V. AIJ 2005 UPT General
Verify the bending capacity and compression capacity of an H section beam.
Details
The member is a 5 m long simply-supported beam. The section used is an H300x150x6.5x9. The steel has a yield strength of 235 MPa, a modulus of elasticity of 205×(10)3 MPa, and a shear modulus of 79×(10)3 MPa.
The member is subject to the following loads:- a -10 kN concentrated force at mid-span in the global Y direction
- a 3 kN concentrated force at mid-span in the global Z direction
- a -40 kN axial force
- a -0.2 kN·m concentrated moment at the left end
Validation
Section Properties
Dimensions:
- Leg, D = 300 mm
- Width, B = 150 mm
- Thickness of web, tw = 6.5 mm
- Thickness of flange, tf = 9 mm
Area, Ax = 4,678 mm2
Moment of inertia about major axis,
Moment of inertia about minor axis,
Major axis section modulus,
Minor axis section modulus,
Torsional constant,
Warping constant,
Radius of gyration about major axis,
Radius of gyration about minor axis,
Section Classification
For webs of beams in compression (Cl. 8.1):
Depth to thickness ratio is OK
.
For webs of beams in bending (Cl. 8.1):
Depth to thickness ratio is OK
.
Allowable Compressive Stress
The slenderness ratio of compression members (Cl. 11.1):
Therefore, λ = 151.7.
Slenderness ratio dividing elastic and inelastic buckling (Cl no 5.5):
λ > Λ, so the allowable compressive stress is given by Cl. 5.4:
Allowable Flexural Stress
Distance between braced points of the compression flange, lb = 5,000 mm.
The yield moment,
The modification factor for allowable flexural stress (Cl. 5.13):
The elastic lateral-torsional buckling moment (Cl 5.12):
The maximum slenderness ratio to achieve the plastic strength (Cl. 5.12):
The elastic slenderness limit:
Here, pλb < λb ≤ eλb , so:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Allowable compressive stress (MPa) | 40.57 | 40.57 | none | |
Allowable flexural stress (MPa) | 74.45 | 74.47 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Japan\AIJ 2005 UPT General.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Oct-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
107 26 0 0; 108 31 0 0;
MEMBER INCIDENCES
54 107 108;
START USER TABLE
TABLE 1
UNIT METER KN
GENERAL
UT_H300X150X6.5X9
0.004678 0.3 0.0065 0.15 0.009 7.21e-05 5.08e-06 9.95e-08 0.000480667 -
6.77333e-05 0.00195 0.0018 0 0 1.07545e-07 0.256
END
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY JAPANESE
54 UPTABLE 1 UT_H300X150X6.5X9
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
107 PINNED
108 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
54 CON GY -10
54 CON GZ 3
JOINT LOAD
108 FX -40
107 MX 0.2
PERFORM ANALYSIS
PARAMETER 1
CODE JAPANESE 2005
SLF 1 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AIJ-2005) V2.1
***********************
ALL UNITS ARE IN - METE KN (U.N.O.)
|-----------------------------------------------------------------------------|
| Member No: 54 Profile : UT_H300X150X6.(UPT) |
| Ratio: 0.913 (PASS) Reference: Eq.6.1 Loadcase: 1 |
|-----------------------------------------------------------------------------|
| Location: 2.500 Criteria: Stress Load Case: 1 (Permanent)|
| Px:(C) 40.000 Vy: 5.000 Vz: -1.500 |
| Tx: 0.200 My: -3.750 Mz: -12.500 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE: 2499.999 MM (UNIT: MM) |
| Ax: 4.67800E+03 Az: 1.80000E+03 Ay: 1.95000E+03 |
| Iz: 7.21000E+07 Iy: 5.08000E+06 J: 9.95000E+04 |
| Zz: 4.80667E+05 Zy: 6.77333E+04 Zx: 1.10556E+04 |
| iZ: 1.24147E+02 iY: 3.29535E+01 Iw: 1.07545E+11 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES (Unit: N/mm2) |
| Fy: 235.000 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 pλb: 0.000 |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Compression) |
| Actual : 151.729 Allowable : 200.000 Ratio : 0.759 |
|-----------------------------------------------------------------------------|
| Section Classification Results : Width to Thickness Ratios |
|-----------------------------------------------------------------------------|
| Compression | Bending |
|-----------------------------------------------------------------------------|
| LC# | Actual | Allowable | LC# | Actual | Allowable |
|-----------------------------------------------------------------------------|
| 1 | 43.3846 | 47.2567 | 1 | 43.3846 | 70.8850 |
|-----------------------------------------------------------------------------|
| CHECKS |Env| Stresses | |
| | Loc. | Demand | L/C |Typ| Actual | Allow |Ratio | Ref. |
| |(MET) |(KN-MET)| | |(N/mm2) |(N/mm2) | | |
|--------------|------|--------|------|---|--------|--------|------|----------|
| Tension | - | - | - | - | - | 156.67| - | Eq.5.1 |
| Compression | 0.000| 40.00| 1| P | 8.55| 40.57| 0.211| Eq.5.4 |
| Bending Z (T)| 2.500| -12.50| 1| P | 26.01| 156.67| 0.166| Eq.5.1 |
| Bending Z (C)| 2.500| -12.50| 1| P | 26.01| 74.47| 0.349| Eq.5.8 |
| Bending Y (T)| 2.500| -3.75| 1| P | 55.36| 156.67| 0.353| Eq.5.1 |
| Bending Y (C)| 2.500| -3.75| 1| P | 55.36| 156.67| 0.353| Eq.5.1 |
| Shear Z | 0.000| -1.50| 1| P | 0.83| 90.45| 0.009| Eq.5.2 |
| Shear Y | 0.000| 5.00| 1| P | 2.56| 90.45| 0.028| Eq.5.2 |
| Comp+ Bend C | 2.500| - | 1| P | - | - | 0.913| Eq.6.1 |
| Comp+ Bend T | 2.500| - | 1| P | - | - | 0.465| Eq.6.2 |
| Ten + Bend T | 2.500| - | 1| P | - | - | 0.519| Eq.6.3 |
| Ten + Bend C | 2.500| - | 1| P | - | - | 0.703| Eq.6.4 |
| Von-Mises | 2.500| - | 1| P | 96.86| 156.67| 0.618| Eq.5.24 |
| |
| INTERMEDIATE RESULTS (Bending) |
| Me: 8.2523E+01 KN-MET My: 1.1296E+02 KN-MET pλb: 0.300 C: 1.000 |
| |
| INTERMEDIATE RESULTS (Von-Mises) |
| Sigmax: 89.920 N/mm2 Tou: 20.787 N/mm2 fm: 96.860 N/mm2 |
|-----------------------------------------------------------------------------|