and columns, but not the tension fields. In order to determine these, a more sophisticated model with a series of inclined pin-ended strips can be used to model the plate wall:

Figure No.7: Strip model for a plate wall Source: CISC 2004: 2-92.

However, since there are limitations for the angle of inclination of the principal stress, this model does not work well for tall and short plate walls. In order for yielding to occur first in the web plate, the beams and columns must be stronger. This is the principle for the capacity design of a plate wall. The ultimate loads in the beams and columns are increased by an amplification factor, equal to: B=

Vre ≤ Rd (S16-01, clause 27.8.2.4) Vf

Where: Vre = 0.5R y Fy wLSin 2α (S16-01, clause 27.8.2.4)

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Where: -

B: Overstrength factor for ductile plate walls. Vre: Probable shear resistance at the base of the wall. Vf: Factored lateral seismic force at the base of the column. Rd: Force modification factor.

To calculate the design moments at each storey, the following procedure must be followed: -

Calculate the design moment at the base as BMf, where Mf is the factored seismic moment at the base of the wall. Extend this moment to a length L, but not less than two storeys from the base. Calculate the design moment at the top of the building as B times the moment in the level below the top. Calculate the design moments in the storeys above L, assuming they have a linear variation from the level above L to the top. The design moment at each level does not need to exceed Rd times the moment at that level.

With these moments, we can calculate the axial forces in the columns. This procedure is illustrated in the following figure:

Figure No.8: Capacity design of ductile plate walls Source: CISC 2004: 2-123.

The top and bottom web plates must also be anchored to stiff elements, so that the plates can develop full tension fields. At the top panel, the web plate must be attached to the beam. At the bottom panel, the web must be attached to the substructure, or alternatively, to a very rigid beam. This is to anchor the vertical components of the tension fields. The horizontal components must also be transferred to the substructure. The columns must also be stiffened at the base, so that the plastic hinges form at a distance at least 1.5 the column depth above the base plate. These stiffeners must resist 1.1Ry the nominal flexural resistance of the column or the tensile load in the column, the one that is greater. Most of the requirements described previously are summarized in the following figure. This figure also shows details for type LD systems, which will be described later:

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Figure No.10: Configuration of eccentrically braced frames Source: Schubak 2005: 6-15.

Figure No.9: Summary of design requirements for ductile plate walls Source: Mitchell 2003: 315.

SFRS with Rd = 4.0

The link beams must be class 1. The web must have a uniform depth, have no penetration or any type of reinforcement, except stiffeners. The resistance of the link is given by the lower value between φVp’ and 2φMp’e, which are defined as:

Ductile SFRS defined in CAN/CSA S16-01 with a force reduction factor of 4.0 are the eccentrically braced frames. We will expose the design philosophy and general requirements of this system according to the CAN/CSA S16-01.

Vp '= Vp

⎞ ⎟ ⎟ ⎠

2

⎛ Pf ⎞ ⎟≤Mp M p ' = 1.18M p ⎜1 − ⎜ ⎟ AF y ⎝ ⎠

Ductile eccentrically braced frames

(S16-01, clause 27.7.2)

Where:

In eccentrically braced frames, the energy dissipating elements are the links, which are the beam segments between the brace connections and the beam. The link is designed to fail either in flexure or shear. Therefore, the columns, braces, beam segments outside the link and connections must be stronger than the link itself and behave elastically. These SFRS have the advantage that they combine the ductile behavior of the moment-resisting frames and the stiffness of the concentrically braced frames, which will be described later (Schubak 2005: 6-15). They can have the following configurations:

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⎛ Pf 1− ⎜ ⎜ AF y ⎝

V p = 0.55wdFy M p = ZFy

(S16-01, clause 27.7.2)

Where: -

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Vp: Plastic shear resistance. Pf: Factored axial force in the link (compression or tension).

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A: Gross area of the beam link. Mp: Plastic moment resistance. e: Length of the beam link. w: Web thickness of the beam link. d: Depth of the beam link.

The length of the link should not be less than its depth. In case Pf/(AFy) > 0.15, the length of the link is determined by: ⎛ Pf Aw ⎞⎛ 1.6 M p ⎟⎜ e ≤ ⎜1.15 − 0.5 ⎜ ⎟⎜ V V A p f ⎝ ⎠⎝ 1.6 M p Vf A ; if w < 0.3 e≤ Vp A Pf

⎞ Aw Vf ⎟; if ≥ 0.3 ⎟ A Pf ⎠

Figure No.11: Forces acting on the beam link Source: Schubak 2005: 6-16.

Short links have a better performance than long links, due to the following reasons: (S16-01, clause 27.7.3)

-

Where: Aw = w(d − 2t ) (S16-01, clause 27.7.3) Where: -

Vf: Factored shear force. Aw: Area of web.

Short links (e < 1.6Mp/Vp): Yield in shear. Long links (e > 2.6Mp/Vp): Yield in flexure. Intermediate links: Yield in both shear and flexure.

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The shear force is constant along the length of the link, so shear strains are uniformly distributed, meaning there are no local strains. All the link contributes to dissipate energy, not only the ends.

The maximum allowed rotation of the link depends on the behavior of the link. This rotation is calculated given the drift of the frame. The drift of the frame is obtained multiplying the drift from the analysis by Rd, to get the maximum inelastic deformation expected in a severe earthquake. The link rotation limits are the following: -

The behavior of the link is related to its length (Schubak 2005: 6-16): -

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0.09 rad for shear yielding. 0.03 rad for flexure yielding. Use linear interpolation to obtain the limits when 1.6Mp/Vp < e < 2.6Mp/Vp.

The relations between the drift and the link rotation are given in the following figure:

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If 1.6Mp/Vp < e < 2.6Mp/Vp, the stiffeners must be placed at 1.5bf from each end of the beam link, and intermediate links are placed according to the spacing criteria previously explained. If e ≥ 5Mp/Vp, the link does not require intermediate stiffeners.

Links with a depth of less than 650mm only need intermediate stiffeners at one side. These must have a width of at least 0.5(bf – 2w), where bf is the width of the flange; and a thickness not less than w or 10mm, take the larger. Figure No.12: Relations between drift and link rotation Source: Schubak 2005: 6-16.

The link must have full-depth web stiffeners at both ends of it, in order to clearly define the length of the link, transfer shear forces over the whole depth, and prevent buckling at the plastic hinges. Both stiffeners must have a combined width of at least (bf – 2w), where bf is the width of the flange; and a thickness not less than 0.75w or 10mm, taking the larger. Both ends of the link must also be braced at both flanges.

If the link is directly connected to the column, the link beam-to-column connection must be able to develop anticipated plastic deformation. In this case, physical test are required to show that the connection is able to develop a rotation of 1.2 times the rotation obtained by multiplying the drifts by Ry. The same standard procedures for physical tests mentioned previously apply for this. However, this requirement may be avoided if all of the following conditions are satisfied: -

Full-depth intermediate stiffeners are also required to make sure that the link will have a ductile behavior. The spacing between them is determined in the following way: -

-

If e < 1.6Mp/Vp, the maximum spacing is (30w – 0.2d) if the rotation of the link is 0.09 rad, and (52w – 0.2d) if the rotation of the link is 0.03 rad or less. Spacing for intermediate angles is obtained by interpolation. If 2.6Mp/Vp < e < 5Mp/Vp, the stiffeners must be placed at 1.5bf from each end of the beam link.

alfredo_bohl_report.doc

-

The link is separated from the column at a short distance, and the beam in this distance is reinforced so that the connection behaves elastically. If e < 1.6Mp/Vp. Full-depth stiffeners are provided at the end of the reinforced location.

As we mentioned previously, the portion of the beam outside the link must behave elastically. The link inelastic straining will induce forces to the beam. So, the beam outside the link is designed for a larger force than the link. This force is equal to 1.3Ry the nominal strength of the link, and the factored resistance

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is equal to the link factored resistance multiplied by Ry/φ. Lateral bracing also needs to be provided at both flanges. If a plastic hinge is expected to form at the link end, then the maximum unbraced length is given by:

ALFREDO BOHL

column, where hs is the storey height. At the base of the top columns, this factor is 0.5/hs. Most of the requirements described previously are summarized in the following figure:

Lcr 25000 + 15000κ = (S16-01, clause 13.7(a)) ry Fy Where: -

Lcr: Unbraced length. ry: Radius of gyration about the weak axis. κ: Ratio of the smaller factored moment to larger factored moment at opposite ends of the unbraced length, positive for double curvature and negative for single curvature. Fy: Yield strength.

The diagonal braces of the frame, although are expected to behave elastically, must be class 1 or 2, since they can carry more load than expected. Sometimes, the brace and link are connected with moment-resisting connections, so that the brace can take some of the loads produce by the straining of the link, and this way, relief the segments of the beam outside the link. Also, the brace-tobeam connection must not extend into the link. The columns and their splices must be designed for secondary moment effects due to the frame drift, and to resist forces due to yielding of the links. Forces due to yielding in the columns are equal to 1.15Ry times the nominal strength of the beam; in the case of multi-storey buildings, this force is taken as 1.3Ry for the top two storeys. The column splices must resist shear forces equal to 0.3/hs times the nominal flexural resistance of the

alfredo_bohl_report.doc

Figure No.13: Summary of design requirements for eccentrically braced frames Source: Mitchell 2003: 315.

