Page 1
Steel Structures 10 - 1Instructional Material Complementing FEMA 451, Design Examples
NEHRP RECOMMENDED PROVISIONSSEISMIC DESIGN OF STEEL STRUCTURES
• Context in NEHRP Recommended Provisions
• Steel behavior
• Reference standards and design strength
• Moment resisting frames
• Braced frames
• Other topics
• Summary
Page 2
Steel Structures 10 - 2Instructional Material Complementing FEMA 451, Design Examples
Steel Design: Context in ProvisionsDesign basis: Strength limit state
Using the 2003 NEHRP Recommended Provisions:Load combination Chap. 4Seismic load analysis Chap. 5Components and attachments Chap. 6Design of steel structures Chap. 8
AISC Seismicand others
Page 3
Steel Structures 10 - 3Instructional Material Complementing FEMA 451, Design Examples
Seismic Resisting SystemsUnbraced Frames•Joints are:
Rigid/FR/PR/Moment-resisting
•Seismic classes are:Special/intermediate/Ordinary/not detailed
Braced Frames• Concentric bracing• Eccentric bracing
Page 4
Steel Structures 10 - 4Instructional Material Complementing FEMA 451, Design Examples
Monotonic Stress-Strain Behavior
Page 5
Steel Structures 10 - 5Instructional Material Complementing FEMA 451, Design Examples
Bending of Steel Beam
M
Strain slightly above yield strain
Section near “plastic”
Extreme fiber reachesyield strain and stress
φ u
ε y
Strain Stress
φ y
εy < ε < εsh σy
σy
σy
εsh
Page 6
Steel Structures 10 - 6Instructional Material Complementing FEMA 451, Design Examples
Plastic Hinge Formation
Page 7
Steel Structures 10 - 7Instructional Material Complementing FEMA 451, Design Examples
Cross - section DuctilityConceptual moment - curvature
M
yφ′
Mp
My
yφ uφφ
u u u
y y y
φ φ εφ φ ε
≤ =′
Page 8
Steel Structures 10 - 8Instructional Material Complementing FEMA 451, Design Examples
Moment CurvatureLaboratory Test -- Annealed W Beam
Page 9
Steel Structures 10 - 9Instructional Material Complementing FEMA 451, Design Examples
Behavior Modes For Beams
OLM Elastic lateral tors. bucklingOHI Inelastic lateral tors. bucklingOJG Inelastic lateral tors. bucklingOJE Idealized behaviorOJK Strain hardening
Mr
Page 10
Steel Structures 10 - 10Instructional Material Complementing FEMA 451, Design Examples
Flexural Ductility of Steel MembersPractical Limits
1 Lateral torsional bucklingBrace well
2 Local bucklingLimit width-to-thickness ratiosfor compression elements
3 FractureAvoid by proper detailing
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Steel Structures 10 - 11Instructional Material Complementing FEMA 451, Design Examples
Local and Lateral Buckling
Page 12
Steel Structures 10 - 12Instructional Material Complementing FEMA 451, Design Examples
Lateral Torsional Buckling
Page 13
Steel Structures 10 - 13Instructional Material Complementing FEMA 451, Design Examples
Local Buckling
ycr tbEk σ
μπσ ≤
−= 22
2
)/)(1(12
b
t
Classical plate buckling solution:
Substituting μ = 0.3 and rearranging:
yFkE
tb 95.0≤
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Steel Structures 10 - 14Instructional Material Complementing FEMA 451, Design Examples
Local Bucklingcontinued
0.38y
b Et F≤
With the plate buckling coefficient taken as 0.7 and an adjustment for residual stresses, the expression for b/t becomes:
This is the slenderness requirement given in the AISC specification for compact flanges of I-shaped sections in bending. The coefficient is further reduced for sections to be used in seismic applications in the AISC Seismic specification
0.3y
b Et F≤
Page 15
Steel Structures 10 - 15Instructional Material Complementing FEMA 451, Design Examples
Welded Beam to Column Laboratory Test - 1960s
Page 16
Steel Structures 10 - 16Instructional Material Complementing FEMA 451, Design Examples
Bolted Beam to Column Laboratory Test - 1960s
Page 17
Steel Structures 10 - 17Instructional Material Complementing FEMA 451, Design Examples
Pre-Northridge Standard
Page 18
Steel Structures 10 - 18Instructional Material Complementing FEMA 451, Design Examples
Following the 1994 Northridge earthquake,
numerous failures of steel beam-to-column moment
connections were identified. This led to a multiyear,
multimillion dollar FEMA-funded research effort known as the SAC joint
venture. The failures caused a fundamental rethinking of
the design of seismic resistant steel moment
connections.
