# 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:

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
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

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
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.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      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|
|         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)
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      |
|                                                                          |
|**************************************************************************|
|*                                                                        *|
|*                         DESIGN SUMMARY  (KIP-FEET)                     *|
|*                         --------------                                 *|
|*                                                                        *|