When modeling eccentrically braced frames, the difficulties arise when we have to model the link. The other elements of the frame can be represented by beam elements. The model we use for the link will depend on its behavior. To model a link which fails in flexure is not a problem, we just have to place plastic hinges at the ends of the link. However, when the link fails in shear, it is difficult to represent it in the model. An approach used in pushover analysis is to replace the link’s plastic moment Mp with an equivalent moment that corresponds to the shear force at which the link reaches its yield point in shear, given by (Schubak 2005: 617): M p = 0.5V p e

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SFRS with Rd = 3.5 Moderately ductile SFRS defined in CAN/CSA S16-01 with a force reduction factor of 3.5 are the moderately ductile moment-resisting frames. We will expose the design philosophy and general requirements of this system according to the CAN/CSA S16-01.

Moderately ductile moment-resisting frames In moderately ductile moment-resisting frames, as in ductile moment-resisting frames, the energy dissipating elements are the beams, so they must be able to undergo inelastic response without stability failures. This type of SFRS can develop a moderately amount of inelastic deformation by formation of plastic hinges in the beams at a short distance from the columns. Since the elements for this type of frames are designed to resist higher forces, they will have larger sections, and most of the general requirements are the same as for the ductile momentresisting frames. However, a few of these requirements are different, and are explained in the preceding paragraphs. The beams must be class 1 or 2 sections. The maximum unbraced length between plastic hinges for beams and columns is given in this case by the same expression used to determine the maximum unbraced length of the portion of the beam outside the link for eccentrically braced frames, repeated here for convenience: Lcr 25000 + 15000κ = (S16-01, clause 13.7(a)) ry Fy

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ALFREDO BOHL

For plastic analysis, the distribution for seismic loads may be taken as varying linearly with zero at one end and the plastic moment at the other, in order to determine κ. Also for the columns, in high seismic areas, the maximum axial load shall be 0.5AFy for all load combinations, because the flexural resistance of the column deteriorates fast when high axial loads are applied, limiting the ductility. The beam-to-column joints and connections must be capable to develop an inter-storey drift angle of 0.03 rad under cyclic loading, this has to be demonstrated by physical testing. Except the fact that joints must be capable to develop this interstorey drift angle, all other requirements described regarding panel zones, joints and connections (which are the same as for ductile moment-resisting frames) do not need to be satisfied if the procedures from appendix J of the CAN/CSA S16-01 are used. Some of these requirements are summarized in figure No.3, shown previously. Modeling issues are the same that those for ductile moment-resisting frames.

SFRS with Rd = 3.0 Moderately ductile SFRS defined in CAN/CSA S16-01 with a force reduction factor of 3.0 are the moderately ductile concentrically braced frames. We will expose the design philosophy and general requirements of this system according to the CAN/CSA S16-01.

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Moderately ductile concentrically braced frames In moderately ductile concentrically braced frames, the energy dissipating elements are the diagonal braces, which carry the lateral loads by axial forces and dissipate energy through inelastic straining. Therefore, columns, beams and connections must be stronger than the braces and have an elastic behavior. In this system, the braces intersect the beams at one point. There are three types of bracing configurations accepted by the CAN/CSA S16-01: -

Tension-compression bracing systems. Chevron braced systems. Tension-only bracing systems.

Alternatively, other systems that can respond inelastically without losing their stability are also permitted. Some common configurations are shown in the following figure:

Figure No.14: Common configurations of concentrically braced frames Source: Schubak 2005: 6-7.

Some bracing systems, like K-bracing, are not allowed, because in this type of systems, the tension brace imposes bending to the column, and plastic hinges tends to form in the clear length of the columns, causing instability of the structure.

alfredo_bohl_report.doc

Figure No.15: Non-permitted configuration of concentrically braced frames Source: Schubak 2005: 6-7.

Systems with concentrically braced frames tend to have a soft-storey response, especially in tall buildings, because inelastic demands tend to concentrate in the lower levels, since they are the first ones to be affected by ground motions; and in the upper levels, due to higher mode effects. That is why height restrictions are imposed for buildings with these systems. Because ground motions may occur in any direction, the structural configuration of these frames must be as symmetric as possible. The dimensions of the diagonal braces must be such that the shear resistance in each storey provided by the tension forces developed in these elements is similar for storey shears acting in opposite directions. For this, the ratio between of the sum of the horizontal components of the factored tensile resistances in opposite directions must be between 0.75 to 1.33. For tension-compression bracing systems, the building can have no more than eight storeys. In these, the brace in compression will buckle after certain amount of cycles, due to deterioration of its strength. So, class 2 sections with low slenderness ratios are required for these braces, the maximum value is 200 (Mitchell 2003: 312). Also, its cross-sectional area should be small so that they yield before the other elements of the frame. So, finding an

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optimum section for the compression braces is not possible sometimes, since it is difficult to obtain low areas and low slenderness ratios. This is still a matter of research (Schubak 2005: 6-9).

Figure No.16: Failure mechanism of tension-compression bracing systems Source: Mitchell 2003: 311.

For chevron bracing systems, the building also can have no more than eight storeys. The beams can also respond inelastically in this kind of system, they must be continuous between columns and across braces, and both flanges must be braced at the brace connection. The problem with this kind of bracing system is that when the compression braces buckles, severe bending in the beam from the tension brace occurs. So, the beams must be strong enough to resist yielding and buckling forces from the braces together with gravity loads, without considering the support from the braces.

ALFREDO BOHL

The force induced due to yielding of the tension brace to the beam is equal to AgRyFy, where Ag is the gross area of the brace, and from the compression brace equal to 0.2AgRyFy. When the brace is connected to the beam from above, the compression force is 1.2 times the compressive resistance of the brace, which is equal to Cr/φ, where Cr is the factored compressive resistance which depends on RyFy. In the case of buildings with four storeys or lower, limited inelastic deformations are allowed in the beams, since this does not affect negatively the response of the structure, as long the beams are class 1 and their connections can resist loads due to formation of plastic hinges in the beam. In this case, the tension force induced to the beam is taken as 0.6AgRyFy. The beam-to-column connections must be able to resist gravity forces along with forces induced by the probable nominal flexural resistance of the beam at the brace connection, in case the tension brace force is less than AgRyFy. Brace connections must be laterally braced. For tension-only bracing systems, the building can have no more than four storeys. The energy dissipation capacity in this kind of frames is limited. The braces are connected the beam-tocolumns connections and must be able to carry all the seismic loads, in tension. The columns must be continuous and of constant cross-section, and its splices must have the moment resistance of the cross-section and a shear resistance of 2ZFy/hs. In relation to the diagonal braces of the three bracing systems, because post-buckling resistance of these elements is required to maintain the stability of the structure and they may fracture prematurely, the limit to its slenderness ratio is:

Figure No.17: Failure of chevron concentrically braced frames Source: Schubak 2005: 6-10.

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kL ≤ 200 (S16-01, clause 27.5.3.1) r Where: -

k: Effective length factor that depends on the boundary conditions of the element. L: Length between the points where formation of plastic hinges is expected. r: Radius of gyration.

When kL/r ≤ 100, the width-to-thickness ratio of the braces must not exceed the following limits: -

For rectangular and square HSS: 300 / Fy .

-

For circular HSS: 1000/Fy. For legs of angles and flanges of channels: 145 / Fy .

-

For other elements: Class 1 cross-sections.

When kL/r = 200, the width-to-thickness ratio of the braces must not exceed the following limits: -

For HSS members: Class 1 cross-sections. For legs of angles: 170 / Fy .

-

For other elements: Class 2 cross-sections.

Linear interpolation is used when 100 < kL/r < 200. In low seismic areas, sections may be class 1 or 2; except for HSS sections, that must be class 1.

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ALFREDO BOHL

Regarding the effective length factor, for cross-bracing, it can be taken as 0.4 for in-plane buckling and 0.5 for out-of-plane buckling. For other types of bracing, it can be taken as 0.5 for inplane buckling and 1.0 for out-of-plane buckling. In brace connections, eccentricities between the brace and supporting elements must be minimized. These connections must be able to resist axial loads due to buckling of the compression brace and tensile yielding of the tension brace. So, the factored resistance must be at least AgRyFy in tension and 1.2 the probable compressive resistance in compression. Buckling of the compression brace will redistribute forces along the elements, and they need to be considered to determine the connection resistance. The post-buckling resistance of the braces can be taken as the lower value between 0.2AgRyFy and the probable nominal compressive resistance. Since the magnitude of ground motions is uncertain, a value of Rd = 1 is used for this calculation. However, the tensile force in the brace does not need to be greater than combined effect of gravity loads and seismic loads corresponding to Rd = 1; this tensile force should be resisted by the net section, and the resistance of it may be multiplied by a factor of Ry/φ. The brace connections must also be detailed to have a ductile rotational performance if high inelastic response is expected, in or out of the plane of the frame, depending on the governing effective slenderness ratio. When plastic hinges are expected to form in the braces, the factored flexural resistance of the brace connection must be at least 1.1ZRyFy, this resistance may also be multiplied by a factor of Ry/φ.

