Seismic Braced Frames - Design Concepts and Connections

Seismic Braced Frames Design Concepts and Connections

Developed by:

Rafael Sabelli, S.E.

DASSE Design Inc.

July 27, 2006 Chicago, IL

The information presented herein is based on recognized engineering principles and is for general information only. While it is believed to be accurate, this information should not be applied to any specific application without competent professional examination and verification by a licensed professional engineer. Anyone making use of this information assumes all liability arising from such use.

Copyright © 2006

By

The American Institute of Steel Construction, Inc.

All rights reserved. This document or any part thereof must not be reproduced in any form without the

written permission of the publisher.

Seismic Braced Frames

Design Concepts and Connections

Developed by:

Rafael Sabelli, S.E.

DASSE Design Inc.

Seismic Braced Frames:Design Concepts and Connections

Performance, Code Requirements, and Detailing ConceptsBut No Hysteresis Diagrams!

Seismic Braced Frames: Design Concepts and Connections

Outline

I. Seismic DesignII. Behavior of Concentrically Braced FramesIII. Special Concentrically Braced Frames (SCBF)

A. Expected PerformanceB. RequirementsC. Design ExampleD. Gusset Plate Design Tools


Outline

IV. Ordinary Concentrically Braced Frames (OCBF)A. SystemB. RequirementsC. Design Example

V. Buckling-Restrained Braced Frames (BRBF)A. SystemB. RequirementsC. Design Example


Ground Rules

1. 2002 & 2005 editions of AISC Seismic and the AISC Specification are used, with differences pointed out.

2. LRFD is used. 3rd Edition LRFD Manual tools are used.3. 2005 edition of ASCE 7 is used.

New to 2005

Part I:

Seismic Design



When are the Seismic Provisions Required?

Depends on Seismic Design CategoryDepends on Seismic Use Group

Seismic Use Group Depends on OccupancyDepends on Soil TypeDepends on Spectrum

Proximity to FaultsCapacity of FaultSoil Types A-E

Spectrum Determined from USGS MapsSite-Specific Spectrum

Soil Type FSite-Specific Spectrum


Seismic Design (Seismic Use Groups I&II)


Seismic Design (Seismic Use Group III)


Seismic Design

Response SpectrumBased on Maximum Credible Earthquake

Design Base ShearDepends on Building PeriodReduced by Factor “R”

R Depends on SystemReflects System DuctilityIncludes System Overstrength


System Ductility

What is “System Ductility”?Ability of System to Maintain Stability After Yielding/Overload of

Some ElementsAbility of Yielding/Overloaded Elements to Deform

If yielding elements fracture, system may lose stabilityAbility of Nonyielding Elements to Withstand Forces Redistributed by

YieldingWhen an element yields, other elements may receive more load

Ability of Nonyielding Elements to Withstand Deformations Caused by Yielding

System displacements increase after yielding, and deformation modes changeSo-called “nonyielding” members may have some inelastic deformation


System Ductility

How is System Ductility Achieved?Designate certain elements to be fuses

Ensure those elements are ductileEnsure other elements do not yield

Determine maximum forces that yielding elements can imposeMaximum forces can be much greater than design forces

Resistance factorConservative design equationsConservative design assumptionsHigher-than-specified material strengthOver-designed elements (e.g., Drift-controlled)

Check strength or ductility at expected drifts


System Ductility

How is System Ductility Achieved?


AISC Seismic

Basic AISC Seismic Design Procedure1. Calculate demands based on applicable

building code

2. Analyze

3. Size fuses (braces)

4. Size other members so fuses will govern


AISC Seismic

Redefines some required strengths based on size of fuse (e.g., the braces)

Gives detailing requirements to ensure ductility of fuses

Was developed based on LRFD LRFD is more consistent with ProcedureLRFD is not required (ASD equations are also included)


2005 AISC Seismic Provisions

Section 1: ScopeSection 2: Referenced StandardsSection 3: General Seismic Design Requirements

Defers to Applicable Building Code (ABC)Section 4: Loads, Load Combinations, Strengths

Loads and CombinationsPer ABCPer ASCE-7 2002 If No ABC

“Amplified Seismic Load” Means Combinations with ΩoEStrengths Per 2005 AISC Specification (i.e., LRFD or ASD)



Section 5: Contract Documents, Shop and Erection2005

Drawings Identify Seismic Load Resisting System

FramesBracesChordsCollectors

Identify Protected ZoneAreas of Expected Inelastic StrainDetrimental Attachments Not Permitted

Shot-in PinsLow-Toughness Welds



Section 6: MaterialsPermissible Materials for yielding members

Fy ≤ 50 ksiElongation ≥ 20%

Material OverstrengthExpected Yield Strength

RyFy

Corresponding Expected Ultimate Strength2005

RTFu

RT Applies only to same member as Ry



Section 7: ConnectionsBolted Connections

PretensionedClass A Faying SurfaceNot to Share Force with Welds

Welded Connections20 ft-lbs @ -0º for the SLRS20 ft-lbs @ -20º and 40 ft-lbs @ 70º for Demand Critical Welds

Welds in CBF are not typically considered “Demand Critical”Protected Zone2005 Defined


Bolts

Bolts

Weld

Vertical force (and possibly the horizontal force) is shared by bolts and welds

THIS IS NOT ALLOWED!


Bolts

Bolted joint is not considered in the transfer of seismic forces.

This is permitted.



Section 8: MembersWidth-Thickness LimitsColumn Requirements

StrengthSplices

Non-Frame Columns2005

Splices


Columns

Σ(1.1RyFyAg sin θ+ 1.1RyFcrAg sin θ)

Strength

or ΩoEθ

1.2D + 0.5L (or 0.9D)

+


Splices

Ru = ½ RyFyAf

For PJP, use Ru ≥ 2 Ωo QE

Transition perAWS D1.1 (2.7.1)


Base Plate2005

Axial: ΣRui

Ru(col) = Σ(1.1RyFyAg sin θ + 1.1RyFcrAg sin θ)or ΩoE (-0.9D-0.2Sds)

Ru(brace connection) = RyFyAg sin θ

1.1RyFyAg

1.1RyFyAg

1.1RyFcrAg

1.1RyFcrAg Vertical component of brace expected strength:

Column required strength:

θ


Base Plate2005

Shear: ΣRu i

Ru(col)= Vu = 2 Mp / hor ΩoE (+1.2D+f1L+0.2Sds)

Ru(brace connection) = RyFyAg cos θ

Vu

Mp

Mp

VuHorizontal component of brace

expected strength:

Column required strength:

θ


Base Plate2005

Flexure: ΣRu

Ru(col) ≤ 1.1RyFyZ

≤ 1.2D + 0.5L + ΩoE0.9D + ΩoE

Ru(brace) ≤ 1.1RyFyZ

For fixed-end braces, add:


Columns not part of the SLRS2005

Splice

Vu

Mp

Vu

Mp

V12

.

Mph∑



Section 13: Special Concentrically Braced FramesBrace RequirementsBrace Connection RequirementsSpecial Requirements for V-Braced FramesColumnsProtected Zone2005



Section 14: Ordinary Concentrically Braced Frames2005

Brace RequirementsSpecial Requirements for V-Braced and K-Braced Frames Brace Connection Requirements



Section 16: Buckling-Restrained Braced Frames2005

Brace RequirementsBrace Connection RequirementsSpecial Requirements for V-Braced FramesBeams and ColumnsProtected Zone



Appendix Q: Quality Assurance2005

Appendix R: Seismic Design Coefficients2005

Only Applicable if Building Code Does Not Define Coefficients for BRBF

Appendix T: Qualification Testing of BRBs2005

Testing Requirements for Buckling-Restrained Braces

Part II:

Concentrically Braced Frames



I. Concentrically Braced Frames

Elastic BehaviorPost-Elastic BehaviorObserved BehaviorDesign Issues


CBF Elastic BehaviorTruss System

Concentrically Braced Frames can be approximately modeled as vertical trusses


CBF Elastic BehaviorFlexure: Connection Fixity

Connection is more similar to rigid connections than to simple ones.


CBF Elastic Behavior

Shear

Overturning

Braces resist shear.

Overturning forces are delivered to columns and base.


Limit States

Members

Connections

Column Splices

Yielding or fracture can occur in:


Limit StatesConnections: Brace End

Brace net section fracture

Brace block shear fracture

Brace-to-gusset weld fracture

Gusset block shear fracture

Gusset tension yield or fracture

Gusset or weld failure at column

Gusset or weld failure at beamGusset buckling



Gusset buckling


Brace Fracture

Courtesy of R. Tremblay


Post-Elastic BehaviorUnfavorable Modes: Connection Fracture

Courtesy of C. Roeder


Connection Instability




Column web yielding

Column web crippling

Column web shear

Beam web yielding, crippling, shear

Beam-column connection, shear

Beam-column connection, axial


Limit StatesConnections: Beam Midspan

Brace net section

Brace block shear

Brace-to-gusset weld

Gusset block shear

Gusset fracture

Gusset or weld failure at beam

Beam web yieldingBeam web crippling

Gusset buckling


Beam Instability



Limit StatesConnections: Base Plate

Shear

Tension

Resistance to horizontal and vertical force components must be provided. Different mechanisms (with different limit states) can be used.


Post-Elastic BehaviorUnfavorable Modes: Connection Fracture

Connection fracture must not be the governing limit state.


Post-Elastic BehaviorUnfavorable Modes: Column Buckling

Column buckling must not be the governing limit state.


Post-Elastic BehaviorUnfavorable Modes: Column Tension Fracture

Column tension fracture must not be the governing limit state.


Column Fracture



Post-Elastic BehaviorUnfavorable Modes: Beam Failure

Beam failure must not be the governing limit state.


Post-Elastic BehaviorPreferred Modes: Brace Buckling

Brace buckling should be a governing limit state.


Brace Buckling: Effect on Other Elements



Post-Elastic BehaviorPreferred Modes: Brace Tension Yielding

Brace yielding should be a governing limit state.


Brace Elongation (Tension Only)



Expected Performance

Diaphragm yieldingRocking

Other Acceptable Modes Rocking or diaphragm yielding may be the governing limit state.


System Behavior with Brace Yielding

Column Flexure

Columns must bend when braces buckle and yield.


Beam Flexure

System Behavior with Brace Yielding

Brace buckling and yielding induce flexural forces in beams in this configuration.


Frame Participation

Flexural forces are induced in rigidly-connected columns and beams due to drift.


Design IssuesConfiguration

Single Diagonal K-Bracing Chevron


Beam Forces

Configuration


Design IssuesConfiguration

2-Story X Zipper


Design IssuesEffective Length

L

K = 1 Brace effective length can be determined easily if pin-type connections are used.


