V. AISC ASD - 二维框架验证

确定如图所示结构构件的允许应力（根据1989 AISC规范）。此外，基于分析结果对这些构件进行规范检验。

Reference

附根据1989 AISC ASD规范逐步手算。第九版。

Details

构件1, 2 = W12X26, 构件3, 4 = W14X43

构件5, 6, 7 = W16X36, 构件8 = L40404, 构件9 = L50506

F = 15 kip (风荷载)

w = 2 kip/ft (恒载 + 活载)

钢材: Fy = 36ksi

Calculations

手算

手动/规范参考AISC钢结构手册，允许应力设计，第九版。

构件1

截面 W12x26, L = 10 ft., a = 7.65 in², S_z = 33.39 in³

根据章节 F2，屈服和侧向扭转屈曲极限状态的较低值：

Mn = Mp = FyZx = 36ksi × 37.2 in³ = 1,339 in·k = 111.3 ft·k

根据手册第5-45页条款 F1-2，L_c = 6.85 ft.

从观察，荷载工况1将控制，

F_x = 25.0 kip (压力), M_z = 56.5 ft·kip

受压翼缘面积 = 6.49*0.38 = 2.466 in²

允许弯曲应力，根据条款 F1-8（手册第5-47页）

f_b = 12. · 1000 · 1.0/[10 · 12 · (12.22/2.466)] = 20.1817 ksi

(kl/r)y = 120/1.5038 = 79.8, 所以 f_a = 15.38 ksi

应力根据表 C-36（手册第3-16页）

f_a = 25./7.65 = 3.268

f_b = 56.5 · 12/33.39 = 20.31 ksi

(kl/r)z = 120/5.1639 = 23.238, 所以 F'_ez = = 276.54 ksi

方程 H1-1，手册第5-54页

3.268/15.38 + 0.85 · 20.31 / [(1-3.268/276.54) · 20.1817] = 1.078

方程 H1-2，手册第5-54页。

3.268/(0.6 · 36) +20.31/20.1817 = 1.1576

因此，方程 H1-2 控制且应力比 = 1.1576

构件2

截面 W12x26, L = 5 ft., a = 7.65 in², Sz = 33.39 in³

从观察，荷载工况1将控制，

F_x = 8.71 kip (压力), M_z = 56.50 ft·kip

由于 L 小于 L_c = 6.85ft，根据条款 F1-1 & F1-2（手册第5-45页）

f_b = 0.66 · 36 = 23.76 ksi

(kl/r)y = 60/1.5038 = 39.90, 所以 f_a = 19.19 ksi

根据表 C-36（手册第3-16页）

f_a = 8.71/7.65 = 1.1385, f_b = 56.5 · 12/33.39 = 20.31 ksi

由于 f_a/F_a 小于 0.15，应用方程 H1-3（手册第5-54页）

1.1385/19.19 + 20.31/23.76 = .0593 + .8548 = 0.9141

构件3

截面 W14X43, L = 11ft., a = 12.6 in², Sz = 62.7 in³

从观察，荷载工况3将控制，

F_x = 25.5 kip (压力), M_z = 112.173 ft·kip

参考条款 F1-2，手册第5-45页。

L_c = 8.4 ft. 因此

f_b = 0.6 · 36 = 21.6 ksi

(kl/r)y = 132/1.8941 = 69.69,

所以 f_a = 16.46 ksi 根据表 C-36（手册第3-16页）

f_a = 25.5/12.6 = 2.024

f_b = 112.173 · 12/62.66 = 21.48 ksi

由于 f_a/F_a 小于 0.15，使用方程 H1-3，手册第5-54页

2.024/16.46 + 21.48/21.6 = 0.123 + 0.994 = 1.117

构件4

截面 W14x43, L = 4ft, a = 12.6 in², Sz = 62.7 in³

从观察，荷载工况3将控制，

F_x = 8.75 kip (拉力), M_z = 112.173 ft·kip

由于 L 小于 L_c = 8.4 ft

f_b = 0.66 · 36 = 23.76 ksi

条款 F1-1（手册第5-45页）

f_a = 8.75/12.6 = 0.694

f_b = 112.73x12/62.66 = 21.48 ksi

组合拉力和弯曲，使用方程 H2-1，手册第5-55页。

0.694/(0.6 · 36) + 21.48/23.76 = 0.032 + 0.904 = 0.936

构件5

截面 W16x36, L = 5ft, a = 10.6 in², Sz = 56.49 in³

从观察，荷载工况3将控制。

F_x = 14.02 kip (压力), M_z =57.04 ft·kip

由于 L 小于 L_c = 7.37（根据条款 F1-2，手册第5-45页）

f_b = 0.66 · 36 = 23.76 ksi

(kl/r)y = 60./1.52 = 39.47

所以 f_a = 19.23 ksi 根据表 C-36（手册第3-16页）

f_a = 14.02/10.6 = 1.32

