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V. AISC N690 1994 Angle

Verify the allowable stress and critical ratio of the brace members in a frame using the AISC N690 1994 code.

Details

Space frame subjected to static loads

The horizontal load is 7.5 kips and the vertical load is 10 kips.

The forces due to loading in member 6 is 2.861 kips (tension) and in member 7 is 7.328 kips (compression). Members 6 and 7 are "truss" members (axial-only).

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

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

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

For members in compression (member 7), the equivalent slenderness ratio per Eqn. 4-4 of AISC ASD p5-311 must also be determined:

(KL/r)equiv = π×√(E/Fe)

where
Fe
=
the elastic buckling strength for flexural torsional buckling taken to be 60.348 ksi. This is defined as the lowest root of the Eqn in AISC ASD (C4-2) page 5-317

Thus, (KL/r)equiv = π×√(29,000/60.348) = 68.86

Axial Tension: Member 6

Actual tensile stress (gross) = P/A = 2.862 / 8.41 = 0.340 ksi

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

Critical ratio = 0.340/21.6 = 0.016

Axial Compression: Member 7

Actual compressive stress = P/A = 7.328 / 8.41 = 0.871 ksi

As this member is made from austenitic stainless steel the allowable compression stress should be determined according to clause Q.1.5.9. As KL/r < 120, then the value of allowable axial stress, Fa, is determined from Eqn. Q1.5-11:

F a = F y 2.15 - F y 2.15   -   6 120 × K l / r = 16.74 - 16.71 - 6 120 68.86 = 10.57   k s i

Check cross-section meets requirements of Q1.9, which sets a limit for any unstiffened element clause Q1.9.1.2 of 75/√(Fy) = 12.67

  • Short leg = B/t = 6/0.625 = 9.5 < 12.67, OK
  • Long leg = D/t = 8/0.625 = 12.8 > 12.67, leg is slender

Since 75/√(Fy) = 12.67 < D/t = 12.8 < 155/√(Fy) = 25.83, Qs is determined by Eqn. QC2-1:

Qs = 1.340 - 0.00447×(b/t)×√(Fy) = 0.9967

Allowable compressive stress, Fa = 0.9967 × 10.57 = 10.54 ksi

Critical ratio = 0.871 / 10.54 = 0.083

Results

Table 1. Verification comparison for AISC_N690_1994_Angle
Parameter Hand Calculation STAAD.Pro Difference Comments
Member 6 (tension) Slenderness ratio 61.76 61.76 negligible  
Actual tensile stress (ksi) 340 340 none
Allowable tensile stress (ksi) 21.6 21.6 none
Critical ratio 0.016 0.016 none  
Member 7 (compression) Critical slenderness ratio 68.86 68.87 negligible
Actual tensile stress (ksi) 0.871 0.87 negligible  
Allowable compressive stress (ksi) 10.54 10.55 negligible  
Critical ratio 0.083 0.083 none  

