V. AIJ 2005 UPT Channel
Verify the bending capacity and compression capacity of a channel section beam.
Details
The member is a 5 m long simply-supported beam. The section used is a C380X100X10.5. 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.
- a 10 kN·m concentrated moment at the left end
- a -3 kN·m concentrated moment at the right end
Validation
Section Properties
Dimensions:
- Depth, D = 380 mm
- Width, B = 100 mm
- Thickness of web, tw = 10.5 mm
- Thickness of flange, tf = 16 mm
Height of web, d = D - 2tf = 348 mm
Area, Ax = 2B×tf + d×tw = 6,854 mm2
Distance from heel to centroid,
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 (Cl. 8.5):
Depth to thickness ratio is OK
.
Allowable Compressive Stress
The slenderness ratio of compression members (Cl. 11.1):
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) | 33.35 | 33.34 | negligible | |
| Allowable flexural stress (MPa) | 102.5 | 102.48 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Japan\AIJ 2005 UPT Channel.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
31 19 0 0; 32 24 0 0;
MEMBER INCIDENCES
16 31 32;
START USER TABLE
TABLE 1
UNIT METER KN
GENERAL
GE_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
*0.004678 0.3 0 0.15 0 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
TABLE 2
UNIT METER KN
WIDE FLANGE
WF_H300X150X6.5X9
0.004678 0.3 0.0065 0.15 0.009 7.21e-05 5.08e-06 9.95e-08 0.00195 0.0018
WF2_H300X150X6.5X9
0.004678 0.3 0.0065 0.15 0.009 7.21e-05 5.08e-06 9.95e-08 0.00195 -
0.0018 0.15 0.009
WF_H300X100-200X7X9-12
0.005253 0.3 0.007 0.1 0.009 7.29942e-05 8.75797e-06 1.71399e-07 0.0021 -
0.0022 0.2 0.012
TABLE 3
UNIT METER KN
ISECTION
IS_I300X150X8
0.3 0.008 0.3 0.15 0.013 0.15 0.013 0.0024 0.0026 2.69e-07
TABLE 4
UNIT METER KN
CHANNEL
CH_C380X100X10.5
0.006854 0.38 0.0105 0.1 0.016 0.000142897 6.11657e-06 4.07351e-07 -
0.0261429 0.00399 0.00213333
TABLE 5
UNIT METER KN
ANGLE
AG_L175X175X15
0.175 0.175 0.015 0.0342 0.00175 0.00175
TABLE 6
UNIT METER KN
TUBE
TB_TUB1501506
0.003363 0.15 0.15 0.006 1.15e-05 1.15e-05 1.79e-05 0.0018 0.0018
TB_RHS200X100X9
0.004867 0.2 0.1 0.009 2.35e-05 7.82e-06 1.93e-05 0.0036 0.0018
TABLE 7
UNIT METER KN
PIPE
PP_PIP165.2X7.1
0.1652 0.151 0.001763 0.001763
TABLE 8
UNIT METER KN
DOUBLE ANGLE
DA_L100X100X13LD
0.1 0.1 0.013 0 4.48744e-06 8.79409e-06 2.73893e-07 0.0294 0.00173333 -
0.00173333 1.94
TABLE 9
UNIT METER KN
TEE
TE_CT100X200X8X12
0.003177 0.1 0.2 0.012 0.008 1.84e-06 8.01e-06 1.3e-07 0.0173 0.000533333 -
0.0016
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
16 UPTABLE 4 CH_C380X100X10.5
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
31 PINNED
32 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
31 MZ 10
32 MZ -3
*148 FX 0.01 FY 0.01 MX 0.8
PERFORM ANALYSIS
PARAMETER 1
CODE JAPANESE 2005
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: 16 Profile : CH_C380X100X10(UPT) |
| Ratio: 0.130 (PASS) Reference: Eq.5.8 Loadcase: 1 |
|-----------------------------------------------------------------------------|
| Location: 0.000 Criteria: Stress Load Case: 1 (Permanent)|
| Px:(C) 0.000 Vy: 1.400 Vz: 0.000 |
| Tx: 0.000 My: 0.000 Mz: 10.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE: 0.000 MM (UNIT: MM) |
| Ax: 6.85400E+03 Az: 2.13333E+03 Ay: 3.99000E+03 |
| Iz: 1.42897E+08 Iy: 6.11657E+06 J: 4.07351E+05 |
| Zz: 7.52090E+05 Zy: 8.28163E+04 Zx: 2.54594E+04 |
| iZ: 1.44391E+02 iY: 2.98732E+01 Iw: 1.44256E+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 (Tension) |
| Actual : 167.374 Allowable : 400.000 Ratio : 0.418 |
|-----------------------------------------------------------------------------|
| Section Classification Results : Width to Thickness Ratios |
|-----------------------------------------------------------------------------|
| Compression | Bending |
|-----------------------------------------------------------------------------|
| LC# | Actual | Allowable | LC# | Actual | Allowable |
|-----------------------------------------------------------------------------|
| - | - | - | 1 | 33.1429 | 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 | - | - | - | - | - | 33.34| - | Eq.5.4 |
| Bending Z (T)| 0.000| 10.00| 1| P | 13.30| 156.67| 0.085| Eq.5.1 |
| Bending Z (C)| 0.000| 10.00| 1| P | 13.30| 102.48| 0.130| Eq.5.8 |
| Bending Y (T)| - | - | - | - | - | 156.67| - | Eq.5.1 |
| Bending Y (C)| - | - | - | - | - | 156.67| - | Eq.5.1 |
| Shear Z | - | - | - | - | - | 90.45| - | Eq.5.2 |
| Shear Y | 0.000| 1.40| 1| P | 0.35| 90.45| 0.004| Eq.5.2 |
| Comp+ Bend C | 0.000| - | 1| P | - | - | 0.130| Eq.6.1 |
| Comp+ Bend T | 0.000| - | 1| P | - | - | 0.085| Eq.6.2 |
| Ten + Bend T | 0.000| - | 1| P | - | - | 0.085| Eq.6.3 |
| Ten + Bend C | 0.000| - | 1| P | - | - | 0.130| Eq.6.4 |
| Von-Mises | 0.000| - | 1| P | 13.31| 156.67| 0.085| Eq.5.24 |
| |
| INTERMEDIATE RESULTS (Bending) |
| Me: 2.1541E+02 KN-MET My: 1.7674E+02 KN-MET pλb: 0.510 C: 1.462 |
| |
| INTERMEDIATE RESULTS (Von-Mises) |
| Sigmax: 13.296 N/mm2 Tou: 0.351 N/mm2 fm: 13.310 N/mm2 |
|-----------------------------------------------------------------------------|