f_b = 57.04 · 12/56.5 = 12.12 ksi

由于 f_a/F_a 小于 0.15，使用方程 H1-3，手册第5-54页

1.32/19.23 + 12.12/23.76 = 0.069 + 0.510 = 0.579

构件6

截面 W16x36, L = 16ft, a = 10.6 in², Sz = 56.49 in³

从观察，荷载工况1将控制。跨中力为

F_x = 5.65 kip (压力), M_z = 71.25 ft·kip

根据AISC ASD 9^th 版规范章节 F，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

因此 F_b（根据 F1-6，手册第5-47页）

[(2/3) – 36 · 107.26 · 107.26/(1,530,000)] · 36 = 14.25 ksi

(Kl/r)y = 192/1.5203 = 126.29

所以 f_a = 9.36 根据表 C-36（手册第3-16页）

f_a = 5.65/10.6 = 0.533

f_b = 71.25x12/56.49 = 15.14 ksi

由于 f_a/F_a 小于 0.15，使用公式 [H1-3，手册第5-54页]

0.533/9.36 + 15.14/14.25 = 0.057 + 1.062 = 1.119

构件7

截面 W16x36, L =4ft, a = 10.6in², Sz =56.49in³

L_c = 7.37ft（条款 F1-2 第5-45页手册）

从观察荷载工况3将控制，F_x = 24.06 kip (拉力), M_z = 62.96 ft·kip

根据条款 F1-1，允许压应力为

f_b = 0.66 Fy = 23.76 ksi

由于截面受拉，根据条款 F1-5（手册第5-45页）

f_b = 0.60 · 36 = 21.60 Ksi

选择以上两个值中的较大者，f_b = 23.76 Ksi

f_a = 24.06/10.6 = 2.2698

f_b = 62.96 · 12/56.49 = 13.37

由于组合拉力和弯曲，使用方程 H 2-1，AISC ASD 9^th 版规范第5-55页。

2.2698/(0.6 · 36) + 13.37(23.76) = 0.105 + 0.5627 = 0.6677

构件8

截面 L4x4x1/4, L = 7.071 ft, a = 1.94 in²

从观察荷载工况1将控制，F_x = 23.04 kip (压力)

Fa 根据AISC ASD 9^th 版规范第5-310页计算。

Q_s = 1.34 – 0.00447 · (4/0.25)·(36)^1/2 = 0.9108

Q_a = 1.0

Q = Q_s · Q_a = 0.9108

C_c= 92.0·π²·E/(Q·F_y)]^1/2 = [2.0·π² · 29000/(0.9108 · 36)]^1/2 = 132.1241

Kl/r = 7.071 · 12/0.795 = 106.73 < C_c.

因此，f_a = 11.6027 ksi（根据方程 4-1 计算）

实际压应力

f_a = 23.04/1.94 = 11.876 ksi

因此，应力比 =

f_a/f_a = 11.876/11.602 = 1.024

构件9

截面 L5x5x3/8, L = 5.657 ft, a = 3.61 in²

从观察，荷载工况1控制，F_x = 48.44 kip (压力)

Fa 根据AISC ASD 9^th 版规范第5-310页计算。

Q_s = 1.34 – 0.00447 · (5/0.375)·(36)^1/2 = 0.9824

Q_a = 1.0

Q = Q_s · Q_a = 0.9824

C_c= 92.0·π²·E/(Q·F_y)]^1/2 = [2.0·π² · 29000/(0.9824 · 36)]^1/2 = 127.2238

(Kl/r)min = 5.657 · 12/0.99 = 68.57 < C_c.

因此，f_a = 16.301 ksi（根据方程 4-1 计算）

实际压应力

f_a = 48.44/3.61 = 13.418 ksi

因此应力比 =

f_a/f_a = 13.418/16.301 = 0.823

Results

构件编号处的控制应力比	手算	STAAD.Pro	差异
1	1.158	1.154	可忽略
2	0.914	0.913	可忽略
3	1.117	1.121	可忽略
4	0.936	0.939	可忽略
5	0.579	0.580	可忽略
6	1.119	1.107	1.1%
7	0.668	0.670	可忽略
8	1.024	1.045	2.1%
9	0.823	0.815	1.0%

Input

文件 C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\09 Steel Design\US\AISC\AISC ASD - 2D Frame validation.STD 通常随程序安装。

STAAD

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

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   |
  -----------------------------------------------------------------------