2006 asce/sei structures congress st. louis, mo may 18-20 1 manual and inelastic-analysis based...
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2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 1
Manual and Inelastic-Analysis Based
Design of Partially-Restrained Frames
Using the 2005 AISC Specifications
By
Christopher M. Foley, PhD, PE John Schaad, MS, EIT Marquette University Jezerinac, Geers, & Associates Milwaukee, WI Dublin, OH
2006 ASCE-SEI Structures CongressSt. Louis, MO
May 18-20
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 2
AISC Specifications are becoming more liberalized in the designer's favor and are beginning to allow software capabilities to be exploited.
There are new demands on the structural engineer to understand phenomena that software is now able to consider.
How do we teach these concepts and specification developments to students?
MOTIVATION FOR PRESENTATION
Focus can now be on SYSTEM BEHAVIOR rather than members or components and designing for target behavior is possible.
Address Wooten's Third Law of Steel Column Design - Corollary Number 2:
"The computer renders obsolete the necessity of rationalizingand simplifying problems - or even of understanding them" (Wooten 1971)
It would be very beneficial to have a manual methodology to get starting sizesfor inelastic analysis-based design.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 3
N
TYPICAL FRAMING PLAN
PR Connections Flexible (pin) Connections
A B C D E30 ft.3@10 ft.
1
2
3
4
30 f
t.
X-Braced Bay
Superimposed DL: 63 psf• Comp. Slab: 46 psf• Ceiling: 2 psf• Fireproofing: 3 psf• MEP systems: 12 psf
Superimposed LL: 30 psf
Steel Framing: 5 psf
30 ft. 30 ft.
30 f
t.30
ft.
Wind, WL: 20 psf
Steel Material: A992
Superimposed DL: 83 psf• Comp. Slab: 46 psf• Ceiling: 2 psf• Fireproofing: 3 psf• MEP systems: 12 psf• Partitions: 20 psf
Superimposed LL: 50 psf
Roof Level:
Floor Level:
Cladding: 25 psf (wall area)
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 4
RIP R
LP
FW
15
15RW
RkR
FkR
bpkR
30
A B C D E
30 3030
FLP
REP
BASE ANALYTICAL MODEL
FIP F
EP
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 5
10 zEI
L
M
0.50 FpbM
10 zEI
L
M
0.50 RpbM
10 zEI
L
M
0.75 pcM
BILINEAR CONNECTION MODELS
FLOOR BEAM ROOF BEAM
BASE PLATE
0.50 FpbM 0.50 R
pbM
0.75 pcM
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 6
AISC APPENDIX 7 - Preliminary Design
Member design can be greatly streamlined if the following constraints on member selection are included.
• Choose a target interstory drift to meet target 2nd order sway amplification:
2, ,
11.15 0.153
10.85
Hu nt H u nt
HLB
P P
HL
• Choose member sizes to avoid stiffness reduction;
*0.50 1.00ub
y
PEI EI
P
• Choose member sizes to avoid effect;P
10.15 1.00u
eL
PB
P
Implies that behavior is "nearly" linear up to first hinge formation.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 7
AISC APPENDIX 1 - Preliminary Design
Local Buckling:
276.02 0.328 u
w y
Ph
t P
29.94 2.10 35.88u
w y
Ph
t P
• Flanges;
0.113u
y
P
P
0.113u
y
P
P
• Webs in Combined flexure and axial compression;
9.152
f
f
b
t
Stability and Nonlinear Geometric Effects
0.675u
y
P
P
Lateral-Torsional Buckling
min 113.43
by
Lr
(column members) (beam members)
min1
2
0.12 0.076 580
by
Lr
M
M
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 8
0.9cap
n
M
M
0.9u
ny
P
P
Moment capacity in presence of axial loading
0.9u
ny
P
P
0.9u
n
M
M
91 1
8 0.9 0.9u u
cap pc pcny ny
P PM M M
P P
min
15 121.96
0.12 0.076 0.5 580yr
Assume column bent in reverse curvature and theinflection point is at 2/3 column height:
Therefore, if miny yr r then;
AISC APPENDIX 1 - Preliminary Design
0.20
11 0.90 0.452
u ucap pc pc
ny ny
P PM M M
P P
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 9
LOADING COMBINATIONS
ASCE 7 - 02 Strength Limit State (with corrections):
1.4 DL
1.2 1.6 0.5 rDL LL LL
1.2 0.5 1.6 rDL LL LL
1.2 0.5 0.5 1.6rDL LL LL WL
ASCE 7 - 02 Serviceability Limit State
DL LL
0.5 0.7DL L W
0.2% notional loads
0.2% notional loads
0.2% notional loads
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 10
DESIGN ASSUMPTIONS
The following assumptions are made in the design:
• Unbraced lengths for columns were taken as the story height.
