V. AIJ 2005 UPT Tee
Verify the bending capacity and compression capacity of a tee section beam.
Details
The member is a 2 m long simply-supported beam. The section used is a CT100x200x8x12. 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 concentrated force at mid-span in the global Y direction
- a -2 kN·m concentrated moment at the left end
- a 2 kN·m concentrated moment at the right end
Validation
Section Properties
Dimensions:
- Leg, D = 100 mm
- Width, B = 200 mm
- Thickness of web, tw = 8 mm
- Thickness of flange, tf = 12 mm
Area, Ax = 3,104 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 bending (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. 5.3:
Allowable Flexural Stress
Distance between braced points of the compression flange, lb = 2,000 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, λb < pλb , so:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Allowable compressive stress (MPa) | 104.2 | 104.24 | negligible | |
Allowable flexural stress (MPa) | 149.4 | 149.04 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Japan\AIJ 2005 UPT Tee.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
127 26 0 20; 128 28 0 20;
MEMBER INCIDENCES
64 127 128;
START USER TABLE
TABLE 1
UNIT METER KN
GENERAL
GE_H300X150X6.5X9
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
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
0.006939 0.38 0.0105 0.1 0.016 0.000145 5.35e-06 3.99e-07 0.0241 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
64 UPTABLE 9 TE_CT100X200X8X12
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
127 PINNED
128 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
64 CON GY -10
JOINT LOAD
127 MZ 2
128 MZ -2
PERFORM ANALYSIS
UNIT MMS KN
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 - MMS KN (U.N.O.)
|-----------------------------------------------------------------------------|
| Member No: 64 Profile : TE_CT100X200X8(UPT) |
| Ratio: 0.867 (PASS) Reference: Eq.5.24 Loadcase: 1 |
|-----------------------------------------------------------------------------|
| Location: 999.999 Criteria: Stress Load Case: 1 (Permanent)|
| Px:(C) 0.000 Vy: 5.000 Vz: 0.000 |
| Tx: 0.000E+00 My: 0.000E+00 Mz: -3.000E+03 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE: 999.999 MM (UNIT: MM) |
| Ax: 3.17700E+03 Az: 1.60000E+03 Ay: 5.33333E+02 |
| Iz: 1.84000E+06 Iy: 8.01000E+06 J: 1.30000E+05 |
| Zz: 2.22491E+04 Zy: 8.01000E+04 Zx: 1.08333E+04 |
| iZ: 2.40658E+01 iY: 5.02120E+01 Iw: 1.07813E+08 |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES (Unit: N/mm2) |
| Fy: 235.000 E : 205000.000 G : 79000.000 |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES |
| Member Length: 1999.999 Lz: 1999.999 Ly: 1999.999 UNL: 1999.999 |
| DESIGN PARAMETERS |
| Kz: 1.000 Ky: 1.000 NSF: 1.000 Cb: 0.000 pλb: 0.000 |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Tension) |
| Actual : 83.105 Allowable : 400.000 Ratio : 0.208 |
|-----------------------------------------------------------------------------|
| Section Classification Results : Width to Thickness Ratios |
|-----------------------------------------------------------------------------|
| Compression | Bending |
|-----------------------------------------------------------------------------|
| LC# | Actual | Allowable | LC# | Actual | Allowable |
|-----------------------------------------------------------------------------|
| - | - | - | 1 | 11.0000 | 15.6538 |
|-----------------------------------------------------------------------------|
| 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 | - | - | - | - | - | 104.21| - | Eq.5.3 |
| Bending Z (T)| 1.000| -3.00| 1| P | 134.84| 156.67| 0.861| Eq.5.1 |
| Bending Z (C)| 0.000| 2.00| 1| P | 89.89| 156.67| 0.574| Eq.5.1 |
| Bending Y (T)| - | - | - | - | - | 156.67| - | Eq.5.1 |
| Bending Y (C)| - | - | - | - | - | 149.04| - | Eq.5.7 |
| Shear Z | - | - | - | - | - | 90.45| - | Eq.5.2 |
| Shear Y | 0.000| 5.00| 1| P | 9.38| 90.45| 0.104| Eq.5.2 |
| Comp+ Bend C | 0.000| - | 1| P | - | - | 0.574| Eq.6.1 |
| Comp+ Bend T | 1.000| - | 1| P | - | - | 0.861| Eq.6.2 |
| Ten + Bend T | 1.000| - | 1| P | - | - | 0.861| Eq.6.3 |
| Ten + Bend C | 0.000| - | 1| P | - | - | 0.574| Eq.6.4 |
| Von-Mises | 1.000| - | 1| P | 135.81| 156.67| 0.867| Eq.5.24 |
| |
| INTERMEDIATE RESULTS (Bending) |
| Me: 9.8026E+01 KN-MET My: 1.8824E+01 KN-MET pλb: 0.600 C: 1.000 |
| |
| INTERMEDIATE RESULTS (Von-Mises) |
| Sigmax: 134.837 N/mm2 Tou: 9.375 N/mm2 fm: 135.811 N/mm2 |
|-----------------------------------------------------------------------------|