SDM Example 3 Steel SMF.pdf

Seismic Design Manual Volume III

Design Example 3Steel Special Moment Resisting Frame

Originally prepared by David Hutchinson, S.E., President, Buehler & Buehler Structural Engineers, Inc. for 1997 UBC

Adapted to 2006 IBC by Kevin S. Moore, Principal, Certus Consulting, Inc.

2006 IBC Adaptation presented by Scott Hooker, S.E., Principal, Buehler & Buehler Structural Engineers, Inc.

September 2007

Example Problem Overview

The problem begins with a forward and general overview and is then divided into the following sections:

1 Earthquake Loads2 Seismic Ground Motion parameters – 2006 IBC3 Building Weights and Mass Distribution4 Seismic Design Requirements for Building Structures – ASCE 7-055 SMF Member Design – AISC 341, 358 and 3606 SMF Beam to Column Connection Design – AISC 341, 358 and 360

Code References

Four-Story Steel Frame Office Building

Building Area: Four levels @ 29,090 s.f. per floorLateral System: Special Moment Resisting Frames

• Roof Dead Load 62psf• Roof Live Load 20psf• Floor Dead Load 69psf• Floor Live Load 80psf• Exterior Wall Weight 10psf

Structural Materials

Wide Flange ShapesPlatesWeld Electrodes

ASTM A992 grade 50ASTM A572 grade 50E70xx

Typical Floor Framing Plan

Frame Elevation at Line A

Basic ground motion parameters based on 2006 IBC Section 1613. All other seismic design provisions and equations taken from ASCE 7-05.

Earthquake Loads Seismic Design Requirements 2006 IBC Section 1613 For Building Structures

ASCE 7-05 Chapter 12

1 - Seismic Design Parameters

Mapped Acceleration parameters SS and S1, taken from maps in 2006 IBC figures 1615 (1) through (14) or ASCE 7-05 figures 22-1 through 22-14, or use of Google Earth and USGS website: earthquake.usgs.gov/research/hazmaps/design

• SS = 1.5g @ T=0.2 sec. • S1 = 0.6g @ T=1.0 sec.

Note: These values are site specific and are based on MCE values for 2% in 50 year probability (≈2,500 year recurrence)

Determine site class per 2006 IBC 1613.5.2 or 1613.5.5• Use site class D in absence of specific geotechnical information per 1613.5.2

Determine site coefficient and adjusted MCE per 2006 IBC 1613.5.3• Required since all mapped accelerations based on site class B• Use table 1613.5.3 values to convert to site class D • Fa=1.0, Fv=1.5• Adjust MCE Spectral Response for site class D

• Sms = Fa SS = 1.0(1.5)=1.5g • Sm1 = Fv S1 = 1.5(0.6) = 0.9g

2 - Seismic Ground Motion Parameters – 2006 IBC Chapter 16

Determine Design Spectral Response = 2/3 MCE per IBC 1613.5.4• SDS = (2/3) SMS = (2/3) 1.5g = 1.0g• SD1 = (2/3) SM1 = (2/3) 0.9g = 0.6g

Note: For coastal California, the use of 2/3 MCE values approximates the 10% in 50 years Design Basis Earthquake (≈ 475 year recurrence) used in UBC. This is not necessarily true in other parts of California or the rest of the United States.

Determine Occupancy Category from 2006 IBC table 1604.5• Office Building use results in Occupancy Category = II

Determine seismic design category (SDC) per 2006 IBC table 1613.5.6(1) and 1613.5.6(2)

• SDS = 1.0g => Category D • SD1 = 0.6g => Category D

Importance Factor from ASCE 7 table 11.5-1• For occupancy category II, I = 1.0

2 - Seismic Ground Motion Parameters – 2006 IBC 1613 (continued)

The design example is based on the following building weight, center of gravity and mass property information.

3 - Building Weights and Mass Distribution

Determine lateral system response parameters per ASCE 7-05 Table 12.2-1 for steel SMF systems type C.1 the following parameters apply:

ASCE 7-05 1997 UBC• R = 8 response modification factor R = 8.5• Ωo= 3 system over-strength factor Ωo= 2.8• Cd = 5.5 deflection amplification factor .7R = 5.95

Example building does not have structural irregularities per ASCE 7-05 12.3.2 and tables 12.3-1 and 12.3-2, however note limits and additional requirements for SDC D-F per ASCE 7-05 sections 12.2.5.5 & 12.3.3

Concrete filled metal deck diaphragms considered rigid per ASCE 7-05 12.3.1.2

4 - Seismic Design Requirements for Building Structures

4 - Seismic Design Requirements for Building Structures (continued)

Check redundancy per ASCE 7-05 12.3.4.2

• ρ = 1.3 for all buildings in SDC D-F. • If one of two exceptions are met, ρ = 1.0.