Effective LengthPlane of Buckling

Out-of-plane(Generally governs if brace

is round or square)

In-Plane(Generally requires brace with weak in-plane

axis and connections fixed out-of-plane)


Effective LengthEnd Fixity / Hinge Location

FixedPin


Effective LengthCross Bracing

Hinged connectionContinuous connection



(with flexural continuity at splice)

L

K = 1(out-of-plane)



(with flexural continuity at splice)



Effective LengthCross Bracing(with flexural continuity at splice)




(without flexural continuity at splice)

K = ?(out-of-plane)

L


Design IssuesGussets: Effective Width

Whitmore limitation

30°

Reality limitation


GussetsEffective Length

Leff K=1.2Astaneh-Asl, Steel Tips # 42“Seismic Behavior and Designof Gusset Plates”


Connections: Compression

L2

(Astaneh, Steel Tips)

K = 1.2

L3

L1

L = Max (L)?

L = Ave (L)?

L = C (L)?L

3 Options (all reasonably reliable)


GussetsEdge Buckling

Le

Le

t34

EFy

⋅≤ (Astaneh-Asl, Steel Tips)


GussetsWorkpoint Location

EccentricConcentric

An eccentric workpoint will induce flexural forces in the framing members.


Eccentric WorkpointModeling of Eccentric Workpoint

Brace goes past column

(no node)

Rigid-end offset in beam

If flexure or shear yielding of beams or columns govern over brace yielding, the frame cannot be considered a Concentrically Braced Frame


GussetsAnalysis: Uniform Force Method

No flexure at beam-column section

eq. eq.

eq.

eq.


GussetsAnalysis: Other Methods

Truss Analogy

αβ

T

Astaneh-Asl, Steel Tips

eq .

eq .Tsin α( )

sin α β+( )

Tsin β( )

sin α β+( )

eq. eq.

eq.

eq.



Component MethodT

e2

e1

eq. eq.

eq.

eq.

Te1

e1 e2+



All shear

Effect of eccentricity should not be neglected (although it often is)

Leads to large gussetsShear: 0.6Fy

Tension: Fy

T

T sin θ( )

T cos θ( )

θ


GussetsFixity of Beam-Column Connection

Rigid ConnectionMoments are accounted

for in design

Connection Similar to Shear plateRotational ductility provided

via bolt deformation

Make sure to follow shear-plate design rules (e.g., max. plate thickness)


GussetsFixity of Beam-Column Connection

Connection Similar to Shear plateRotational ductility provided

via bolt deformation

Make sure to follow shear-plate design rules (e.g., max. plate thickness)

Part III:

Special Concentrically Braced Frames



SCBF

Expected performance

Unfavorable modes

AISC Seismic requirements

Design example



Braces

Primary location of inelastic demands

Buckling

Tension yielding


Post-Elastic BehaviorPreferred Modes: Brace Tension Yielding

Δ

F

Consider maximum effects due to brace force (RyFyAg)

RyFyAg


Post-Elastic BehaviorPreferred Modes: Brace Buckling

Δ

F

Consider maximum effects due to brace force (sometimes P = RyPn, sometimes P = 0.3Pn)

RyPn

0.3Pn


Com

pres

sion

Interior column seismic axial load effect is zero

Tens

ion

Traditional Overturning Assumption

Column Axial Load Distribution

W14

x370

W14

x370

HSS3

x3x1 / 4


Interior column Seismic axial load effect is not zero

Buckled brace (0.3Pn)Overturning

Distribution with Buckling

Column Axial Load Distribution

Yielding brace (RyFyAg)


Beam Design

C ≥ 0.3 Pn

C < Ry Pn

~~ ~~

Yield Mechanism

Cbelow Ry Fy Ag

CaboveRy Fy Ag

~ ~

~~F (left) F (right)

Forces

(Maximum axial force in beam)

C ≥ 0.3 Pn


Beam Design

C < Ry Pn

~~ ~~

Yield Mechanism

C ≥ 0.3 Pn (Maximum flexural force in beam)

CRy Fy Ag

~ ~

Forces



ConnectionsMinor inelasticityNo Fracture

Framing MembersSmall flexural forcesMinor inelasticity


Unfavorable Modes

Connection fracture

Column buckling

Beam failure


AISC Seismic

Basic AISC Seismic Design Procedure1. Calculate demands based on applicable

building code

2. Analyze

3. Size fuses (braces)

4. Size other members so fuses will govern


AISC Seismic

4. Size other members

Use expected brace capacity

Eliminate conservative design assumptions

Do not use φ for brace expected strength

Use expected material strength (RyFy) of brace

Consider other sources of conservatism


Other Sources of Conservatism

Brace effective lengthOut-of-straightness in equation of nominal

compression strengthFoundation Uplift

Size of footingParticipation of slab and grade beams-catenary action?

Other?


Bracing Members

Fundamental Requirement

φPn ≥ Pu

Required strength is not redefined by AISC Seismic


Bracing Members: Limitations

Exception:2005

if columns are designed for expected brace capacity of

Slenderness§ 13.2a2005K l⋅

r4

EFy

≤

4EFy

K lr

< 200≤

.

Ry Fy Ag sin θ( ) Ry Fcr Ag sin θ( )+( )∑



RyFyAg sin θ1

2

1

2

1

1

2 RyFcrAg sin θ+

ΩoE =

θ

Where columns can resist loads that include the expected brace strengths, kl/r can be as high as 200.



λpsCompactness

Slender

Non-compactCompact

Seismicallycompact

λps λp λr

Element slenderness (λ)

Mn



θ

Slender

Non-compact

Compact

Seismically compact

Mn

λpsCompactness


Local Buckling

Courtesy of S. MahinU.C. Berkeley, 2004


Local Buckling



Bracing Members: LimitationsLateral force distribution

Δ

F

Δ

F

F

F


Bracing Members: LimitationsBuilt-Up Members

Global buckling OK

Local buckling NOT PERMITTED


Connections

Connection fractureNOT PERMITTED

Member tension yielding OK

Tension

φRn ≥ RyFyAg


Connections

Old Codes (i.e., Uniform Building Code)ΩoPu

AISC Seismic

Ry: 1.1 – 1.5 φPn/Pu: 1.1 – ?FyAg/Pcr: 1.3 – 1.7 Overstrength: 1.6 – ?

RyFyAg


Connections

Buckling: 3 hinges

Flexure (Compression)

1

3

2

1

2

3

1

OK (fixed end)

1

OK(pinned end)


Pinned-End Gusset Hinging



Fixed-End Brace Connection


ConnectionsFlexure (Compression)

No Hinge ZoneGusset must fracture or weld must break to permit rotation


Connections

FixedφRn ≥ 1.1 Z Ry Fy

PinnedProvide accommodating detail (2t offset)

Flexure (Compression)


2t Offset

Fold line

2t

Fold line

2t

Provide accommodating detail (2t offset)Recommendation: Detail: 2t + ¾” ± ¾”

Design: 2t + 1½”


2t

2t Offset at Concrete Fill

Fold lineStyro-foam (1” ea. side per 6”depth)

2t

Fold line


Tearing of Gusset (No Hinge Zone)

From Astaneh-Asl, Seismic Behavior and Design of Gusset Plates, Steel Tips 1998

Crack formed by gusset plate folding


Folding of Gusset (Hinge Zone)


Gusset plate fold line


Folding of Gusset (Hinge Zone)




Estimate maximum compression force from braceConsider true brace lengthConsider connection fixityConsider material overstrengthShortcut: compression strength is always less than

tension strength



Stocky

Intermediate

Slender

CompressionFailure

Squashing

Inelastic buckling

Elastic buckling

DesignStrength

ExpectedStrength

AISCRequirements

Slenderness(KL/r)

φ Fy Ag Ry Fy Ag Ry Fy Ag

φ 0.658

Fy

Fe Fy A 0.658?

Ry Fy

Fe Ry Fy A 0.658

Fy

Fe Ry Fy A

φ 0.877 Fe A Fe A Ry 0.877 Fe A

Fe Aπ2 E I

(KL)2



L2

(Astaneh, Steel Tips)

K = 1.2

L3

L1

L = Max (L)?

L = Ave (L)?

L = C (L)?L

3 Options (all reasonably reliable)


ConfigurationsChevron



T C

or

T = RyFyAg

C = 0.3Pn

T C



Forces apply toBeams

Connections

Columns etc.

Beam must be continuous and strong enough for gravity


2-story X-bracing resists unbalanced load caused by the buckled brace.

The beam does not need to be designed for this load.

Braces on floor above support beam

Configurations2-Story X


ConfigurationsK-Bracing


Along a given brace line, both tension compression braces should be used (or a penalty applies)

Sum of horizontal components for brace compression forces or tension forces should be at least 30% and shall not exceed 70%

ConfigurationsSingle Diagonal


All compression or tension systemSum of horizontal components in either

compression or tension ≥ 0.7VNo Good

V

100%V50%V

50%V

ConfigurationsSingle Diagonal

V


0.30V ≤ Tension ≤ 0.70.30V ≤ Compression ≤ 0.7

OK

0.30V ≤ Tension ≤ 0.70.30V ≤ Compression ≤ 0.7

OK

V

ConfigurationsX-Bracing Chevron Bracing

V50%V

50%V 25%V

25%V

25%V

25%V


0.30V ≤ Compression = 0.74 ≥ 0.70.30V ≥ Tension = 0.26 ≤ 0.7

No Good

Tension and compression force distribution based on relative stiffness of frame members

ConfigurationsCombination

V

26%V

26%V

48%V


Except if the compression only brace system is designed for:

1.2 PD + 0.5PL + 0.2S + ΩoPe

0.9 PD - ΩoPe

Configurations


Columns

λpsCompactness

Splices

Vu = ΣMp/h

Mu = ½ Mp i+1

Mp i+1

Mp i

Vu


Protected Zone(2005 Seismic Provisions)

dd

LL/4

Gussets

Braces atexpected hingelocations

Miscellaneous attachments (cladding, plumbing, etc.) not permitted in the Protected Zone

Break



Design Example

5 x 30’ = 150’

5 x

30’

= 15

0’

ASCE 7 2005AISC Seismic 2005


Base Shear

Bingo

HazardSds = 1.00

Sd1 = 0.635

Ta = 0.484 sec.

V = 0.167 W

T

V


Load Combinations

1.2D + f1L + E

0.9D ± E

1.40D + 0.5L + ρQE

0.7D ± ρQE

1.40D + 0.5L + ΩoQE

0.7D ± ΩoQE

f1 = 0.5E = ρ QE + 0.2SDS D

Basic Special (Amplified Seismic Load)

1.2D + f1L + Em

0.9D ± Em

Em = Ωo QE + 0.2SDS D


Redundancy (ρ)

Ω o effective( )Ω o

ρ

If ρ > 1.0, the strength ratio of members designed for the Amplified Seismic Load to those designed for the Basic Load Combinations will be less than Ωo.