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If plastic hinges are allowed to be formed in beams in chevron braced systems, the tensile force in the connection can be reduced. In this case, it can be taken as the maximum value between the tensile force due to yielding of the beam or 1.2 the probable compressive resistance of the brace. The beams, columns, and connections excepting brace connections, must be able to resist loads due to yielding of the braces and redistribution of forces due to buckling. The columns and their splices must be designed for secondary moment effects due to the frame drift. Columns in multi-storey buildings, including those that do not form part of the SFRS, must be continuous and have a constant cross-sectional area over a minimum of two storeys, except for tension-only bracing systems, to prevent soft-storey response. Class 4 sections are not allowed for columns, and columns in brace bays must be class 1 or 2, because they play a major role in resisting lateral loads and are subjected to large axial forces during an earthquake. Columns in brace bays must be designed for a flexural resistance of 0.2ZFy, and considering single curvature (κ = -1). The columns splices must have a shear resistance equal to 0.4/hs times the nominal flexural resistance of the columns. Most of the requirements described previously are summarized in the following figure. This figure also shows details for type LD systems, which will be described later:

Figure No.18: Summary of design requirements for concentrically braced frames Source: Mitchell 2003: 315.

Modeling concentrically braced frames is fairly simple, using beam elements to represent the longitudinal axis of the beams, columns and braces. We must just take into account that the braces in compression are expected to buckle. If we use a linear model, these braces must be omitted or have a limited carrying capacity corresponding to post-yielding. If we use a nonlinear model, the elements that represent the compression braces should reflect their hysteretic behavior (Schubak 2005: 6-11).

SFRS with Rd = 2.0 Limited ductile SFRS defined in CAN/CSA S16-01 with a force reduction factor of 2.0 are the moment-resisting frames with

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limited ductility, the limited ductility concentrically braced frames and the limited ductility plate walls. We will expose the design philosophy and general requirements of these systems according to the CAN/CSA S16-01.

Moment-resisting frames with limited ductility In moment-resisting frames with limited ductility, as in ductile and moderately ductile moment-resisting frames, the energy dissipating elements are the beams, so they must be able to undergo inelastic response without stability failures. This type of SFRS can develop a limited amount of inelastic deformation by formation of plastic hinges in the beams at a short distance from the columns. Since the elements for this type of frames are designed to resist higher forces, they will have even larger sections than the moderately ductile moment-resisting frames, and most of the general requirements are the same as for this system. However, a few of these requirements are different, and are explained in the preceding paragraphs. This type of systems cannot be used in high seismic areas and may be used in buildings not exceeding 12 storeys. The beams must be class 1 or 2 sections. Columns must be class 1 and be Ishaped. The beam-to-column joints and connections must have a moment resistance equal to the lower value between 1.1RyMpb, or the effect of combined gravity and seismic loads multiplied by two. The shear resistance of the connection must be enough to resist shears due to gravity loads and due to moments applied at each end equal to the moment resistance of the connection. The

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ALFREDO BOHL

beam flanges are to be directly welded to the columns flanges. Partial-joint-penetration-groove welds and fillet welds must not be used to resist tensile forces in the connections. Alternatively, the beam-to-column joints and connections must be capable to develop an inter-storey drift angle of 0.02 rad under cyclic loading, this has to be demonstrated by physical testing. Some of these requirements are summarized in figure No.3, shown previously. Modeling issues are the same that those for moderately ductile moment-resisting frames.

Limited ductility concentrically braced frames In limited ductility concentrically braced frames, as in moderately ductile concentrically braced frames, the energy dissipating elements are the diagonal braces, which carry the lateral loads by axial forces and dissipate energy through inelastic straining. Since the elements for this type of frames are designed to resist higher forces, they will have larger sections than the moderately ductile concentrically braced frames, and most of the general requirements are the same as for this system. However, a few of these requirements are different, and are explained in the preceding paragraphs. For both tension-compression and chevron bracing systems, the maximum height is 12 storeys. This is because, since the sections are bigger, the frames have a greater lateral resistance,

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and it is more unlikely that they will have a soft-storey response. For chevron systems, in case they have four storeys or less, the beams do not need to be designed for forces due to buckling and yielding of the braces as long as they are class 1, and as long as the braces and beam-to-column connections can resist the forces due to buckling of the braces. Also, the beam must be able to support gravity loads without considering the support provided by the braces. Tension-only bracing systems cannot have more than eight storeys, and the columns must be continuous and of constant crosssection over a minimum of two storeys. The diagonal braces for this system, in case of single-storey or two-storey buildings, can have a maximum slenderness ratio of 300. Diagonal braces also do not have limits in their width-tothickness ratios if their slenderness ratio is greater than 200, since very little inelastic straining is expected in these cases. In low seismic areas, the braces can be class 2 or less compact, and the width-to-thickness ratio of the legs of the angles should not exceed 170 / Fy . In low seismic areas, ductile rotational behavior of the bracing connections is not required if the slenderness ratio of the braces is greater than 100, and columns splices in columns that do not form part of the SFRS do not need to have shear resistance for loads due to yielding of the braces and redistribution of forces due to buckling. Some of these requirements are summarized in figure No.18, shown previously.

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ALFREDO BOHL

Modeling issues are the same that those for moderately ductile moment-resisting frames.

Limited ductility plate walls In limited ductility plate walls, the energy dissipating element is the web plate; not the framing elements as in ductile plate walls. The web plate dissipates a limited amount of energy by yielding. Since the elements for this type of systems are designed to resist higher forces, they will have even larger sections than the ductile plate walls. Plate webs must still satisfy minimum requirements, and must have a factored shear and flexural resistance greater or equal to the corresponding factored loads. Because the beams and columns are not expected to yield, they do not have any special requirements. Also, there is no need for moment-resisting connections, and these can be designed conventionally. Buildings with this type of system cannot exceed 12 storeys. Some of these requirements are summarized in figure No.9, shown previously. Modeling issues are the same that those for ductile plate walls.

SFRS with Rd < 2.0 SFRS defined in CAN/CSA S16-01 with a force reduction factor lower than 2.0 are the cantilever column structures and conventional construction. It is the first time that the CAN/CSA S16-01 considers requirements for these types of systems.

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Cantilever column structures This type of structures consists of beam-column systems with little redundancy, which is fixed at the base and free at the upper end. They are assigned an Rd = 1; except when the elements have class 1 cross-sections, an Rd = 1.5 is assigned in this case. As general requirements, the base connections must resist a moment of 1.1Ry times the nominal flexural resistance of the column. The amplification factor that takes into account P-delta effects should not be greater than 1.25.

Conventional construction This type of structures can dissipate some energy through yielding and friction, available if conventional construction requirements are satisfied. They are assigned an Rd = 1.5. As general requirements, the SFRS of these structures must have ductile failure modes or be designed for greater loads in high seismic areas; these design loads are equal to the combined effects of gravity and seismic loads multiplied by two in very high seismic areas, and by 1.5 in other cases. The elements and connections must have factored resistances corresponding to the factored load effects, but design loads for connections can be limited to Ry times the nominal strength of the joined elements. Connections for moment resisting-frames or braced frames should be used.

Deduction of the Ro factors for SFRS We have covered so far the main aspects related to the ductility-related force modification factor, Rd. We will now expose briefly the most relevant aspects of the overstrength-related force

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ALFREDO BOHL

modification factor, Ro. As we mentioned previously, the new NBCC takes into account in a more explicit way the overstrength in structures, by identifying the sources of it and assigning factors that consider each of these sources. The product of all these factors is the Ro factor. We will explain how these factors have been derived for the SFRS described (Mitchell 2003: 314 – 316). The Rsize factor accounts for overstrength arising from restricted choices of sizes of elements and rounding up of dimensions. It is taken as 1.05 for steel structural shapes. For web plates, it is taken as 1.10 considering that its thickness is rounded up to the next plate thickness available. The Rφ factor accounts for overstrength due to the difference between the nominal and factored resistances, equal to 1/φ. Since φ is equal to 0.9 for ductile failure in steel structures, this factor is equal to 1.11. The Ryield factor is the ratio of the “actual” yield strength to the minimum specified yield strength. It is taken as 1.10, which is the mean ratio of the actual and minimum specified yield strength for W shapes. The Rsh factor accounts for overstrength due to development of strain hardening. It depends on the yielding and the level of inelastic deformations. For eccentrically braced frames, it is approximately 1.30 when the link yields in shear and 1.15 when it fails in flexure; it has been considered as 1.15 to be more conservative. For plastic hinges in beams, this factor is approximately 1.15, so this is the value assigned for ductile and moderately ductile moment-resisting frames. For moment-resisting frames with limited ductility, this factor is 1.05, since lower inelastic deformations are expected. In tension elements, this factor

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is approximately 1.05; this is the value assigned to concentrically braced frames, because only braces in tension develop strain hardening. For plate walls, the web plates develop strain hardening due to the tension fields; it has been assigned a value of 1.05. The Rmech factor accounts for overstrength arising from for the additional resistance that can be developed before a collapse mechanism forms in the structure. For moment-resisting frames, this factor is greater than 1.00 when plastic hinges form in the columns after the beams, it is taken conservatively as 1.00. Overstrength in concentrically braced frames arises when the compression brace buckles and an additional force is required so that the tension brace yields; but Rmech is taken also conservatively as 1.00, due to deterioration of compressive resistance under cyclic loading. For eccentrically braced frames, the collapse mechanism forms once the link has yielded, so this factor is 1.00. For ductile plate walls, overstrength arises due to the fact that the collapse mechanism occurs once the web plate has first yielded and then the framing system, and because the compression that develops in these elements provides an additional resistance. So, Rmech is taken as 1.10. For limited ductility plate walls, it is taken as 1.05. The values of the Ro factors in the 2005 NBCC for SFRS are summarized in this table:

Table No.2: Summary of Ro factors for SFRS in the 2005 NBCC Source: Mitchell 2003: 316.