Page 19
Steel Structures 10 - 19Instructional Material Complementing FEMA 451, Design Examples
Bottom Flange Weld Fracture Propagating Through Column Flange and Web
Page 20
Steel Structures 10 - 20Instructional Material Complementing FEMA 451, Design Examples
Beam Bottom Flange Weld Fracture Causing a Column Divot Fracture
Page 21
Steel Structures 10 - 21Instructional Material Complementing FEMA 451, Design Examples
Northridge Failure
• Crack through weld
• Note backup barand runoff tab Bottom flange
of beam
Beamweb
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Steel Structures 10 - 22Instructional Material Complementing FEMA 451, Design Examples
Northridge Failure
Columnflange
Backup bar
Beam flangeand web
Page 23
Steel Structures 10 - 23Instructional Material Complementing FEMA 451, Design Examples
Northridge Failures
Column Flange HAZ Lamellar Tear
Weld Weld Fusion Column Divot
Page 24
Steel Structures 10 - 24Instructional Material Complementing FEMA 451, Design Examples
Flexural Mechanics at a Joint
12
12
Beam Moment Fw
Fy
1 2w yF Z F Z⋅ > ⋅
21 1 2
Cross Sections
Fw
Fy
Page 25
Steel Structures 10 - 25Instructional Material Complementing FEMA 451, Design Examples
Welded Steel Frames
• Northridge showed serious flaws. Problems correlated with:
- Weld material, detail concept and workmanship- Beam yield strength and size- Panel zone yield
• Repairs and new design- Move yield away from column face(cover plates, haunches, “dog bone”)
- Verify through tests• SAC Project: FEMA Publications 350 through 354
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Steel Structures 10 - 26Instructional Material Complementing FEMA 451, Design Examples
Reduced Beam Section (RBS) Test SpecimenSAC Joint Venture
Plastic Rotation (% rad)
Mom
ent (
MN
-m)
-4 -2 0 2 4-4
-2
0
2
4
Graphics courtesy of Professor Chia-Ming Uang, University of California San Diego
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Steel Structures 10 - 27Instructional Material Complementing FEMA 451, Design Examples
T-stub Beam-Column TestSAC Joint Venture
Photo courtesy of Professor Roberto Leon, Georgia Institute of Technology
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Steel Structures 10 - 28Instructional Material Complementing FEMA 451, Design Examples
T-Stub Failure Mechanisms
Net section fracture in stem of T-stub
Plastic hinge formation -- flange and web local buckling
Photos courtesy of Professor Roberto Leon, Georgia Institute of Technology
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Steel Structures 10 - 29Instructional Material Complementing FEMA 451, Design Examples
Rotation (rad)-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Mom
ent (
k-in
)
-7000-6000-5000-4000-3000-2000-1000
01000200030004000500060007000
Mom
ent (
kN-m
)
-700-600-500-400-300-200-1000100200300400500600700
FS-03 - Moment/Rotation
T-Stub Connection Moment Rotation Plot
Graphic courtesy of Professor Roberto Leon, Georgia Institute of Technology
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Steel Structures 10 - 30Instructional Material Complementing FEMA 451, Design Examples
Extended Moment End-Plate Connection Results
Photo courtesy of Professor Thomas Murray, Virginia Tech
Page 31
Steel Structures 10 - 31Instructional Material Complementing FEMA 451, Design Examples
Extended Moment End-Plate Connection Results
Total Plastic Rotation (rad)-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
Mom
ent a
t Col
umn
Cen
terli
ne (i
n-ki
ps)
-25000
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
25000
(b) Moment vs Plastic Rotation(a) Moment vs Total Rotation
Total Rotation (rad)-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08
Mom
ent a
t Col
umn
Cen
terli
ne (i
n-ki
ps)
-25000
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
25000
Graphics courtesy of Professor Thomas Murray, Virginia Tech
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Steel Structures 10 - 32Instructional Material Complementing FEMA 451, Design Examples
Ductility of Steel Frame JointsLimits
Welded Joints- Brittle fracture of weld- Lamellar tearing of base metal- Joint design, testing, and inspection
Bolted Joints- Fracture at net cross-section- Excessive slip
Joint Too Weak For Member- Shear in joint panel
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Steel Structures 10 - 33Instructional Material Complementing FEMA 451, Design Examples