The effective overstrength factor is therefore reduced.This is not good.


Vertical Distribution

Fiwi hi

k⋅

.

wi hik⋅∑


Horizontal Distribution

0.47 V 0.53 V0.03 V

0.03 V

5%

V


Redundancy per ASCE 7 2005

ρ = 1.0

Regular

Perimeter bracing

≥ 2 bays per side


Frame Analysis

ModelTruss

Fix in-plane,Pin out-of-plane

Fix if requiredfor beam flexuralstrength


Brace Design

CompressionPu = 1.4D + 0.5L + E

= 1.4(19k) + 0.5(7k) + (178k)

= 209k

TensionPu = 0.7(19k) – (178k)

= 159k


Brace Design

(12” offset in connections; verify later in connection design)

HSS 8.750x0.312

L 13ft( )2 15ft( )2+ 2 1.0ft( )− 17.85ft

Fy 42ksiK l⋅

r71.64 Fe 55.9ksi A 7.71in2

42ksi 7.71⋅ in2φPn 0.9 0.658

4255.9

⎛⎜⎝

⎞⎟⎠ 213k AISC 2005

Specification


Brace Design

Check compactness

λps 0.044EFy

36.5

Dt

8.75in0.93 0.312in( )⋅

30.1 OK

Actual thickness is 93% of nominal for A500


Required Strength in Tension

AISC Seismic Provisions 13.3.aRy Fy Ag

Other Limiting Maximum ForceConsider Variability of Force DistributionConsider Dynamics (Not only Statics)

Greater Than Previous RequirementsBrace Design ForceAmplified Seismic Load

3Rw /8 x Brace Design ForceWo x Brace Design Force


Brace Connection: Tension

Required StrengthRu = Ry Fy Ag

= 1.4 (42 ksi) (7.71 in.2)

= 453k

(= 2.14 Pu)

Note: Ry values revised in AISC Seismic 2005


Typical Detailing of Reduced Section at Knife Plate

Radius = 1/2 t2

Grind Smooth

HSS BraceGusset Platet1

2” max.

t2 = t1 + 1/8“


Demand versus Capacity

Net-Section reinforcement is always required

RyFyAg

Demand

φRTFuUAnet

Capacity

Anet

Ag= 1.3 1.1 (U = 0.9)

A500 Gr. B A53

Ry Fy

φRTFuU

≥Expected Tensile StrengthNew to 2005 AISC Seismic


Facture at the Reduced Section

Kobe, 1995


U.C. Berkeley, 2004

Courtesy of S. Mahin, P. Uriz


Brace Reinforcement



Brace Reinforcement




AssumptionsGusset width ~ 2 dbr (2 x 8.75” = 17.5”)

Gusset thickness (tg):

453k / (0.9 x 36 ksi x 17.5”) = 0.80”;Use ⅞”

dbr

Gusset width



Net Section FractureAremoved = 2 [tg + ⅛”] tbr

= 2 [⅞” + ⅛”] 0.29”

= 0.58 in.2

Anet = 7.71 in.2 – 0.58 in.2 = 7.13 in.2



Required AreaφRTFuAe ≥ RyFyAg

= 1.4 x 42 ksi x 7.71in.2 /(0.75 x 1.3 x 58 ksi)

= 8.01 in.2 ( > Ag!)

Reinforcement required

Ae ≥ RyFyAg /φRTFu


Reinforcement

Add 2 sections of HSS 9.625 x 0.500(I.D. = 8.7”)


Reinforcement

Assume L = 18”

Ae,req = Ag

Assume x = D / π = 9.625” / π = 3.1”_

U = 1 – x / L = 0.83_

Anet = Ae / U = 9.33 in.2Provision requires higher load (RyFyAg) be considered only when Ae < Ag


Reinforcement

0.93 x 0.50” = 0.465”

AreinfAnet req( ) Anet brace( )−

2 plates1.10in2

RR

9.625in2

t2

− 4.58in


Reinforcement

c

2 ½”

breq1.10in2

0.465in2.36in

creq 2R sin12

180o b π r

⎛⎜⎝

⎞⎟⎠

⎡⎢⎣

⎤⎥⎦

2.40in

A2.5 in2.4 in

1.10in2 1.15in2b


Reinforcement

Fillet weld:

Connect reinforcement to develop capacity:Ry Fy A 1.15in2 1.4 42ksi( ) 67 k

L 2(5 in) = 10 in

s516

φRn 16 20.75

5 20.6 70⋅ ksi( )10in 70 k OK


Reinforcement

5/16

2” max

5”5”



Use L = 2D = 17.5” 18”

Brace block shearφRn 4 0.75( ) t L⋅ 0.6Fu( )⋅ Ru≥

LRu

4 0.75( ) t 0.6Fu( )⋅≥ 15in

LD



Brace-to-gusset weldL 18in

φRn 4 0.75( ) s2

2⋅ L⋅ 0.6FEXX( )⋅ Ru≥

sRu

4 0.75( )⋅2

2⋅ L⋅ 0.6 FEXX⋅( )⋅

≥516

in OK


Brace Connection: TensionGusset block shear

At

Av





Gusset Block Shear

Ant = Agt = [8.75” + 2 (5/16”) ] x ⅞” = 8.20 in.2

φRn = 0.75 [ 0.6 Fy Agv + Ubs Fu Ant ]= 867k ≥ Ru OK

Tension is uniform, Ubs = 1.0

Agv = 2 x 18” x ⅞” = 31.5 in.2


Brace Connection: TensionGusset block shear

Uniform gusset tension

D2D

2D

Brace welds


Gusset Design (Method 1)Sabelli Method

Width required =

= 16”Use 2D = 18”

W = 18”

Ru

φFy t⋅

D


Gusset Design (Method 1)

HINGE ZONE


Gusset Analysis (Method 1)

T

e c

e b

Tbeam

Tcol

Concentric Workpoint

Tbeam Tec

ec eb+⋅

Tcol Teb

ec eb+⋅

eq. eq.eq

.eq

.


Gusset Analysis (Method I)

T

e c

e b

Tbeam

Tcol

Modified Workpoint

ec eb

TbeamT2

TcolT2

eq. eq.

eq.

eq.


Gusset Design: Method IIUniform force method

θ

e b12

d b=

e c12

d c=

2α

2β


Uniform Force Method

Assume β 5in

Note: Assumed size must be verified by checking gusset width and combined shear & tension at gusset joints to beam & column

α β eb+( )tan θv( )

α 5in 8.95in+( )tan 49.1o( ) 9.24in

r α ec+( )2 β eb+( )2+ 21.3in

(For zero moment on welded interfaces)


HSS Columns

Do not rely on HSS wall to resist horizontal component(The same applies to webs of WF columns)



Vucβr

Pu 106k

Hucec

rPu 145k

Vubeb

rPu 190k

Hubαr

Pu 190k



Check gusset tension

Or use conservative shortcut:

w1

w2

w w1 w2+

ew2

w1−

wef 4e2 w2+ 2e−

wef 2 min w1 w2,( )

From Popov, Mechanics of Materials



w1 7.99in w2 9.27in

w 17.3in e 0.6in

wef 0.928w 16.0 in

Compare : 2w1 16.0in


Gusset Yield across Width

φRn φt w Fy

OKφRn 0.978

in 16in 36ksi 454k


Combined Tension and Shear at Gusset Edges Stresses

von Mises yield criterion

σ≤ φFy

T

A

⎛⎜⎝

⎞⎟⎠

2

3V⎛

⎜⎝

⎞⎟⎠

2

+A

T

φFy A

⎛⎜⎝

⎞⎟⎠

2

3V⎛

⎜⎝

⎞⎟⎠

2

+ ≤ 1φFy A


Gusset Yield at Vertical Section

Huc

φ Fy t 2 β

⎛⎜⎝

⎞⎟⎠

2

3Vuc

φ Fy t 2 β

⎛⎜⎝

⎞⎟⎠

2

+ 0.83

OK

Don’t forget to deduct weld access hole for flange weld, if used.


Gusset Yield at Horizontal Section

Vub

φ Fy t 2 α

⎛⎜⎝

⎞⎟⎠

2

3Hub

φ Fy t 2 α

⎛⎜⎝

⎞⎟⎠

2

+ 0.74

OK


Gusset-to-Flange Weld

Size welds for

and

Option I

1.25 Vub2 Hub

2+

1.25 Vuc2 Huc

2+

(1.25 “Ductility Factor” anticipates local stresses higher than average stress. Revised from 1.4 in 2005 Manual)



Size welds to develop gusset shear capacity

Option II (My Recommendation)

Rn Ry 0.6Fy t≥

2s( )2

20.6FEXX 0.66 Fy t≥

s 0.47 t≥ (A36) s 0.56t≥ (A572 Gr. 50)



Size welds to develop gusset tension capacity

Option II (continued)

Rn RyFy t≥

2s1.5 ( )2

20.6FEXX 1.1 Fy t≥

s 0.53 t≥ (A36) s 0.62t≥ (A572 Gr. 50)

(1.5 per Appendix J)

Use ½ t Use 5/8 t


Gusset Welding Options

Alternative

CJP

7/16

0.5 x ⅞ = 7/16


Check Beam Web Local Yielding

Ru Vub 190k

W18x40

φRn 1.0 2α 2.5kb+( )Fy tw

φRn 385k Vub> OK


Check Column Web Local Yielding

Ru Huc 145k

W12x152

φRn 1.0 2β 5kc+( )Fy tw

φRn 885k Huc> OK


Check Detail for Compression

Ru Ry Fcr Ag Brace expectedcompression strength

Assume L 13ft( )2 15ft( )2+ 2 3.0ft( )− 14ft

Fcr 34.61ksi

Ru 374k

L


Gusset Stability

L

L 14in K 1.2

rt

120.253in

Klr

66 Fe 64.9ksi

φRn 0.9 0.658

Fy

Fe

⎛⎜⎜⎝

⎞⎟⎟⎠ Fy A

φRn 0.9 28.5( )78

in 17.3in2 389k

A = t Wef


Check Brace Length Assumption

L 14in

LL2

L2 Db/2cos(θ) = 12in

L2 + (L – Lhinge) = 24in

> 12in (for lower-bound brace strength)

< 36in (for upper-bound brace strength)


Gusset Edge Stability

Le

t34

EFy

≤ (Astaneh, Steel Tips)

Le

t21.3

Le 21.3t≤ 18.6 in

Le


Gusset Edge Stability

Le

Le = 10” OK

b

b/t ≤ λps

t

Where gusset meets λps, edge buckling is prevented. My recommendation only, not code.


