SDM Example 3 Steel SMF Design of Entire Building GOOD

Seismic Design Manual Volume III Design Example 3 Steel 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 2 3 4 5 6

Earthquake Loads Seis Seismi micc G Gro roun und d Mot Motio ion n par param amet eter erss – 2006 2006 IBC IBC Buil Buildi ding ng Wei Weigh ghts ts and and Mass Mass Dis Distr trib ibut utio ion n Seismi Seismicc Desi Design gn Requir Requireme ements nts for Buildi Building ng Struct Structure uress – ASCE ASCE 7-05 7-05 SMF SMF Mem Membe berr Desi Design gn – AISC AISC 341, 341, 358 358 and and 360 360 SMF SMF Beam Beam to Colu Column mn Conn Connec ecti tion on Des Desig ign n – AISC AISC 341, 341, 358 358 and and 360 360

Code References

Four-Story Steel Frame Office Building

 

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

Roof Dead Load Roof Live Load Floor Dead Load Floor Live Load Exte Exteri rior or Wall Wall Weig Weight ht

62psf 20psf 69psf 80psf 10ps 10psf f

Code References

Four-Story Steel Frame Office Building

 

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

Roof Dead Load Roof Live Load Floor Dead Load Floor Live Load Exte Exteri rior or Wall Wall Weig Weight ht

62psf 20psf 69psf 80psf 10ps 10psf f

Structural Materials   

Wide Flange Shapes Plates Weld Electrodes

ASTM A992 grade 50 ASTM A572 grade 50 E70xx

Typical Floor Framing Plan

Frame Elevation at Line A

1 - Seismic Design Parameters 

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

Earthquake Loads 2006 IBC Section 1613

Seismic Design Requirements For Building Structures ASCE 7-05 Chapter 12

2 - Seismic Ground Motion Parameters – 2006 IBC Chapter 16 

Mapped Acceleration parameters S S 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 1613 (continued) 

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

3 - Building Weights and Mass Distribution 

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

4 - Seismic Design Requirements for Building Structures



Determine lateral system response parameters per ASCE 7-05 Table 12.2-1 for s teel SMF systems type C.1 the following parameters apply: ASCE 7-05 • R= 8 • Ωo= 3 C d = 5.5 •





response modification factor system over-strength factor deflection amplification factor

1997 UBC R = 8.5 Ωo= 2.8 .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 (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

4 - Seismic Design Requirements for Building Structures (continued) 

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

E = E h – E v

equation 12.4-2

•

E h = ρQ E where Q E = seismic forces from V or FP; ρ = per 12.3.4.2

•

E v = 0.2SDS D where SDS = design spectral short period response

Note: E v = 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 + ρQ E + L + 0.2S

Load combo 5

ASCE 7-05 2.3.2

(0.9 - 0.2 SDS)D + ρQ E + 1.6H Load combo 7 ASCE 7-05 2.3.2 Note: • 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 = E mh + E v equation 12.4-5 •

Em = E mh - E v equation 12.4-6

•

E mh = ΩoQ E where Q E = seismic forces V or FP; Ωo = per table 12.2-1

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

E v = 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 + ΩoQ E + L + 0.2S

Load combo 5

ASCE 7-05 2.3.2

(0.9 - 0.2 SDS)D + ΩoQ E + 1.6H Note: • L and H same as previous

Load combo 7

ASCE 7-05 2.3.2








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

4 - Seismic Design Requirements for Building Structures (continued) 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 feet x=0.8 per table 12.8-2 Ta=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 analysis Ty = 1.305 N-S Tx = 1.165 E-W



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



Note: Per 1997 UBC Tmax = 130% Ta for Zone 4 Tmax = 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 C s

•

=

S DS ( R ) I

=

1.0 g (8 ) 1.0

Cs need not exceed

=

0.125 g

S D1 for T ≤ T L T ( R ) I

=

0.6 g 0.974( 8 ) 1.0

=

0.077 g

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

(0.5) S1 ( R ) I

=

0.038 g


Vertical distribution per ASCE 7-05 12.8.3 • Fx = horizontal force at each level X • Fx = CvxV where: k = exponent related to building period k W h k = 1 for T ≤ 0.5s C vx = n x x k = 2 for T ≥ 2.5s k W i hi ∑ Use linear interpolation between 0.5 and 2.5 1=1 for 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 n • V x = ∑ F i = story shear = sum of levels above i =1

• •

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-S Mt =.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