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ALFREDO BOHL

Structures with combined SFRS We have exposed the Rd and Ro factors that are used for different types of SFRS. However, when we have structures with combined SFRS, some special considerations need to be taken into account (NBCC 2005 Part 4: 22): -

-

If a particular value of Rd is used, then the corresponding Ro must be used. For combinations of different types of SFRS in the same direction in the same storey, the product RdRo shall be taken as the lowest value of RdRo of all of these. For vertical variations of RdRo, not including penthouses whose weight is less than 10% of the level below, the value of RdRo in a particular direction must be less or equal than the lowest value of RdRo used for the storeys above. If it can be demonstrated by physical testing or analysis that the seismic response of a structure is equivalent to one particular SFRS, then this SFRS qualifies as a good representation of the structural system, and the corresponding Rd and Ro can be used.

Physical tests to evaluate the behavior of connections in moment-resisting frames As we mentioned previously, connections in type D and MD frames must be tested physically to ensure that they satisfy certain deformation criteria under cyclic loads. When performing these tests, the test assemblies must represent the prototype characteristics, and the test loading the deformation magnitude and cyclic nature. These design procedures are specified in the appendix J of the CAN/CSA S16-01, which provides a list of

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references with guidelines. The inelastic cyclic behavior of a connection is a function of the size of the elements, bracing arrangements, and welding details and procedures. The Federal Emergency Management Agency (FEMA) conducted a project in which they tested several types of momentresisting connections after the Nortridge earthquake, in order to investigate their performance. This project ended with the publication of four engineering practice guidelines documents (FEMA 2000 a, b, c, d) for design and evaluation of momentresisting frames (CISC 2004: vii). In these documents, they specify prequalified connections that may be used if the prototype connection size and details are similar to those tested. In case these prequalified connections are used and satisfy these conditions, physical tests are not necessary. Some of these prequalified connections will be mentioned later.

Table No.3: Inter-storey drift angle limits for various performance levels Source: FEMA 350 2000: 3-75.

The drift angle capacity is measured according to the following figure:

The procedures that will be described to perform the physical tests are the ones described in the FEMA 350 document, in chapter 3. These tests are for connections that do not form part of those that are prequalified, or for a qualified connection that is used outside its parametric limits.

Figure No.19: Angular rotation of test assembly Source: FEMA 350 2000: 3-75.

Testing procedure For each given combination of beam and column size, tests of at least two specimens must be performed. The results obtained must be able to predict the mean value of the drift angle capacity, θ, of the connection, given the following performance levels:

alfredo_bohl_report.doc

The test specimens must satisfy certain conditions. The size of the beam used in the specimen must be at least the largest depth and heaviest weight used in the structure. The column must represent the expected inelastic action of the column in the real structure for the beam selected, and must provide a flexural strength consistent with the requirements of strong-column-weakbeam connections. Also, the tested column must have a height similar to the real column, so that the drift angles obtained are representative of the real structure.

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In relation to the loading history, it is divided into steps, and the peak deformation at each step j is given by θj, a predetermined value of the drift angle. The number of cycles to be performed at the load step j is denoted as nj. The loading history is shown in the following table: Table No.5: Minimum qualifying total inter-storey drift angle capacities for OMF and SMF systems Source: FEMA 350 2000: 3-77.

In the case that the clear-span-to-depth ratio of the beam in the real steel frame is less than eight, it is expected that it will have larger strains in the flanges, so the drift angle capacities indicated can be increased using the following expressions: 8d ⎛ L − L' ⎞ ⎜1 + ⎟θ SD (FEMA 350, equation 3-70) L ⎝ L ⎠ ⎛ L − L' ⎞ θ 'U = ⎜1 + ⎟θ U (FEMA 350, equation 3-71) L ⎠ ⎝

θ ' SD =

Table No.4: Numerical values of θj and nj Source: FEMA 350 2000: 3-76.

Where:

Acceptance criteria

-

For the connection to have an acceptable performance, the mean value of the drift angle capacity at strength degradation and at connection failure must not be less than the values shown in the following table, for ordinary moment frames (OMF) and special moment frames (SMF):

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θ’SD: Increased qualifying strength degradation drift angle capacity. θSD: Basic qualifying strength degradation drift angle capacity. θ’U: Increased qualifying ultimate drift angle capacity. θU: Basic qualifying ultimate drift angle capacity. L: Distance between the longitudinal axis of the columns. L’: Distance between plastic hinges in the beam. d: Depth of the beam.

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ALFREDO BOHL

These limits in the drift angles capacities where determined after extensive probabilistic evaluations of several structural systems. If these requirements are met, then there is a 90% chance that the frames will be protected against global collapse of the structure, and a 50% chance that local collapse will not occur.

Analytical prediction of structural behavior The connection tests results must be supported with the development of analytical design procedures, so that the same connections with different sizes can be used for design. These analytical models should be able to identify the strength and deformation demands, as well as limit states, of the elements that are part of the connection. Figure No.20: Physical test of a beam-to-column connection Source: Chen, Yeh and Chu 1996: 1295.

Example of a physical test of a beam-to-column connection The following figure shows an example of a full-scale beam-to-column connection assembly used in a physical test. It is a reduced beam section connection, a special moment-resisting connection that will be explained later. The beam section is Htype, with section H600×300×12×20; and the column section is a box type, with section HSS500×500×20×20. In this case, this test was carried to investigate the performance of this connection when it is subjected to a large shear and bending moment. A force is being applied at the end of the beam to simulate this situation. Five different specimens were tested.

Design of moment-resisting connections for seismic applications We have seen how physical tests are conducted to evaluate the performance of moment-resisting connections. Understanding the structural behavior of connections is not easy, since it is affected by several factors, like geometric alterations, hole drilling for bolts, welding, among others. A connection is considered adequate when it has enough rotational capacity, since this affects strongly the energy dissipation capacity of the frame. The connection must be properly detailed in order to achieve this. Some types of connections, which are commonly used in standard practice, do not have enough rotational capacity to withstand strong earthquakes. One of these is the typical welded

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flange-bolted web moment connection, in which the beam is connected to the columns by bolting the beam web to the shear tab of the column plate, and then welding the beam flange to the column plate. This arrangement is shown in the following figure. Its lack of rotational capacity has been demonstrated in a research project held in Taiwan, in which 37 prototypes of this type of connection were tested. Eight of these specimens had a brittle failure (Chen, Yeh and Chu 1996: 1292).

ALFREDO BOHL

publication, which cover most of the practical applications in Canada. These prequalified connections must satisfy certain criteria and size limitations so that they can be used in design, since they must have similar sizes and details to those that were tested to predict their performance. They apply to frames with wide-flange beams and columns subjected to strong axis bending only, and column cross-sections must be within the depth of W360 sections. The three types of connections described in this document are: -

Bolted unstiffened end plate connection. Bolted stiffened end plate connection. Reduced beam section connection.

The general design procedure of these connections is as follows: Figure No.21: Welded flange-bolted web moment connection Source: Chen, Yeh and Chu 1996: 1292.

That is why ductile moment-resisting connections for seismic applications must satisfy more rigorous design and detail requirements. The appendix J of the CAN/CSA S16-01 contains a list of references with guidelines of the design procedures for different types of these connections used in type D and MD frames; that were prequalified by FEMA after they conducted a project in which they tested several prototypes of connections. One of these publications is “Moment Connections for Seismic Applications”, developed by the CISC, which contains design procedures of three types of prequalified beam-to-column momentresisting connections that were provided in the FEMA 350. Prototype testing will not always be possible for new designs, so these connections may be used in these cases. This part of the report will focus on these three connections contained in this CISC

alfredo_bohl_report.doc

-

Identify undesirable brittle failure modes, and the primary and other yielding mechanisms. Determine the probable peak rotational capacity of the primary yielding mechanism. Determine the dimensions of the elements so that they have nominal resistances (φ = 1) against all brittle failure modes at least equal to the probable yield capacity of the primary yielding mechanism, to assure that this mechanism occurs before the others.

When the plastic hinges are expected to form in the beams, the probable plastic moment at the location of the hinge is: M pr = C pr R y Fy Z e

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ALFREDO BOHL

Where: C pr =

Fy + Fu 2 Fy

Z e = bt (d − t ) +

w (d − 2t )2 4

Where: -

Mpr: Probable peak plastic hinge moment. Cpr: Factor that considers effects of strain hardening, additional reinforcement, among others. RyFy: Probable yield stress, where Ry = 1.1. The product RyFy must be at least 385 MPa, and Fy should not be less than 350 MPa. Ze: Effective plastic modulus of the beam. It is equal to the plastic modulus of the beam, Zb, when the section is not reduced. Fu: Specified minimum tensile strength. b: Flange width of the section. t: Flange thickness of the section. d: Depth of the section. w: Web thickness of the section.

Figure No.22: Shear at plastic hinges Source: CISC 2004: 25.