• The compression flange for beams in positive flexure is fully braced.
• The compression flange for girders subjected to negative flexure is braced at column lines and at beam lines.
• Compression forces in beams is negligible.
• Columns are pin-pin for minor axis bending.
• Beams are non-composite with floor system.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 11
Plastic Hinges:
MECHANISM 1 - BEAM STRENGTH
uPuP
- beam hinge
- connection hinge
ssu b n
pb M pb
M M
M M
M
M pbM
pbM
ssuM
1
ssu
b nM
MM
1.4 DL1.2 1.6DL LL
Plastic hinges form in beamsindicating SCWB behavior.
FuIP
RuIP R
uIP
FuIP
Loading Combinations:
Simplified GravityLoad Analysis:
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 12
PP
M 3
2
8e
PaM
L
BEAM SERVICEABILITY
Moment Diagram - Kotylar (1996)
2
2
81m
aM Pa
L
12
1mb
EI
k L
Moment-Area Principle Yields
2 2 23 4 2424CL
PaL a a
EI
L
aa
mbkmbk
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 13
BEAM DESIGN
10bL
Assume connection strength at 50% of the plastic moment capacity: 0.50M
Assume that the beams are bent in reverse curvature:
Serviceability:
Compute the ultimate simply-supported beam moment.
Compute the required strength of the PR beam.
1 2 0.50M M
Using the unbraced length establish: minyr
10 Assume that beam connection stiffness results in PR behavior:
Check total, DL and LL deflections at mid-span.
Strength:
Select a beam for strength considerations.
Check that connections do not exceed yield moment at service level loads.
Adjust beam size as required.
Beams Selected: W16x40 (roof) W21x55 (floor)
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 14
MECHANISM 2 - Gravity and Notional Loading
Plastic Hinges:
- beam hinge
- connection hinge
30
15
10 20
15
15
FuIP
RuIPR
uN
FuN
Plastic hinges formin beams indicating
SCWB behavior.
FuEP
RuEP
Loading combinations applied in a non-proportional manner (e.g. gravity load first and then lateral load to failure) will likely result in a sway mechanism forming.
Gravity and notional loading are assumed to be applied in a proportional manner - therefore, a combined mechanism is targeted.
FuIP
RuIP
FuLP
RuLP
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 15
MECHANISM 3 - Gravity and Lateral Loading
Lateral and gravity loading combinations are applied in a proportional manner - therefore, a combined mechanism is targeted.
RuH
FuH
Previous beam design indicates that plastic hinges will NOT form when gravityloading at the following magnitude is applied:
1.2 0.5 rDL LL LL
Plastic Hinges:
- beam hinge
- connection hinge
30
15
10 20
15
15
FuIP
RuIP
Plastic hinges formin beams indicating
SCWB behavior.
FuEP
RuEP
FuIP
RuIP
FuLP
RuLP
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 16
16 40W
,2cap M pcol bm
M M
SIZING FOR TARGET MECHANISMS
SCWB criteria can be used to help ensure assumed targeted mechanisms form.
16 40W 16 40W
21 55W
16 40W
,22cap M pcol bm
M M
,1 ,2
2cap cap M pcol col bmM M M
,1 ,2cap cap M pcol col bmM M M
21 55W 21 55W 21 55W
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 17
16 40W 16 40W 16 40W 16 40W
12 58W
12 58W
12 58W
12 58W
FRAME FOR FURTHER EVALUATION
The framework shown below is the system that will be used for displacement evaluation.