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

•

δ x

=

C d δ xe I e

=

5.5δ xe = 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


P-∆ Effects and stability coefficient per ASCE 12.8.7 •

P-∆ need not be considered if sta bility coefficient θ ≤ 0.10 where: P x Δ

θ = V h C x sx d

Px = total vertical load at and above level x (no load factor need exceed 1.0) ∆ = design story drift resulting from V X Vx = seismic shear acting between levels x & x-1 hsx = the story height below level x Cd = deflection amplification factor 0.5

0.5

= 0.091 ≤ 0.25 where: β C d 1.0 x5.5 β is the ratio of shear force to shear strength at level considered and may be conservatively taken as 1.0

θ max

•

=

=

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

4 - Seismic Design Requirements for Building Structures (continued)



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 W14x176 column •



A992 A992

Fy = 50 ksi Fy = 50 ksi

Fu = 65 ksi Fu = 65 ksi

AISC 341-05 requires use of expected strength = F ye = R yFy where R y = 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

M DL

V DL

= 1 ,042

k − in

= 16.4 kips

M LL

V LL

= 924

k − in

= 13.3 kips

M seis

V seis

= ± 3 ,083

k − in

= ± 19.0 kips

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 ± Ev Eh = 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) = 41.0 k 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

5 - Check W27x84 Beam for AISC 358 Limitations 

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

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

Flange:

b t

=

bf

2tf

≤

0.3 E F y

=

7.78 ≤ 0.3

29,000ksi 50ksi

=

7.22n.g .

• 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” b f − y

2t f

• Web:

h t w

≤

2.45 E F y

=

(9.96 − 1.27) 2(0.64)

h t w

=

=

6.79o.k .

(26.7 − 2(0.64)) 0.46

= 55.3 ≤

2.45

29,000ksi 50ksi

= 59o.k .

5 – Beam Bracing Required per AISC 341-05 

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 : Lb

=

0.086r y E F y

=

0.086(2.07)(29,000) 50

= 103.3in = 8.60 ft

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

Required brace strength at hinge per AISC 341-05 9.8: M M Pbr = 0.06 u at hinges (0.02 u elsewhere) ho ho

where Mu=Mr =R yZFy ho=d b-tf =26.7-0.64=26.06” Note: At RBS, Mr =R yZeFy = 1.1(169)(50)=9,300k-in (Section 6 has calculation for Z e=169 at RBS) Pbr =

0.06(9,300) 26.06

=

21.4k

5 – Beam Bracing Required per AISC 341-05 (continued) Check brace capacity per AISC 13 th 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:



1 10 M r C d ( ) φ Lb ho

β br =

where φ=0.75 Mr =13,420k-in (per above) Cd=2.0 at brace closest to hinge and = 1.0 elsewhere L b=brace spacing per above ho=26.7” per above β br =

•

Brace axial stiffness = k =

1

10(13,420)(2.0) ( ) = 163.5k / in 0.75 84in(26.7in)

Ag E

k =

L

cos 2 θ

where θ = tan −1 (

3.65in 2 (29,000) 152.4in

26.7 12.5 ft (12)

) = 10.090

cos 2 (10.09) = 673 k o.k . in

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

Flexural strength per AISC 360 F2 W27x24: L p

= 1.76r y

E F y

= 87.7" > 84" o.k. ∴ M n =

M p

=

Fy Z x

Flexural strength = φ bMn=0.9(50)(244)=10,980k-in D



C

=

5,004 k − in( M max( D + L + E )) 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 D

C

=

48.6k (V max( D + L + E )) 331.6

=

0.15<1.0 o.k.

5 - Frame Column at 2nd Story M DL

=

236k − in

M LL

=

201k − in

M seis

= ±3,970k − in

V DL

=

3.1 kips

V LL

=

2.7 kips

V seis

= ±56.8 kips

P DL

= 113 kips

P LL

=

78 kips

= ±28 kips

Pseis

5 - Load Combinations 

Same basic load combinations used for bea m 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 5.3.2 1. Rolled or built-up sections per AISC 358-05 2.3 Allows use of: Built-up I-shaped columns Boxed WF columns Built-up box columns Flanged 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 Box columns Boxed WF columns in orthogonal frames

= 36” max = 24” max = 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

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

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

Flange:

Web:

∴

b t

h tw

=

bf

2tf

≤

E

≤ 3.14

where

C a

0.3

F y =

E

bf

F y

2tf

= 5.97 ≤

0.3

(1 − 1.54C a ) = 13.7 ≤ 3.14

Pu

φ b P y

=

Pu

0.9 F y A y

=

29,000ksi 50ksi

29,000 50

256 0.9(50)(51.8)

=

=

7.22o.k .