Multistory FrameLaboratory Test
Page 34
Steel Structures 10 - 34Instructional Material Complementing FEMA 451, Design Examples
Flexural DuctilityEffect of Axial Load
0.10 ==∞=p
pc
y MM
PPe
57.0MM
55.0PP"10.5e
p
pc
y
===
28.0MM
76.0PP"75.1e
p
pc
y
===
0.7rLx
=
W12x36
Page 35
Steel Structures 10 - 35Instructional Material Complementing FEMA 451, Design Examples
Axial StrutLaboratory test
45rL=
Page 36
Steel Structures 10 - 36Instructional Material Complementing FEMA 451, Design Examples
Cross Braced FrameLaboratory test
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Steel Structures 10 - 37Instructional Material Complementing FEMA 451, Design Examples
Tension Rod (Counter) BracingConceptual Behavior
H
Δ
“Slapback”For cycle 2
H
Page 38
Steel Structures 10 - 38Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced Frame
Page 39
Steel Structures 10 - 39Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FrameLab test of link
Page 40
Steel Structures 10 - 40Instructional Material Complementing FEMA 451, Design Examples
Steel Behavior• Ductility
- Material inherently ductile- Ductility of structure < ductility of material
• Damping- Welded structures have low damping- More damping in bolted structures dueto slip at connections
- Primary energy absorption is yielding ofmembers
Page 41
Steel Structures 10 - 41Instructional Material Complementing FEMA 451, Design Examples
Steel Behavior• Buckling
- Most common steel failure under earthquake loads- Usually not ductile- Local buckling of portion of member- Global buckling of member- Global buckling of structure
• Fracture- Nonductile failure mode under earthquake loads- Heavy welded connections susceptible
Page 42
Steel Structures 10 - 42Instructional Material Complementing FEMA 451, Design Examples
NEHRP Recommended ProvisionsSteel Design
• Context in NEHRP Recommended Provisions
• Steel behavior
• Reference standards and design strength
Page 43
Steel Structures 10 - 43Instructional Material Complementing FEMA 451, Design Examples
Page 44
Steel Structures 10 - 44Instructional Material Complementing FEMA 451, Design Examples
Using Reference StandardsStructural Steel
Both the AISC LRFD and ASD methodologies are presented in a unified format in both the Specification for Structural Steel Buildings and the Seismic Provisions for Structural Steel Buildings.
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Steel Structures 10 - 45Instructional Material Complementing FEMA 451, Design Examples
Page 46
Steel Structures 10 - 46Instructional Material Complementing FEMA 451, Design Examples
Other Steel MembersSteel Joist Institute
Standard Specifications, 2002
Steel CablesASCE 19-1996
Steel Deck InstituteDiaphragm Design Manual, 3rd Ed., 2005
Page 47
Steel Structures 10 - 47Instructional Material Complementing FEMA 451, Design Examples
NEHRP Recommended ProvisionsSteel Design
• Context in NEHRP Recommended Provisions
• Steel behavior
• Reference standards and design strength
• Moment resisting frames
Page 48
Steel Structures 10 - 48Instructional Material Complementing FEMA 451, Design Examples
Steel Moment Frame Joints
Frame Test θi Details
Special Req’d 0.04 Many
Intermediate Req’d 0.02 Moderate
Ordinary Allowed NA Few
Page 49
Steel Structures 10 - 49Instructional Material Complementing FEMA 451, Design Examples
Steel Moment Frame Joints
u pa bM M
b+
≈ ⋅
*y y yF R F= ⋅
* *1 1.7u y yf
a bF F Z Fb A d+
≈ ⋅ ⋅ ≈
Page 50
Steel Structures 10 - 50Instructional Material Complementing FEMA 451, Design Examples
Panel Zones
Special and intermediate moment frame:
• Shear strength demand:
Basic load combination or φRyMp of beams• Shear capacity equation
• Thickness (for buckling)
• Use of doubler plates
Page 51
Steel Structures 10 - 51Instructional Material Complementing FEMA 451, Design Examples
Steel Moment Frames• Beam shear: 1.1RyMp + gravity
• Beam local buckling - Smaller b/t than LRFD for plastic design
• Continuity plates in joint per tests
• Strong column - weak beam rule- Prevent column yield except in panel zone- Exceptions: Low axial load, strong stories, top story,and non-SRS columns
Page 52
Steel Structures 10 - 52Instructional Material Complementing FEMA 451, Design Examples
Steel Moment Frames
• Lateral support of column flange- Top of beam if column elastic- Top and bottom of beam otherwise- Amplified forces for unrestrained
• Lateral support of beams- Both flanges- Spacing < 0.086ryE/Fy