We will now check the columns and/or beams to ensure second-order effectsare "small" and the frame is serviceable with respect to interstory drift.
12 58W
12 58W 21 55W 21 55W 21 55W 21 55W
12 58W
12 58W
12 58W
12 58W
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 18
2
1 2 1 2 6
12i
ib c k
V h h L h h E
E I I R
Exterior Sub-Assembly
Interior Sub-Assembly
2
1 2 1 2 6
6 2e
eb c k
V h h L h h E
E I I R
SUB-ASSEMBLAGE DISPLACEMENTS
Using modifications to the work of Englekirk (1994), displacement expressionsfor interior, exterior and column base segments can be generated.
Partially Restrained Column Bases
31
1
31
3c
cbc kb
EIVh
EI R h
For simplicity, we will assume inflection points at 1/2 first story height and mid-height of the second story columns.
2L 2L
kR
kR
iV
iV1 2
i
h hR V
L
RcI
cI
bI bI1h
2h
kRcI
eV
eV
bI
1 2i
h hR V
L
2L
cI 1h
2h
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 19
Exterior and Interior Columns:
2nd Floor Beam: 21 55W
12 58W
Assume inflection points at mid-heights: 1 2 7.5 90h h
, 10 765,278Ik bp
EIR k in rad
L
, 10 918,333k beam
EIR k in rad
L
Connection and base plate stiffness:
"SMALL" 2nd ORDER EFFECTS AND SERVICEABILITY
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 20
1.2 1.6 0.5 rDL LL LL with notional loading
21.118 180 360 180 6(29,000) 1
0.04612(29,000) (1,140) (475) (918,333) 2i
2(0.559) 180 360 180 6(29,000) 1
0.046(29,000) (1,140) 2(475) (918,333) 2e
3(0.559)(90) 3(29,000)(475)1 0.02
3(29000)(475) (765,278)(90)ecb
0.06Etot OK
3(1.118)(90) 3(29,000)(475)1 0.02
3(29000)(475) (765,278)(90)icb
0.07Itot OK
"SMALL" 2nd ORDER EFFECTS - STRENGTH L.S.
4.47H k, 1,666u ntP k
180L
max
0.074H at 1st story
4.470.559
8e
kV k
1.118iV k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 21
1.2 0.5 1.6rDL LL LL W without notional loading
28.10 180 360 180 6(29,000) 1
0.3312(29,000) (1,140) (475) (918,333) 2i
2(4.05) 180 360 180 6(29,000) 1
0.266(29,000) (1,140) 2(475) (918,333) 2e
3(4.05)(90) 3(29,000)(475)1 0.11
3(29000)(475) (765,278)(90)ecb
0.37Etot OK
3(8.10)(90) 3(29,000)(475)1 0.23
3(29000)(475) (765,278)(90)icb
0.56Itot OK
"SMALL" 2nd ORDER EFFECTS - STRENGTH L.S.
32.4H k, 1,368u ntP k
180L
max
0.65H at 1st story
32.44.05
8e
kV k
8.10iV k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 22
0.5 0.7rDL LL LL W
23.55 180 360 180 6(29,000) 1
0.1412(29,000) (1,140) (475) (918,333) 2i
2(1.78) 180 360 180 6(29,000) 1
0.116(29,000) (1,140) 2(475) (918,333) 2e
3(1.78)(90) 3(29,000)(475)1 0.05
3(29000)(475) (765,278)(90)ecb
0.16Etot OK
3(3.55)(90) 3(29,000)(475)1 0.10
3(29000)(475) (765,278)(90)icb
0.28Itot OK
SERVICEABILITY LIMIT STATE
without notional loading
400 0.45L
14.18H k, 1,176u ntP k
180L
max
0.33H at 1st story
14.21.78
8e
kV k
3.55iV k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 23
16 40W 16 40W 16 40W 16 40W
12 58W
12 58W
12 58W
12 58W 12 58W
The framework shown below is the system that resulted from the serviceability and 2nd order effects evaluation.