(1 − 1.54(0.110)) = 62.8o.k .

0.110 < 0.125

5 - Check W14x176 column flexural and axial capacity 

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 < L p ∴

Mnx = M px = FyZx & Mny = M py = 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 G=

∑ ( I / L ) ∑ ( I / L ) c

c

y

y

Gtop

=

Gbott =

2(2140 / 12.5) 2(2850 / 28)

= 1.68

(2140 / 12.5) + (2140 / 14) 2(2850 / 28)

= 1.59

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



Axial capacity continued … K x L x r x K y L y r y

•

=

=

1.5(12.2)(12) 6.43 1.2(12.2)(12) 4.02

=

34.3

=

43.9

Check flexural buckling stress limit per AISC 360-05 E3

K 1 r

<

4.71

E F y

=

4.71

29,000 50

= 113in

o.k.

F y

π 2 E ]F y where F e = KL 2 ( ) 50 r F cr = [0.658148.5 ](50) = 43.4ksi

∴ F cr = [0.658

F e

=

π 2 (29,000) 43.9 2

= 148.5ksi

φPn = φ cFcr Ag = 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 stresses 

Check combined axial and flexural per AISC 360-05 H1 Pu max

φ Pn

D / C =



224 k

=

2025 Pr

2 Pc

k

=

0.11 < 0.2 ∴ equation (H1-1b) applies

M rx

+(

M cx

+

M ry M cy

)=

Pu

2φ Pn

+

M u

φ b M n

=

256 2(2025)

+

4401 14,400

=

0.369 < 1.0o.k

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 D

C

=

62.5k (V max( D + L + E )) 341

=

.183<1.0 o.k.

Prequalified Moment Frame Connections from MSC January 2007




6 - RBS design considerations per AISC 358-05 

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



0.5b bf ≤ a ≤ 0.75b bf 0.65d ≤ b ≤ 0.85d 0.1b bf ≤ c ≤ 0.25b bf R =

4c 2 + b 2 8c

6 – RBS design procedure per AISC 358 5.8 

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:

⎛ b f ⎞ 0.45(9.96 ) ⎟⎟ = = 2.24in 2 ⎝ 2 ⎠

c = 0.45⎜⎜

∴ R =



4c 2 + b 2 8c

4(2.25)

2

=

+ 22

8(2.25)

∴ Use

2 1 " cut 4

2

=

28.0 in radius

Plastic hinge assumed to occur at the center of the curved cut such that Sh = a + b/2 = 6 + 22/2 = 17 in


Determine distance between plastic hinges (L’) is used to determine forces for joint analysis L=28 ft L' = L − 2 sh − d c ∴





L' = 28' (12) − 2(17" ) − 15.2" = 286.8 / 12 = 23.9 ft

Step 2: Determine Ze at RBS per AISC 358-05 5.8 Z e=Z x-2ct f (d-t bf ) 2c=2(2.25”)=4.5” Z e=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 M pr = C pr R y F y Z e C pr =

F y + F u

2 F y

accounts for peak connection strength = C pr =

≤ 1.2

50 + 65 2(50)

= 1.15

M pr = 1.15(1.1)(50)(169) = 10,686k − in

Note: M pr 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 b eam section. This is verified below.


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

V pr = V P

2 M pr L'

=

2(10,686) 12(23.9)

= 74.5 kips

(V D ) + 0.5(V L ) ± V pr

= 1.2

(

)

(

)

∴V P = 1.2 16.4 + 0.5 13.3 + 74.5 = 101kips =

VRBS

(16.4) + 0.5(13.3) − 74.5 = 48.2 kips = V'RBS

∴V P = 1.2


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

(

M f = M pr + V P (sh ) = 10,686 + 101 6 + 22 M f

= −10,686 + [−48(6 + 22

2





= M pr + M v = M pr

( + V (s P

) = 12,403k − in

)] = −11,505k − in

* M pb = M pr + M v = M pr + V P sh * M pb

2

h

) 10,686 101 (6 22 2 15.2 2) 13,170k in + dc ) = 10,686 + 48(6 + 22 + 15.2 ) = 11,867 k − in 2 2 2 + dc

2

=

+

+

+

=

−

Moment at column face (M f ) used for beam flange-to-column weld and panel zone strength check below * Moment at column centerline ( M pb ) used to check weak beam/strong column condition below Note: The moment due to gravity loads occurring between plastic hinge and face of column may be neglected per AISC 358 5.8 Step 5.


