# V. IS 801-Pipe subject to axial compression and bending

Verification example for a cold-formed beam subject to axial compression and bending moment according to IS:801-1975.

## Details

The section used is an ST 101.6x2.6CHS (pipe) section. The beam is a 6 m span subject to axial compression and bending moments. Both ends of the span are fixed.

Material properties:
• E = 203,400 MPa
• Fy = 353.0 MPa
Design forces:
• P = ±2.5 kN
• Mz = 3.88 kN·m
• Vy = 3.88 kN
Section properties:
• Outer diameter, OD = 101.6 mm
• Thickness, t = 2.6 mm
• Area, A = 8.09 cm2
• Moment of inertia about the major axis, Izz = 99.1 cm3
• Section modulus about the major axis, Zxx = 19.51 cm3

## Verification

Compressive Stress

Allowable compression stress:

$C e = 2 π 2 E F y = 2 π 2 × 203,404 353.1 = 106.6$
$Q = 1$
$C e Q = 106.6 1.0 = 106.6 < K L r = 1.0 ( 600 ) 3.50 = 171.4$

Therefore, the allowable compressive stress:

Actual stress in compression

Stress ratio in compression: 3.09 / 35.65 = 0.087

Bending Stress

Avg. diameter = 101.6 mm - 2.6 mm = 99.0 mm

$D t = 99.0 2.6 = 38.1 < 232,000 F y = 232,000 353.1 = 657.0$

Per Cl. 6.8, the maximum allowable stress in bending:

F = 0.6 × Fy = 0.6 × 353.1 = 211.9 MPa

Actual bending stress:

Stress ratio in bending: 198.9 / 211.9 = 0.939

Tensile Stress

Allowable tension stress:

F = 0.6 × Fy = 0.6 × 353.1 = 211.9 MPa

Actual stress in tension
Stress ratio in tension: 3.09 / 211.9 = 0.015

Calculation of Allowable Shear Stress

Allowable shear stress:

Fv = 0.4 × Fy = 0.4 × 353.1 = 141.2 MPa

Shear area:

Actual shear stress:

Stress ration in shear: 9.35 / 141.2 = 0.066

## Results

Table 1. Comparison of results
Allowable compression stress (MPa) 35.65 35.660 negligible
Actual compression stress (MPa) 3.09 3.090 none
Compression stress ratio 0.087 0.087 none
Allowable bending stress (MPa) 211.9 211.854 negligible
Actual bending stress (MPa) 198.9 198.857 negligible
Allowable tensile stress (MPa) 211.9 211.854 negligible
Actual tensile stress (MPa) 3.09 3.090 none
Tension stress ratio 0.015 0.015 none
Allowable shear stress (MPa) 141.2 141.236 negligible
Actual shear stress (MPa) 9.349 9.349 none
Shear stress ratio 0.066 0.066 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\India\IS 801-Pipe subject to axial compression and bending.STD is typically installed with the program.

The following design parameters are used:
• The effect of cold work of forming strengthening is not considered by specifying the parameter CWY 0
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 02-Apr-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
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 COLDFORMED AUSTRALIAN
1 TABLE ST 101.6x2.6CHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
1 UNI GY -0.169
1 CON GX -5
1 UNI GY -1.01
1 UNI GY 1.893
1 UNI GY -0.158
1 1.0 2 1.0
1 0.75 3 0.75
1 0.75 2 0.75 4 0.75
PERFORM ANALYSIS
PARAMETER 1
CODE IS801
TRACK 2 ALL
CWY 0 ALL
CHECK CODE ALL
FINISH


                        STAAD.Pro CODE CHECKING - ( IS:801 )   v3.0
***********************
ALL UNITS ARE IN - METE  KN   (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1  SECTION: 101.6X2.6CHS          LEN:    6.000   LOC:   0.000   |
| STATUS: PASS    RATIO:   0.951               REF: 6.7.1b      LC:      6    |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Fx:(C)        1.875       Fy:        -3.879          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:      -3.879       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                            (Unit:   CM) |
|  Ag:         8.09000       Az:     4.14956            Ay:     4.14956       |
|  Cz:         5.08000       Cy:     5.08000            Z0:     0.00000       |
|  Iz:        99.10001       Iy:    99.10001             J:   198.20002       |
|  Sz:        19.50788       Sy:    19.50788                                  |
|  Rz:         3.49996       Ry:     3.49996            Cw:   656.18642       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                  (Unit: MPa) |
|  Fy:   353.090        Fu:   449.993      E: 203404.356       G:  77968.401  |
|  Fya(compression):   353.090             Fya(bending):   353.090            |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:     6.000      Lz:     6.000 Ly:     6.000 Lb:     6.000    |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000     Ky:   1.000   NSF:  1.000   Cb:   0.000                    |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|  Actual:     171.431      Allowable:     200.000      Ratio:   0.857        |
|-----------------------------------------------------------------------------|
| CHECKS:                             |      Stresses       |                 |
|              | Loc. | Demand |  L/C |  Actual  |  Allow   |Ratio | Ref CL   |
|              |(MET) |(KN-MET)|      | (MPa)    | (MPa)    |      |          |
|--------------|------|--------|------|----------|----------|------|----------|
| Tension      | 3.500|   -2.50|     5|    3.090 |  211.854 | 0.015| 6.1      |
| Compression  | 0.000|    2.50|     5|    3.090 |   35.660 | 0.087| Cl.6.8   |
| BendZComp    | 0.000|    3.88|     6|  198.857 |  211.854 | 0.939| 6.3      |
| BendZTens    | 0.000|    3.88|     6|  198.857 |  211.854 | 0.939| 6.3      |
| BendUnbraced |  -   |   -    |  -   |    -     |    0.000 |  -   |          |
| BendYComp    |  -   |   -    |  -   |    -     |  211.854 |  -   | 6.3      |
| BendYTens    |  -   |   -    |  -   |    -     |  211.854 |  -   | 6.3      |
| Shear Z      |  -   |   -    |  -   |    -     |  141.236 |  -   | 6.4.1    |
| Shear Y      | 0.000|   -3.88|     6|    9.349 |  141.236 | 0.066| 6.4.1    |
| Axial+Bend   | 0.000|   -    |     6|    -     |     -    | 0.951| 6.7.1b   |
| Bend+Shear   | 0.000|   -    |     6|    -     |     -    | 0.066| 6.4.3    |
|-----------------------------------------------------------------------------|
| Effective Section Properties:(cm)                                           |
|  Ae:   8.090 SzTop:  19.508 SzBot:  19.508 SyLeft:  19.508 SyRight:  19.508 |
| Intermediate Results:  Cb =  0.000                                          |
|-----------------------------------------------------------------------------|
NOTE: Torsion and deflections have not been considered in the design.