V.AIJ 2005 Check for MISES parameter

Verify the Von Mises stresses per the AIJ 2005 code of a beam in a frame.

Details

A cantilever beam is subject to the following forces at the free end. The cantilever member is a pair of C12X30, back-to-back.

Fx = 5 kN

Fy = -15 kN

Fz = 5 kN

Mx = 10 kN·m

My = -6.667 kN·m

The member is steel with the following material properties:

E = 205,000 MPa

Fy = 200 MPa

The section forces at the fixed-end of the left cantilever are taken from the STAAD.Pro analysis:

Fx = -5 kN

Fy = -15 kN

Fz = -5 kN

Mx = -10 kN·m

My = 15 kN·m

Mz = 25 kN·m

Validation

From the section forces, σx and τxy at the cross-section at the fixed end are calculated:

From these, the Von Mises stress, fm, is calculated as:

For permanent loading conditions, k = 1 and ft = Fy/1.5 = 133.3 N/mm2

The ratio = fm / (k × ft ) = 346.17 / (1 × 133.3) = 2.596

Results

Table 1. Comparison of results
σx (N/mm2) 63.98 63.983 negligible
τxy (N/mm2) 196.4 196.415 negligible
fm (N/mm2) 346.17 346.16 negligible
ft (N/mm2) 133.3 133.3 negligible
Ratio 2.596 2.596 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Japan\AIJ 2005 Check for MISES parameter.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 28-Apr-15
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 1.667 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
CONSTANTS
MATERIAL STEEL ALL
MEMBER PROPERTY AMERICAN
1 TABLE D C12X30 SP 0.1
SUPPORTS
1 FIXED
2 FX 5 FY -15 FZ 5 MX 10 MY -6.6667
PRINT ANALYSIS RESULTS
PRINT MEMBER PROPERTIES ALL
PARAMETER 1
CODE JAPANESE 2005
MISES 1 MEMB 1
FYLD 200000 ALL
TRACK 2 MEMB 1
CHECK CODE MEMB 1
FINISH


                        STAAD.Pro CODE CHECKING - (AIJ-2005)   V2.1
***********************
ALL UNITS ARE IN - METE  KN   (U.N.O.)
|-----------------------------------------------------------------------------|
|   Member No:       1        Profile:D   C12X30           (AISC SECTIONS)      |
|  Ratio:    2.596  (FAIL)  Reference: Eq.5.24           Loadcase:       1    |
|-----------------------------------------------------------------------------|
|  Location:    0.000  Criteria:     Stress      Load Case:     1  (Permanent)|
|  Px:(T)       -5.000       Vy:        15.000          Vz:      -5.000       |
|  Tx:         -10.000       My:        15.002          Mz:      25.005       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE:    0.000 MM              (UNIT: MM)         |
|  Ax:     1.13677E+04       Az: 2.73233E+03            Ay: 7.89676E+03       |
|  Iz:     1.34859E+08       Iy: 5.54743E+07             J: 6.56703E+05       |
|  Zz:     8.84901E+05       Zy: 4.25031E+05            Zx: 5.16057E+04       |
|  iZ:     1.08919E+02       iY: 6.98569E+01            Iw: 8.08857E+10       |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES   (Unit: N/mm2)                                         |
|  Fy:         200.000      E :   205000.000          G :     79000.000       |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES                                                           |
|  Member Length:     1.667      Lz:     1.667 Ly:     1.667  UNL:      1.667 |
| DESIGN PARAMETERS                                                           |
|  Kz:   1.000     Ky:   1.000   NSF:  1.000   Cb:   0.000    pλb:  0.000     |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Tension)                                              |
|  Actual :     23.863      Allowable :    400.000      Ratio :  0.060        |
|-----------------------------------------------------------------------------|
| Section Classification Results :    Width to Thickness Ratios               |
|-----------------------------------------------------------------------------|
|            Compression              |             Bending                   |
|-----------------------------------------------------------------------------|
|  LC#   |    Actual   |   Allowable  |   LC#   |    Actual   |   Allowable   |
|-----------------------------------------------------------------------------|
|   -    |      -      |       -      |      1  |    10.7824  |     76.8375   |
|-----------------------------------------------------------------------------|
| CHECKS                              |Env|     Stresses    |                 |
|              | Loc. | Demand |  L/C |Typ| Actual | Allow  |Ratio |   Ref.   |
|              |(MET) |(KN-MET)|      |   |(N/mm2) |(N/mm2) |      |          |
|--------------|------|--------|------|---|--------|--------|------|----------|
| Tension      | 0.000|   -5.00|     1| P |    0.44|  133.33| 0.003| Eq.5.1   |
| Compression  |  -   |   -    |  -   | - |   -    |  129.59|  -   | Eq.5.3   |
| Bending Z (T)| 0.000|   25.00|     1| P |   28.26|  133.33| 0.212| Eq.5.1   |
| Bending Z (C)| 0.000|   25.00|     1| P |   28.26|  131.65| 0.215| Eq.5.7   |
| Bending Y (T)| 0.000|   15.00|     1| P |   35.30|  133.33| 0.265| Eq.5.1   |
| Bending Y (C)| 0.000|   15.00|     1| P |   35.30|  133.33| 0.265| Eq.5.1   |
| Shear Z      | 0.000|   -5.00|     1| P |    1.83|   76.98| 0.024| Eq.5.2   |
| Shear Y      | 0.000|   15.00|     1| P |    1.90|   76.98| 0.025| Eq.5.2   |
| Comp+ Bend C | 0.000|   -    |     1| P |   -    |    -   | 0.479| Eq.6.1   |
| Comp+ Bend T | 0.000|   -    |     1| P |   -    |    -   | 0.477| Eq.6.2   |
| Ten + Bend T | 0.000|   -    |     1| P |   -    |    -   | 0.480| Eq.6.3   |
| Ten + Bend C | 0.000|   -    |     1| P |   -    |    -   | 0.476| Eq.6.4   |
| Von-Mises    | 0.000|   -    |     1| P |  346.17|  133.33| 2.596| Eq.5.24  |
|                                                                             |
| INTERMEDIATE RESULTS (Bending)                                              |
|  Me: 3.7016E+03 KN-MET  My: 1.7698E+02 KN-MET   pλb:   0.600  C:  1.750     |
|                                                                             |
| INTERMEDIATE RESULTS (Von-Mises)                                            |
|  Sigmax:    63.993 N/mm2   Tou:   196.415 N/mm2  fm:   346.167 N/mm2        |
|-----------------------------------------------------------------------------|