Step 6: Expected plastic moment capacity of beam (gross section) per AISC 358-05 5.8 M pe=Z bR yFy=(244)(1.1)(50)=13,420 k-in



Step 7: Check that M f does not exceed φdM pe per AISC 358-05 5.8 φ d M pe

= 1.0(13,420) = 13,420k − in > 12,403 =

M f

Note: If φ d M pe ≥ M f no additional calculations required and CJP weld at beam flange to column flange is acceptable. If φ d M pe < M f 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 V u

=

2 M pr L1

+ V gravity = V pr + V gravity = V RBS

as previously calculated = 101 kips.

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

=

331.6 > 101kips ok

6 – RBS design procedure per AISC 358 5.8 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



0.4 1.8b f t bf

t cf

≥

t cf

≥

t cf

= 1.31 ∴

•

bf

6

F yb R yb F yc R yc

=

0.4 (1.8)(9.96)(0.64)

50(1.1) 50(1.1)

= 1.35

= 1.66in

continuity plate required.

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


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


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

•

Therefore, contact area of continuity plate and column flange A pb

•

where W pb

= W pb t cont − pl

= bcont − pl − ( k 1col +

1 ") 4

The required continuity plate area is determined from AISC 360-05 J7 φ Rct = 0.9(1.8) F y A pb 476

≥

A pb

≥

W pb

k = W pb max − ( 1col +

0.9 x1.8F y

where W pb max ∴ t cont − pl =

A pb W pb

=

=

=

(

Mf

d b − t bf 476

0.9(1.8)(50)

)= =

12,403 26.7 − 0.64

=

476kips

5.88in 2

1 " ) = 7.435 − (1.625 + 0.25) = 5.56in 4

bcf − t cw

2 5.88in 2 5.56in

=

7.435

= 1.06in

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


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

∑φ F A

a. T=

y

b. T= φ V nw

pb

=

2(0.9)50(5.56) = 500kips

= φ (0.6) F y A pw = 1.0(0.6)(50)(5.67) = 173kips

W

where A pw = (dc - 2tcf - 2(k+1.5in) x tcont-pl A pw = (15.2 - 2(1.31) - 2(1.91 - 1.5) x c. T= φ R y d. T=

=

469kips = panel zone capacity as determined in Step 11

φ d M pc

∑ d − t y

•

1.0 = 5.67in2

bf

=

2(

0.9(13,420) 26.7 − 0.64

) = 927kips

Weld to have capacity to resist smallest of above = 173 kips. Minimum double sided fillet = Dmin

=

Dmin

=

Ru

2(1.392k )(d c in

− 2t cf − 2( k + 1.5in))

k

173

2(1.392)(5.67in)

= 10.8

Use double sided ¾” fillet weld


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

H = 162 d p

=

26.7 − (0.64 / 2) = 26.38"

Mf = 12,430 & 11,505 from previous

Ru

=

F f

=

∑ M

f

d p

=

12,430 + 11,505 26.38

= 907 kips


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

⎡

2 ⎤ 3bcf t cf

⎢⎣

d b d c t w ⎥⎦

= φ (0.6) F y d c t w ⎢1 +

⎥

⎡ 3(15.7)(1.32) 2 ⎤ φ Rv = 1.0 x0.6 x50 x15.2 x0.83⎢1 + ⎥ = 469 < 907 n.g. add doubler plates ⎣⎢ 26.7 x15.2 x0.83 ⎦⎥ •

Check minimum panel zone thickness per Section AISC 341 9.3b t z

≥

(d z + w z ) / 90

t z

=

0.83"

≥

[(26.38) + (15.2 − 2(1.31) ) / 90] = 0.43

minimum thickness o.k .

Note: Adding ½” to each side of the column web and replacing t w 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.


Step 12: Check column-beam moment ratio (strong col-weak beam) per AISC 358-05 5.8 * ∑ M pc * ∑ M pb

≥ 1.0

* where M pc yc − = Z c ( F

Pu =

224 k 51.8

∑ M *pc

=

=

Puc ) Ag

4.32

2(320)(50 − 4.32) = 29,232

* M pb pr + M v = M

∑ M *pb = 13,170 + 11,867 * ∑ M pc * ∑ M pb 

=

29, 232 25,037

= 1.17 > 1.0o.k .

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

•

>

2.0

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%R yFy bf t bf (no minimum stiffness requirement)

6 -Fabrication Considerations 

  

 

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 grinding Protected 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 W QA/QC requirements per AISC 341 Appendix Q

Additional Design Examples

SDM Example 3 Steel SMF Design of Entire Building GOOD

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