Beam Web Stability

α

N=2α

Ru

Ru VubFcr

FyVub

34.6ksi42ksi

0.82Vub 157k

N 2α 18.5in

α 9.24ind2

> 8.95in


Beam Web Stability

φRn 0.75 0.8 tw2⎛

⎝⎞⎠ 1 3

Nd

twtf

⎛⎜⎝

⎞⎟⎠

32

+

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

E Fy tftw

φRn 226k Ru> OK


Column Web Stability

βRuN = 2β = 10”

Convert load based on expected tension strength to one based on expected compression strength

Ru HucFcrFy

119k


Column Web Stability

φRn 0.75 0.8 tw2⎛

⎝⎞⎠ 1 3

Nd

twtf

⎛⎜⎝

⎞⎟⎠

32

+

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

E Fy tftw

φRn 281k Ru> OK


Shear in Beam and Column

Beam

ColumnVu 1.4D 0.5L+ 1.0 Huc 1k+( )+

Vu 0 0+ 146k+ 146k

φVn 0.9 0.6Fy( ) d 2tf−( )tw 427k

Vu 1.4D 0.5L+ 1.0 Vub 210k+( )+

Vu 1.4 15k( ) 0.5 6k( )+ 1.0 190k 210k+( )+ 423k

φVn 143k

2 braces connect to this gusset


Shear in Beam Web

1. Use deeper, heavier beam (re-analysis required)

2. Use reinforcement

Options

Aw ≥423k

φ 0.6Fy15.7in2

3. Use beam stub


Shear in Beam Web

LShear P

WebArea tw d 2 K 1.5in+( )−[ ] (deduct weld-access holes)

0.315in 15.9in( ) 5.00in2

Area 10.7in2 (A572 Gr. 50)

15.9in34

in⎛⎜⎝

⎞⎟⎠

11.9in


Shear Reinforcement

k+1.5” (TYP)

P ¾ A572 Gr. 50 L


Shear Reinforcement

15.9”

9.25”9.25”

18.5”(= 2β)

Vu

Vu10.6 in2

15.6 in2420 k 285 k


Shear Reinforcement

a l

ex

k lx l

l

l 15.9in K l⋅ 18.5in K 1.16in

x 0.401 (Table) a 0.181

C 5.7ex 9.25in x l⋅− 2.87in

φRn C C1⋅ D⋅ l⋅

DminPu

C C1⋅ l⋅

420k5.7 1.0( )⋅ 15.9in

4.6

USE 516

in WELD


Beam-to-Column Connection

(CJP web & reinforcement)

(Collector Fpx)

Vu 420k

Mu 26.5ft k Beam moment from model⋅

Pu Ωo 37.9k 75.8k

Pu Huc(i) – 0.3 Hc(i+1) 186 k

(based on postelastic mode)


Postelastic mode

0.3 Pn

0.3 Hc(i+1)

Ry Fy A

Huc(i)

Pu

Can be reduced somewhat by collector force (as shown in design of beam to follow)

Need not be considered in conjunction with full shear



Beam moment from model:26.5 ft-kip

Beam moment from connection forces:Hub (Db/2) - Vub (α)= 190 kip (9in) - 190 kip (9in)= 0 in-kip

e b12

d b=

e c12

d c=

2α

2β

Hub

Vub

This moment will be > 0 for methods other than UFM



CJP Flange OK (Alternatively, use a PJP or fillets)

Flange forceMu

d tf−

12

Pu+ 111 k

57.6k0.9Fy Af

0.76Pu

Pnφ



φRn 0.8 0.6 70⋅ ksi( ) 6.02in E

φRn 111 k≥

E 0.55in≥

916

in PJP WELD OK


Connection Design

k+1.5”

HSS 9.625 x 0.500 x 2.5”x 12”

5/16 18

LP ⅞

CJP

2.5” ± ¾”

5/16

2” max

5”5”

5/16

3 sides

or CJP18.57/16

or CJP107/16

P ¾ x16x18.5 A572 Gr. 50 L

Lunch Break


Bay size Plate A36 Brace BeamL = 15 ft Material Fy = 36 (ksi) Material Material A992H = 13 ft Fu = 58 (ksi) Fy 50 (ksi)

49.1 deg. Dimensions Section W18X46Analysis Width adustment factor 1.00 Fy 42 (ksi) Stiffening

Suggested Ry 1.4 Not = 7/8 in. 3/4 in. Fu 58 (ksi) No

Slot width 1 in. 1 in. RT 1.31.25 L L 4.54

(in.) (in.) SectionGusset K = 1.2 Gusset lap with brace (min.) = 16.63 16.63

Control Horizontal = 17.00 17.00 Reinforcement (2 plates) ColumnVertical = 10.00 10.00 Material Material A992

Width and angle (beam side) = 8.29 13 deg t = 3/8 in. Fy 50 (ksi)

Precision Width and angle (col. side) = 8.29 13 deg Suggested Section W12X1520.125 (in.) b = 4.00 4.00 in. Stiffening

Welds eh = 0 (in.) A/ Ae = 0.94 NoFEXX 70 (ksi) Hinge tolerance 1 (in.) No

s Max. Useful Shoulder 1 (in.)

Brace weld 5/16 in. 7/16 in. Weld gap (hor) 0 (in.) 4.55Suggested Weld gap (vert) 0 (in.) L = 14.00 (in.)

Beam weld 7/16 in. 7/16 in. Max. Overslot 2 (in.) Fy 42 (ksi)

Column weld 7/16 in. 7/16 in. Buckling length 12.9 (in.) Ry 1.3No s 5/16 (in.) Orientation Strong

Limit States OK! Ru φRn Ru/φRn

Brace (kip) (kip)Net-section rupture J4-2 462 489 0.94Brace shear rupture J4-4 462 677 0.68Brace shear yield J4-3 462 633 0.73Brace weld J2-4 462 463 1.00

GussetGusset block shear J4-5 462 1088 0.42Tension Yield J4-3 462 470 0.98Gusset buckling J4-6 329 386 0.85

Gusset at columnYield (σvm) J4-1 244 284 0.86Tension rupture J4-2 150 381 0.39Shear rupture J4-4 104 228 0.46Column weld J2-4 244 374 0.65

Gusset at beamYield (σvm) J4-1 412 482 0.85Tension rupture J4-2 198 647 0.31Shear rupture J4-4 199 388 0.51Beam weld J2-4 194 313 0.62

ColumnWeb yielding J10-2 150 870 0.17Web crippling J10-4, 5a, 5b 107 1438 0.07

BeamWeb yielding J10-2 198 397 0.50Web crippling J10-4, 5a, 5b 141 160 0.88

Gusset edge buckling Length Limit Length/LimitAt column (Steel Tips) 9.2 in. 18.6 in. 0.49At beam (Steel Tips) 2.8 in. 18.6 in. 0.15

Beam-to-column connection forces Eccentric moment Vertical and horizontal dimensions Diagonal dimensionsHcol 150 (kip) Mecc 0 (in.-kip) Max. gusset height 23.3 in. Width 18.7 in.Vbm 198 (kip) Max gusset length 29.4 in. Length 32.2 in.M 0 (in.-kip) Area 685 in.2 Area 602 in.2

Stiffener length 0.0 in.

A500 Round Grade B

Factor to account for weld stress concentrations

Edge length measured

Edge length measured


HSS8.625X.312

Specification Equation

Web stiffener?

to brace end

Edge stiffener?

Edge stiffener?Gusset b/t at end of

brace =

Gusset b/t at end of brace =

to brace end

Workpoint horizontal eccentricity Web stiffener?

Edge stiffener?

A572 Gr.42Vertical and horizontal dimensions

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

-20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0


Connection at Beam Midspan

T = Ru

= 453kC = Ru

= 374k Conservatively set C = RyFyA


Connection at Beam Midspan

Same as brace at beam-column connection:

Gusset thickness

Brace reinforcement

Brace block shear capacity

Gusset-to-brace weld

Gusset block shear capacity


Gusset LengthL

e = d/2

Vu 2Tu cos θ( )≤ 685k

Mu Vud2

6130 in k⋅


Combined Shear and Tension

=

Compression

Brace forces

Tension

Shear

Flexureσ=4M/tL2

σ=V/tL


Gusset Length

4Mu

t L2

φFy

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

2

3

Vu

t L

φFy

⎛⎜⎜⎝

⎞⎟⎟⎠

2

+ 1≤

Lmin 46in


Gusset Length

8in. is ½required width

8insin θ( )

d

2

tan θ( )

Lmin 2

d

2

tan θ( )8in

sin θ( )+

⎛⎜⎜⎝

⎞⎟⎟⎠

45in

8in


Gusset Yielding

Use L = 48” and t = ⅞”Gusset Width:

w1 = 8.5”

w2 = 21.1”

e 6.3in

Wef 19.6in

φRn φ Wef t Fy 555k Ru> OK


Gusset at Flange

Use CJPor

7/16

4Mu

t L2

⎛⎜⎜⎝

⎞⎟⎟⎠

2

3Vu

t L

⎛⎜⎝

⎞⎟⎠

2

+ 0.92 φFy


w

w/2

M

T

V

C

V

Check Combined Shear and Tension


Check Beam Web

Beam web cripplingw 48in

Ru CMw2

255k

Nw2

24 in

W18x40

φ Rn 0.75 0.8tw2 ⎛

⎝⎞⎠ 1 3

Nd

t wt f

⎛⎜⎝

⎞⎟⎠

3

2

+

⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

E Fy tftw

φ Rn 265k OK


Check Compression in Plate

L = 13.0”

L 13in K 1.2

rt

120.253in

Klr

62 Fe 74.3ksi

φRn 0.9 0.658

Fy

Fe

⎛⎜⎜⎝

⎞⎟⎟⎠ Fy A

φRn 0.9 29.4( )78

in 19.6in2 416k

A = t Wef

OK


Gusset Edge Buckling

Le

Le

t34

EFy

≤ (Astaneh-Asl, Steel Tips)


Gusset Edge Buckling

Le

Add stiffener to reduce unbraced length of plate edge


Beam Stability

Brace flanges for strength

Pbr = Mbr/ho = 160 in-kip /(18.1”-0.605”) = 9.1 kip

Mbr 0.024Ry Z F Ly

n Lb Cb

Mbr 0.0241.1(90.7in3)50ksi(360in.)

3(90in.)1.0160 in-kip

Torsional BracingLRFD C4b(a)


Beam Stability

Brace flanges for stiffness

βbr = βT /ho2 = 14,600 kip-in/radian /(18.1”-0.605”)2 = 48 kip/in

β T2.4(RyFyZ)2L

nφEIyCb2

β T2.4 [1.1(90.7in3)50ksi]2 360in.