• Exception a:• Requires each level that resists more than 35% of the base shear to be evaluated with

selected elements removed. If no more than 33% reduction in capacity occurs and the resulting system does not have an extreme torsional irregularity, ρ = 1.0

• Exception b: • Building must be regular in plan at all levels• For each level resisting more than 35% of base shear, the LFRS must have at least two

bays of perimeter seismic resisting framing at each side in each orthogonal direction• The example meets exception b requirements and results in ρ = 1.0

Note: Per 1997 UBC SDM Example 3A, ρ = 1.25

Seismic load effect per ASCE 7-05 12.4.2• E = Eh + Ev equation 12.4-1

• E = Eh – Ev equation 12.4-2

• Eh = ρQE where QE = seismic forces from V or FP; ρ = per 12.3.4.2

• Ev = 0.2SDS D where SDS = design spectral short period response

Note: Ev = 0 when SDS ≤ 0.125 or in equation 12.4-2 where determining demands on soil – foundation interface.

Seismic load combinations – LRFD per ASCE 7-05 12.4.2.3

(1.2 + 0.2 SDS)D + ρQE + L + 0.2S Load combo 5 ASCE 7-05 2.3.2

(0.9 - 0.2 SDS)D + ρQE + 1.6H Load combo 7 ASCE 7-05 2.3.2Note:

• L may be taken as 0.5L where L is less than 100psf except for garages or public assembly areas.

• H is zero if lateral earth pressures counteract E. If H is used as resistance to E, H shall not occur in above equations but shall be included in resistance.

• Equations for ASD also shown in example, however LRFD used for example.


Seismic load effect including overstrength factor per ASCE 7-05 12.4.3• Em = Emh + Ev equation 12.4-5

• Em = Emh - Ev equation 12.4-6

• Emh = ΩoQE where QE = seismic forces V or FP; Ωo = per table 12.2-1

Note: Emh need not exceed maximum force determined by a rational, plastic mechanism analysis or non-linear response using realistic expected material strength

• Ev = 0.2SDS D same as previous

Seismic load combinations with overstrength factor – LRFD per ASCE 7-05 12.4.3.2

(1.2 + 0.2 SDS)D + ΩoQE + L + 0.2S Load combo 5 ASCE 7-05 2.3.2

(0.9 - 0.2 SDS)D + ΩoQE + 1.6H Load combo 7 ASCE 7-05 2.3.2Note:

• L and H same as previous


Direction of loading (orthogonal effects): ASCE 7-05 12.5.4 for SDC D through F• Shared columns or intersecting walls• Non-parallel systems

Analysis procedure: ASCE 7-05 Table 12.6-1• Lists acceptable analysis techniques given the SDC, structural characteristics and

occupancy category• Example building with SDC = D, regular and T<3.5Ts, has no restrictions on

analysis procedure. • Where 3.5Ts=3.5SD1/SDS=3.5(0.6/1.0)=2.15s

Seismic weight: ASCE 7-05 12.7.2• Requires portion of storage loads, partitions, equipment and portions of snow load

to be included in seismic weight• Building dead load includes 10 psf for partitions as “given” for this example and

meets requirement

Structural modeling: ASCE 7-05 12.7.3• Certain horizontal irregularities require 3-D model• Example is regular and does not require 3-D model. However, 3-D model is used

to determine force distribution to frames based on rigid analysis


∴

Approximate period determination per ASCE 7-05 12.8.2.1• Ta=CT (hn)

x where:CT=0.028 for steel SMF per table 12.8-2 hn=building height in feetx=0.8 per table 12.8-2Ta=0.028(55.5)0.8=0.696

Note: Per method A of 1997 UBC Ta =CT(hn)

¾

T=0.03(55.5) ¾=0.71

Period determined by computer analysisTy = 1.305 N-STx = 1.165 E-W

Upper limit on calculated period per ASCE 7-05 12.8.2Tmax = CuTa where Cu = coefficient from table 12.8-1 = 1.4 in exampleTmax = 1.4 x .696 = 0.974S for N-S & E-W

