V.AIJ 2002 Check for MISES parameter
Verify the von Mises stress calculations per the AIJ 2002 code using a cantilever beam.
Details
Japanese Angle section L250X250X35, E = 205,000 MPa, Fy = 200 MPa
- Fx = 10 kN
- Vz = 5 kN
- Vy = 5 kN
- T = 5 kN·m
Verification
The maximum of the left-hand side of the von Mises stress equation apparently occurs at the fixed support of the beam. Section forces at the fixed end are calculated as below.
- FX = -10 KN
- FY = -5 KN
- FZ = -5 KN
- MX = -5 KN-m
- MY = 25 KN-m
- MZ = -25 KN-m
The standard AIJ calculation is used (MISES 1). From these section forces, σx and τxy at the section of the fixed end are calculated:
=0.615 + 29.809 + 70.244 = 100.668 N/mm2 |
= 27.57 N/mm2 |
From σx and τxy , fm is calculated:
For permanent loading, k = 1 and ft = fy/1.5 = 133.33 N/mm2
Therefore, the ratio = fm/k×ft = 111.419/(1 × 133.33) = 0.836
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
fm (N/mm2) | 111.42 | 111.42 | none | |
ft (N/mm2) | 133.33 | 133.33 | none | |
σx (N/mm2) | 100.668 | 100.669 | negligible | |
τxy (N/mm2) | 27.569 | 27.57 | negligible | |
Ratio | 0.836 | 0.836 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Japan\AIJ 2002 Check for MISES parameter.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 27-Apr-15
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY JAPANESE
1 TABLE ST L250X250X35
*1 TABLE ST H100X50X5
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FX 10 FY 5 FZ 5 MX 5
PERFORM ANALYSIS PRINT STATICS LOAD
PRINT MEMBER PROPERTIES ALL
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE JAPANESE 2002
*TMP 1 ALL
*KZ 1.5 ALL
FYLD 200000 ALL
MISES 1 ALL
*MBG -1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AIJ-2002) V2.1 *********************** ALL UNITS ARE IN - METE KN (U.N.O.) |-----------------------------------------------------------------------------| | Member No: 1 Profile:ST L250X250X35 (JAPANESE SECTIONS) | | Ratio: 0.836 (PASS) Reference: Eq.5.16 Loadcase: 1 | |-----------------------------------------------------------------------------| | Location: 0.000 Criteria: Stress Load Case: 1 (Permanent)| | Px:(T) -10.000 Vy: -5.000 Vz: -5.000 | | Tx: -5.000 My: 25.000 Mz: -25.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES AT DISTANCE: 0.000 MM (UNIT: MM) | | Ax: 1.62600E+04 Az: 5.83333E+03 Ay: 5.83333E+03 | | Iz: 3.79328E+07 Iy: 1.48256E+08 J: 6.63950E+06 | | Zz: 3.55901E+05 Zy: 8.38661E+05 Zx: 1.89700E+05 | | iZ: 4.83000E+01 iY: 9.54873E+01 Iw: 2.99365E+10 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES (Unit: N/mm2) | | Fy: 200.000 E : 205000.000 G : 79000.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES | | Member Length: 5.000 Lz: 5.000 Ly: 5.000 UNL: 5.000 | | DESIGN PARAMETERS | | Kz: 1.000 Ky: 1.000 NSF: 1.000 Cb: 0.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS (Tension) | | Actual : 103.520 Allowable : 400.000 Ratio : 0.259 | |-----------------------------------------------------------------------------| | Section Classification Results : Width to Thickness Ratios | |-----------------------------------------------------------------------------| | Compression | Bending | |-----------------------------------------------------------------------------| | LC# | Actual | Allowable | LC# | Actual | Allowable | |-----------------------------------------------------------------------------| | - | - | - | 1 | 7.1429 | 14.1421 | |-----------------------------------------------------------------------------| | 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 | 0.62| 133.33| 0.005| Eq.5.1 | | Compression | - | - | - | - | - | 77.53| - | Eq.5.3 | | Bending Z (T)| 0.000| -25.00| 1| P | 70.24| 133.33| 0.527| Eq.5.1 | | Bending Z (C)| 0.000| -25.00| 1| P | 70.24| 133.33| 0.527| Eq.5.1 | | Bending Y (T)| 0.000| 25.00| 1| P | 29.81| 133.33| 0.224| Eq.5.1 | | Bending Y (C)| 0.000| 25.00| 1| P | 29.81| 133.33| 0.224| Eq.5.1 | | Shear Z | 0.000| -5.00| 1| P | 0.86| 76.98| 0.011| Eq.5.2 | | Shear Y | 0.000| -5.00| 1| P | 0.86| 76.98| 0.011| Eq.5.2 | | Comp+ Bend C | 0.000| - | 1| P | - | - | 0.750| Eq.6.1 | | Comp+ Bend T | 0.000| - | 1| P | - | - | 0.750| Eq.6.2 | | Ten + Bend T | 0.000| - | 1| P | - | - | 0.755| Eq.6.3 | | Ten + Bend C | 0.000| - | 1| P | - | - | 0.746| Eq.6.4 | | Von-Mises | 0.000| - | 1| P | 111.42| 133.33| 0.836| Eq.5.16 | | | | INTERMEDIATE RESULTS (Bending) | | C: 0.000 | | | | INTERMEDIATE RESULTS (Von-Mises) | | Sigmax: 100.669 N/mm2 Tou: 27.570 N/mm2 fm: 111.420 N/mm2 | |-----------------------------------------------------------------------------|