Page 53
Steel Structures 10 - 53Instructional Material Complementing FEMA 451, Design Examples
Prequalified Connections
See FEMA 350: Recommended Seismic Design Criteria forNew Steel Moment-Frame Buildings
-Welded Unreinforced Flange -Bolted Unstiffened End Plate Connection-Welded Free Flange Connection -Bolted Stiffened End Plate Connection-Welded Flange Plate Connection -Bolted Flange Plate Connection-Reduced Beam Section Connections
See ANSI/AISC 358-05, Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications
-Reduced Beam Section Connections-Bolted Stiffened and Unstiffened Extended Moment End Plate Connections
Page 54
Steel Structures 10 - 54Instructional Material Complementing FEMA 451, Design Examples
Welded Coverplates
Page 55
Steel Structures 10 - 55Instructional Material Complementing FEMA 451, Design Examples
Reduced Beam Section (RBS)
Page 56
Steel Structures 10 - 56Instructional Material Complementing FEMA 451, Design Examples
Extended End Plate
Page 57
Steel Structures 10 - 57Instructional Material Complementing FEMA 451, Design Examples
Excellent Moment Frame Behavior
Page 58
Steel Structures 10 - 58Instructional Material Complementing FEMA 451, Design Examples
Excellent Moment Frame Behavior
Page 59
Steel Structures 10 - 59Instructional Material Complementing FEMA 451, Design Examples
Excellent Moment Frame Behavior
Page 60
Steel Structures 10 - 60Instructional Material Complementing FEMA 451, Design Examples
Special Moment FramesExample
5 at
25'
-0"
N
7 at 25'-0"
Page 61
Steel Structures 10 - 61Instructional Material Complementing FEMA 451, Design Examples
Special Moment Frames
The following design steps will be reviewed:• Select preliminary member sizes• Check member local stability• Check deflection and drift• Check torsional amplification• Check the column-beam moment ratio rule• Check shear requirement at panel zone• Select connection configuration
Page 62
Steel Structures 10 - 62Instructional Material Complementing FEMA 451, Design Examples
Special Moment Frames
Select preliminary member sizes – The preliminary member sizes are given in the next slide for the frame in the East-West direction. These members were selected based on the use of a 3D stiffness model in the program RAMFRAME. As will be discussed in a subsequent slide, the drift requirements controlled the design of these members.
Page 63
Steel Structures 10 - 63Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Preliminary Member Sizes
Page 64
Steel Structures 10 - 64Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Check Member Local Stability
bf
tf
twhc
Check beam flange:(W33x141 A992)
Upper limit:
Check beam web:
Upper limit:
6.012
f
f
bt=
0.3 7.22y
EF
=
49.6c
w
ht
=
3.76 90.6y
EF
=
OK
OK
Page 65
Steel Structures 10 - 65Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Check Deflection and DriftThe frame was checked for an allowable story drift limit of 0.020hsx. All stories in the building met the limit. Note that the NEHRP Recommended Provisions Sec. 4.3.2.3 requires the following check for vertical irregularity:
2
3
5.17 .268 . 0.98 1.33.14 .160 .
d x story
d x story
inC in
inCin
⎛ ⎞⎜ ⎟Δ ⎝ ⎠= = <
Δ ⎛ ⎞⎜ ⎟⎝ ⎠
Therefore, there is no vertical irregularity.
Page 66
Steel Structures 10 - 66Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Check Torsional Amplification
The torsional amplification factor is given below. If Ax < 1.0 then torsional amplification is not required. From the expression it is apparent that if δmax / δavg is less than 1.2, then torsional amplification will not be required.
2
max
1.2xavg
A δδ
⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠
The 3D analysis results, as shown in FEMA 451, indicate that none of the δmax / δavg ratios exceed 1.2; therefore, there is no torsional amplification.
Page 67
Steel Structures 10 - 67Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Member Design NEHRP Guide
Member Design Considerations - Because Pu/φPn is typically less than 0.4 for the columns, combinations involving Ω0 factors do not come into play for the special steel moment frames (re: AISC Seismic Sec. 8.3). In sizing columns (and beams) for strength one should satisfy the most severe value from interaction equations. However, the frame in this example is controlled by drift. So, with both strength and drift requirements satisfied, we will check the column-beam moment ratio and the panel zone shear.