Note: Per 1997 UBC Tmax = 130% Ta for Zone 4Tmax = 1.30 x 0.71 = 0.925S


Calculation of seismic response (base shear) coefficient per ASCE7-05 12.8.1.1

• Cs = seismic response coefficient

• Cs need not exceed for governs for example

Note: TL = response spectrum long period transition = 8 seconds in example

• Cs shall not be less than 0.01

• For structures with S1 ≥ 0.6g, Cs shall not be less than

Seismic base shear per ASCE 7-05 12.8.1• V = CsW• V = 0.077W = 0.077(8180Kip) = 630K

Note: Per 1997 UBC V= 0.082W for Zone 4 and no near source effects


gg

IRS

C DSs 125.0

)0.18(

0.1

)(===

g

IR

S038.0

)(

)5.0( 1 =

g.g

TT L 0770)0.1

8(974.0

6.0 ==≤)(

1

IRT

SD

Vertical distribution per ASCE 7-05 12.8.3• Fx = horizontal force at each level X• Fx = CvxV where:

k = exponent related to building periodk = 1 for T ≤ 0.5sk = 2 for T ≥ 2.5sUse linear interpolation between 0.5 and 2.5for T = 0.974s, k = 1.237

• See tables 3-3 from example for vertical force distribution

Horizontal distribution of forces per ASCE 7-05 12.8.4• = story shear = sum of levels above

• Example based on rigid diaphragm, distribution of forces per stiffness and location• Torsional moments to include both natural and accidental torsion where

Mt = 5% of the building length perpendicular to the direction considered Mt =.05(204) Fx = 10.2 Fx N-SMt =.05(144) Fx = 7.2 Fx E-W

• See tables 3-4, 3-5, and 3-6 from example for torsional moments and horizontal force distribution


∑=

=n

iix FV

1

∑=

= nkii

kxx

vx

hW

hWC

11

Story drift determination per ASCE 7-05 12.8.6• ∆ = story drift = story displacement at C.M. relative to floor below

• δxe = total elastic building deflection at level x

• = increased deflection based on both elastic and estimated inelastic displacements

Note: ∆ and δx are determined from linear elastic analysis. Upper limit of CuTa not required for drift analysis per ASCE 7-05 12.8.6.2

• Recalculate seismic base shears, torsional moments and force distribution using calculated period with out upper limit

• Table 3-7 show building deflections, drifts, drift ratios, and stability coefficients based on calculated periods

Story drift limit per ASCE 7-05 12.12• Allowable drift limits given in table ASCE 7-05 12.12-1• For steel SMF 4 stories or less with walls and ceilings that can accommodate drift

and occupancy II, the allowable drift ∆a = 0.025 hsx

Note: ASCE 7-05 12.12.1.1 requires drift for buildings comprised of solely moment frames to be limited to ∆ ≤ ∆a/ρ


xee

xedx I

C δδδ 5.5==

P-∆ Effects and stability coefficient per ASCE 12.8.7

• P-∆ need not be considered if stability coefficient θ ≤ 0.10 where:

θ =

Px = total vertical load at and above level x (no load factor need exceed 1.0)

∆ = design story drift resulting from VX

Vx = seismic shear acting between levels x & x-1hsx = the story height below level xCd = deflection amplification factor

where:

β is the ratio of shear force to shear strength at level considered and may be conservatively taken as 1.0

• Where 0.10 <θ < θ max, P-∆ effects must be determined by rational analysis or displacements and member forces multiplied by 1/(1- θ)If θ >θ max, the structure may be unstable and shall be redesigned


25.0091.05.50.1

5.05.0max ≤===

xCdβθ

dsxx

x

ChV

P Δ

Modify story drift and stability coefficient for reduced frame stiffness associated with RBS connections

• AISC 358-05 5.8 indicates that SMF design must consider reduced stiffness associated with the use of RBS connections. In lieu of more precise analysis, an elastic story drift using gross section properties multiplied by 1.1 may be used for flange reductions up to the maximum of 50% (interpolation may be used for lesser flange reductions)

• From the example: (∆/h)max = 0.023 x 1.1 = 0.025 ≤ 0.025 ok

θ x 1.1 = 0.079 < θmax ok

Note: Analysis model used for example is based on a centerline analysis which is considered a reasonable approximation of primary element deflections and panel zone distortions


5 – SMF Frame Member Design

Steel SMF member design governed by 2006 IBC 2205.2.2 which requires compliance with AISC 341 for SDC D, E, and F.

