V. AISC ASD - 2D Frame Validation
Determine the allowable stresses (per 1989 AISC code) for the members of the structure as shown in the figure. Also, perform a code check for these members based on the results of the analysis.
Problem
Members 1, 2 = W12X26, Members 3, 4 = W14X43
Members 5, 6, 7 = W16X36, Memb 8= L40404, Memb 9 = L50506
F = 15 kip (wind load)
w = 2 kip/ft (dead load + live load)
Steel: Fy = 36ksi
Hand Calculation
Manual / Code refers to AISC Manual of Steel Construction, Allowable Stress Design, ninth edition.
Member 1
Size W12x26, L = 10 ft., a = 7.65 in2, Sz = 33.39 in3
Per Section F2 is the lower value for the yielding and lateral-torsional buckling limit states:
Mn = Mp = FyZx = 36ksi × 37.2 in3 = 1,339 in·k = 111.3 ft·k
From clause F1-2, page 5-45 of Manual, Lc = 6.85 ft.
From observation Load case 1 will govern,
Fx = 25.0 kip (compression), Mz = 56.5 ft·kip
Area of compressive flange = 6.49*0.38 = 2.466 in2
Allowable bending stress, per Clause F1-8 (page 5-47 of Manual)
fb = 12. · 1000 · 1.0/[10 · 12 · (12.22/2.466)] = 20.1817 ksi
(kl/r)y = 120/1.5038 = 79.8, so fa = 15.38 ksi
Stresses per Table C-36 (page 3-16 of manual)
fa = 25./7.65 = 3.268
fb = 56.5 · 12/33.39 = 20.31 ksi
(kl/r)z = 120/5.1639 = 23.238, so F'ez = = 276.54 ksi
Equation H1-1, page 5-54 of Manual
3.268/15.38 + 0.85 · 20.31 / [(1-3.268/276.54) · 20.1817] = 1.078
Equation H1-2, page 5-54 of Manual.
3.268/(0.6 · 36) +20.31/20.1817 = 1.1576
Therefore, equation H1-2 governs and ratio = 1.1576
Member 2
Size W12x26, L = 5 ft., a = 7.65 in2, Sz = 33.39 in3
From observation load case 1 will govern,
Fx = 8.71 kip (compression), Mz = 56.50 ft·kip
Since L is less than Lc = 6.85ft, per Clauses F1-1 & F1-2 (page 5-45 of Manual)
fb = 0.66 · 36 = 23.76 ksi
(kl/r)y = 60/1.5038 = 39.90, so fa = 19.19 ksi
Per Table C-36 (page 3-16 of Manual)
fa = 8.71/7.65 = 1.1385, fb = 56.5 · 12/33.39 = 20.31 ksi
Since fa/Fa less than 0.15, apply equation H1-3 (page 5-54 of Manual)
1.1385/19.19 + 20.31/23.76 = .0593 + .8548 = 0.9141
Member 3
Size W14X43, L = 11ft., a = 12.6 in2, Sz = 62.7 in3
From observation load case 3 will govern,
Fx = 25.5 kip (compression), Mz = 112.173 ft·kip
Referring to clause F1-2, page 5-45 of Manual.
Lc = 8.4 ft. Therefore
fb = 0.6 · 36 = 21.6 ksi
(kl/r)y = 132/1.8941 = 69.69,
so fa = 16.46 ksi per Table C-36 (page 3-16 of Manual)
fa = 25.5/12.6 = 2.024
fb = 112.173 · 12/62.66 = 21.48 ksi
since fa/Fa less than 0.15, use equation H1-3, page 5-54 of Manual
2.024/16.46 + 21.48/21.6 = 0.123 + 0.994 = 1.117
Member 4
Size W14x43, L = 4ft, a = 12.6 in2, Sz = 62.7 in3
From observation, load case 3 will govern,
Fx = 8.75 kip (tension), Mz = 112.173 ft·kip
Since L is less than Lc = 8.4 ft
fb = 0.66 · 36 = 23.76 ksi
Clause F1-1 (page 5-45 of Manual)
fa = 8.75/12.6 = 0.694
fb = 112.73x12/62.66 = 21.48 ksi
Combined tension and bending, use equation H2-1, page 5-55 of Manual.
0.694/(0.6 · 36) + 21.48/23.76 = 0.032 + 0.904 = 0.936
Member 5
Size W16x36, L = 5ft, a = 10.6 in2, Sz = 56.49 in3
From observation, load case 3 will govern.