We will now simply ensure that the member sizes chosen will result in thetargeted mechanisms forming at levels higher than the strength limit statecombinations.
12 58W
12 58W
12 58W
12 58W 21 55W
FRAME FOR MECHANISM ANALYSIS
12 58W
21 55W 21 55W 21 55W
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 24
30
15
10 20
15
15
FuIP
RuIP
RR uP N F
F uP N
FuIP
RuIP
MECHANISM 2 - Combined Mechanism
1.2 1.6 0.5 rDL LL LL
1.2 0.5 1.6 rDL LL LL
1.2 0.5 1.6rDL LL LL WL RR uP H F
F uP H
RP
FP
RR uP N F
F uP N
p pbM M
, , ,min 0.75 ,p col p col cap colM M M
, 0.5p con pbM M
y nyP P
y g yP A F
y g yP A F
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 25
EVALUATION OF DESIGN USING INELASTIC ANALYSIS
The frame designed preliminarily using the preceding procedure was checkedusing MASTAN2 (Ziemian and McGuire).
The following loading combinations were evaluated:
0.5 0.7rDL LL LL W
1.2 1.6 0.5 rDL LL LL
1.2 0.5 1.6 rDL LL LL
DL LL
1.2 0.5 1.6rDL LL LL W
The yield surface of MASTAN2 was manipulated as follows:
ny
P
P
, ,p base p col
M Mor
M M 1.0
1.0
Default MASTAN2 yield surfaceconnects end points.
,ny y col gP F A
, , ,min ,x y col p base p colZ F M M
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 26
EVALUATION OF DESIGN USING INELASTIC ANALYSIS
1.2 1.6 0.5 2.11r ultDL LL LL
0.0 0.5 1.0 1.5 2.0 2.5 3.00.0
0.5
1.0
1.5
2.0
2.5
Displacement (in.)
Node 15 - Horiztonal
Node 15
Elem. 35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.000
0.025
0.050
0.075
0.100
P/P
y
M/Mp
Element 35 - Right
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 27
EVALUATION OF DESIGN USING INELASTIC ANALYSIS
1.2 0.5 1.6 2.08r ultDL LL LL
Node 15
0.00 0.25 0.50 0.75 1.000.0
0.5
1.0
1.5
2.0
2.5
Displacement (in.)
Node 15 - Horiztonal
Elem. 39
Elem. 35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.00
0.01
0.02
0.03
0.04
0.05
Element 35 - Right Element 39 - Right
P/P
y
M/Mp
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 28
EVALUATION OF DESIGN USING INELASTIC ANALYSIS
1.2 0.5 1.6 2.04r ultDL LL LL W
Node 15
0 2 4 6 8 100.0
0.5
1.0
1.5
2.0
2.5
Displacement (in.)
Node 15 - Horiztonal
Elem. 39 Elem. 35
Elem. 100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.0
0.1
0.2
0.3
0.4
0.5
Element 35 - Right Element 39 - Right Element 100 - Bottom
P/P
y
M/Mp
ALR = 1.0
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 29
SERVICEABILITY EVALUATION OF DESIGN
0.5 0.7rDL LL LL W
DL LL
0.0 0.1 0.2 0.3 0.40.0
0.2
0.4
0.6
0.8
1.0
1.2
App
lied
Load
Rat
io
Displacement (in.)
1st InterStory Drift 2nd InterStory Drift Roof Level Drift
No connections hit yieldmoment at service levels.
Typical limit on interstory drift is:
1800.45
400is
1 0.28is
No connections hit the yield moment
Vertical beam deflections were well below acceptable thresholds
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 30
CONCLUDING REMARKS
An approximate methodology for sizing members within the context of AISCAppendices 1 and 7 has been outlined.
The method has been shown to be relatively accurate given its overall simplicity.
The advantage of the approach is that it focuses on "system" behavior whilemaintaining flexibility to consider beam-columns, beams, and connections.