Example members: W27x84 beam A992 Fy = 50 ksi Fu = 65 ksiW14x176 column A992 Fy = 50 ksi Fu = 65 ksi

• AISC 341-05 requires use of expected strength = Fye = RyFy where Ry = 1.1 per AISC 341-05 table I-6-1 for A992

Check Frame for P-Δ Instability• AISC 360-05 Chapter C notes that any method that considers P-Δ and P-δ effects is

acceptable. This Chapter also has provisions for approximating second order effects.

Where: P-Δ = second order effect of displacements of braced points (story deflection)P-δ = second order effect of displacements between braced points (loads

between levels)

• Computer analysis/design program such as SAP and ETABS have provisions to consider second order effects.

• AISC 360-05 Appendix 7 and AISC 341-05 commentary C3 also have provisions for considering P-Δ effects.

• SDM Example illustrates AISC 341 commentary C3 approach.

5 - Frame Beam at 3rd Floor

in k,M DL −= 0421 in kM LL −= 924 in k,M seis −±= 0833

kips4.16=DLV kips3.13=LLV kips0.19±=seisV

5 – ASCE 7-05 Load Combinations

D + L = 1.2D + 1.6L – ASCE 7-05 2.3.2

D + L + E = ASCE 7-05 12.4.2.3

D + L - E =ASCE 7-05 12.4.2.3

where: E = Eh ± EvEh = ρ QE = 1.0QE

Ev = 0.2SDSD = 0.2(1.0g)D = 0.2D

(1.2 + 0.2SDS)D + ρQE + 0.5L + 0.2S ASCE 7-05 12.4.2.3

(0.9 - 0.2SDS)D –ρQE – 1.6H ASCE 7-05 12.4.2.3

MD+L = 1.2(1042) + 1.6 (924) = 2729k-in

VD+L = 1.2(16.4) + 1.6(13.3) = 41.0k

MD+L+E = [1.2 + 0.2(1.0)] 1042 + 1.0 (3083) + 0.5(924) + 0 = 5004k-in

VD+L+E = [1.2 + 0.2(1.0)]16.4 + 1.0(19) + 0.5(13.3) + 0 = 48.6k

Check Beam Limits per AISC 358-05 5.3.1

1. Rolled or built-up I shaped sections per AISC 358-05 2.3.2

2. Depth limited to W36 or 36” max depth for built-up

3. Weight limited to 300 lbs/ft

4. Flange thickness limited to 1¾”

5. Clear span to depth = 7 or greater for SMF (= 5 or greater for IMF)

6. Meet width/thickness ratios of AISC 341.Note: May use width at end of center ⅔ of radius cut to determine flange

width/thickness. This will be further illustrated below.

5 - Check W27x84 Beam for AISC 358 Limitations

Check width-thickness ratios per AISC 341 Table I-8-1.

• Flange:

• Check flange width at end of center 2/3 of radius cut per note above. This results in an effective flange width of bf - y where y=b - R+(r2-x2)½ = 2.25-2.8+(282-7.332)½ =1.27”

• Web:

5 – Limiting Width -Thickness Ratios per AISC 341-05

yFE

tf

bf

t

b3.0

2≤= ..22.7

50

000,293.078.7 gn

ksi

ksi =≤=

..79.6)64.0(2

)27.196.9(

2ko

t

yb

f

f =−=−

yw FE

t

h45.2≤ ..59

50

000,2945.23.55

46.0

))64.0(27.26(ko

ksi

ksi

t

h

w=≤=−=

Beam Bracing• AISC 358-05 5.3.1 #7 refers to AISC 341-05 9.8 for required bracing strength and

spacing.• Additional lateral bracing is also required at reduced sections unless the beam

supports concrete structural slab connected between the protected zones with welded shear connectors.

• Max brace spacing per AISC 341-05 9.8 :

place braces at ¼ points = 7.0 ft on center (84in)

• Required brace strength at hinge per AISC 341-05 9.8:

where Mu=Mr=RyZFy

ho=db-tf=26.7-0.64=26.06”

Note: At RBS, Mr=RyZeFy = 1.1(169)(50)=9,300k-in (Section 6 has calculation for Ze=169 at RBS)

5 – Beam Bracing Required per AISC 341-05

ftinF

ErL

y

yb 60.83.103

50

)000,29)(07.2(086.0086.0====

elsewhere) 02.0( hingesat 06.0o

u

o

ubr h

M

h

MP =

kPbr 4.2106.26

)300,9(06.0 ==

Check brace capacity per AISC 13th Edition table 4-12• For 5x5x3/8” angle brace with KL = 12’-0”

φcPn=22.2kips o.k.