3(0.75)29,000ksi(22.5in.4)(1.0)214,600 kip-in/radian

Pbr/βbr = 9.1 kip/48 kip/in = 0.19 in.

Torsional BracingLRFD C4b(a)


Beam BracingCheck strength and stiffness:

Δ ≤ 0.19 in.

9.1 kip.

9.1 kip.

Consider deflection due to angle compression, beam flexure, and bolt oversize (if not designed as slip-critical)


Beam Bracing

9/16

L3x3x¼W/ ⅞” A325 SCEACH END


Verify Hinge Zone

2t+¾” = 2.5” OK

2t+¾”

L=4.8

”


Check Vertical Area

H = 24”Av = Ht = 21 in.2

Ru Pu sin θ( ) 237k

φRn 0.9 21⋅ in2 0.6⋅ Fy 408k OK

Designers may consider the strength of the beam web in resisting this shear. Gusset force analysis should be consistent with such an assumption.


Check Vertical Area

(OK to shape P : Hreq = 13.5”)L

H = 14”

Ru Pu sin θ( ) 237k

φRn 0.9 21⋅ in2 0.6⋅ Fy 408k OK

Av = Ht = 12.8 in.2


Chevron ConfigurationTop Story

HSS6.125x0.250


Forces from Braces

Tension yieldingRyFyAg = 235k

Post-bucking0.3Pn = 28k

Vertical force:(RyFyAg -0.3Pn ) sin(θ) = 135k

Horizontal force:(RyFyAg +0.3Pn ) cos(θ) = 199k


Forces from BracesBrace @ ¼ points

199k99k 99k

135k68k 68k

ME = 506 ft-k; Mu = 521 ft-k

Pu = 99k


Moment Magnification

B1Cm

1Pu

Pe−

Cm 1.0-0.2Pu/Pe = 0.99

Pe 3445 k B1 1.0

W24x62

Table C-C1.1


Forces from Braces

Use W24x62Lp 4.84ft Lr 13.3ft Lb 7.5ft

φMp 0.9Fy Z 6885in k⋅ Cb 1.67

φMn Cb φMp BF Lb Lp−( )−⎡⎣ ⎤⎦

φMn 1.67 6885in k⋅ 258k 7.5ft 4.84ft−( )−[ ] 10350in k⋅

φMn φMp 6885in k⋅


Forces from Braces

φPn 0.9 0.658

Fy

Fe

⎛⎜⎜⎝

⎞⎟⎟⎠ Fy A

Klr

7.5 ft 12⋅inft

1.38in65.2

Fe 67.3ksi Fcr 36.6ksi

φPn 590 k


Combined Flexure and Compression

Pu

φPn0.165 0.2<

12

Pu

φPn

Mu

φMn+ 0.99 OK


Check Support

Ru = 68k

OK (AISC LRFD Manual Table)

P ⅜ w/ 4 ⅞”Ø A325N BoltsL

ColumnW12x96 OK by inspection


Column Forces

Elastic AnalysisColumn SeismicForces

Postelastic AnalysisColumn SeismicForces

Significant for low buildings and top stories of taller buildings


End Moments

Mu = 521ft-kProvide W24x55 in adjacent bays

W24x55W24x62W24x55

Check end moments


Column Design

Basic code forces from modelPu 1.4D 0.5L+ Ωo QE⋅+

Pu 1.4 257k( ) 0.5 93k( )+ 2.0 388k( )+

Pu 1182k


Column Moments

B1Cm

1Pu

Pe−

W12x152

K 1.0 L 18ft rx 5.66in

K l

rx

26.2


Column Moments

Fex417 ksi A 44.7in2

Pe 18,631k

Cm 1.0

B1 1.07


Column Moments

B21

1

.

PuΔoh

ΣH L

⎛⎜⎝

⎞⎟⎠∑−

ΣPu 1.4 ΣD 0.5 ΣL+

ΣPu 1.4 11,600k( ) 0.5 4 100psf( ) 23,700ft2( )⎡⎣ ⎤⎦+

ΣPu 21,000k


Column Moments

Δoh Δm Cd Δe 5.5 0.249in( ) 1.37in

ΣH V 1940k

L 18ft 216in

B2 1.07 Δe = elastic displacement from modelCd = code displacement amplification factor


Column Moments

Mnt 1.4(3.4ft-k)+0.5(1.2ft-k)=5.4ft-k

Mlt 20.0k

Mu B1 M +nt B2 Mlt 27.2ft k⋅


Column Moments

φPn 0.9 0.658

Fy

Fe

⎛⎜⎜⎝

⎞⎟⎟⎠ Fy A

φPn 1440k

Pu

φPn0.82


Column Moments

W12x152 Cb 1.67 φMp 911ft k⋅

Lp 11.3ft Lb 18ft BF 5.59k

φMn Cb φMp BF Lb Lp−( )−( )φMn 1460ft k⋅ φMp>

φMn φMp 911ft k⋅Pin-based column assumed.


Column Moments

Pu

φPn0.82

Pu

φPn

89

Mu

φMn+ 0.85 OK Moments can often

be neglected


Column Splice

Third Story

SpliceLocated in middle 1/3 of clear height(4’ above slab preferred)


Column Splice

VuΣMp

Hc

Fy Z1 Z2+( )13ft 18in−

Vu50 ksi 147 in3 243 in3+( )

13ft12in

ft18in−

Vu 141k


Column Splice

P 9/16 x 6 ½ x 13 ESL

φRn 0.9 0.6( ) 36 ksi 612

in⎛⎜⎝

⎞⎟⎠

2916

in⎛⎜⎝

⎞⎟⎠

142k OK

Vu 141k


Column Splice

Weldper AISC Manual

weld-group table

6½”

6½”

C1 1.0 70ksi

L 612

in K l L

K 1 x 0.333

L a L x L+

ex a L L x L− 0.67L

a 0.67 C 3.03


Column Splice

t1 = 0.550”

t2 = 0.870”

gap = 0.16”1

Dmin

12

Vu

C C L116

in3.616

in

4USE

1in WELD

t2 t1−

20.16

316

in< OK

Column web above

Column web below


Column Splice

Mu12

Mn12

Z Fy 3680in k⋅

Mu

d tf−311k

CJP: φRn 0.9 50ksi( ) 0.900in 12.2⋅ in 494k OK

PJP: E( )2.0Ru

0.8 0.6·70ksi( ) 12.2in≥ 1.52 in use CJP

= Ru


Column Splice

CJP Transition

12.5

AWS D1.12.7.1

Where

12.5

Ru

φ Rn

13

≥


Columns not part of the SLRSSplice

Vu

Mp

Mp

Vu

V12

.

Mph∑

Bearing


Beam Design

C ≥ 0.3 Pn

C ≤ Ry Fcr Ag

~~ ~~Yield Mechanism

C Ry Fy Ag

CRy Fy Ag

~ ~

~~F4 (left) F4 (right)

Forces(Maximum Pu)

Above: (Ry Fy Ag +0.3 Pn)cosθ = (253k+28k)cos(40.9o) = 199k

Below: (Ry Fy Ag +0.3 Pn)cosθ = (277k+54k)cos(40.9o) = 250k

F4(left) = F4(right) = ½ (250k-199k) = 26k

Pu = F4(left) + (Ry Fy Ag5 - 0.3 Pn4)cosθ = 163k

4th Floor


Beam Moments

M1.4D+0.5L = 117 ft-kip

MΩ.E = 42 ft-kip

M1.4D+0.5L+Ω.E = 159 ft-kip

Forces from model


Beam Moment Magnification

W18x40

Major Minor

K 1.0 K 1.0

L 30ft L 7.5ft

r 7.21in r 1.27in

K l

r49.9

K l

r70.7

Fe 57.2ksi

A 11.8 in2

Pe 675k

Fe 104ksi

A 11.8 in2

Pe 1355k(for momentmagnification)

(for compressionstrength)



30’

Cm 1.0-0.4Pu/Pe = 0.95

Table C-C1.1



B1Cm

1Pu

Pe−

1.0≤

0.95

11631355

−1.08

B2 1.07 (from column design)


Beam Moments

Mu B1 117 ft k⋅ B2 42 ft k⋅ 162ft k⋅+


Beam Design

φPn 0.9 0.658

Fy

Fe

⎛⎜⎜⎝

⎞⎟⎟⎠ Fy A

φPn 409k

Pu

φPn0.39


Beam Design

7.5’ 7.5’ 7.5’ 7.5’

M1 = 40 ft-kip

Mc = 60 ft-kip

Mb = 84 ft-kipMa = 120 ft-kip

M2 = Mmax. = 162 ft-kip

Cb12.5Mmax

2.5 Mmax 3 Ma+ 4 Mb+ 3 Mc+1.58


Beam Design

W18x40 Cb 1.58 φMp 294ft k⋅

Lp 4.49 ft Lb 7.5 ft BF 11.7 k

φMn Cb φMp BF Lb Lp−( )−( )φMn 409 ft k⋅ φMp>

φMn φMp 294 ft k⋅


Beam Design

Pu

φPn0.39

Pu

φPn

89

Mu

φMn+ 0.88


Base Connection


Base Connection

TensionPu Pu(col) Pu(brace conn) sin θ( )+

Pu 0.7D Ωo QE− Ry Fy Ag sin θ( )−

Pu 0.7 257 k( ) 2.0 388 k( )−

1.4− 42 ksi( ) 13.38 in2 sin 50.2o( )Pu 1200k

Pu(col) Pu(brace conn)


Base Connection

Mu 0 (Neglect column base fixity and brace connection moment)

Vu Ωo QE Ry Fy Ag cos θ( )+ (Brace)

Vu 2.0 0.5k( ) 787k cos 50.2o( )+

Vu 505k

Vu(col)

Mu(brace conn)Mu(col)

Pu(brace conn)


Base Connection

F1554 Grade 55 (with weldability and toughness supplementary requirements)

φRn 0.75 0.75Fu( )Ab 42ksi Ab⋅ Fu 75ksi

Areq'd 28in2 Use (9) 2"φ F1554 Gr.55


Base Connection

Shear

Use P 1¼ x 4½” A572 Gr. 50 L

Vu 505k

2 φ Fy A 505k≥

φRn 2 0.9( ) 50ksi 1.125⋅ in 4.5⋅ in 506k

505k


Base Connection

φRn 0.75U Fu AnFu 65ksi An Ag

U505k

0.75Fu A≥ 0.92

Use L 2w≥ → U = 1.0"

L = 9" L = 9"


Base Connection

WeldsφRn 2 0.75( ) s

22

L 0.6FEXX( )

Ru12

505k 253k

s 0.63 Too big!≥

Use longer weld length: L = 15"

s38

in φRn 251k

⅜ 15


Base Plate Gusset Design

Locate horizontal force resistance to move resultant vertical force to centroid of bolt group (or design bolt group for eccentric moment)

596k

1k

605k504k 505k

1201k

787k





Force to columnGusset vertical force

605k10.5in

10.5in 1.125in+⋅ 546k

L 27in s12

(Double fillet)

φRn 601k



605k - 546k = 59k

Force to base plate

Use same weld (utilize gusset in stiffening base plate)

½


Anchorage Design

ACI 318 2002Appendix D

EmbedmentSpacingEffect of eccentricity

No eccentricity in our design

Edge distanceetc.


