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
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
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:
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:
Allowable compressive stress, Fa = 0.9967 × 10.57 = 10.54 ksi
Critical ratio = 0.871 / 10.54 = 0.083
Results
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 2024\Samples \Verification Models\09 Steel Design\US\AISC\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 |
| * |<---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
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 |
| * |<---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 |
|* *|
| |
|--------------------------------------------------------------------------|