The flexural and shear strength demands at different critical sections can also be determined from equilibrium:

For a wide-flange section, the plastic modulus can be calculated using the expression shown above (Wong 2003: 2). The shear at the plastic hinge location can be determined from static equilibrium of the beam, as it is shown in the following figure: Figure No.23: Strength demands at critical sections Source: CISC 2004: 25.

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We will expose the design philosophy and general requirements of these three connections.

Bolted unstiffened end plate connection (BUEP) The BUEP connection consists of the beam being welded to an end plate, extended above and below the flanges. The beam flange-to-plate joints have complete-penetration-groove welds, and the beam web is connected to the plate with fillet or completejoint-penetration-groove welds. Then, the end plate is bolted to the column using eight bolts. This type of connection can be used for type D, MD and LD frames. The connection is showed in the following figure:

ALFREDO BOHL

type LD frames, panel zone yielding may occur alone. There must not be any significant yielding in the end plate, bolts and welds. The connection must be proportioned to preclude the following failure modes:

Mode 1: Bolt tension This failure mode is avoided by selecting a bolt type that can resist the moment at the column face. The following equation must be satisfied: 0.75 Ab Fu ≥

M cf

2(d1 + d 2 )

Where: -

Ab: Nominal cross-sectional area of one bolt. Fu: Minimum tensile strength of the bolt, equal to 825 MPa for bolts A325M, and 1035 MPa for bolts A490M. Mcf: Moment at the face of the column. d1: Defined in figure No.24. d2: Defined in figure No.24.

Mode 2: Bolt shear This failure mode is avoided satisfying the following equation: Figure No.24: Bolted unstiffened end plate connection Source: CISC 2004: 26.

The basic idea in the design procedure is that yielding in the connection can occur as a combination of beam flexure and panel zone yielding simultaneously, or beam flexure alone. For

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3 Ab (0.5Fu ) ≥ Vcf Where Vcf is the shear at the column face. A comment regarding this empirical formula is that the factor of three in the

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right hand side is part of the test results that were performed to derive it. Given that Ab is the area of only one bolt, this formula seems to be too conservative, considering that this connection has eight bolts.

Mode 4: End plate shear This failure mode is avoided if the end plate has this minimum thickness:

Mode 3: End plate flexure

tp ≥

This failure mode is avoided if the end plate has this minimum thickness: tp ≥

⎧⎪ ⎡bp ⎛ 1 1 ⎞ 2 ⎤ bp 0.8 Fyp ⎨(d b − pt )⎢ ⎜ + ⎟ + (p f − s) ⎥ + ⎜ ⎟ g ⎦⎥ 2 ⎪⎩ ⎣⎢ 2 ⎝ p f s ⎠

s = bp g

⎛ d b 1 ⎞⎫⎪ ⎜ + ⎟⎬ ⎜p ⎟ ⎝ f 2 ⎠⎭⎪

M cf

1.1Fyp b p (d p − t b )

Where:

M cf

Where:

-

dp: Depth of the plate. tb: Beam thickness.

Mode 5 a: Beam flange tension effect on column flange without continuity plates If the column flange thickness satisfies the following equation, proceed to check mode 6. If not, continuity plates or a bigger column cross-section should be used:

Where: -

ALFREDO BOHL

⎛ M cf ⎞ ⎜⎜ ⎟⎟C1 d t − b b ⎠ tc ≥ ⎝ 2 Fyc c

tp: End plate thickness. Fyp: End plate yield strength, taken as 250 MPa. db: Depth of the beam. pt: Defined in figure No.24. bp: Defined in figure No.24. pf: Defined in figure No.24. s: Defined in equation. g: Defined in figure No.24.

Where: C1 =

g − k1 2

Where:

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tc: Column flange thickness. C1: Defined in equation. Fyc: Column yield strength. c: Defined in figure No.24. k1: Distance from centerline of column web to flange toe of fillet, is a property of the section found in the tables of the CISC HSC.

ALFREDO BOHL

Where: -

Yc: Defined in equation. s: Defined in equation. C1: Defined in equation. C2: Defined in equation. bc: Width of column flange.

Mode 5 b: Beam flange tension effect on column flange with continuity plates

Mode 6: Beam flange compression effect on column without continuity plates

If continuity plates are provided and the column flange thickness satisfies the following equation, proceed to check mode 7. This is the minimum thickness that the column flange can have:

If the column web thickness satisfies the following equation, continuity plates or a bigger column cross-section should be used:

M cf

tc ≥

wc <

2(d b − t b ) 0.8 Fyc Yc

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(d b − t b )(6k e + 2t p + t b )Fyc

Where:

Where: 2 ⎞ ⎛c ⎞⎛ 1 ⎛4 Yc = ⎜ + s ⎟⎜⎜ + ⎟⎟ + (C 2 + C1 )⎜ + ⎝c ⎝2 ⎠⎝ C 2 C1 ⎠ g C1 = − k1 2 b −g C2 = c 2 C1C 2 (2bc − 4k1 ) s= C 2 + 2C1

M cf

-

2⎞ ⎟ s⎠

wc: Column web thickness. ke: Is the k-distance of the column section for engineering design, is a property of the section found in the table No.4.1 of this CISC publication.

If continuity plates are provided, they must satisfy the following requirements: -

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For one-sided connections, their thickness must be at least half of the thickness of the beam flanges. For two-sided connections, their thickness must be at least equal to the thickness of the thicker beam flange.

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Usually, it is less expensive to use a bigger column section than to use continuity plates. The arrangement of continuity plates in one-sided connections is shown in the following figure:

ALFREDO BOHL

Where: -

w’: Panel zone thickness. Cy: Defined in equation. Mc: Moment at the centerline of the column. h: Average storey height. db: Distance from one edge of the end plate to the centre of the beam flange at the opposite direction. RycFyc: Probable yield stress of the column. dc: Depth of the column. Se: Effective section modulus of the beam. It is equal to the section modulus of the beam, Sb, when the section is not reduced.

The average storey height is calculated using the heights above and below the connection, except in the following cases: Figure No.25: Continuity plates for one-sided connection Source: CISC 2004: 32.

-

Mode 7: Panel zone shear

-

For one-sided connections, this failure mode is avoided if the panel zone has this minimum thickness: ⎛ h − db ⎞ CyMc ⎜ ⎟ h ⎠ ⎝ w' < 0.9(0.6 R y Fyc d c )(d b − t b )

When the column has a pinned base, it is the sum of the storey height below and half of the storey height above. In top level connections, it is the storey height for pinned base columns, and half of it otherwise.

For two-sided connections, plastic hinges can be formed in both beams. The same expressions apply for this case. If doubler plates are used, then w’ can be taken as the sum of the thicknesses of the column web and the doubler plates. Also, the following equation must be satisfied: d '+b' ≤ 90 w'

Where: Cy =

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Se C pr Z e

Where:

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CANADIAN SEISMIC DESIGN OF STEEL STRUCTURES

d’: Panel zone depth. b’: Panel zone width.

Usually, it is less expensive to use a bigger column section than to use doubler plates. The arrangement of continuity and doubler plates in two-sided connections is shown in the following figure:

ALFREDO BOHL

The minimum span-to-depth ratio, for type D and MD frames, is seven; and for type LD frames is five. Also, the maximum flange thickness of the beam is 19mm, and the maximum bolt diameter is 1½”.

Bolted stiffened end plate connection (BSEP) The BSEP connection consists of the beam being welded to an end plate. The beam flange-to-plate joints have completepenetration-groove welds, and the beam web is connected to the plate with fillet or complete-joint-penetration-groove welds. The end plate extensions at the top and bottom of the beam are stiffened with vertical stiffeners that extend outward from beam flanges. Then, the end plate is bolted to the column using 16 bolts. This type of connection can be used for type D, MD and LD frames. The connection is showed in the following figure:

Figure No.26: Continuity and doubler plates for two-sided connection Source: CISC 2004: 33.

Other restrictive parameters The expected location of the plastic hinge measured from the face of the column, x, is given by: x = tp +

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db 3

Figure No.27: Bolted stiffened end plate connection Source: CISC 2004: 27.

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The basic idea in the design procedure is that yielding in the connection can occur as a combination of beam flexure and panel zone yielding simultaneously, or beam flexure alone. For type LD frames, panel zone yielding may occur alone. There must not be any significant yielding in the end plate, bolts and welds. The connection must be proportioned to preclude the following failure modes:

-

ALFREDO BOHL

ts: Defined in figure No.27. bp: Defined in figure No.27. Tb: Minimum bolt pretension. The minimum bolt pretensions are shown in the following

table:

Mode 1: Bolt tension This failure mode is avoided by selecting a bolt type that can resist the moment at the column face. The following equations must be satisfied: 0.75 Ab Fu ≥ 0.75 Ab Fu ≥

M cf

3.4(d 2 + d 3 ) 3.25 × 10 −6 p f tp

0.895

d bt

1.91

ts

0.591

0.327

Pcf =

0.965

+ Tb

Mode 2: Bolt shear

M cf

6 Ab (0.5Fu ) ≥ Vcf

d b − tb

Where: d2: Defined in figure No.27. d3: Defined in figure No.27. pf: Defined in figure No.27. Pcf: Axial force at the column face. dbt: Diameter of the bolts.

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bp

This failure mode is avoided satisfying the following equation:

Where:

-

Pcf

Table No.6: Minimum bolt pretensions Source: AISC-LRFD 1999: 60.