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\N690\1994\AISC N690 1994 Angle.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 26-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
**************************************************************
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
PRINT MEMBER PROPERTIES all
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
4 FX 7500
6 FY -10000
PERFORM ANALYSIS
************************************************************
PARAMETER 1
CODE AISC N690 1994
* Material strength
FU 58000  MEMB 6 7
FYLD 36000  MEMB 6 7
* Net area reduced by 10%
NSF 0.9 MEMB 6 7
* Austenitic stainless steel
STYPE 1  MEMB 6 7
* Effective length factors 0.85 in both axes
LX 1 MEMB 6 7
KY 0.85  MEMB 6 7
KZ 0.85  MEMB 6 7
*
TRACK 2 ALL
CHECK CODE MEMB 6 7
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (  ANSI N690-1994)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ==| |==     ------------ |
  |MEMBER   6  *  |  AISC SECTIONS              |     | |       AX =   8.41  |
  |            *  | ST  L806010                 |     | |  --Z  AY =   3.33  |
  |DESIGN CODE *  |                             |     | |       AZ =   2.50  |
  |ANSI N690-94*  ===============================   ==| |==     SY =  11.99  |
  |            *                                                SZ =   5.16  |
  |            *  |&lt;---LENGTH (FT)=    7.81 --->|               RY =   2.81  |
  |*************                                                RZ =   1.29  |
  |                                                                          |
  |                  0.0 (KIP-FEET)                                          |
  |PARAMETER        |L0                                     L0  STRESSES     |
  |IN KIP  INCH     |L0                                     L0  IN KIP  INCH |
  |---------------  +L0                                     L0  -------------|
  | KL/R-Y=  28.34  |L0                                     L0  FA  =  21.60 |
  | KL/R-Z=  61.76  +L0                                     L0  fa  =   0.34 |
  | UNL   =  93.72  |L0                                     L0  FCZ =   0.00 |
  | CB    =   0.00  +L0                                     L0  FTZ =   0.00 |
  | CMY   =   0.00  |L0                                     L0  FCY =   0.00 |
  | CMZ   =   0.00  +L0                                     L0  FTY =   0.00 |
  | FYLD  =  36.00  |L0                                     L0  fbz =   0.00 |
  | NSF   =   0.90  +---+---+---+---+---+---+---+---+---+---|   fby =   0.00 |
  | DFF   =   0.00   0.0                                        Fey = 165.72 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez =  34.91 |
  | (KL/R)max =  68.87              (WITH LOAD NO.)             FV  =   0.00 |
  |                                                             fv  =   0.00 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE      -2.9         0.0        0.0         0.0         0.0      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         1           0          0           0           0      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        ANSI Q1.6-2      0.016              1               |
  |          2.86 T          0.00         0.00             0.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
      STAAD SPACE                                              -- PAGE NO.    5
 ALL UNITS ARE - POUN INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
  |--------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    6
                       STAAD.PRO CODE CHECKING - (  ANSI N690-1994)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ==| |==     ------------ |
  |MEMBER   7  *  |  AISC SECTIONS              |     | |       AX =   8.41  |
  |            *  | ST  L806010                 |     | |  --Z  AY =   3.33  |
  |DESIGN CODE *  |                             |     | |       AZ =   2.50  |
  |ANSI N690-94*  ===============================   ==| |==     SY =  11.99  |
  |            *                                                SZ =   5.16  |
  |            *  |&lt;---LENGTH (FT)=    7.81 --->|               RY =   2.81  |
  |*************                                                RZ =   1.29  |
  |                                                                          |
  |                  0.0 (KIP-FEET)                                          |
  |PARAMETER        |L0                                     L0  STRESSES     |
  |IN KIP  INCH     |L0                                     L0  IN KIP  INCH |
  |---------------  +L0                                     L0  -------------|
  | KL/R-Y=  28.34  |L0                                     L0  FA  =  10.55 |
  | KL/R-Z=  61.76  +L0                                     L0  fa  =   0.87 |
  | UNL   =  93.72  |L0                                     L0  FCZ =   0.00 |
  | CB    =   0.00  +L0                                     L0  FTZ =   0.00 |
  | CMY   =   0.00  |L0                                     L0  FCY =   0.00 |
  | CMZ   =   0.00  +L0                                     L0  FTY =   0.00 |
  | FYLD  =  36.00  |L0                                     L0  fbz =   0.00 |
  | NSF   =   0.90  +---+---+---+---+---+---+---+---+---+---|   fby =   0.00 |
  | DFF   =   0.00   0.0                                        Fey = 165.72 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez =  34.91 |
  | (KL/R)max =  68.87              (WITH LOAD NO.)             FV  =   0.00 |
  |                                                             fv  =   0.00 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE       7.3         0.0        0.0         0.0         0.0      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         1           0          0           0           0      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        ANSI Q1.6-2      0.083              1               |
  |          7.33 C          0.00         0.00             0.00              |
  |*                                                                        *|
  |**************************************************************************|
  |                                                                          |
      STAAD SPACE                                              -- PAGE NO.    7
 ALL UNITS ARE - POUN INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================