Required brace stiffness per AISC 360-05 Appendix 6.3.1.b:

where φ=0.75Mr=13,420k-in (per above) Cd=2.0 at brace closest to hinge and = 1.0 elsewhereLb=brace spacing per aboveho=26.7” per above

• Brace axial stiffness = where

5 – Beam Bracing Required per AISC 341-05 (continued)

)10

(1

ob

drbr hL

CM

φβ =

inkininbr /5.163)

)7.26(84

)0.2)(420,13(10(

75.0

1 ==β

θ2cosL

EAk g= 01 09.10)

)12(5.12

7.26(tan == −

ftθ

..673)09.10(cos4.152

)000,29(65.3 22

koink

in

ink ==

Flexural strength per AISC 360 F2

W27x24:

Flexural strength = φbMn=0.9(50)(244)=10,980k-in

0.46<1.0 o.k.

Shear strength per AISC 360 G2

• h/tw previously checked for compliance with AISC 341-05 Table I-8-1

Vn=.6FyAw

Shear strength = φVn=0.9(0.6)(50)(0.46)(26.7)=331.6k

0.15<1.0 o.k.

5 – Check beam flexural and shear strength per AISC 360-05

xypn ZFMM o.k. "84"7.8776.1 ==∴>==y

yp F

ErL

=−

−= ++

ink

MC

D ELD

980,10

)in(k004,5 )max(

== ++

6.331

)(6.48 )max( ELDVkC

D

∴

inkM DL −= 236

inkM LL −= 201

inkM seis −±= 970,3

kips1.3=DLV

kips7.2=LLV

kips8.56±=seisV

kips113=DLP

kips78=LLP

kips28±=seisP

5 - Frame Column at 2nd Story

5 - Load Combinations

Same basic load combinations used for beam design

• PD+L = 1.2(113) + 1.6(78) = 260 Kips

• MD+L = 1.2(236) + 1.6(201) = 604.8 K-in

• VD+L = 1.2(3.1) + 1.6 (2.7) = 8.0K

• PD+L+E = [1.2 + 0.2(1.0)] 113 + 1.0 x 28 + 0.5 x 78 = 225 Kips

• MD+L+E = [1.2 + 0.2(1.0)]236 + 1.0 x 3970 + 0.5 x 201 = 440 K-in

• VD+L+E = [1.2 + 0.2(1.0)]3.1 + 1.0 x 56.8 + 0.5 x 2.7 = 62.5 K

• PD-E = [0.9 – 0.2(1.0)]113 – 1.0 x 28 = 51.1 K

• MD-E = [0.9 – 0.2(1.0)]236 – 1.0 x 3970 = -3805 K-in

• VD-E = [0.9 – 0.2(1.0)]3.1 – 1.0 x 56.8 = -54.6K

5 - Check W14x176 Column for Limits of AISC 358

Check column limits per AISC 358-05 5.3.21. Rolled or built-up sections per AISC 358-05 2.3

Allows use of: Built-up I-shaped columnsBoxed WF columnsBuilt-up box columnsFlanged cruciform columns

Built-up sections must be CJP welded at joints and 12” above and below (PJP groove or fillet OK elsewhere)

2. Beams must be connected to flanges (not webs)

3. Depth: WF, built-up I shapes and flanged cruciform = 36” maxBox columns = 24” maxBoxed WF columns in orthogonal frames = 24” max

4. No weight limit

5. No flange thickness limit

6. Width/thickness ratios of AISC 341.05 I.8.1 must be met

7. Lateral bracing per AISC 341.05 section 9.7

Check flange and web width/thickness ratios per AISC 341-05 Table I-8-1

Flange:

Web:

where

5 - Limiting width – thickness ratios per AISC 341-05

yF

E

tf

bf

t

b3.0

2≤= ..22.7

50

000,293.097.5

2ko

ksi

ksi

tf

bf =≤=

125.0110.0)8.51)(50(9.0

256

9.0<====

yy

u

yb

ua AF

P

P

PC

φ

..8.62))110.0(54.11(50

000,2914.37.13)54.11(14.3 koC

F

E

tw

ha

y

=−≤=−≤∴

Flexural capacity per AISC 360 F2

For W14 x 176 LP = 14.2ft, Lr = 73.2ft

With Lu = 13.5 feet – 2.5½ = 12.2 feet < Lp

Mnx = Mpx = FyZx & Mny = Mpy = FyZy

φMnx = 0.9(50)(320) = 14,400 k-in

φMny = 0.9(50)(163) = 7,735 k-in

Axial capacity per AISC 360 E3• Determine effective length factor, K per alignment charts in AISC 360

commentary figure C-C2.4

5 - Check W14x176 column flexural and axial capacity

68.1)28/2850(2

)5.12/2140(2 ==topG∑∑=

)/(

)/(

yy

cc

LI

LIG

59.1)28/2850(2

)14/2140()5.12/2140( =+=bottG

∴

Axial capacity continued …

• Check flexural buckling stress limit per AISC 360-05 E3

o.k.

where

φPn = φ cFcrAg = 0.9 x 43.4 x 51.8 = 2025K

Note: SDM example illustrates AISC 360-05 chapter C approach for amplifying first order elastic analysis to approximate second-order effects.