2.58

A comment regarding this empirical formula is that the factor of six in the right hand side is part of the test results that were performed to derive it, as in the expression to avoid bolt shear for BUEP connections. Given that Ab is the area of only one bolt, this formula seems to be too conservative, considering that this connection has sixteen bolts.

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1

Mode 3: End plate flexure

⎛ A ⎞ 3 C3 α m = Ca ⎜⎜ f ⎟⎟ 1 ⎝ Aw ⎠ (d bt ) 4 g d C3 = − bt − k1 2 4

This failure mode is avoided if the end plate has a minimum thickness of at least the greater of these two values: tp ≥ tp ≥

154 × 10 −6 p f 0.9

0.9

g 0.6 Pcf

0.1

267 × 10 −6 p f d bt t s

0.25

0.15

0.9

Where:

0.7

d bt t s b p 0.7

g 0.15 Pcf

bp

-

0.3

Where g is defined in figure No.27. The column flanges must be at least as thick as the end plate.

-

Mode 4: End plate shear This failure mode is avoided by the effect of the stiffeners, which are proportioned as shown in figure No.27.

Mode 5: Beam flange tension effect on column flange without continuity plates If the column flange thickness satisfies the following equation, proceed to check mode 6. If it is not satisfied and continuity plates are used, proceed to check mode 7: tc ≥

ALFREDO BOHL

α m Pcf C 3

0.9 Fyc (3.5 p b + c )

αm: Defined in equation. C3: Defined in equation. pb: Defined in figure No.27. c: Defined in figure No.27. Ca: Factor equal to 0.128 for bolts A325M and 0.131 for bolts A490M. Af: Flange area. Aw: Web area.

Mode 6: Beam flange compression effect on column without continuity plates If the column web thickness satisfies the following equation, continuity plates or a bigger column cross-section should be used: wc <

M cf

(d b − t b )(6k e + 2t p + t b )Fyc

The requirements for continuity plates are the same as those for BUEP connections.

Where:

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ALFREDO BOHL

Mode 7: Panel zone shear This failure mode is avoided if the same expressions as in BUEP connections are satisfied. In case of using doubler plates, the same requirements also apply.

Other restrictive parameters The expected location of the plastic hinge measured from the face of the column, x, is given by: x = t p + Ls Where Ls is the horizontal length of the stiffener. The minimum span-to-depth ratio, for type D and MD frames, is seven; and for type LD frames is five. Also, the maximum flange thickness of the beam is 25mm, and the maximum bolt diameter is 1½”.

Figure No.28: Reduced beam section connection Source: CISC 2004: 28.

Reduced beam section connection (RBS) The RBS connection is one in which the acting forces are kept within its resistance by reducing the flexural resistance of the beam at a certain distance from the connection, so that yielding and plastic hinging occurs in the beam. The top and bottom beam flanges have circular radius cuts for this purpose. The flanges of the beam are connected to the columns only with complete joint penetration groove welds. A shear tab, that can be bolted or welded, is used for the web connection. This type of connection can be used for type D and MD frames, not type LD frames. The connection is showed in the following figure:

alfredo_bohl_report.doc

Since the beam has been weakened, the frame drifts will be larger. It has been observed that this increase in the drift varies between 7 to 9% for flange reductions of 40 to 50%, respectively. So, if a model with beam elements has been used to analyze the structure, the drifts obtained must be increased by 7 to 9%. The basic idea in the design procedure is that yielding in the connection can occur as a combination of the reduced beam flexure and panel zone yielding simultaneously, or as reduced beam flexure alone. There must not be any significant yielding in the beam-flange-to-column joints and the beam web. The

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connection must be proportioned to preclude the following failure modes:

We then calculate the moment at the face of the column, Mcf, using the scheme shown in figure No.23. The flexural failure is avoided satisfying the following equation:

Mode 1: Connection flexure

M cf ≤ R y Fy Z b

The location, length and depth of the beam flanges reduction is selected between these limits:

Where:

0.50b ≤ a ≤ 0.75b 0.65d ≤ s ≤ 0.85d 0.20b ≤ c ≤ 0.25b

Where: -

a: Defined in figure No.28, usually taken as 0.5b. b: Width of the beam. s: Defined in figure No.28, usually taken as 0.65d. d: Depth of the beam. c: Defined in figure No.28, usually taken as 0.2b.

The width of the reduced beam flange should have a maximum value of 14.6t, where t is the thickness of the flange. Then, the effective plastic modulus of the reduced section of the beam, Ze, must be determined, using:

ALFREDO BOHL

-

RyFy: Probable yield stress, taken as 385 MPa. Zb: Plastic modulus of the gross beam section.

If this equation is not satisfied, the value of c is increased and all previous steps are repeated, taking into consideration that it c must not be greater than 0.25b. Once the final dimensions of the reduced section are determined, we calculate the moment at the face of the column and the moment at the column centerline using these values and the scheme in figure No.23.

Mode 2: Connection shear The shear at the face of the column is determined by the following equation: Vcf =

c = 0.2b be = 0.6b

2M cf L − dc

+ Vg

Where: -

With this, we calculate the probable peak plastic hinge moment, using Cpr = 1.15:

Vcf: Shear at the face of the column. Vg: Shear due to gravity loads, as shown in figure No.22.

M pr = C pr R y Fy Z e

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This shear force is used to design the connection of the beam to the column. If a complete joint penetration groove weld is used, no further calculations are required. If a bolted shear tab is used, the tab and the bolts must be designed to resist this shear force, using a resistance factor of unity (φ = 1). The tab must be connected to the column using complete joint penetration groove welds or full depth fillets.

The requirements for continuity plates are the same as those for BUEP and BSEP connections.

Other restrictive parameters The expected location of the plastic hinge measured from the face of the column, x, is given by:

Mode 3: Panel zone shear

x=a+

This failure mode is avoided if the same expressions as in BUEP and BSEP connections are satisfied. In case of using doubler plates, the same requirements also apply.

Continuity plates If the column flange thickness, in milimetres, is less than the greater of the following two expressions, then continuity plates must be provided to the connection: t c ≤ 0.4 1.8bb t b tc ≤

R yb Fyb R yc Fyc

bb 6

Where: -

bb: Unreduced beam flange width. tb: Beam flange thickness. RybFyb: Probable yield stress of the beam. RycFyc: Probable yield stress of the column.

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ALFREDO BOHL

s 2

The minimum span-to-depth ratio is seven. Also, the maximum flange thickness is 44mm; and the maximum relation be/2t is 7.3, where be is the reduced beam flange width.

Special seismic steel framing systems Up to now, this report has been focused in reviewing the main aspects of seismic design of steel structures for framing systems and connections types that are well-known and are commonly used in the construction industry of Canada. Requirements for these systems are extensively covered in the CISC HSC, FEMA documents, the American Institute of Steel Construction (AISC) publications, among others. However, there are also many non-conventional steel framing systems for seismic applications that are very innovative in their design and they may be implemented in the codes in the next years. New systems are continuously being developed by researchers, since many aspects of seismic steel design still remain as a challenge. The clause 27 of the CAN/CSA S16-01 states that when special steel framing systems are used in structures, their design should be based on published research results, design guidelines,

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ALFREDO BOHL

observed performance in past earthquakes, or special investigation. The level of safety using these systems must be similar to the one that is established in the CAN/CSA S16-01. The last part of this report will be focused in describing two of these special systems. The first one is the special truss moment frame, which provides savings in costs and time of construction compared to conventional systems. The second one is the frictiondamped steel frame. Different types of damping devices have been developed in the past years and are added to the structure to dissipate more energy during an earthquake. We will describe some of these devices.

Special truss moment frames (STMF) The STMF is a specially designed SFRS that reduces the earthquake damage of steel structures. This design was the result of a research that was developed at the University of Michigan. The system is designed in such a way that when it is subjected to earthquake loading, inelastic deformation is moved to some segments of the truss that are specially designed. This truss has several diagonal members in a segment at the midspan designed for this purpose, they absorb most of the energy and dissipate it by yielding. The ductile behavior of this system is similar to that of the eccentrically braced frames, since all the inelastic deformation is taken by the special segment, which acts as the link. After the earthquake, the diagonal members that were damaged can easily be repaired or replaced (USACE: 7-101). A STMF with an X-braced configuration is shown in the following figure:

Figure No.29: Special truss moment frame Source: USACE: 7-103.

This type of system must satisfy certain special design requirements that are described in a document made by the US Army Corps of Engineers (USACE), in chapter 7. These requirements are covered in the preceding paragraphs. These trusses are limited to a span length of 18m and a depth of 8m. The truss elements outside the special segment and the columns are designed elastically. The length of the special segment ranges from 0.1 to 0.5 times the total length of the span. The panels in the special segment should have a length-todepth ratio that ranges from 0.67 to 1.5. They may have a Vierendeel of X-braced configuration, but not a combination of them. In the Vierendeel configuration, a weakened beam with holes in it is used for energy dissipation. If diagonal elements are used in the special segment, they must have an X-pattern arrangement and be interconnected at the points of crossing, and must be separated by vertical elements.

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They must also be made of identical cross-sections. The interconnection nodes of diagonal members must have a design strength enough to resist a force equal to 0.25 times the nominal tensile strength of the member.

