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V. AISC N690 1984 Angle

Verify the allowable stress and critical ratio of the brace members in a frame using the AISC N690 1984 code.

Details

The forces due to loading in member 6 is 2,666.18 lbs (tension) and in member 7 is 7,104.23 lbs (compression). Members 6 and 7 are "truss" members (axial-only).

Space frame subjected to static loads

Both member 6 and 7 are L 80x60x10, grade A36 steel (Fy = 36 ksi, Fu = 58 ksi).

Assume a net section factor of 0.9, an effective length factor of 0.85, and Ct = 0.9.

Validation

L = 5 2 + 6 2 ( 12 in/ft ) = 93.726 in

Slenderness ratio (same for both members) using the minimum value of r: kL/rz = 0.85(93.726)/1.29 = 61.76

For member 6, kL/rz = 61.76 < 300

For member 7, kL/rz = 61.76 < 200

Axial Tension: Member 6

Corrected area, Ac = Ct×Ax = 7.57 in2

Actual tensile stress = P/A = 2,666.18 / 7.57 = 352.2 psi

Allowable tensile stress (Tension capacity) = 0.6×Fy = 0.6×36 = 21.6 ksi

Critical ratio = 352.2/21600 = 0.016

Axial Compression: Member 7

Actual compressive stress = P/A = 7,104.23 / 8.41 = 844.74 psi

C c = 2 π 2 E Q s Q a F y = 126.2

(kL/r)min < Cc', allowable compression stress, Fa = 17.2 ksi

Critical ratio = 844.74 / 17,200 = 0.049

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Member 6 (tension) Slenderness ratio 61.76 61.76 none  
Actual tensile stress (psi) 352 352 none
Allowable tensile stress (psi) 21,600 21,600 none
Critical ratio 0.016 0.016 none
Member 7 (compression) Slenderness ratio 61.76 61.76 none
Actual tensile stress (psi) 845 845 none
Allowable tensile stress (psi) 17,200 17,200 none
Critical ratio 0.049 0.049 none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\N690\1984\AISC N690 1984 Angle.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 26-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 60 0 0; 3 120 0 0; 4 0 72 0; 5 120 72 0; 6 60 72 0;
MEMBER INCIDENCES
1 1 4; 2 4 6; 3 6 5; 4 5 3; 5 6 2; 6 1 6; 7 6 3;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.9e+07
POISSON 0.3
DENSITY 0.283
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 36000 FU 58000 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TO 5 TABLE ST W8X48
6 7 TABLE ST L806010
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 TO 3 FIXED
MEMBER TRUSS 
6 7
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
4 FX 7500
6 FY -10000
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES LIST 6 7
SECTION 0 0.25 0.5 0.75 1 MEMB 6 7
PRINT MEMBER SECTION FORCES LIST 6 7
PRINT MEMBER FORCES LIST 6 7
PRINT MEMBER STRESSES LIST 6
PARAMETER 1
CODE AISC N690 1984
CMY 1 ALL
CMZ 1 ALL
CT 0.9 ALL
FU 58000 ALL
FYLD 36000 ALL
KY 0.85 ALL
KZ 0.85 ALL
UNT 60 ALL
UNB 60 ALL
MAIN 200 ALL
NSF 0.9 ALL
RATIO 1 ALL
TMAIN 300 ALL
STYPE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