The formulas for displacement have been show to be accurate for preliminarydesign purposes and they provide the engineer with significant problem feel.
Small multiple-story multiple-bay frames can be sized using the procedure tocontrol second-order effects and the resulting designs have significant reservestrength.
The best use of the methodology would be to demonstrate the importantprovisions in the new AISC (2005) specifications in a simplified manner so thatalgorithms for computer implementation can be developed.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 31
REFERENCES
Englekirk, R. (1994) Steel Structures - Controlling Behavior ThroughDesign, John Wiley & Sons, Inc., New York, NY.
Foley, C.M. and Schinler, D. (2003) "Automated Design of Steel Frames Using Advanced Analysis and Object-Oriented Evolutionary Computation", Journal of Structural Engineering, 129 (5), pp. 648-660.
Kotylar, N. (1996) "Formulas for Beams with Semi-Rigid Connections"Engineering Journal, AISC, Fourth Quarter, pp. 142-146.
Wooten, J. (1971) "Wooten's Third Law and Steel Column Design",Engineering Journal, 2nd Quarter, pp. 1-3.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 32
Extra slides showing detailed computationsto follow this slide.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 33
,
3050 5 3,750
2F
E LLP psf lbs
SERVICE LOADING
Gravity Loading
Roof Floor
,
3088 5 25 15
2
25 15 5 14,100
FE DLP psf psf
psf lbs
,
15 3068 5 25
2 2
1525 5 8,850
2
RE DLP psf psf
psf lbs
,
3088 10
2
25 15 10 16,950
FI DLP psf
psf lbs
,
3030 5 2,250
2R
E LLP psf lbs
,
3050 10 7,500
2F
I LLP psf lbs
,
3068 10
2
1525 10 12,075
2
RI DLP psf
psf lbs
,
3030 10 4,500
2R
I LLP psf lbs
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 34
SERVICE LOADING (continued)
15 9020
2 2
6,750
RW psf
lbs
Wind Loading
9020 152
13,500
FW psf
lbs
Leaning Columns
Roof Floor
, 88 60 120
125 60 15 2
2
339,300
FL DLP psf
psf
lbs
,
150 60 120
2
180,000
FL LLP psf
lbs
, 68 60 120
15 125 60 2
2 2
256,050
RL DLP psf
psf
lbs
,
130 60 120
2
108,000
RL LLP psf
lbs
Roof Floor
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 35
AISC APPENDIX 7 - DIRECT ANALYSIS
Design Analysis Requirements
,n in planeP computed using 1.0in planeK
Out of plane strength defined in usual manner.
Column Nominal Strength
Analysis must incorporate geometric nonlinearity: P P and
• AISC amplification factors allowed if reduced stiffness is used;
2
1
10.85
nt H
BP
HL
Interstory drift, , and axial force demands computed using;H
* 0.8 bEI EI 4 1 0.50r r rb
y y y
P P P
P P P
1
1
1
m
r
e
CB
P
P
and construction/erection imperfections.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 36
AISC APPENDIX 7 (continued)
Design Analysis Requirements (continued)
P • effects can be omitted when; 1 1.00B
0.15r eLP P
• Story out-of-plumb imperfections must be included through notional loading;
0.002i iN Y
Out-of-plumbness can be directly inserted into the analytical model (1/500).
• If second-order amplification is less than 50% notional loads need only need only be applied with gravity load combinations.
• Computer software capable of conducting geometrically nonlinear analysis is allowed.
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 37
AISC APPENDIX 1 - INELASTIC ANALYSIS AND DESIGN
Material Limitations:
The yield strength of members shall not exceed 65 ksi.
Local Buckling:
2.753.76 1
0.90r
w y y
Ph E
t F P
1.12 2.33 1.490.90
r
w y y y
Ph E E
t F P F
• Flanges;
0.1250.9
r
y
P
P
0.1250.9
r
y
P
P
• Webs in Combined flexure and axial compression;
0.382
f
f y
b E
t F
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 38
AISC APPENDIX 1 (continued)
Stability and Nonlinear Geometric Effects
• First order (mechanism) analysis can be used provided second-order effects are considered. Second order inelastic analysis is permitted.