Vne =

-

⎞ ⎟ + R y (Pnt + 0.3Pnc )Sinα ⎟ ⎠

Vne: Overall vertical nominal shear strength of the special segment. Ry: Factor defined in clause 27 of the CAN/CSA S16-01, taken as 1.1. Mnc: Nominal flexural strength of the chord element of the special segment. Ls: 0.9 times the length of the special segment. EI: Flexural elastic stiffness of the chord elements of the special segment. L: Span length of the truss. Pnt: Nominal tension strength of the diagonal elements of the special segment. Pnc: Nominal compression strength of the diagonal elements of the special segment. α: Angle of the diagonal elements of the special segment, measured from the horizontal plane.

The width-to-thickness ratio of the elements of the special segment must not exceed the following limits:

Regarding the elements and connections outside the special segment, all of these must have a design strength in order to resist the factored gravity loads, plus the lateral loads necessary to develop the expected overall vertical nominal shear resistance of the special segment, which is given by:

alfredo_bohl_report.doc

Ls

⎛ L − Ls + 0.07 EI ⎜⎜ 3 ⎝ Ls

Where:

The web members in the special segment must not have bolted connections. The chord members must not be spliced within the special segment and within half the panel length measured from the end of the special segment, and must have a constant cross-section. The axial forces in the web diagonal members in the special segment due to factored dead and live loads must not exceed 0.03AgFy, where Ag is the gross area of the member, to limit their strength degradation. When yielding occurs in the system, the special segment must develop its nominal shear resistance, through the nominal flexural strength of the chord elements and the nominal axial tensile and compressive strengths of the diagonal web elements. All these elements are proportioned in such a way that at least 25% of the shear resistance is provided by the chord elements. The required axial strength of the chord elements must not exceed 0.45φAgFy, taking φ = 0.9. The end connections of the diagonal elements in the special segment must have a design strength of at least the nominal tension strength of the web element, given by RyFyAg.

3.4 R y M nc

ALFREDO BOHL

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-

Diagonal web elements: 2.5. Angles: 137 / Fy .

-

Flanges and webs of tee sections in chord elements: 137 / Fy .

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The top and bottom chords of the trusses must be laterally braced at the ends of the special segment. Intermediate braces are also required.

and the Sumitomo friction device. Friction dampers offer the following advantages (UPC: 28 – 29): -

The advantages of the STMF compared to other SFRS are the following (Emerging Construction Technologies):

-

Provides substantial cost and time savings and a better level of performance. Its weight is about 20% less than common framing systems carrying the same gravity loads. Fabrication costs are reduced in about 20% compared to common framing systems. Welded connections can be visually inspected without the need of additional tests.

-

Friction dampers are designed in such a way they have moving parts that will slide over each other during a strong earthquake. Friction is created between these sliding elements, which dissipates energy built up in the structure. There are several types of friction damping devices, like the basic sliding joint, the rotation sliding joint, the dual level joint, the Pall friction device

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They have high energy dissipation capacity. Their behavior is not seriously affected by repeated cycles of displacement. The friction force between surfaces can be controlled, through the prestressing (normal) force. They can absorb a big amount of energy and then dissipate it. They are not affected by fatigue. However, they also have some disadvantages:

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Friction-damped steel frames (FDSF) Damping devices are used in structures to increase their energy dissipation capacity, in order to reduce oscillations, and therefore, the structural and nonstructural damage. There are different types of dampers, like viscous dampers, visco-elastic dampers, Coulomb friction dampers, metallic dampers, among others. We will describe some of the friction dampers used in steel structures.

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Sliding surfaces tend to heat. They do not contribute to dissipate energy of the structure before they start slipping. Changes in the sticking-sliding conditions of the damper may introduce high frequencies to the structural response.

We will describe the main features of these damping devices.

Basic sliding joint (BSJ) The BSJ consists in incorporating slots in the bolt holes between steel plates, so that friction between the surfaces of steel plates dissipates energy. This type of joint is capable of repeated cycles of displacement without losing strength, stability or energy dissipation capacity. Their performance is influenced by three factors (Butterworth 1999: 1 – 2): -

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Maintenance of contact pressure between sliding surfaces.

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Maintenance of an approximately constant coefficient of friction between sliding surfaces. Avoiding brittle failure when the joint reaches the limit of its sliding range.

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In the case shown in figure No.30, since two plates are used, the slip force is 2Nslip. The BSJ is used in concentrically braced frames with diagonal and chevron configuration:

The BSJ is shown in the following figure:

Figure No.31: Applications of the basic sliding joint Source: Butterworth 1999: 2.

Figure No.30: Basic sliding joint Source: Butterworth 1999: 2.

The friction resistance in this device requires a normal force acting at the interface. This force is applied through the bolt placed at the joint. The normal force can be modified by adjusting the tension in the bolt. The slip force between surfaces is determined by: N slip = nN b µ Where: -

Nslip: Slip force. n: Number of bolts. Nb: Tension in one bolt. µ: Coefficient of friction.

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In the diagonal bracing system, the braces require that the compression capacity is greater than the slip load of the SBJ to have and adequate seismic performance. In the chevron bracing system, the braces must be designed for compression, to resist the reversible sliding in the SBJ, but their cross-sections are smaller than in a typical chevron system (Butterworth 1999: 2 – 3).

Rotating sliding joint (RSJ) The RSJ is used in moment-resisting frames. The energy dissipation is achieved by friction between the surfaces of steel plates through a rotational action. It was developed by Tang and Popov (Butterworth 1999: 4). The RSJ is shown in the following figure:

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of the bottom flange, using higher tension at the interface or more bolts. The centre of rotation is closer to the top flange; this is convenient, for example, to avoid damage in concrete floor slabs (Butterworth 1999: 5). The DLJ is shown in the following figure:

Figure No.32: Rotating sliding joint Source: Butterworth 1999: 4.

When the joint is subjected to a moment, it behaves elastically until the beam flange reaches the slip level of the sliding connections. The beam will then start to rotate around the central pivot, shown in figure No.32, until the bolts reach the end of their slots. The maximum moment is given approximately by: M slip = nN b µD Where: -

Mslip: Slip moment. D: Beam depth.

In the case shown in figure No.32, since two friction interfaces are used in both flanges, the slip moment is 2Mslip.

Dual level joint (DLJ) The DLJ is also used in moment-resisting frames, and also dissipates energy by friction between the surfaces of steel plates through a rotational action. However, it differs from the RSJ because it has a dual slip level capacity. This is achieved by making the slip force of the top flange of the beam higher than that alfredo_bohl_report.doc

Figure No.33: Dual level joint Source: Butterworth 1999: 5.

Under the action of an increasing moment, the joint responds elastically until the bottom flange starts to slip once its threshold or slip moment has been reached. This causes plastic rotation around a centre of rotation in the top flange until the bolts in the bottom flange reach the end of the slots. The joint starts rotating elastically again, without any slipping, until the slip moment at the top flange is reached. The top flange then starts slipping, while the bottom flange rotates plastically around a centre of rotation. When the bolts in the top flange reach the end of the 4/6/2005

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slots, the joint rotates elastically again until it reaches the yield point. This dual action has the following advantages in the design: -

The lower threshold level provides sufficient strength for loads arising from the design earthquake. The upper threshold level provides a strength reserve for extreme events. If the bottom flange fails to slip, energy can still be dissipated by the top flange when it reaches its slip moment. If the top flange fails to slip, all the slip will eventually occur in the bottom flange.

The required length of the slots is determined by (Butterworth 1999: 6): L = Dθ + d

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are interconnected by horizontal and vertical link members using bolts. These links assure that when the forces acting on the device, through the braces, are high enough to initiate slip on the tension diagonal, the compression diagonal also slips an equal amount in the opposite direction; resulting in frictional sliding occurring at the interface (Aiken 1993: 11). This device is shown in the following figure:

Figure No.34: Pall friction device Source: Aiken 1993: 12.

The friction resistance in the device requires a normal force acting at the interface. This force is applied through a bolt placed at the intersection of the diagonals, and it can be modified by adjusting the tension in the bolt, as in the BSJ (Aiken 1993: 12). The following figure shows how this friction device works:

Where: -

L: Length of the slot. θ: Inelastic rotation of the joint. d: Bolt diameter.

Pall friction device The Pall friction device is used in concentrically braced frames with cross-bracing configuration. This type of damper was developed by Dr. Avtar Pall during his doctoral studies. It consists of rigid diagonal brace elements, with slotted holes in them, that have a friction interface (friction hinges) at their intersection. They

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Figure No.35: Installation of Pall dampers in cross-bracing systems Source: UPC: 33.

A patented version of this device is now available in the market and has been used in many new and retrofitted buildings in

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Canada (Butterworth 1999: 3). One of the most famous cases is the Concordia University’s Webster Library building in downtown Montreal, which has 150 Pall friction dampers installed. Other buildings that have this damping device are the Casino on lle Ste. Helene in Montreal, and the Space Agency in St. Hubert, Quebec.

Sumitomo friction device The Sumitomo friction device is used in concentrically braced frames with chevron configuration. It consists of a cylindrical steel casing device with friction copper pads, with pieces of granite inside, that slide directly on the inner surface of the case. They are typically installed on the underside of the beams of the frames. This device was designed and developed by Sumitomo Metal Industries, Ltd, Japan; and was originally used for railway cars (Aiken 1993: 4). They have the following configuration:

Figure No.37: Installation of Sumitomo dampers in chevron systems Source: Aiken 1993: 6.