 |-----------------------------------------------------------------------------|
      6  ST   L806010                  (AISC SECTIONS)
                           PASS      Q1.5.1.1          0.016         1
                    -2666.18 T          0.00           0.00        0.00
 |-----------------------------------------------------------------------------|
 | SLENDERNESS CHECK:    ACTUAL RATIO:  61.76 ALLOWABLE RATIO: 300.00          |
 | ALLOWABLE STRESSES:   (UNIT - POUN INCH)                                    |
 | AX.TENS: 2.16E+04                     COMPRESS:1.72E+04                     |
 |                                                                             |
 | ACTUAL STRESSES: (UNIT - POUN INCH)                                         |
 | AX.TENS: 3.52E+02                     COMPRESS:0.00E+00                     |
 |-----------------------------------------------------------------------------|
 | SECTION PROPERTIES: (UNIT - INCH)                                           |
 | AXX:   8.41  AYY:   3.33  AZZ:   2.50  RZZ:  1.29  RYY:  2.81               |
 | SZZ:       5.16  SYY:      11.99                                            |
 |-----------------------------------------------------------------------------|
 | PARAMETER: (UNIT - POUN INCH)                                               |
 | KL/R-Z: 61.76   KL/R-Y: 28.34   UNL:   60.0   CMZ:  1.00   CMY:  1.00       |
 | CB: 0.00   FYLD: 36000.00   FU: 58000.00   NET SECTION FACTOR: 0.90         |
 | CT:  0.90   STEEL TYPE:  1.0                                                |
 |-----------------------------------------------------------------------------|
 | CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS POUN-INCH)                      |
 | CLAUSE       RATIO  LOAD       FX        VY        VZ        MZ        MY   |
 | TENSION      0.016    1    2.67E+03       -         -         -         -   |
 | COMPRESSION  0.000    1    2.67E+03       -         -         -         -   |
 | COMP&BEND    0.000    1    2.67E+03       -         -    0.00E+00 0.00E+00  |
 | TEN&BEND     0.016    1    2.67E+03       -         -    0.00E+00 0.00E+00  |
 | SHEAR-Y      0.000    1        -     0.00E+00       -         -         -   |
 | SHEAR-Z      0.000    1        -          -    0.00E+00       -         -   |
 |-----------------------------------------------------------------------------|
      7  ST   L806010                  (AISC SECTIONS)
                           PASS      Q1.5.1.3.1        0.049         1
                     7104.23 C          0.00           0.00        0.00
 |-----------------------------------------------------------------------------|
 | SLENDERNESS CHECK:    ACTUAL RATIO:  61.76 ALLOWABLE RATIO: 200.00          |
 | ALLOWABLE STRESSES:   (UNIT - POUN INCH)                                    |
 | AX.TENS: 2.16E+04                     COMPRESS:1.72E+04                     |
 |                                                                             |
 | ACTUAL STRESSES: (UNIT - POUN INCH)                                         |
 | AX.TENS: 0.00E+00                     COMPRESS:8.45E+02                     |
 |-----------------------------------------------------------------------------|
 | SECTION PROPERTIES: (UNIT - INCH)                                           |
 | AXX:   8.41  AYY:   3.33  AZZ:   2.50  RZZ:  1.29  RYY:  2.81               |
 | SZZ:       5.16  SYY:      11.99                                            |
 |-----------------------------------------------------------------------------|
 | PARAMETER: (UNIT - POUN INCH)                                               |
 | KL/R-Z: 61.76   KL/R-Y: 28.34   UNL:   60.0   CMZ:  1.00   CMY:  1.00       |
 | CB: 0.00   FYLD: 36000.00   FU: 58000.00   NET SECTION FACTOR: 0.90         |
 | CT:  0.90   STEEL TYPE:  1.0                                                |
 |-----------------------------------------------------------------------------|
 | CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS POUN-INCH)                      |
 | CLAUSE       RATIO  LOAD       FX        VY        VZ        MZ        MY   |
 | TENSION      0.000    1    7.10E+03       -         -         -         -   |
 | COMPRESSION  0.049    1    7.10E+03       -         -         -         -   |
 | COMP&BEND    0.049    1    7.10E+03       -         -    0.00E+00 0.00E+00  |
 | TEN&BEND     0.000    1    7.10E+03       -         -    0.00E+00 0.00E+00  |
 | SHEAR-Y      0.000    1        -     0.00E+00       -         -         -   |
 | SHEAR-Z      0.000    1        -          -    0.00E+00       -         -   |
 |-----------------------------------------------------------------------------|