• Sufficient rotational ductility in columns preserved through limiting axial load levels;
0.90 0.75 0.675r y g yP F A P
Lateral-Torsional Buckling
4.71b
y
L E
r F
1
2
0.12 0.076b
y y
L M E
r M F
(targeted for column members)
(targeted for beam and beam-column members)
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 39
AISC APPENDIX 1 (continued)
Axial Capacity, Moment Capacity and Combined Forces
0.90r c nP P P 0.90 0.9 1.6r c p yM M M M
81
0.9 9 0.9r r
n p
P M
P M
1
2 0.9 0.9r r
n p
P M
P M
0.9r
p
M
M
0.9r
n
P
P
0.900.9
r
p
M
M
0.200.9
r
n
P
P
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 40
BEAM DESIGN - STRENGTH
217
1 1 0.5
144.7
ssu
b n reqM
MM
k ft
Roof Beams Floor Beams
1
2
1.4 12.08 16.9
1.2 12.08 1.6 4.5 21.7
u
u
P k
P k
1
2
1.4 16.95 23.7
1.2 16.95 1.6 7.5 32.3
u
u
P k
P k
32.3 10 323ssuM k k ft 21.7 10 217ss
uM k k ft
323
1 1 0.5
215.3
ssu
b n reqM
MM
k ft
10bL (negative bending)
Assume connection strength at 50% of the plastic moment capacity: 0.50M
At the strength limit state, beams are bent in reverse curvature and ratio ofend moments is 0.50.
min
10 121.31
0.12 0.076 0.5 580yr
min
1.49yr
Try W14x30 Try W16x36177b n pM M k ft
min
1.52yr
240b n pM M k ft
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 41
10
BEAM DESIGN - SERVICEABILITY (continued)
Roof Beams Floor Beams
12.08 4.5 16.6P k 16.95 7.5 24.4P k
0.42CL tot
Assume that beam connection stiffness results in PR behavior:
10.91
21
mb
EI
k L
429,000 448
10360
360,889
zmb
ksi inEIk
Lk in rad
429,000 291
10360
234,417
zmb
ksi inEIk
Lk in rad
10.83
21
mb
EI
k L
W14x30 W16x36
120a 120a
7.50.42 0.13
24.4CL LL
0.16CL tot
4.50.16 0.04
16.6CL LL
Check total, DL and LL deflections at mid-span.
12.080.16 0.12
16.6CL DL
16.950.42 0.29
24.4CL DL
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 42
BEAM DESIGN - SERVICEABILITY (continued)
Roof Beams Floor Beams
12.08 4.5 16.6P k 16.95 7.5 24.4P k
10.91
21
mb
EI
k L
10.83
21
mb
EI
k L
W14x30 W16x36
120a 120a
3
2
8(24.4)(120) (0.83)180.0
(360) (12)eM k ft
Ensure end moments are less than connection yield moment at service loads.
0.5 177 88 134M pM NG 0.5 240 120 180M pM NG
3
2
8(16.6)(120) (0.91)134.3
(360) (12)eM k ft
connection yield moments may be exceeded at service
Revise to W16x40 Revise to W21x55
1.35 1.31yr 1.57 1.31yr
473b n pM M k ft 274b n pM M k ft
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 43
SIZING FOR TARGET MECHANISMS (continued)
Interior 2nd Story Column Exterior 2nd Story Column
Interior 1st Story Column Exterior 1st Story Column
2 max14.2 21.7 35.9uP k
1 max22.9 32.3 55.2uP k
2 max3 21.7 65.1uP k
2 max11.8 16.8 28.6uP k
1 max3 32.3 96.9uP k
2 max3 16.8 50.4uP k
,2274cap col
M k ft
,1 ,2
473cap capcol colM M k ft
,1 ,2236cap capcol col
M M k ft
15yK L min
1.96yr
,2137cap col
M k ft
Gravity loading combinations will be used (axial load in columns greatest).