Column Connection to Base PL

Pu 596k + 546k = 1142k

Pu2

571k

PJP: 571k

0.8 0.6( ) 70ksi 12.5⋅ in1.36 in

Use CJP

CJP



RecommendUse CJP or similar weld toexceed element capacity

ORMake sure capacity exceeds footing rocking + grade beam hinging



CJP

⅜


Base Plate

T

e

T39

1200k 400k

e 518

in M 2050in k⋅

φMn φ Z Fy φbt2

4 Fy

b 20in t 3.0in≥


Base Plate Alternatives

A grout pocket with shear lugs can resist shear

Grout



Small shear forces can be resisted by bending of the anchor rods

Do not assume bearing in grout

GroutSlab

Footing



Column bearing can transfer horizontal force

φRn 0.65 0.85f'c( )b f y

y505k

0.65 0.85 4× ksi( ) 12.5in≥

18iny ≥


Completion of Design

Design of FoundationsConsider Steel Piles

Design of Diaphragms, Chords, and CollectorsInteraction with Architectural and Mechanical Systems

Define Protected Zone of BracesEstimate Brace Out-of-Plane Displacement


Protected Zone

dd

LL/4

Protect areas of expected high inelastic strain from attachments with low-toughness welds or shot-in pins


Estimate Brace Transverse Displacement

L`T

L

Δb

L'T L Δb+



Δoop

L`C

L

Δb

L'C L Δb−

Δoop

L'T

2

⎛⎜⎝

⎞⎟⎠

2 L'C

2

⎛⎜⎝

⎞⎟⎠

2

−



L'T L Δb+

L'C L Δb−

~ C d0.5 F Ay

EAL

~ 3Fy L

EΔb Cd

Pu

EAL

ΔoopL'T2

⎛⎜⎝

⎞⎟⎠

2 L'C2

⎛⎜⎝

⎞⎟⎠

2

− ~ 1.5 LFyE

~ L20

~ 10”

This is a simplified method that is likely to overestimate out-of-plane deformations.

~ ½Fy

EΔb

Part III b:

Detailing Tools and Tricks



Detailing Tools and Tricks

Controlling Gusset Plate SizeAvoid:

“One size fits all scheduling”30o fan

ConsiderSpecifying gusset widthModified WorkpointOther “smart” details

Set up spreadsheets to graph the design


Graphing Calculationy

10 5 0 5 10 15 20 25 30 35 40 45 50 55 6015

10

5

0

5

10

15

20

25

30

35

40

45

50

55

CLBeam

TOSlab

CLCol

Gusset Width


30o Fan Width


30o

30o


30o Fan Width


Very Big Gussets


Case Study: Recent SCBF Design

Recent SCBF DesignLarge Brace30o from Horizontal

Attempt 4 alternate design methods to reduce gusset size


Case Study: Alternative 1

Uniform Force MethodGusset proportioned for

zero moments at horizontal and vertical welds

20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14020

10

0

10

20

30

40

50

60

70

80

CLBeam

TOSlab

CLCol

LV LH+ 104 in=

.

Actual design

Alternate

Alternate total weld:104 in. (Actual design total weld: 136 in.)



Uniform Force MethodGusset proportioned to

provide required tension area

Gusset proportioning creates moments at horizontal and vertical welds

20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14020

10

0

10

20

30

40

50

60

70

80

CLBeam

TOSlab

CLCol

LV LH+ 87 in= .

Alternate total weld:87 in.



Component MethodGusset width matches

required area

20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14020

10

0

10

20

30

40

50

60

70

80

CLBeam

TOSlab

CLCol

LV LH+ 69 in= .Alternate total weld:69 in.



Component MethodGusset width matches

required areaModified workpoint usedLarge moment must be

resisted by frameMoment is large due to

low angle and deep beam 20 10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 14020

10

0

10

20

30

40

50

60

70

80

CLBeam

TOSlab

CLCol

LV LH+ 68 in= Tu eccentricity0 0,⋅ 2236kip ft⋅=Alternate total weld:68 in.


Case Study: Cost Comparison

Design Cost Factor

Actual Design 1.70UFM, no moment 1.45UFM, with moment 1.05Component, concentric 1.00 (baseline for comparison)Component, eccentric 1.25

Part IV:

Ordinary Concentrically Braced Frames



Limitations

Height Limits Separated by Seismic Design Category:

B&C D E FNL 35 35 NP (NL = Not Limited) (NP = Not Permitted)



Limited inelasticity

Minor connection damage

Rocking

High strength

Diaphragm yielding

Brace buckling and yielding


Design Requirements

AISC Seismic 2002

R = 5, Ωo = 2.0

(Equivalent to R = 2.5 and Ωo = 1.0, ρ not considered)

All members & connections:Amplified seismic load1.2D + 0.5L + ΩoE0.9D - ΩoE


AISC Seismic 2002 Requirements

Ru = RyFyAg

for braces

Bracing connection

V-Braced framesKL r

4.23EFy

≤



R = 3.25, Ωo = 2.0 (ASCE 7 05, Supp. #1)

K- & V-Braced frames

Braces: meet λps

K lr

4EFy

≤



V-Braced Frames2005

T = RyFyAg C = 0.3Pn

BeamSimilar requirement to SCBF

Out-of-Plane BracingUnbalance Load

or T = ΩoE



K-Braced Frames2005

T = RyFyAg

C = 0.3Pn

Similar requirement

Note:Need for out-of-

plane bracing.K-bracing is not

recommended.(T = ΩoE is not allowed)



Bracing connectionsRu = Lesser of

RyFyAg

Amplified seismic load (1.2D + 0.5L + ΩoE)

Maximum that can be delivered by the system



Bracing connectionsBolt slip

Ru = Basic Load Combination =1.2D + 0.5L + E (i.e., Not the Amplified Seismic Load)2005

Required slip << Required bearingstrength strength

Permits oversize holes


Design Example

5 x 30’ = 150’

5 x

30’

= 15

0’



Base Shear

Bingo

HazardSds = 1.0

Sd1 =0.635

Ta = 0.18 sec.

V = 0.308 W

T

V


Load Combinations

1.2D + f1L + E

0.9D ± E

1.40D + 0.5L + ρQE

0.7D ± ρQE

1.40D + 0.5L + ΩoQE

0.7D ± ΩoQE

f1 = 0.5E = ρ QE + 0.2SDS D


1.2D + f1L + Em

0.9D ± Em



Vertical Distribution

Fiwi hi

k⋅

.

wi hik⋅∑


Horizontal Distribution

0.47 V 0.53 V0.03 V

0.03 V

5%

V


Redundancy (ASCE 7 2005)

ρ = 1.0

Regular

Perimeter bracing

≥ 2 bays per side


Frame Analysis

ModelTruss

Fix in-plane,Pin out-of-plane


Brace Design

CompressionPu = 1.4D + 0.5L + E

= 1.4(19 ) + 0.5(7) + (339)

= 369k


Brace Design

(12” offset in connections; verify later in connection design)

HSS 11.25x0.375

L 13ft( )2 15ft( )2+ 2 1.0ft( )− 17.85ft

Fy 42ksiK l

r55.6 Fcr 34.8ksi A 7.73in2

φPn 374k OK



Required StrengthRu = Ry Fy Ag

= 1.4 (42 ksi) (11.94 in.2)

= 702k

(= 1.90 Pu)



Amplified seismic loadRu = 1.4D + 0.5L + ΩoE

= 1.4(16.5k) + 0.5(5.2k) + 2.0(339 k)

= 692k

(= 0.99Ry Fy Ag = 1.87 Pu)

Might as well use Ry Fy Ag



AssumptionsGusset width ~ 2 dbr (2 x 11.25” = 22.5”)

Gusset thickness (tg):

702k / (0.9 x 36 ksi x 22.5”) = 0.96”;Use 1” A36 PL

dbr

Gusset width



Net Section FractureAremoved = 2 [tg + ⅛”] tbr

= 2 [1” + ⅛”] 0.35”

= 0.79 in.2

Anet = 11.94 in.2 – 0.79 in.2 = 11.12 in.2



Required AreaφRTFuAe ≥ Ru

= 702k / (0.75 x 1.3 x 58 ksi)= 12.4 in.2 ( > Ag)

• Reinforcement required• Or use the Amplified Seismic Load and

a larger brace

Ae ≥ Ru / φRTFu

Note: if the Amplified Seismic Load is used for Ru, RTcannot be used for Rn


OCBF Gusset Connection

Same limit states as SCBF

No “hinge-zone” requirements(No reason not to provide, however)


OCBF Gusset Connection

OR

No “hinge-zone” “Hinge-zone”


No Hinge Zone Detail

30o

Whitmore width(must not exceed

actual width for calculations)30o



L – Gusset buckling (very small)

Le – Gusset edge buckling

Le

L

Le

Le

t34

EFy

⋅≤



LeLe

t34

EFy

⋅≤



Design bracing connections for the required strengthCheck all connection limit states covered for SCBF

No hinge-zone detailing required

Design column spliceNet Tension under the Amplified Seismic Load

Design base anchorageSame as SCBF

Part V:

Buckling-Restrained Braced Frames



Buckling Restrained Braced Frames

Introduction to BRBF SystemBuckling Restrained BracesBuckling Restrained Braced Frame SystemAdvantages of Buckling-Restrained Braced Frames

AISC Seismic RequirementsDesignTesting

Design Example


What is a Buckling-restrained Brace? Two Definitions

De-Coupled Stress and Buckling(Mechanics Definition)

Balanced Hysteresis(Performance Definition)

Stress resisted by steel coreBuckling resisted by sleeve


BRB Definitions Explained: Conventional Bracing

Brace behavior is asymmetric with respect to tension and compression and is subject to strength and stiffness degradation