5 - Check W14x176 column flexural and axial capacity (continued)

3.3443.6

)12)(2.12(5.1 ==x

xx

r

LK

9.4302.4

)12)(2.12(2.1 ==y

yy

r

LK

inF

E

r

K

y

11350

000,2971.471.4

1 ==<

yF

F

cr FF e

y

]658.0[=∴ ksi

rKL

EFe 5.148

9.43

)000,29(

)(2

2

2

2

=== ππ

ksiFcr 4.43)50](658.0[ 5.148

50

==

Check combined axial and flexural per AISC 360-05 H1

equation (H1-1b) applies

Shear strength per AISC 360 G2

• h/tw previously checked for compliance with AISC 341-05 Table I-8-1

Vn=.6FyAw

φ Vn = 0.9(0.6)(50)(15.2)(0.830) = 341K

.183<1.0 o.k.

5 - Check W14x176 column stresses

∴<== 2.011.02025

224maxk

k

n

u

P

P

φ

koM

M

P

P

M

M

M

M

P

PCD

nb

u

n

u

cy

ry

cx

rx

c

r .0.1369.0400,14

4401

)2025(2

256

2)(

2/ <=+=+=++=

φφ

∴

== ++

341

)(5.62 )max( ELDVkC

D

Prequalified Moment Frame Connections from MSC January 2007


Overall Requirements of AISC 358 for RBS Connections

• RBS connections pre-qualified for use in SMF and IMF Systems

• Beam and column limitations per AISC 358-05 5.3.1 and 5.3.2 – reviewed in Section 5

• Beam-column relationships per AISC 358-05 5.4• Panel zones limited per AISC 341-05 9.3 for SMF• Column-beam moment ratio limited per AISC 341-05 9.6

• Beam flange to column flange welds per AISC 358-05 5.5• Must be CJP welds in conformance with Section 7.3 and appendix W of AISC 341• Weld access hole geometry shall conform to AISC 360 J1.6

• Beam web to column connection per AISC 358-05 5.6• Required web connection strength based on probable beam strength per

AISC 358-05 5.8-9• For SMF, must use CJP weld extending between flange weld access holes. Shear

plate permitted as backing with ⅜” minimum thickness. Holes for erection bolts are O.K.

Note: AISC 358-05 is based on post-Northridge Earthquake research and testing conducted by SAC Joint Venture, University of Texas as well as the provisions of FEMA 350.

6 - RBS design considerations per AISC 358-05

Step 1: Flange cut parameters per AISC 358-05 5.8

0.5bbf ≤ a ≤ 0.75bbf

0.65d ≤ b ≤ 0.85d

0.1bbf ≤ c ≤ 0.25bbf

6 – RBS design procedure per AISC 358 5.8

c

bcR

8

4 22 +=

Step 1 continued: Flange cut parameters per AISC 358-05 5.8

For W27x84: 0.5bf=4.98in 0.75bf=7.47in use a=6.0in

0.65d=17.36in 0.85d=22.7in try b=22.0in

• Depth of cut “c” to result in 20-50% of flange removed

• With 45% reduction in flange area:

Plastic hinge assumed to occur at the center of the curved cut such that

Sh = a + b/2 = 6 + 22/2 = 17 in

( )cut4

12Use2422

96.9450

2450 " in .

.b.c f ∴==⎟⎟

⎠

⎞⎜⎜⎝

⎛=

( )( ) radius 0.28

2528

222524

8

4 2222

in .