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Steel Structures 10 - 68Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Column-Beam Moment Ratio
Per AISC Seismic Sec. 9.6*
* 1.0pc
pb
MM
Σ>
Σ
where ΣM*pc = the sum of the moments in the column above and
below the joint at the intersection of the beam and column centerlines. ΣM*pc is determined by summing the projections of the nominal flexural strengths of the columns above and below thejoint to the beam centerline with a reduction for the axial force in the column.ΣM*
pb = the sum of the moments in the beams at the intersection of the beam and column centerlines.
Page 69
Steel Structures 10 - 69Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Column-Beam Moment Ratio
Column – W14x370; beam – W33x141
* 22
*
5002 736 50109
66,850
ucpc c yc
g
pc
P kipsM Z F in ksiA in
M in kips
⎛ ⎞ ⎡ ⎤⎛ ⎞Σ = Σ − = −⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦⎝ ⎠Σ = −
Adjust this by the ratio of average story height to average clear height between beams.
* 268 . 160 .66,850 75,300251.35 . 128.44 .pc
in inM in kips in kipsin in
+⎛ ⎞Σ = − = −⎜ ⎟+⎝ ⎠
Page 70
Steel Structures 10 - 70Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Column-Beam Moment RatioFor beams:
( )
( )( ) ( ) ( )
*
' 2
' 2'
2
(1.1 )
. ./ 2 / 2 25.61 .
222 / 2
1.046 248.8 .2 25,700
12 2
248.8 .
pb y p v
v p h
h
c b
p
p
p p
M R M M
with M V S
S dist fromcol centerline to plastic hinged d in
V shear at plastic hinge location
wLMV M wL
L
klf inin kips
in
Σ = Σ +
=
=
= + =
=
+⎡ ⎤= + =⎣ ⎦
⎛ ⎞⎜ ⎟− +⎜ ⎟⎝ ⎠= 221.2kips=
Page 71
Steel Structures 10 - 71Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Column-Beam Moment Ratio
*
(221.2 )(25.61 .) 5,665
(1.1 )
2[(1.1)(1.1)(25,700 ) 5,665 ] 73,500
v p h
pb y p v
M V S kips in in kips
andM R M M
in kips in kips in kips
= = = −
Σ = Σ +
= − + − = −
The ratio of column moment strengths to beam moment strengths iscomputed as:
*
*75,300 1.02 1.0073,500
pc
pb
M in kipsRatio OKM in kips
Σ −= = = > ∴Σ −
Other ratios are also computed to be greater than 1.0
Page 72
Steel Structures 10 - 72Instructional Material Complementing FEMA 451, Design Examples
SMF Example –Panel Zone CheckThe 2005 AISC Seismic specification is used to check the panel zone strength. Note that FEMA 350 contains a different methodology, but only the most recent AISC provisions will be used. From analysis shown in the NEHRP Design Examples volume(FEMA 451), the factored strength that the panel zone at Story 2 of the frame in the EW direction must resist is 1,883 kips.
2 23 (3)(16.475 .)(2.66)0.6 1 (0.6)(50 )(17.92 .)( ) 1(33.3 .)(17.92 .)( )
537.6 315
( ) determined :
(1
cf cfv y c p p
b c p p
v p
v u
b t inR F d t ksi in td d t in in t
R t
The required total web plus doubler plate thickness is byR Rφ
⎡ ⎤ ⎡ ⎤= + = +⎢ ⎥ ⎢ ⎥
⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦= +
=
.0)(537.6 315) 1,883
2.91 .
