V. AIJ 2005 Check for MISES parameter 2
Determine the von Mises stress in a slender, cantilever beam subjected to a load at the end per the AIJ 2005 code.
Details
A cantilever beam of length 0.3 meters is subjected to a permanent joint load of 3 kN in the Y direction and 2 kN in the Z direction as well as a 0.008 kN·m torque applied at the end. Axial tension of 10 kN is also applied to the member. An H100x50x5 section is used from the Japanese steel tables.
Section properties
- D = 100 mm, B = 50 mm, tf = 7 mm, tw = 5 mm
- Ix = 15,000 mm4
- Ax = 1185 mm2, Ay = 500 mm2, Az = 467 mm2
- Zx = Ix/tmax = 15,000/7 = 2,143 mm3, Zy = 5,920 mm3, Zz = 37,400 mm3
The maximum of the left hand side of the von Mises stress equation apparently occurs at the fixed end of the beam. Section forces at the fixed end are as follows:
- -10.0 kN (Tension)
- 0.6 kN·m (Bending-Y)
- 0.9 kN·m (Bending-Z)
- -3.0 kN (Shear-Y)
- -2.0 kN (Shear-Z)
- -0.008 kN·m (Torsion
Material
- FYLD = 300 MPa
- E = 2.05E+05 MPa
- G = E/2.6 MPa
Validation
From these section forces, σx and τxy at the section of the fixed end are calculated as follows:
From σx and τxy, fm is calculated:
Since ft = FYLD/1.5 = 300.0 MPa/15 = 200.0 N/mm2 and k = 1 for permanent loading,
- Ratio = 135.22/(200.0 · 1) = 0.676 < 1, So OK.
Results
Result Type | Reference | STAAD.Pro Result | Difference | Comments |
---|---|---|---|---|
von Mises Stress, fm (N/mm2) | 135.22 | 135.21 | negligible |
STAAD Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Japan\AIJ 2005 Check for MISES parameter 2.std is typically installed with the program.
- The standard AIJ calculation for the von Mises stresses is used per the
MISES 1
parameter. - An unsupported length of 2 mm is specified using the
UNL 0.002
parameter. - A steel yield strength of 300 GPa is specified using the
FYLD 300000
parameter.
STAAD SPACE VERIFICATION FOR VON MISES STRESSES IN AIJ 2005
START JOB INFORMATION
ENGINEER DATE 18-AUG-10
END JOB INFORMATION
UNIT MMS KN
JOINT COORDINATES
1 0 0 0; 2 300 0 0;
MEMBER INCIDENCES
1 1 2;
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY JAPANESE
1 TABLE ST H100x50x5x7
UNIT MMS KN
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
UNIT METER KN
LOAD 1 LC1
JOINT LOAD
2 FX 10 FY 3 FZ 2 MX 0.008
PERFORM ANALYSIS
LOAD LIST 1
PRINT MEMBER FORCES LIST ALL
PARAMETER 1
CODE JAPANESE 2005
UNL 0.002 ALL
MISES 1 ALL
TRACK 2 ALL
FYLD 300000 ALL
CHECK CODE ALL
FINISH
Output
STAAD.Pro CODE CHECKING - (AIJ-2005) V2.1
***********************
ALL UNITS ARE IN - METE KN (U.N.O.)
|-----------------------------------------------------------------------------|
| Member No: 1 Profile:ST H100X50X5X7 (JAPANESE SECTIONS) |
| Ratio: 0.676 (PASS) Reference: Eq.5.24 Loadcase: 1 |
|-----------------------------------------------------------------------------|
| Location: 0.000 Criteria: Stress Load Case: 1 (Permanent)|
| Px:(T) -10.000 Vy: -3.000 Vz: -2.000 |
| Tx: -0.008 My: 0.600 Mz: -0.900 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE: 0.000 MM (UNIT: MM) |
| Ax: 1.18500E+03 Az: 4.66667E+02 Ay: 5.00000E+02 |
| Iz: 1.87000E+06 Iy: 1.48000E+05 J: 1.53000E+04 |
| Zz: 3.74000E+04 Zy: 5.92000E+03 Zx: 2.18571E+03 |
| iZ: 3.97248E+01 iY: 1.11756E+01 Iw: 3.20013E+08 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES (Unit: N/mm2) |
| Fy: 300.000 E : 205000.000 G : 79000.000 |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES |
| Member Length: 0.300 Lz: 0.300 Ly: 0.300 UNL: 0.002 |
| DESIGN PARAMETERS |
| Kz: 1.000 Ky: 1.000 NSF: 1.000 Cb: 0.000 pλb: 0.000 |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Tension) |
| Actual : 26.844 Allowable : 400.000 Ratio : 0.067 |
|-----------------------------------------------------------------------------|
| Section Classification Results : Width to Thickness Ratios |
|-----------------------------------------------------------------------------|
| Compression | Bending |
|-----------------------------------------------------------------------------|
| LC# | Actual | Allowable | LC# | Actual | Allowable |
|-----------------------------------------------------------------------------|
| - | - | - | 1 | 14.0000 | 62.7376 |
|-----------------------------------------------------------------------------|
| CHECKS |Env| Stresses | |
| | Loc. | Demand | L/C |Typ| Actual | Allow |Ratio | Ref. |
| |(MET) |(KN-MET)| | |(N/mm2) |(N/mm2) | | |
|--------------|------|--------|------|---|--------|--------|------|----------|
| Tension | 0.000| -10.00| 1| P | 8.44| 200.00| 0.042| Eq.5.1 |
| Compression | - | - | - | - | - | 189.47| - | Eq.5.3 |
| Bending Z (T)| 0.000| -0.90| 1| P | 24.06| 200.00| 0.120| Eq.5.1 |
| Bending Z (C)| 0.000| -0.90| 1| P | 24.06| 200.00| 0.120| Eq.5.7 |
| Bending Y (T)| 0.000| 0.60| 1| P | 101.35| 200.00| 0.507| Eq.5.1 |
| Bending Y (C)| 0.000| 0.60| 1| P | 101.35| 200.00| 0.507| Eq.5.1 |
| Shear Z | 0.000| -2.00| 1| P | 4.29| 115.47| 0.037| Eq.5.2 |
| Shear Y | 0.000| -3.00| 1| P | 6.00| 115.47| 0.052| Eq.5.2 |
| Comp+ Bend C | 0.000| - | 1| P | - | - | 0.627| Eq.6.1 |
| Comp+ Bend T | 0.000| - | 1| P | - | - | 0.627| Eq.6.2 |
| Ten + Bend T | 0.000| - | 1| P | - | - | 0.669| Eq.6.3 |
| Ten + Bend C | 0.000| - | 1| P | - | - | 0.585| Eq.6.4 |
| Von-Mises | 0.000| - | 1| P | 135.21| 200.00| 0.676| Eq.5.24 |
| |
| INTERMEDIATE RESULTS (Bending) |
| Me: 6.0918E+06 KN-MET My: 1.1220E+01 KN-MET pλb: 0.600 C: 1.750 |
| |
| INTERMEDIATE RESULTS (Von-Mises) |
| Sigmax: 133.854 N/mm2 Tou: 11.034 N/mm2 fm: 135.212 N/mm2 |
|-----------------------------------------------------------------------------|