.

c

bcR =+=+=∴


Determine distance between plastic hinges (L’) is used to determine forces for joint analysis

L=28 ft

Step 2: Determine Ze at RBS per AISC 358-05 5.8 Ze=Zx-2ctf(d-tbf)2c=2(2.25”)=4.5”Ze=244-4.5(0.64)(26.7=0.64)=169in3

Step 3: Determine probable maximum moment strength at RBS per AISC 358-05 5.8

accounts for peak connection strength =

Note: Mpr must be limited such that the projected moment demand at the face of the column Mf is less than the expected strength of the full beam section. This is verified below.

ch dsLL' −−= 2


eyyprpr ZFRCM =

2.12

≤+

=y

uypr F

FFC 15.1

)50(2

6550 =+=prC

inkM pr −== 686,10)169)(50)(1.1(15.1

ft L' 9.2312/8.286"2.15)"17(2)12('28 ==−−=∴

( )( ) kips

.L'

MV pr

pr 5.7492312

686,1022===

( ) ( ) prLDP VVVV ±+= 5.02.1

( ) ( ) RBSVkips1015.743.135.04.162.1 ==++=∴ PV


( ) ( ) RBSV'kips2.485.743.135.04.162.1 ==−+=∴ PV

Step 4: Determine shear at center of RBS per AISC 358-05 5.8

Moment at column face (Mf) used for beam flange-to-column weld and panel zone strength check belowMoment at column centerline ( ) used to check weak beam/strong column condition belowNote: The moment due to gravity loads occurring between plastic hinge and face of

column may be neglected per AISC 358 5.8 Step 5.


( ) inkdcsVMMMM hPprvprpb −=+++=++=+= 867,11)22.15

2226(48686,102

*

( ) inkdcsVMMMM hPprvprpb −=+++=++=+= 170,13)22.15

2226(101686,102

*

( ) ( ) inksVMM hPprf −=++=+= 403,122226101686,10

inkM f −−=+−+−= 505,11)]2226(48[686,10

*pbM

Step 5: Determine probable maximum moment at the face and center of column per AISC 358-05 5.8

Step 6: Expected plastic moment capacity of beam (gross section) per AISC 358-05 5.8

Mpe=ZbRyFy=(244)(1.1)(50)=13,420 k-in

Step 7: Check that Mf does not exceed φdMpe per AISC 358-05 5.8

Note: If no additional calculations required and CJP weld at beam flange to column flange is acceptable. If the flange cut depth should be increased (not to exceed 50%) to reduce Mf.

Step 8: Check shear strength per AISC 358-05 5.8

as previously calculated = 101 kips.

Shear check of beam per chapter G of AISC 360 as checked in Section 5 previously

ok


fped MinkM =>−== 403,12420,13)420,13(0.1φ

fped MM ≥φ

fped MM <φ

RBSgravityprgravitypr

u VVVVL

MV =+=+=

1

2

kipsVn 1016.331 >=φ

Step 9: Design web-to-column connection per AISC 358-05 5.8• AISC 358-05 5.6 requires CJP connection at web to column face, therefore, no

further calculations required.

Step 10: Check continuity plate requirements per AISC 358-05 5.8 and AISC 358-05 2.4.4

continuity plate required.

• Minimum thickness per AISC 358-05 2.4.4a• tcont-pl ≥ tbf / 2 for one sided connection• tcont-pl ≥ thickest tbf for two sided connection


35.1)1.1(50

)1.1(50)64.0)(96.9)(8.1(4.08.14.0 ==≥

ycyc

ybybbffcf RF

RFtbt

inb

tf

cf 66.16=≥

31.1=cft ∴


Step 10 continued: Check continuity plate requirements per AISC 358-05 5.8

• AISC 358-05 3.6 requires corner clip to be at least 1½” beyond “k” along web and clipped to avoid interference with flange radius but not to exceed “k1” + ½” along flanges


435.72

where max =−

= cwcfpb

tbW

inkWW colpbpb 56.5)25.0625.1(435.7)"411(max =+−=+−=

inin

in

W

At

pb

pbplcont 06.1

56.5

88.5 2

===∴ −

Step 10 continued: Check continuity plate requirements per AISC 358-05 5.8

• Therefore, contact area of continuity plate and column flange

where

• The required continuity plate area is determined from AISC 360-05 J7

Use two pairs of 1”x7½” continuity plates aligned with beam flanges

)"411( +−= − colplcontpb kbWplcontpbpb tWA −=

kipstd

MfAFR

bfbpbyct 476

64.07.26

403,12)()8.1(9.0 =

−=

−≥=φ

288.5)50)(8.1(9.0

476

8.19.0

476in

FxA

ypb ==≥

Step 10 continued: Check continuity plate requirements per AISC 358-05 5.8• Per AISC 358-05 2.4.4b, welds must have capacity to resist the smallest of:

a. Sum of design strength in tension of contact areas of continuity plates at column flanges that have frame beams attached

b. Design strength in shear of the contact area of the continuity plate with column web

c. Design strength in shear of the column panel zone

d. Sum of the expected yield strengths of the beam flanges transmitting forces to the continuity plates

Note: AISC 358-05 2.4.4b requires use of CJP welds of continuity plates to column flanges, therefore no calculations are required at this interface. However, the connection between continuity plates and column web must be checked.