Pcr

Ry Ag Fy

Compression

Tension


0 31 2

Com

pres

sion

Stre

ngth

Slenderness Parameter λc

BRB Definitions Explained: Sleeved Column

Sleeve achieves π2EI/L2

Stress is zeroNo material stress limit

Ag Fy

π2

E I

L2Steel core achieves Fy

λc ~ 0kl/r ~ 0


Advantages of BRBFPerformance of Braces

Balanced Hysteresis

Slightly Stronger in

Compression

Hysteretic Energy DissipationHysteretic Stability

StrengthStiffness

Long Fracture Life

Ag Fy

-β Ag Fy


Advantages of BRBF Design of Frames

Force DistributionNo Penalty for Single

Diagonals

Design of Chevron FramesModerate Beam

Requirements


BucklingRestrained

Brace

Unbonded Brace

Buckling-Restrained Brace Types

PowerCatBrace

ACMEBracing

Company


Buckling-Restrained Brace Assembly

Core

Buckling-Restrained Brace Assembly

Sleeve


Buckling-Restrained Brace Mechanics

Unbonded Brace Type

DecouplingBucklingRestraint

Encasing mortar

Yielding steel core

Steel tube

Debonding material between steel core and mortar





Courtesy ofK.C. Tsai

Courtesy ofSTAR Seismic


Alternative Connections

Courtesy ofSTAR Seismic

Courtesy ofCoreBrace

Direct bolting of core

Direct welding of core


Use of Proprietary Braces

Engineer Specifies:Brace StrengthBrace Core Area (or stiffness)Maximum and Minimum Fy (based on coupon test)

Manufacturer Provides:Braces that meet the specificationTest data that qualifies the braces


Design Procedure

Base ShearUsing Applicable Building

Code (ABC)Using R from Appendix R

Force-Based DesignTruss analysis to determine

required strength of bracesElastic analysis with assumed

brace stiffness


Brace Stiffness

Non-Yielding

Zone

Non-Yielding

Zone

Kbr = P/Δ

Δ ~ PLy/AyE

Ly = 0.5-0.8 L(depending on brace type and configuration)

Kbr = 1.3-2.0 AyE /L

FlexibilityL y

E A sc.L L y

E A nonyielding.


Effect of ConfigurationCourtesy of

Ian AikenShort BraceShort Yield LengthYield Length

Smaller Fraction of Overall Length

Brace Effectively Stiffer


Design Procedure

Determine required brace strengthDetermine brace stiffnessCheck drift Determine brace displacements at Δm

Compare required displacements and strength to existing testsPlan and conduct new tests?

Determine brace overstrengths at ΔmRequires test data

Calculate required strength of columns, beams, and connections based on brace capacity


Brace Capacity

Adjusted for Various Factorsω Strain-Hardeningβ Compression OverstrengthRy Material Overstrength

If Fy is used as core yield strength Fysc, Ry is taken from Section 6.If core yield strength Fysc is taken from material coupon test, Ry = 1.0.


Design Procedure

Option I: Project-Specific TestingDetermine required number of

testsDifferent strengths to be testedTest bracesDetermine system design

factorsAlternative: assume system

design factors prior to testing

Option II: Specification of Tested BracesConsult manufacturers about

brace strengths required and assumed stiffness

Specify required brace strength and minimum core area

Obtain system design factors from manufacturer’s test data


ASCE 7 2005 (with Supplement 1)

Identical to AISC Seismic Appendix RDefines 3 Systems

Basic BRBF SystemBRBF System with Rigid Beam-Column ConnectionsBRBF/SMF Dual System

Gives R, Ωo and Cd ValuesGives Height LimitsGives Coefficients for Determination of Approximate Period


R Values7 for Basic BRBF System8 for BRBF System with Rigid Beam-Column Connections8 for BRBF/SMF Dual System

Ωo Values2 for Basic BRBF System21/2 for BRBF System with Rigid Beam-Column Connections 21/2 for BRBF/SMF Dual System

Cd Values51/2 for Basic BRBF System5 for BRBF System with Rigid Beam-Column Connections 5 for BRBF/SMF Dual System



Height Limits Separated by Seismic Design Category:B&C D E FNL 160 160 100 for Basic BRBF System

(NL = Not Limited)

NL 160 160 100 for BRBF System with Rigid Beam-Column Connections

NL NL NL NL for BRBF/SMF Dual System

Coefficients for Determination of Approximate PeriodCr= 0.03x = 0.75(Similar to EBF)



AISC Seismic Provisions: Section 16

ScopeBrace RequirementsBracing Connection RequirementsSpecial Requirements Related to ConfigurationsFraming MembersProtected Zone


Brace RequirementsConstruction

Steel CoreBuckling-Restraining System

CoreResists 100% of Axial Force from Building-Code ForcesStrength

φPysc = 0.9 Fysc Asc

(Fysc = Specified Minimum or Measured Fy)Must Be Notch ToughNo Splices Permitted



Brace RequirementsBuckling-Restraining Mechanism

CasingBeams, Columns, GussetsRestrain Core at Drifts up to 2.0 Δm.

TestingTesting per Appendix T Two Types Required to Qualify Use of Brace Designs

AxialSubassemblage with Rotations

Test Can Qualify as Both Types (Subassemblage Test Always is also Brace Test)



Possible Subassemblages

Eccentric Loading of Brace

Loading of Braced FrameLoading of Brace and Column

Loading of Brace with Constant Imposed Rotation


TestingTesting Used to Establish Brace Expected Strength

Adjusted Brace StrengthsCompressionC’ = βωRyPysc

TensionT’ = ωRyPysc

Ry = 1.0 If Fy Is Based on Coupon TestsFactors

Factors Taken from Test Results within 2.0 Δm.Compression Strength Adjustment Factor β = Cmax/Tmax

Strain-Hardening Adjustment Factor ω = Tmax/FyA



Bracing ConnectionsRequired Strength

110% of the Adjusted Brace Strength in Compression1.1 β ω Ry Pysc

StabilityBased on Tested ConditionsDesign Conditions Must Match Tests

Bracing of BRB Gusset-Plate DesignGusset-Plate Stiffeners



Special Requirements Related to ConfigurationsK-Bracing is Not Permitted V-Braced Frames

Design Beam (and its Connections and Supporting Members) for Adjusted Brace Strengths

Provide Beam Stability Bracing Corresponding to Plastic Design of Beam

Consider Beam Deflection in Determining Brace Ductility Demands for Testing



Qb = sin(θ)(ωRyAscFy - βωRyAscFy)(θ = Angle from Horizontal)

β = 1.1 (for some types of BRBs)

ΔQb = QbL3/48EI

Special Requirements Related to ConfigurationsV-Braced Frames




Δv

Brace Elongation:

Δb = Δv sinθ

Beam Vertical Displacement

θ


Beams and ColumnsUse Seismically Compact ShapesDesign for Adjusted Brace StrengthsColumn Splices

Shear from Mp at top and bottom of column 50% of φMp of Smaller Section

Protected ZoneSteel CoreGussets


Vu

Mp

Mp

Vu

βωRyAscFy

ωRyAscFy

βωRyAscFy

ωRyAscFy


Beams and ColumnsUse Seismically Compact ShapesDesign for Adjusted Brace StrengthsColumn Splices

Shear from Mp at top and bottom of column 50% of φMp of Smaller Section

Protected ZoneSteel CoreGussets


βωRyAscFy ωRyAscFy

βωRyAscFyωRyAscFy


Verify Adequate PerformanceStabilityDuctilityAchieve Full Tension StrengthNo Excessive Compression Overstrength

Establish Design Coefficientsβ = Cmax / Tmax

ω = Tmax / FyA

AISC Seismic Provisions: Appendix T


Types of Testing

Project-SpecificSuite of Tests Designed to Satisfy Appendix T Requirements

From Other SourcesPublic Domain

Published StudiesSufficient Number and Range to Satisfy Appendix T RequirementsSufficiently Documented to Satisfy Appendix T Requirements

Brace ManufacturerExisting Test DataSufficient Number and Range to Satisfy Appendix T RequirementsSufficiently Documented to Satisfy Appendix T Requirements


-2.5-2

-1.5

-1-0.5

00.5

1

1.52

2.5

Loading Sequence2@Δby 2@½Δbm 2@Δbm 2@1½Δbm 2@2Δbm 2@1½Δbm

Appendix T: Verify Adequate Performance

Maximum DeformationRelates to Undesirable Local and Global Buckling Modes2.0 Times Design Story Drift

Relates Expected Drift to Traditional Cd Value Range


Cumulative Ductility2@Δby 2@½Δbm 2@Δbm 2@1½Δbm 2@2Δbm 2@1½Δbm

020406080

100120140160180200220240

Cumulative Inelastic Strain

Most Significant Fracture Index

200 Times Yield Strain



Acceptance CriteriaPositive Incremental StiffnessNo Fracture or InstabilityPmax ≥ Pysc ( = A Fy )Pmax ≤ 1.3 Tmax



Design Example

5 x 30’ = 150’

5 x

30’

= 15

0’

Note: 2 braced frames

per side (vs. 3 for SCBF)


R = 8


Base Shear

Bingo

HazardSds = 1.00

Sd1 = 0.635

Ta = 0.726 sec.

V = 0.109 W

T

V


Load Combinations

1.2D + f1L + E

0.9D ± E

1.40D + 0.5L + ρQE

0.7D ± ρQE

1.40D + 0.5L + ΩoQE

0.7D ± ΩoQE

f1 = 0.5E = ρ QE + 0.2SDS D


1.2D + f1L + Em

0.9D ± Em



Vertical Distribution of Forces

100%12711902

93%118121623

80%101832404

61%77943205

36%4595459Roof

% ofTotalBaseShear

Story Shear

kip

Brace LevelStory Force

kip

DiaphragmLevel


Preliminary Design of Braces

y

usc F

PA φ=

θcos2 FPu =

Assume braces resist 100% of story shear

Design braces precisely to calculated capacity

(Pu = φPn = φFyAsc)

F

θ


Preliminary Design of Braces

7.63260.950.21

6.00205.340.92

5.18177.140.93

3.96135.440.94

2.3379.840.95

in.2kipdeg.

Core Area Asc

Brace Force Pu

Brace Angle θ

Brace Level


Consult Brace Manufacturer

Does the manufacturer’s suite of tests cover the brace forces and deformations in the design?

What are the appropriate brace overstrength factors to be used in the design of beams and columns?

What are the appropriate stiffness values for braces to be used in the analytical model?