W8x40
W12x58
W12x58
W8x40
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 44
COLUMN DESIGN - Out-of-Plane Buckling
Interior Column: Exterior Column:
W12x58 W8x40
1.4 DL
1.2 1.6 0.5 rDL LL LL
1.2 0.5 1.6 rDL LL LL 14.2 21.7
18.8 24.0 78.7
uP
k
Only first-story columns and gravity load combinations will be checked at this point.
1.4 DL
3 21.7
3 24.0 137.1
uP
k
1.2 1.6 0.5 rDL LL LL
12.4 16.9
19.7 23.7 72.7
uP
k
3 16.9
3 23.7 121.8
uP
k
1.0 15minor uK L ft
11.8 16.8
22.9 32.3 83.8
uP
k
3 16.8
3 32.3 147.3
uP
k
1.2 0.5 1.6 rDL LL LL
299 84c nP k k OK 527 147c nyP k k OK
W12x58 W8x40
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 45
COLUMN DESIGN - Cross-Section Stability Checks
Interior Column: Exterior Column:W12x58 W8x40
1.2 1.6 0.5 rDL LL LL 1.2 1.6 0.5 rDL LL LL
11.8 16.8 22.9 32.3 83.8uP k 3 16.8 3 32.3 147.3uP k
585y g yP A F k 850y g yP A F k
7.21 9.152
f
f
b
t 7.82 9.15
2f
f
b
t
27.0 29.94 2.10 57.8u
w y
Ph
t P
840.14 0.675
585u
y
P
P
1470.17 0.675
850u
y
P
P
17.6 29.94 2.10 58.7u
w y
Ph
t P
W12x58 W8x40
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 46
kR
RcI
bI1h
2h
eV
eV
2L
cI
2L 2L
kR
kR
iV
iV1 2
i
h hR V
L
RcI
cI
bI bI1h
2h
kRcI
eV
eV
bI
1 2i
h hR V
L
2L
cI 1h
2h
FLOOR-LEVEL SUBASSEMBLAGES
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 47
COLUMN DESIGN - Out-of-Plane Buckling
Interior Column: Exterior Column:
W10x45 W8x35
1.4 DL
1.2 1.6 0.5 rDL LL LL
1.2 0.5 1.6 rDL LL LL 14.2 21.7
18.8 24.0 78.7
uP
k
Only first-story columns and gravity load combinations will be checked at this point.
1.4 DL
3 21.7
3 24.0 137.1
uP
k
1.2 1.6 0.5 rDL LL LL
12.4 16.9
19.7 23.7 72.7
uP
k
3 16.9
3 23.7 121.8
uP
k
1.0 15minor uK L ft
11.8 16.8
22.9 32.3 83.8
uP
k
3 16.8
3 32.3 147.3
uP
k
1.2 0.5 1.6 rDL LL LL
260 84c nP k k OK 332 147c nP k k OK
W10x45 W8x35
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 48
COLUMN DESIGN - Cross-Section Stability and LTB Checks
Interior Column: Exterior Column:W10x45 W8x35
1.2 1.6 0.5 rDL LL LL 1.2 1.6 0.5 rDL LL LL
11.8 16.8 22.9 32.3 83.8uP k 3 16.8 3 32.3 147.3uP k
515y g yP A F k 665y g yP A F k
8.1 9.152
f
f
b
t 6.47 9.15
2f
f
b
t
22.5 29.94 2.10 56.29r
w y
h P
t P
840.16 0.675
515r
y
P
P
1470.22 0.675
665r
y
P
P
20.5 29.94 2.10 57.99r
w y
h P
t P
W10x45 W8x35
min
1801.59 2.03
113.43yr min
1801.59 2.01
113.43yr
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 49
LOADING COMBINATIONS
1.4 256.1 358.5RuLP k
1.4 339.3 475.0FuLP k
Leaning Columns
1.4 DL
Floor Beam Loads
1.4 16.9 23.7FuIP k
1.4 14.1 19.7FuEP k
Roof Beam Loads