Step 10 continued: Continuity plate connection to web per AISC 358-05 5.8

• Determine required capacity based on criteria noted above

a. T=

b. T=

where Apw = (dc - 2tcf - 2(k+1.5in) x tcont-pl

Apw = (15.2 - 2(1.31) - 2(1.91 - 1.5) x 1.0 = 5.67in2

c. T= = panel zone capacity as determined in Step 11

d. T=

• Weld to have capacity to resist smallest of above = 173 kips.

Minimum double sided fillet =

Use double sided ¾” fillet weld


kipsAF pby 500)56.5(50)9.0(2 ==∑φ

kipsAFV pwynwW 173)67.5)(50)(6.0(0.1)6.0( ===φφ

kipsRy 469=φ

kipstd

M

bfy

pcd 927)64.07.26

)420,13(9.0(2 =

−=

−∑φ

))5.1(22)(392.1(2min

inktdink

RD

cfc

u

+−−=

8.10)67.5)(392.1(2

173min ==

inD

k

162=H

"38.26)2/64.0(7.26 =−=pd

kips90738.26

505,11430,12 =+=== ∑p

ffu d

MFR


Mf = 12,430 & 11,505 from previous

Step 11: Check column panel zone per AISC 358-05 5.8• Comply with AISC 358-05 5.4, AISC 341-05 9.3 and AISC 360-05 J10.6

• Check minimum panel zone thickness per Section AISC 341 9.3b

Note: Adding ½” to each side of the column web and replacing tw in above equation with 0.83+1/2”+1/2”=1.83 results in panel zone capacity = 926kips>907 OK

Note: AISC 341 9.3c requires doubler plates to be welded to column flanges with CJP or fillet to develop shear capacity of doubler and shall be welded at top and bottom to transmit portion of shear to be resisted by doubler.

( ) 90/zzz wdt +≥

( ) ( )[ ] . ./"tz o.k thicknessminimum43090)31.1(22.1538.2683.0 =−+≥=

Step 11 continued: Check column panel zone per AISC 358-05 5.8• Capacity per AISC 360 J10.6


⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

wcb

cfcfwcyv tdd

tbtdFR

231)6.0(φφ

platesdoubler add n.g. 90746983.02.157.26

)32.1)(7.15(3183.02.15506.00.1

2

<=⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

xxxxxxRvφ

6 – RBS design procedure per AISC 358 5.8Step 12: Check column-beam moment ratio (strong col-weak beam) per AISC 358-05 5.8

Column lateral bracing at beam to column connection per AISC 358 5.32• Bracing required at top flange of beam only if

• If above not true, bracing required at top and bottom flanges either directly or indirectly

• Direct bracing achieved through beams or bracing attached directly to column flanges or deck/slab attached near column flange

• Indirect bracing achieved through stiffness of members and connections not directly attached to flanges, but rather act through column web or stiffener plates

• Bracing to have 2% of beam flange strength = 2%RyFybftbf (no minimum stiffness requirement)

where0.1*

*

≥∑

∑

pb

pc

M

M

232,29)32.450)(320(2* =−=∑ pcM

867,11170,13* +=∑ pbM

32.48.51

224 ==k

uP

0.2*

*

>∑

∑

pb

pc

M

M

..0.117.1037,25

232,29*

*

koM

M

pb

pc >==∑

∑

vprpb MMM +=*

)(*

g

ucyccpc A

PFZM −=

Radius cut at RBS to be thermally cut and grind parallel to flange to surface roughness of 500 micro-inches.All transitions to be rounded to minimize notch effects and abrupt transitions. Gouges and notches up to ¼” may be repaired by welding and grindingProtected zone requirements (zone = from face of column to end of radius cut)

• Tack welds, erection aids, gouging and cutting to be avoided or repaired per EOR• Headed studs not permitted (puddle welds of decks OK)• No permanent welded, bolted, screwed, shot-in or other construction permitted (holes

for shear plate erection bolts OK)Welding requirements per AISC 341 Appendix WQA/QC requirements per AISC 341 Appendix Q

6 -Fabrication Considerations

Additional Design Examples

SDM Example 3 Steel SMF.pdf

Documents

Transcript of SDM Example 3 Steel SMF.pdf