1.66 ., :1.25 . ( 1.25 . 0.625 . )
required
doubler
p
p
p
t kips
t in
The column web thickness is in therefore the required doubler plate thickness ist in therefore use one in plate or two in plates
+ =
=
=
Page 73
Steel Structures 10 - 73Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Connection Configuration
Page 74
Steel Structures 10 - 74Instructional Material Complementing FEMA 451, Design Examples
SMF Example – Connection Configuration
Page 75
Steel Structures 10 - 75Instructional Material Complementing FEMA 451, Design Examples
Special Moment FramesSummary
Beam to column connection capacitySelect preliminary member sizesCheck member local stabilityCheck deflection and driftCheck torsional amplificationCheck the column-beam moment ratio ruleCheck shear requirement at panel zoneSelect connection configuration
• Prequalified connections
• Testing
Page 76
Steel Structures 10 - 76Instructional Material Complementing FEMA 451, Design Examples
NEHRP Recommended ProvisionsSteel Design
• Context in Provisions• Steel behavior• Reference standards and design strength• Seismic design category requirement• Moment resisting frames• Braced frames
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Steel Structures 10 - 77Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced FramesBasic Configurations
X Diagonal K
VInverted V K
Page 78
Steel Structures 10 - 78Instructional Material Complementing FEMA 451, Design Examples
Braced Frame Under Construction
Page 79
Steel Structures 10 - 79Instructional Material Complementing FEMA 451, Design Examples
Braced Frame Under Construction
Page 80
Steel Structures 10 - 80Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced Frames
Special AISC Seismic R = 6Chapter 13
Ordinary AISC Seismic R = 3.25Chapter 14
Not Detailed for Seismic R = 3AISC LRFD
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Steel Structures 10 - 81Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced Frames
Dissipate energy after onset of global buckling by avoiding brittle failures:
• Minimize local buckling
• Strong and tough end connections
• Better coupling of built-up members
Page 82
Steel Structures 10 - 82Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced FramesSpecial and Ordinary
Bracing members:
- Compression capacity = φcPn
- Width / thickness limits
Generally compact
Angles, tubes and pipes very compact
- Overall
- Balanced tension and compressionyF
Er
KL 4<
Page 83
Steel Structures 10 - 83Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced FramesSpecial concentrically braced frames
Brace connectionsAxial tensile strength > smallest of:
• Axial tension strength = RyFyAg
• Maximum load effect that can be transmitted to brace by system.
Axial compressive strength ≥ 1.1RyPn where Pn is the nominal compressive strength of the brace.
Flexural strength > 1.1RyMp or rotate to permitbrace buckling while resisting AgFCR
Page 84
Steel Structures 10 - 84Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced FramesV bracing:• Design beam for D + L + unbalanced brace forces,
using 0.3φPc for compression and RyFyAg in tension• Laterally brace the beam• Beams between columns shall be continuous.K bracing:• Not permitted
Page 85
Steel Structures 10 - 85Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced FramesBuilt-up member stitches:
• Spacing < 40% KL/r• No bolts in middle quarter of span• Minimum strengths related to Py
Column in CBF:• Same local buckling rules as brace members• Splices resist moments
Page 86
Steel Structures 10 - 86Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced Frame
Example
E-W direction
Page 87
Steel Structures 10 - 87Instructional Material Complementing FEMA 451, Design Examples
Concentrically Braced Frame Example
The following general design steps are required:• Selection of preliminary member sizes• Check strength• Check drift• Check torsional amplification• Connection design
Page 88
Steel Structures 10 - 88Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced Frames
Link
Brace
Beam
Page 89
Steel Structures 10 - 89Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced Frame Under Construction
Page 90
Steel Structures 10 - 90Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced Frame Under Construction
Page 91
Steel Structures 10 - 91Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced Frames
Eccentric bracing systems R Cd