Test Extrapolation

From designer’s perspective:Axial:

50% Prototype Strength ≤ Specimen Strength ≤ 150% Prototype StrengthSubassemblage:

Specimen Strength≥ Prototype Strength

Manufacturer’s perspective:Axial:

67% Specimen Strength ≤ Prototype Strength ≤ 200% Specimen Strength Subassemblage:

Prototype Strength ≤ Specimen Strength


Required Tests

391—130260.91

308—103205.32

266—89177.13

203—68135.44

120—4079.85

kipkip

Applicable Test Range

Brace Force Pu

Brace Level


Example of a Manufacturer’s Brace Axial Test Range

1.351.145204.23937—31242.3469ST2

1.271.095953.37664—22144.0332BT3

1.411.126013.81458—15342.7229BT2

1.361.106163.51250—8343.1125BT1

ωβΣΔb/Δbyin.kipksikip

Overstrength at Maximum

Displacement

Cumul-ative

Ductility

Maximum Dis-

placement

Qualification Range

Measured Yield

Stress

Nominal Strength

Test ID

Brace Axial Tests

Courtesy of ACME Bracing

Use largest values of β and ω for design


Brace Axial Test Qualification Range

0 100 200 300 400 500 600 700 800 900 1000

BT1

BT2

BT3

ST2

Test

ID

kips

Example of a Manufacturer’s Brace Axial Test Range


Δbm=3.51”

Δbm=3.81”

Δbm=3.37”

Δbm=4.23”


Example of a Manufacturer’s Subassemblage Brace Test Range

2.281.351.145204.23469—042.3469ST2

2.461.391.115734.31619—043.5619ST1

%ωβΣΔb/Δbyin.kipksikip

Max-imum

Rotation

Overstrength at Maximum

Displacement

Cumul-ative

Ductility

Maximum Dis-

placement

Qualification Range

Measured Yield

Stress

Nominal Strength

Test ID

Subassemblage Tests



Example of a Manufacturer’s Subassemblage Brace Test Range


Subassemblage Test Qualification Range

0 100 200 300 400 500 600 700

ST1

ST2

Test

ID

kips

Δbm=4.31”θbm=2.46%

Δbm=4.23”θbm=2.28%


Brace Stiffness

150%1370169 112 28120.008.832611144%1164131 107 23815.006.622052139%981119 119 23813.255.791773134%657107 131 2389.254.031354129%36395 143 2385.252.32805

kip/inin.in.in.in.2in.2kip

CKKbrLnyLyLbrAnyAscPuBrace Level

Manufacturer’s input requiredTypically included in design documents

(Brace stiffness

ratio)


Design Frame

Perform elastic analysis to determine distribution of forces between frame and braces

Compute overstrength factor in order to size columns and beams


Sources of Overstrength

?−1.11FyAsc/φPuDesign

1.05−1.00CTolFabrication Tolerance

1.20−1.00RyMaterial

1.50−1.20ωStrain-Hardening

1.20−1.03βCompression

Typical RangeSymbolSource of Overstrength


Overstrength of Manufacturer’s Braces

1.03CTolFabrication Tolerance

42ksi/38ksi =1.11RyMaterial

1.41ωStrain-Hardening

1.14βCompression

ACME ValueSymbolSource of Overstrength


Project-Specific Overstrength Factor

u

Tolscyyo P

CAFRβω=Ω

If braces are designed precisely to their demand:

(If Pu = φPn = φFyAsc)

03.2900.0

03.111.141.114.1 =×××==Ωφ

βω Tolyo

CR

If ρ = 1.0Pu = QE


Project-Specific Overstrength Factor

u

Tolscyyo P

CAFRρβω=Ω

=Ωφ

ρβω Tolyo

CR

If ρ ≠ 1.0Pu = ρQE

QE = Pu/ρ


Design Frame

Iterate on 3 sets of load combinations:Basic Seismic Load

1.2D+f1L+E0.9D-E Modify brace areas for Demand/Capacity = 1.0

Amplified Seismic Load (with Project-Specific Ωo)1.2D+f1L+ΩoE0.9D-ΩoEModify beams and columns for Demand/Capacity ≤ 1.0

DriftCdEModify brace areas if drift is excessive


Design Frame

Three options if Pu < φFyAscDesign for uniform brace demand/capacity ratio

May lead to braces, beams, and columns significantly larger than requiredCompute Ωo based on lowest brace demand/capacity ratio

May lead to beams and columns significantly larger than requiredDo a separate analysis of each beam and column with actual

overstrength of each connected braceMost work

Pu = φFyAsc in the Design Example


Beam Design

Fhor = (βωRyFyAscCTol + ωRyFyAscCTol)cosθ = (β + 1) ωRyFyAscCTolcosθ

Fver = (βωRyFyAscCTol - ωRyFyAscCTol)sinθ = (β - 1) ωRyFyAscCTolsinθ

ωRyFyAscCTol βωRyFyAscCTol

Compute unbalance forces on beamsApply forces to beams in model


Vertical Unbalance Forces

162504655317.6350.21

03343664176.0040.92

74293163605.1840.93

05222412753.9640.94

13Roof131421622.3340.95

kipkipkipkipin.2deg.

ωRyFyAscCTolβωRyFyAscCTolAscθ

Net Vertical Force

Diaphragm Level

Vertical Force

Adjusted Tension Strength

Adjusted Compression

Strength

Core Area

Brace Angle

Brace Level


116%

110%

112%

102%

99%

Percentage of Preliminary Core Area

8.83

6.62

5.79

4.03

2.32

in.2Asc

Core Area

302.11

226.42

198.03

137.74

79.35

kip

Pu

Brace Force

BraceLevel

Final Frame Design



0.260.0122128.831036.622

0.120.0121045.793054.034

0.210.01613Roof2.325

in.in/kipkipin.2ΔvAsc

Vertical Displacement

Beam Flexibility

Fbm

Net Vertical Force

Diaphragm Level

Core Area

Brace Level



Δv

Brace Elongation:

Δb = Δv sinθθ


Brace Axial Deformation

)cos(θmbm Δ=Δ

byscy

udbm AF

PC Δ=Δ

Brace Elongation:

Based on calculated drift

Based on 2% drift (required for qualifying tests)

(If Pu = φPn = φFyAsc)

bydC Δ= φ

bedbm C Δ=Δ


Brace Deformations

1.59%2.21 0.22 21611.65%1.95 0.19 15621.71%2.02 0.20 15631.78%2.10 0.21 15641.85%2.18 0.22 1565

in.in.in.2Δm/H

2ΔbmΔbeH

Rotation Angle

Maximum Deformation

Elastic Deformation

Story Height

Brace Level

Based on Calculated Forces


Brace Deformations

2.77 2.00%21612.36 2.00%15622.36 2.00%15632.362.00%15642.36 2.00%1565in.in.

2ΔbmH

Maximum Deformation

Rotation AngleStory HeightBrace LevelBased on 2% Drift


Brace Deformations

BT2, BT3ST1, ST22.960.200.261BT1, BT2ST1, ST22.530.170.262BT1, BT2ST1, ST22.440.080.123

BT1ST1, ST22.440.080.124BT1ST1, ST22.490.140.215

in.in.in.ΔbΔv

Applicable Brace Tests

Applicable Subassemblage

Tests

Total Deformation

Brace Deformation

Vertical Displacement

Brace Level

From Beam Displacement


613

460

402

280

161

Required Connection

Strength1.1βωRyFyAscCTol

kip

8.83

6.62

5.79

4.03

2.32

in.2Asc

Core Area

302.11

226.42

198.03

137.74

79.35

kip

Pu

Brace Force

BraceLevel

Final Frame Design



Design bracing connections for the required strengthCheck all connection limit states covered for SCBF

No hinge-zone detailing

Design column spliceSame as SCBF

Design base anchorageSame as SCBF

Specify Protected Zone

Part VI

Wrap up



Understand the likely yield mechanism(s) of your structure.

Design and detail yielding members for ductility.Design non-yielding members for the largest forces

that the yielding mechanism can deliver.

Remember


Acknowledgements

Professor Stephen MahinProfessor Hassan Astaneh-AslPatxi Uriz

University of California at Berkeley

Professor Charles RoederUniversity of Washington

Ian AikenSeismic Isolation Engineering

Professor Robert TremblayÉcole Polytechnique, Montreal

Professor K.C. TsaiNational Center for Research on Earthquake Engineering

Tom SabolEngelkirk and Sabol

Walterio LópezRutherford&Chekene

Images have been contributed by:

Thank You


Suggested Design References:

ACI (2002), Building Code Requirements for Structural Concrete, ACI 318-02, American Concrete Institute, Farmington Hills, MI.

AISC (2001), Load and Resistance Factor Design Manual of Steel Construction, 3rd Ed., American Institute of Steel Construction, Inc., Chicago.

AISC (2006), SCBF Gusset-Plate Design Aid: SCBF Gusset.xls, Steel Tools, www.AISC.org (in development).

AISC (2006), Seismic Design Manual, American Institute of Steel Construction, Inc., Chicago (in press).

AISC (2002), Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Inc., Chicago.

AISC (2005), Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Inc., Chicago (in press).

AISC (2005), Specification for Structural Steel Buildings, ANSI/AISC 360-05, American Institute of Steel Construction, Inc., Chicago, IL.

ASCE (2005), ASCE 7-05, Minimum Design Loads for Buildings and Other Structures (with Supplement Number One), American Society of Civil Engineers, Reston.

Astaneh-Asl, A., (1998). Seismic Behavior and Design of Gusset Plates for Braced Frames, Steel Tips, Structural Steel Education Council, Moraga, California.

Astaneh-Asl, A., Cochran, M., and Sabelli, R. (2006). Notes on Seismic Detailing of Gusset Plates, Steel Tips, Structural Steel Education Council, Moraga, California (in press).

Bruneau, M., Uang, C.M., and Whittaker, A., (1998). Ductile Design of Steel Structures, McGraw-Hill.

López, W. and Sabelli, R., (2004). Seismic Design of Buckling-Restrained Braced Frames, Steel Tips, Structural Steel Education Council, Moraga, California.

Sabelli, R., (2003). “Concentrically Braced Frames,” 2000 IBC Structural/Seismic Design Manual Volume 3, Steel and Concrete Building Design Examples, ICC, Whittier, California.

Sabelli, R., (2006). “Concentrically Braced Frames,” 2006 IBC Structural/Seismic Design Manual Volume 3, Steel and Concrete Building Design Examples, ICC, Whittier, California (in press).

Tamboli, A., (1999). Handbook of Structural Steel Connection Design and Details, McGraw-Hill.

Tremblay, R., (2001). “Seismic Behavior and Design of Concentrically Braced Steel Frames”, Engineering Journal, AISC, Third Quarter.

Uang, C.M. and Nakashima, M. (2003). “Steel Buckling-Restrained Frames,” Earthquake Engineering: Recent Advances and Applications, Chapter 16, Y. Bozorgnia and V.V. Bertero, eds., CRC Press, Boca Raton, FL.

American Institute of Steel Construction, Inc. One East Wacker Drive, Suite 700Chicago, IL 60601-1802

312.670.2400 www.aisc.org

There's always a solution in steel.

Seismic Braced Frames - Design Concepts and Connections

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