Fx = 14.02 kip (compression), Mz =57.04 ft·kip
Since L is less than Lc = 7.37 (per Clause F1-2, page 5-45 of Manual)
fb = 0.66 · 36 = 23.76 ksi
(kl/r)y = 60./1.52 = 39.47
so fa = 19.23 ksi per Table C-36 (page 3-16 of Manual)
fa = 14.02/10.6 = 1.32
fb = 57.04 · 12/56.5 = 12.12 ksi
Since fa/Fa less than 0.15, use equation H1-3, page 5-54 of Manual
1.32/19.23 + 12.12/23.76 = 0.069 + 0.510 = 0.579
Member 6
Size W16x36, L = 16ft, a = 10.6 in2, Sz = 56.49 in3
From observation, load case 1 will govern. Forces at midspan are
Fx = 5.65 kip (compression), Mz = 71.25 ft·kip
From Chapter F of the AISC ASD 9Pth P ed. specs., with Cb = 1.0,
(102,000Cb/Fy)1/2 =53.229
(510,000Cb/Fy)1/2 =119.02
L/rT = 192/1.79 = 107.26
53.229 < 107.26 < 119.02
Therefore Fb (as per F1-6, page 5-47 of Manual)
[(2/3) – 36 · 107.26 · 107.26/(1,530,000)] · 36 = 14.25 ksi
(Kl/r)y = 192/1.5203 = 126.29
so fa = 9.36 per Table C-36 (page 3-16 of Manual)
fa = 5.65/10.6 = 0.533
fb = 71.25x12/56.49 = 15.14 ksi
Since fa/Fa less than 0.15 use formula [H1-3, page 5-54 of Manual]
0.533/9.36 + 15.14/14.25 = 0.057 + 1.062 = 1.119
Member 7
Size W16x36, L =4ft, a = 10.6in2, Sz =56.49in3
Lc = 7.37ft (Clause F1-2 page 5-45 of Manual)
From observation load case 3 will govern, Fx = 24.06 kip (tension), Mz = 62.96 ft·kip
From Clause F1-1, the allowable compressive stress is
fb = 0.66 Fy = 23.76 ksi
Since section is in tension, per Clause F1-5 (page5-45 of Manual)
fb = 0.60 · 36 = 21.60 Ksi
Choosing the larger of above 2 values, fb = 23.76 Ksi
fa = 24.06/10.6 = 2.2698
fb = 62.96 · 12/56.49 = 13.37
Since combined tension and bending, use equation H 2-1, page 5-55 of the AISC ASD 9Pth P ed. specs.
2.2698/(0.6 · 36) + 13.37(23.76) = 0.105 + 0.5627 = 0.6677
Member 8
Size L4x4x1/4, L = 7.071 ft, a = 1.94 in2
From observation load case 1 will govern, Fx = 23.04 kip (Comp.)
Fa is computed as per page 5-310 of the AISC ASD 9Pth P ed.specs.
Qs = 1.34 – 0.00447 · (4/0.25)·(36)1/2 = 0.9108
Qa = 1.0
Q = Qs · Qa = 0.9108
Cc= 92.0·π2·E/(Q·Fy)]1/2 = [2.0·π2 · 29000/(0.9108 · 36)]1/2 = 132.1241
Kl/r = 7.071 · 12/0.795 = 106.73 < Cc.
Hence, fa = 11.6027 ksi (computed per equation 4-1)
Actual compressive stress
fa = 23.04/1.94 = 11.876 ksi
Therefore, Ratio =
fa/fa = 11.876/11.602 = 1.024
Member 9
Size L5x5x3/8, L = 5.657 ft, a = 3.61 in2
From observation, load case 1 governs, Fx = 48.44 kip (Comp.)
Fa is computed as per page 5-310 of the AISC ASD 9Pth P ed. specs.
Qs = 1.34 – 0.00447 · (5/0.375)·(36)1/2 = 0.9824
Qa = 1.0
Q = Qs · Qa = 0.9824
Cc= 92.0·π2·E/(Q·Fy)]1/2 = [2.0·π2 · 29000/(0.9824 · 36)]1/2 = 127.2238
(Kl/r)min = 5.657 · 12/0.99 = 68.57 < Cc.
Hence, fa = 16.301 ksi (computed per equation 4-1)
Actual compressive stress
fa = 48.44/3.61 = 13.418 ksi
Therefore Ratio =
fa/fa = 13.418/16.301 = 0.823
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC ASD - 2D Frame validation.STD is typically installed with the program.
STAAD PLANE VERIFICATION PROBLEM NO 13
START JOB INFORMATION
ENGINEER DATE 22-Sep-18
END JOB INFORMATION
*
* THIS DESIGN EXAMPLE IS VERIFIED BY HAND CALCULATION
* FOLLOWING AISC-89 CODE.