Building frame system or part ofdual system w/ special moment frame
With moment resisting connections 8 4at columns away from links
Without moment resisting connections 7 4at columns away from links
These connectionsdetermine classification
Page 92
Steel Structures 10 - 92Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesDesign Procedure
1. Elastic analysis2. Check rotation angle; reproportion as required3. Design check for strength4. Design connection details
Page 93
Steel Structures 10 - 93Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesExample
Page 94
Steel Structures 10 - 94Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesRotation Angle
1. Compute total Δ = Cd ΔE
2. Deform model as rigid-plastic mechanism with hinges at ends of line
3. Compute rotation angle at end of link
p
p
p
p
p
p
p
p
VM
LVM
whenforeInterpolat
VM
Lwhenradians
VM
Lwhenradians
6.26.1
6.202.0
6.108.0
<<
≥≤
≤≤
α
α
α
4. Check limits (Sec. 15.2g)
Page 95
Steel Structures 10 - 95Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesRotation Angle Example
8.5' 3.0' 8.5'
12.6
7'
θ
Δ
α
From computer analysis:
Total drift:
From geometry:
0.247e inΔ =
4(0.247) 0.99 .d eC inΔ = Δ = =
( )
max
20 0.99 0.0433 12.67 12
1.63.0 ' 3.52'
0.08 0.043
p
y
L rade
MBecause e
F
rad rad OK
α θ
α
⎛ ⎞⎛ ⎞ ⎛ ⎞= = =⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠
= < =
= >
Page 96
Steel Structures 10 - 96Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesRotation Angle
• Rotation angle limits based on link beam equivalent length
- Short links yield in shear and are allowedgreater rotation
• Rotation angle may be reduced in design by:
- Increasing member size (reducing Δe)- Changing geometric configuration(especially changing length of link beam)
Page 97
Steel Structures 10 - 97Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesLink Design
• Provide strength V and M per load combinations• Check lateral bracing per AISC Lpd
• Local buckling (width to thickness of web and flange) per AISC Seismic
• Stiffeners (end and intermediate) perAISC Seismic
Page 98
Steel Structures 10 - 98Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesBrace Design
⎟⎠⎞⎜
⎝⎛⋅> linkofstrengthshear
designfromforceaxialR25.1Strength y
Page 99
Steel Structures 10 - 99Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesBrace Design Example
Check axial strength of 15.26 ft long TS 8 x 8 x 5/8 Fy = 46 ksi:
( )
( )( )
2 2
2 2
4676.4
(1)(15.26) 1261.2
2.99
61.2 4.71 118.3 0.658
(29,000) 76.461.2
0.658 46 35.8
0.9 16.4 35.8 528
y
e
FF
cr yy
e
cr
c n c g cr
KLr
E F FF
EF ksiKLr
F ksi
P A F kip
π π
φ φ
= =
⎛ ⎞⎜ ⎟< = ∴ =⎜ ⎟⎝ ⎠
= = =⎛ ⎞⎜ ⎟⎝ ⎠⎛ ⎞
= =⎜ ⎟⎝ ⎠= = =
Page 100
Steel Structures 10 - 100Instructional Material Complementing FEMA 451, Design Examples
Eccentrically Braced FramesBrace Design Example
( )( )( )
( )( )( )( )
0.9(0.6 ) 0.9 0.6 50 16.4 0.43 190
2 0.9 50 1052(0.9) / 262.5
3 12
w
p
n y
n
V F d t kip
or
V M e kip
φ
φ
= ⎡ ⎤= =⎣ ⎦
= = =
( ) ( )
( ) ( )85.2 120.2
1901.25 1.1 120.2 369 52885.2
e link e brace
u
V kip and P kip
P OK
= =
⎛ ⎞∴ = = <⎜ ⎟⎝ ⎠
Page 101
Steel Structures 10 - 101Instructional Material Complementing FEMA 451, Design Examples
NEHRP Recommended ProvisionsSteel Design
• Context in NEHRP Recommended Provisions
• Steel behavior
• Reference standards and design strength
• Moment resisting frames
• Braced frames
• Other topics
Page 102
Steel Structures 10 - 102Instructional Material Complementing FEMA 451, Design Examples
Special Truss Moment Frame
• Buckling and yieldingin special section
• Design to be elasticoutside special section
• Deforms similar to EBF
• Special panels to be symmetric X orVierendeel
Page 103
Steel Structures 10 - 103Instructional Material Complementing FEMA 451, Design Examples
Special Truss Moment Frame
Geometric Limits:
5.2tb,diagonalsbarFlat
23
dL
32
5.0LL1.0
'6d'65L
p
s
≤
<<
<<
≤≤
Page 104
Steel Structures 10 - 104Instructional Material Complementing FEMA 451, Design Examples
Special Truss Moment Frame
( )2
2 sin 0.3pcp nt cd
s
i i p
MV P P
L
F h V L
α⎛ ⎞
= + +⎜ ⎟⎝ ⎠
=∑ ∑
Page 105
Steel Structures 10 - 105Instructional Material Complementing FEMA 451, Design Examples
Special Truss Moment Frame
Page 106
Steel Structures 10 - 106Instructional Material Complementing FEMA 451, Design Examples
Special Truss Moment Frame
Page 107
Steel Structures 10 - 107Instructional Material Complementing FEMA 451, Design Examples
General Seismic DetailingMaterials:
