# V.AIJ 2005 Check for MISES parameter 2

A slender, cantilever beam subjected to a load at the end.

## Given

A cantilever beam of length 0.3 meters is subjected to a permanent joint load of 3 kN in the Y direction and 2 kN in the Z direction as well as a 0.008 kN·m torque applied at the end. Axial tension of 10 kN is also applied to the member. An H100x50x5 section is used from the Japanese steel tables.

Section properties

• D = 100 mm, B = 50 mm, tf = 7 mm, tw = 5 mm
• Ix = 15,000 mm4
• Ax = 1185 mm2, Ay = 500 mm2, Az = 467 mm2
• Zx = Ix/tmax = 15,000/7 = 2,143 mm3, Zy = 5,920 mm3, Zz = 37,400 mm3

The maximum of the left hand side of the von Mises stress equation apparently occurs at the fixed end of the beam. Section forces at the fixed end are as follows:

• -10.0 kN (Tension)
• 0.6 kN·m (Bending-Y)
• 0.9 kN·m (Bending-Z)
• -3.0 kN (Shear-Y)
• -2.0 kN (Shear-Z)
• -0.008 kN·m (Torsion

Material

• FYLD = 300 MPa
• E = 2.05E+05 MPa
• G = E/2.6 MPa

## Solution

From these section forces, σx and τxy at the section of the fixed end are calculated as follows:

 $σ x = | F x A x | + | M y Z y | + | M z Z z |$ $= | − 10 , 000 1 , 185 | + | 600 , 000 5 , 920 | + | − 900 , 000 37 , 400 |$ = 8.44 + 101.35 + 24.06 = 133.85 N/mm2

 $τ x y = | M x Z x | + | F y A y | 2 + | F z A z | 2$ $= | − 8 , 000 2 , 143 | + | − 3 , 000 500 | 2 + | − 2 , 000 467 | 2$ $= 3.73 + 6 2 + 4.28 2$ = 11.10 N/mm2

From σx and τxy, fm is calculated:

$f m = σ x 2 + 3 τ x y 2 = ( 133.85 ) 2 + 3 ( 11.10 ) 2 = 135.22 N / m m 2$

Since ft = FYLD/1.5 = 300.0 MPa/15 = 200.0 N/mm2 and k = 1 for permanent loading,

• Ratio = 135.22/(200.0 · 1) = 0.676 < 1, So OK.

## Comparison

Table 1. Comparison of results
von Mises Stress, fm (N/mm2) 135.22 135.21 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ is typically installed with the program.

STAAD SPACE VERIFICATION FOR VON MISES STRESSES IN AIJ 2005
START JOB INFORMATION
ENGINEER DATE 18-AUG-10
END JOB INFORMATION
UNIT MMS KN
JOINT COORDINATES
1 0 0 0; 2 300 0 0;
MEMBER INCIDENCES
1 1 2;
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY JAPANESE
1 TABLE ST H100x50x5x7
UNIT MMS KN
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
UNIT METER KN
2 FX 10 FY 3 FZ 2 MX 0.008
PERFORM ANALYSIS
PRINT MEMBER FORCES LIST ALL
PARAMETER 1
CODE JAPANESE 2005
UNL 0.002 ALL
MISES 1 ALL
TRACK 2 ALL
FYLD 300000 ALL
CHECK CODE ALL
FINISH


## Output

                        STAAD.Pro CODE CHECKING - (AIJ-2005)   V2.1
***********************
ALL UNITS ARE IN - METE  KN   (U.N.O.)
|-----------------------------------------------------------------------------|
|   Member No:       1        Profile  : ST  H100X50X5X7   (JAPANESE SECTIONS)  |
|  Ratio:    0.676  (PASS)  Reference: Eq.5.24           Loadcase:       1    |
|-----------------------------------------------------------------------------|
|  Location:    0.000  Criteria:     Stress      Load Case:     1  (Permanent)|
|  Px:(T)      -10.000       Vy:        -3.000          Vz:      -2.000       |
|  Tx:          -0.008       My:         0.600          Mz:      -0.900       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE:    0.000 MM              (UNIT: MM)         |
|  Ax:     1.18500E+03       Az: 4.66655E+02            Ay: 5.00000E+02       |
|  Iz:     1.87000E+06       Iy: 1.48000E+05             J: 1.53000E+04       |
|  Zz:     3.74000E+04       Zy: 5.92000E+03            Zx: 2.18571E+03       |
|  iZ:     3.97248E+01       iY: 1.11756E+01            Iw: 3.20013E+08       |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES   (Unit: N/mm2)                                         |
|  Fy:         300.000      E :   205000.000          G :     79000.000       |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES                                                           |
|  Member Length:     0.300      Lz:     0.300 Ly:     0.300  UNL:      0.002 |
| DESIGN PARAMETERS                                                           |
|  Kz:   1.000     Ky:   1.000   NSF:  1.000   Cb:   0.000    pλb:  0.000     |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Tension)                                              |
|  Actual :     26.844      Allowable :    400.000      Ratio :  0.067        |
|-----------------------------------------------------------------------------|
| Section Classification Results :    Width to Thickness Ratios               |
|-----------------------------------------------------------------------------|
|            Compression              |             Bending                   |
|-----------------------------------------------------------------------------|
|  LC#   |    Actual   |   Allowable  |   LC#   |    Actual   |   Allowable   |
|-----------------------------------------------------------------------------|
|   -    |      -      |       -      |      1  |    14.0000  |     62.7376   |
|-----------------------------------------------------------------------------|
| 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 |    8.44|  200.00| 0.042| Eq.5.1   |
| Compression  |  -   |   -    |  -   | - |   -    |  189.47|  -   | Eq.5.3   |
| Bending Z (T)| 0.000|   -0.90|     1| P |   24.06|  200.00| 0.120| Eq.5.1   |
| Bending Z (C)| 0.000|   -0.90|     1| P |   24.06|  200.00| 0.120| Eq.5.7   |
| Bending Y (T)| 0.000|    0.60|     1| P |  101.35|  200.00| 0.507| Eq.5.1   |
| Bending Y (C)| 0.000|    0.60|     1| P |  101.35|  200.00| 0.507| Eq.5.1   |
| Shear Z      | 0.000|   -2.00|     1| P |    4.29|  115.47| 0.037| Eq.5.2   |
| Shear Y      | 0.000|   -3.00|     1| P |    6.00|  115.47| 0.052| Eq.5.2   |
| Comp+ Bend C | 0.000|   -    |     1| P |   -    |    -   | 0.627| Eq.6.1   |
| Comp+ Bend T | 0.000|   -    |     1| P |   -    |    -   | 0.627| Eq.6.2   |
| Ten + Bend T | 0.000|   -    |     1| P |   -    |    -   | 0.669| Eq.6.3   |
| Ten + Bend C | 0.000|   -    |     1| P |   -    |    -   | 0.585| Eq.6.4   |
| Von-Mises    | 0.000|   -    |     1| P |  135.21|  200.00| 0.676| Eq.5.24  |
|                                                                             |
| INTERMEDIATE RESULTS (Bending)                                              |
|  Me: 6.0918E+06 KN-MET  My: 1.1220E+01 KN-MET   pλb:   0.600  C:  1.750     |
|                                                                             |
| INTERMEDIATE RESULTS (Von-Mises)                                            |
|  Sigmax:   133.854 N/mm2   Tou:    11.034 N/mm2  fm:   135.212 N/mm2        |
|-----------------------------------------------------------------------------|