Design procedure for friction-damped steel frames Structures that have dampers installed in them are usually designed using dynamic analysis, time-history analysis or performance based design. There are no standard procedures for the design of dampers in the present codes, so their design is based on results obtained in previous research projects.

Figure No.36: Longitudinal section of the Sumitomo friction device Source: UPC: 38.

The way this type of damper is implemented in steel buildings is shown in the following figure:

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A code design procedure for friction-damped steel frames has been developed and proposed by Yaomin Fu and Sheldon Cherry, and has been published in the Journal of Structural Engineering in 1998. The name of this article is “Simplified Seismic Code Design Procedure for Friction-Damped Steel Frames”. These authors have developed a method to establish a ductility-related force modification factor for friction-damped steel frames. This allows to use the quasi-static analysis approach established in the code to analyze this type of structures, it may be applied to steel structures having any of the friction dampers

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described previously. We will show how the Rd factor is determined using this method. This method was developed by analyzing a single-degreeof-freedom viscous damped system, which has also a friction damper installed in it. This model may represent a storey segment of a friction-damped frame or an equivalent single-degree-offreedom system of a multi-storey building subjected to a ground motion.

Figure No.39: Force-displacement relation of a trilinear system Source: Fu and Cherry 1998: 57.

This system is characterized by three parameters, the added stiffness ratio, the slip ratio and the yield ductility. These parameters are defined as:

Figure No.38: Single-degree-of-freedom model of a friction-damped system Source: Fu and Cherry 1998: 56.

The concept this method is based on is that the friction damper installed in the system will add stiffness to it. Considering an elasto-plastic behavior, when the system is subjected to a ground motion, the total stiffness of the system is the sum of the stiffness of the primary system (system without the friction damper) and the stiffness provided by the damper. When the threshold level of the damper is reached, it starts slipping and stiffness is only provided by the primary linear system. Then, when the system reaches its yield point, it can no longer sustain increasing forces. This type of system is called a trilinear system, its nonlinear behavior is shown in the following figure:

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αa =

Ka Kf

µs =

u max us

µy =

u max uy

Where: -

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αa: Added stiffness ratio. Ka: Added stiffness provided by the friction damper. Kf: Stiffness of the primary system. µs: Slip ratio. umax: Maximum displacement of the system. us: Displacement at which the friction damper starts to slip. µy: Yield ductility. In building codes, the common assumption is that it is equal to the Rd factor.

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uy: Yield displacement.

Rsd =

The friction damper will increase the period and energy dissipation capacity of the primary linear system. The trilinear system is usually analyzed using an equivalent linear system, whose stiffness and viscous damping ratio can be determined from the parameters of the nonlinear system. The equivalent normalized stiffness, normalized energy dissipated and damping ratio of this linear system can be determined by: K eo = α a E do = α a

ξe = ξo +

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ln µ s + 1

µs

+

µs3

+

-

µy

µy3

E do πK eo

Keo: Equivalent normalized stiffness. Edo: Equivalent normalized energy dissipated. ξe: Equivalent viscous damping ratio. ξo: Viscous damping ratio of the primary system, usually equal to 2% for steel structures.

K eo

−3

4

e

The normalized restoring force of a friction-damped system, Rf, is defined as the ratio between the restoring force of the equivalent linear system and the primary system. It can be obtained using the following expression:

⎛α 1 ⎞⎟ R f = Rsd ⎜ a + ⎜µ ⎟ ⎝ s µy ⎠ Recalling the definition of the force reduction factor (ratio between the elastic and design base shear), and using these expressions, the authors arrived to the following expression to determine the Rd factor for steel friction-damped multi-degree-offreedom systems:

The normalized displacement of a friction-damped system is defined as the ratio between the spectral displacement of the equivalent linear system and the primary system. It can be obtained using the following expression:

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o

− Bξ o

Rsd: Normalized displacement of the friction-damped system. B: Constant whose values vary between 18 and 65, leading to the upper and lower bounds of damping reduction factors. The authors have considered a value of 30, to have an average reduction factor.

Where: -

− Bξ e

Where:

ln µ y + 1

(µ s − 1)2 (µ y − 1)2

(1 − e )ξ (1 − e )ξ

Rd =

f e R f (α a , µ s = 1, µ y = 1) = f y R f (α a , µ s ≥ 1, µ y ≥ 1)

Where:

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Conclusions

their flexibility and have high energy dissipation capacity, but their large inter-storey drifts may cause severe P-delta effects and nonstructural damage. On the other hand, ductile plate walls have very large stiffness, but may be more expensive. Also, calculating the tension fields in the plate web and determining the yielding sequence of the plate and the framing system is still a problem, due to the limitations of the strip model. The eccentrically braced frames have a good performance because they combine the ductile behavior of the moment-resisting frames and the stiffness of the concentrically braced frames. However, since all the energy dissipation is restricted to the link, the collapse mechanism forms once this element has yielded; while other SFRS are more redundant. The concentrically braced frames have high stiffness, but cannot be used in tall buildings, since they tend to have a softstorey response due to concentration of inelastic demands in the lower and upper levels. There may be cases in which the optimum solution will be a combination of different SFRS.

An overall overview of the seismic design of steel structures in Canada has been carried out. The design procedures for SFRS, moment-resisting connections, and some special framing systems, which are spread in various documents and publications, have all been organized in this report, to provide a practical tool for structural engineers. Although this is a very extensive topic which is constantly in change, the most important issues about steel seismic design have been presented and discussed.

Physical testing of connections is important to evaluate their performance during earthquakes. Alternatively, prequalified connections may be used for design. However, there may be cases in which it might not be possible to use the prequalified connections, and physical tests are usually very expensive and cannot be afforded by small engineering companies. More research is needed to develop design procedures for various types of connections with different element sections, rather than only wideflange sections.

Each of the SFRS presented have their own advantages and disadvantages, as we have seen, and these must be taken into consideration to decide which of them is more convenient to design a particular building. Here we present a summary of them. Ductile moment-resisting frames absorb less shear forces due to

Finally, it is important to mention that, although the codes give provisions and recommendations for various kinds of systems, they do not contain the answers to all of the structural problems that engineers may encounter. It is necessary to go beyond of what the code says to find more safe and economic solutions. Systems

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fe: Elastic base shear. fy: Design base shear.

So, when designing this type of structures, the structural designer has to specify the added stiffness ratio, the slip ratio and the yield ductility, depending on the desired performance of the structure. Then, the Rd factor can be determined, and the quasistatic analysis may be used to determine the internal forces and displacements. This method was developed while the 1995 NBCC was the current code. Therefore, to be able to adapt this method to the 2005 NBCC, an Ro factor must be assigned to this type of structures. Overstrength in friction-damped structures arises due to the fact that energy is first dissipated by friction, and then by yielding.

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like the special truss moment frame and the friction-damped steel frame are examples of these, and may be implemented in future codes.

Sheng-Jin Chen, C. H. Yeh and J. M. Chu (1996) “Ductile Steel Beam-to-Column Connections for Seismic Resistance”, Journal of Structural Engineering, Vol. 122, No.11: 1292 – 1299.

References

Joe Wong (2003) “Plastic Analysis of Standard Shapes Loaded by Impact”, University of British Columbia.

Canadian Institute of Steel Construction (2004) “Handbook of Steel Construction” (8th. Edition), Quadratone Graphics Ltd, Toronto, Ontario. Denis Mitchell, Robert Tremblay, Erol Karacabeyli, Patrick Paultre, Murat Saatcioglu and Donald L. Anderson (2003) “Seismic Force Modification Factors for the Proposed 2005 Edition of the National Building Code of Canada”, Canadian Journal of Civil Engineering, 30: 308 – 327. Dennis Chu (2003) “Comparative Case Studies of Beam and Column Design: A Comparison of the Canadian and US Standards”, University of British Columbia. Robert Schubak (2005) “CIVL 505: Seismic Response of Structures” (Lecture Notes, Chapter 6), University of British Columbia. Canadian Commission on Building and Fire Codes (2005) “National Building Code of Canada” (Part 4: Structural Design). Canadian Institute of Steel Construction (2004) “Moment Connections for Seismic Applications” (1st. Edition).

American Institute of Steel Construction (1999) “Load and Resistance Factor Design Specification for Structural Steel Buildings”. Web page: www.hnd.usace.army.mil/techinfo/ti/809-04/ch7c.pdf Web page: www.new-technologies.org/ECT/Civil/truframe.htm Web page: www.tdx.cesca.es/TESIS_UPC/ AVAILABLE/TDX1217103-104653/03Chapt02.pdf John W. Butterworth (1999) “Seismic Response of MomentResisting Steel Frames Containing Dual-Level Friction Dissipating Joints”, NZSEE Conference, Rotorua. Ian D. Aiken, Douglas K. Nims, Andrew S. Whittaker and James M. Kelly (1993) “Testing of Passive Energy Dissipation Systems”, Earthquake Spectra, Vol. 9, No.3. Yaomin Fu and Sheldon Cherry (1998) “Simplified Seismic Code Design Procedure for Friction-Damped Steel Frames”, Canadian Journal of Civil Engineering, 26: 55 – 71.

Federal Emergency Management Agency (2000) “Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings” (FEMA 350).

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