• Limit to lower strengths and higher ductilities
Bolted Joints:• Fully tensioned high strength bolts• Limit on bearing
Page 108
Steel Structures 10 - 108Instructional Material Complementing FEMA 451, Design Examples
General Seismic DetailingWelded Joints:
• AWS requirements for welding procedure specs• Filler metal toughness
• CVN > 20 ft-lb @ -20°F, or AISC Seismic App. X• Warning on discontinuities, tack welds, run offs,
gouges, etc.Columns:
• Strength using Ωo if Pu / φPn > 0.4• Splices: Requirements on partial pen welds and
fillet welds
Page 109
Steel Structures 10 - 109Instructional Material Complementing FEMA 451, Design Examples
Steel DiaphragmExample
φVn = φ (approved strength)
φ = 0.6
For example only:Use approved strength as 2.0 x working load inSDI Diaphragm Design Manual
Page 110
Steel Structures 10 - 110Instructional Material Complementing FEMA 451, Design Examples
Steel Deck Diaphragm ExampleL
dVE VE
wE
plf500w0ww
'40d'80L
ELD ===
==
( ) plf4176.02
5002vv
plf50040
20000v;kip202LwV
ESDI
EE
E
==φ
=
====
Deck chosen:1½ “, 22 gage with welds on 36/5 pattern and 3sidelap fasteners, spanning 5’-0”
Capacity = 450 > 417 plf
Page 111
Steel Structures 10 - 111Instructional Material Complementing FEMA 451, Design Examples
Welded Shear Studs
Page 112
Steel Structures 10 - 112Instructional Material Complementing FEMA 451, Design Examples
Shear Stud Strength - AISC 2005 Specification
Qn = 0.5 Asc ( fc’ Ec)1/2 ≤ Rg Rp Asc Fu
Rg = stud geometry adjustment factorRp = stud position adjustment factor
Note that the strength reduction factor for bending has been increased from 0.85 to 0.9. This results from the strength model for shear studs being more accurate, although the result for Qn is lower in the 2005 specification.
Page 113
Steel Structures 10 - 113Instructional Material Complementing FEMA 451, Design Examples
Rg = 1.0 Rg = 1.0* Rg = 0.85 Rg = 0.7
Shear Studs – Group Adjustment Factor
*0.85 if wr/hr < 1.5
Qn = 0.5 Asc ( fc’ Ec)1/2 ≤ Rg Rp Asc FuRg = stud group adjustment factor
Page 114
Steel Structures 10 - 114Instructional Material Complementing FEMA 451, Design Examples
Shear Studs – Position Adjustment Factor
Rp = 0.75 (strong)= 0.6 (weak)
Rp = 1.0 Rp = 0.75
DeckNo Deck
Qn = 0.5 Asc ( fc’ Ec)1/2 ≤ Rg Rp Asc FuRp = stud position adjustment factor
Page 115
Steel Structures 10 - 115Instructional Material Complementing FEMA 451, Design Examples
Shear Studs – Strength Calculation Model Comparison
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
AISC Predicted Stud Strength, QN (k)
Expe
rim
enta
l Stu
d St
reng
th, Q
e (k)
S Studs2S StudsW Studs
Qe=QN
0
5
10
15
20
25
0 5 10 15 20 25
Predicted Stud Strength, Qsc (k)
Expe
rimen
tal S
tud
Stre
ngth
, Qe (
k)
Qe=Qsc
AISC Seismic prior to 2005
Virginia Tech strength model
Page 116
Steel Structures 10 - 116Instructional Material Complementing FEMA 451, Design Examples
Shear Studs – Diaphragm Applications
Shear studs are often used along diaphragm collector members to transfer the shear from the slab into the frame. The shear stud calculation model in the 2005 AISC specification can be used to compute the nominal shear strengths. A strength reduction factor should be used when comparing these values to the factored shear. There is no code-established value for the strength reduction factor. A value of 0.8 is recommended pending further development.
Page 117
Steel Structures 10 - 117Instructional Material Complementing FEMA 451, Design Examples
Inspection and TestingInspection Requirements
• Welding:- Single pass fillet or resistance welds
> PERIODIC- All other welds
> CONTINUOUS
• High strength bolts:> PERIODIC
Page 118
Steel Structures 10 - 118Instructional Material Complementing FEMA 451, Design Examples
Inspection and TestingShop Certification
• Domestic:- AISC- Local jurisdictions
• Foreign:- No established international criteria
Page 119
Steel Structures 10 - 119Instructional Material Complementing FEMA 451, Design Examples
Inspection and TestingBase Metal Testing
• More than 1-1/2 inches thick
• Subjected to through-thickness weld shrinkage
• Lamellar tearing
• Ultrasonic testing
Page 120
Steel Structures 10 - 120Instructional Material Complementing FEMA 451, Design Examples
NEHRP Recommended ProvisionsSteel Design
• Context in Provisions
• Steel behavior
• Reference standards and design strength
• Moment resisting frames
• Braced frames
• Other topics
• Summary