1.4 12.1 16.9RuIP k
1.4 8.85 12.4RuEP k
Notional Loading (applied laterally)
0.002 2 12.4 11 16.9 358.5
0.002 2 19.7 11 23.7 475.0 2.69
FuN
k
0.002 2 12.4 11 16.9 358.5 1.14RuN k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 50
LOADING COMBINATIONS (continued)
1.2 1.6 0.5 rDL LL LL
Leaning Columns
Floor Beam LoadsRoof Beam Loads
Notional Loading (applied laterally)
1.2 16.9 1.6 7.5 32.3FuIP k
1.2 14.1 1.6 3.75 22.9FuEP k
1.2 12.1 0.5 4.5 16.8RuIP k
1.2 8.85 0.5 2.25 11.8RuEP k
1.2 256.1 0.5 108.0 361.3RuLP k
1.2 339.3 1.6 180.0 695.2FuLP k
0.002 2 11.8 11 16.8 361.3
0.002 2 22.9 11 32.3 695.2 3.33
FuN
k
0.002 2 11.8 11 16.8 361.3 1.14RuN k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 51
LOADING COMBINATIONS (continued)
1.2 0.5 1.6 rDL LL LL
Leaning Columns
Floor Beam LoadsRoof Beam Loads
Notional Loading (applied laterally)
1.2 16.9 0.5 7.5 24.0FuIP k
1.2 14.1 0.5 3.75 18.8FuEP k
1.2 12.1 1.6 4.5 21.7RuIP k
1.2 8.85 1.6 2.25 14.2RuEP k
1.2 256.1 1.6 108.0 480.1RuLP k
1.2 339.3 0.5 180.0 497.2FuLP k
0.002 2 11.8 11 16.8 361.3
0.002 2 18.8 11 24.0 497.2 3.09
FuN
k
0.002 2 14.2 11 21.7 480.1 1.49RuN k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 52
LOADING COMBINATIONS (continued)
1.2 0.5 1.6rDL LL LL WL
Factored Wind Loading
1.6 6.75 10.8RuH k
1.6 13.5 21.6FuH k
Leaning Columns
Floor Beam LoadsRoof Beam Loads
Notional Loading (applied laterally)
Second-order effects will be "small" and thus, no notional loading.
1.2 12.1 0.5 4.5 16.8RuIP k
1.2 8.85 0.5 2.25 11.8RuEP k
1.2 16.9 0.5 7.5 24.0FuIP k
1.2 14.1 0.5 3.75 18.8FuEP k
1.2 339.3 0.5 180.0 497.2FuLP k
1.2 256.1 0.5 108.0 361.3RuLP k
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 53
R
R
bI
eV
kR
bI
con
b
kR
cI
c
bI cI
cI
kR
21 2
6e
bb
V L h h
EI
31 2
12e
cc
V h h
EI
21 2econ
k
V h h
R
FLOOR-LEVEL - EXTERIOR
eV
eV
eV
eVeVR
1h
2h
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 54
bI
iV
kR
bI
con
b
kR
cI
c
bI cI
cI
kR
21 2
12i
bb
V L h h
EI
31 2
12i
cc
V h h
EI
21 2
2i
conk
V h h
R
FLOOR-LEVEL - INTERIOR
iV
R
R
1h
2h
2006 ASCE/SEI Structures CongressSt. Louis, MO
May 18-20 55
21 21 2
12
6i
ii
b c k
V EK
L h h Eh h
I I R
Exterior Sub-AssemblyInterior Sub-Assembly
21 21 2
6
6
2
ee
e
b c k
V EK
L h h Eh h
I I R
STORY STIFFNESS
Concrete floor diaphragm provides displacement compatibility. Thisleads to relationship between interior and exterior shear;
1 2 1 26 6
2 2i
eb c k b c k
L h h L h hV E EV
I I R I I R
i e
Portal frame assumptions regarding shear distribution met when;
1 2 1 2
2 2i
eb c b c
V L h h L h hV
I I I I