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
F_y = 353.0 MPa

Design forces:

P = ±2.5 kN
M_z = 3.88 kN·m
V_y = 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, I_zz = 99.1 cm³
Section modulus about the major axis, Z_xx = 19.51 cm³

Verification

Compressive Stress

Radius of gyration, $r_{x} = \sqrt{\frac{I_{zz}}{A}} = \sqrt{\frac{99.1}{8.09}} = 3.50 cm$

Allowable compression stress:

C_{e} = \sqrt{\frac{2 π^{2} E}{F_{y}}} = \sqrt{\frac{2 π^{2} \times 203,404}{353.1}} = 106.6

Q = 1

\frac{C_{e}}{\sqrt{Q}} = \frac{106.6}{\sqrt{1.0}} = 106.6 < \frac{K L}{r} = \frac{1.0 (600)}{3.50} = 171.4

Therefore, the allowable compressive stress:

F_{c} = \frac{12 π^{2} E}{23 {(\frac{K L}{r})}^{2}} = \frac{12 π^{2} \times 203,404}{23 {(171.4)}^{2}} = 35.65 MPa

Actual stress in compression

f_{c} = \frac{P}{A} = \frac{2.5 \times 10^{3}}{8.09 \times 10^{2}} = 3.09 MPa

Stress ratio in compression: 3.09 / 35.65 = 0.087

Bending Stress

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

\frac{D}{t} = \frac{99.0}{2.6} = 38.1 < \frac{232,000}{F_{y}} = \frac{232,000}{353.1} = 657.0

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

F = 0.6 × F_y = 0.6 × 353.1 = 211.9 MPa

Actual bending stress:

f_{b} = \frac{M}{Z_{xx}} = \frac{3.88 \times 10^{3}}{19.51} = 198.9 MPa

Stress ratio in bending: 198.9 / 211.9 = 0.939

Tensile Stress

Allowable tension stress:

F = 0.6 × F_y = 0.6 × 353.1 = 211.9 MPa

Actual stress in tension

f_{t} = \frac{P}{A} = \frac{2.5 \times 10^{3}}{8.09 \times 10^{2}} = 3.09 MPa

Stress ratio in tension: 3.09 / 211.9 = 0.015

Calculation of Allowable Shear Stress

Allowable shear stress:

F_v = 0.4 × F_y = 0.4 × 353.1 = 141.2 MPa

Shear area:

A_{z} = 0.5 \times 2 π (10.16 / 2) 0.26 = 4.15 {cm}^{2}

Actual shear stress:

f_{v} = \frac{V_{y}}{A_{z}} = \frac{3.88 (10)}{4.15} = 9.349 MPa

Stress ration in shear: 9.35 / 141.2 = 0.066

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
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

STAAD.Pro Input File

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
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1(DL)
MEMBER LOAD
1 UNI GY -0.169
1 CON GX -5
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GY -1.01
LOAD 3 LOADTYPE None  TITLE LOAD CASE 3
MEMBER LOAD
1 UNI GY 1.893
LOAD 4 LOADTYPE None  TITLE LOAD CASE 4
MEMBER LOAD
1 UNI GY -0.158
LOAD COMB 5 COMBINATION LOAD CASE 5
1 1.0 2 1.0 
LOAD COMB 6 COMBINATION LOAD CASE 6
1 0.75 3 0.75 
LOAD COMB 7 COMBINATION LOAD CASE 7
1 0.75 2 0.75 4 0.75 
PERFORM ANALYSIS
LOAD LIST 5 TO 7
PARAMETER 1
CODE IS801
TRACK 2 ALL
CWY 0 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                        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 has not been considered in the design.