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 25 0 0; 3 0 10 0; 4 25 11 0; 5 0 15 0; 6 25 15 0; 7 5 15 0;
8 21 15 0;
MEMBER INCIDENCES
1 1 3; 2 3 5; 3 2 4; 4 4 6; 5 5 7; 6 7 8; 7 8 6; 8 3 7; 9 4 8;
MEMBER PROPERTY AMERICAN
1 2 TABLE ST W12X26
3 4 TABLE ST W14X43
5 TO 7 TABLE ST W16X36
8 TABLE ST L40404
9 TABLE ST L50506
MEMBER TRUSS
8 9
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 2 PINNED
LOAD 1 DL + LL
MEMBER LOAD
5 TO 7 UNI Y -2
LOAD 2 WIND FROM LEFT
JOINT LOAD
5 FX 15
LOAD COMBINATION 3
1 0.75 2 0.75
PERFORM ANALYSIS
LOAD LIST 1 3
PRINT MEMBER FORCES
PARAMETER 1
CODE AISC
TRACK 1 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.Pro CODE CHECKING - (AISC 9TH EDITION) v1.0 *********************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= * 1 ST W12X26 (AISC SECTIONS) FAIL AISC- H1-2 1.154 1 25.00 C 0.00 56.50 10.00 ----------------------------------------------------------------------- | MEM= 1, UNIT KIP-INCH, L= 120.0 AX= 7.65 SZ= 33.4 SY= 5.3| | KL/R-Y= 79.8 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 20.21 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 15.38 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- 2 ST W12X26 (AISC SECTIONS) PASS AISC- H1-3 0.913 1 8.72 C 0.00 56.50 0.00 ----------------------------------------------------------------------- | MEM= 2, UNIT KIP-INCH, L= 60.0 AX= 7.65 SZ= 33.4 SY= 5.3| | KL/R-Y= 39.9 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 19.20 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- * 3 ST W14X43 (AISC SECTIONS) FAIL AISC- H1-3 1.121 3 25.50 C 0.00 -112.20 11.00 ----------------------------------------------------------------------- | MEM= 3, UNIT KIP-INCH, L= 132.0 AX= 12.60 SZ= 62.5 SY= 11.3| | KL/R-Y= 69.7 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 21.60 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 16.46 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- 4 ST W14X43 (AISC SECTIONS) PASS AISC- H2-1 0.939 3 8.83 T 0.00 -112.20 0.00 ----------------------------------------------------------------------- | MEM= 4, UNIT KIP-INCH, L= 48.0 AX= 12.60 SZ= 62.5 SY= 11.3| | KL/R-Y= 25.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 19.85 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- 5 ST W16X36 (AISC SECTIONS) PASS AISC- H1-3 0.580 3 14.02 C 0.00 -57.00 5.00 VERIFICATION PROBLEM NO 13 -- PAGE NO. 6 ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= ----------------------------------------------------------------------- | MEM= 5, UNIT KIP-INCH, L= 60.0 AX= 10.60 SZ= 56.4 SY= 7.0| | KL/R-Y= 39.5 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 19.23 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- * 6 ST W16X36 (AISC SECTIONS) FAIL AISC- H1-3 1.107 1 5.65 C 0.00 -71.25 8.00 ----------------------------------------------------------------------- | MEM= 6, UNIT KIP-INCH, L= 192.0 AX= 10.60 SZ= 56.4 SY= 7.0| | KL/R-Y= 126.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 14.45 | | FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 9.36 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- 7 ST W16X36 (AISC SECTIONS) PASS AISC- H2-1 0.670 3 24.13 T 0.00 63.00 0.00 ----------------------------------------------------------------------- | MEM= 7, UNIT KIP-INCH, L= 48.0 AX= 10.60 SZ= 56.4 SY= 7.0| | KL/R-Y= 31.6 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 | | FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.88 FT= 21.60 FV= 14.40 | ----------------------------------------------------------------------- * 8 ST L40404 (AISC SECTIONS) FAIL AISC- H1-1 1.045 1 23.03 C 0.00 0.00 0.00 ----------------------------------------------------------------------- | MEM= 8, UNIT KIP-INCH, L= 84.9 AX= 1.93 SZ= 0.8 SY= 1.7| | KL/R- = 108.4 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 | | FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 11.42 FT= 21.60 FV= 0.00 | ----------------------------------------------------------------------- 9 ST L50506 (AISC SECTIONS) PASS AISC- H1-1 0.815 3 48.55 C 0.00 0.00 0.00 VERIFICATION PROBLEM NO 13 -- PAGE NO. 7 ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= ----------------------------------------------------------------------- | MEM= 9, UNIT KIP-INCH, L= 67.9 AX= 3.65 SZ= 1.8 SY= 3.9| | KL/R- = 68.8 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 | | FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 16.32 FT= 21.60 FV= 0.00 | -----------------------------------------------------------------------