# V. IS 800 2007 - WSD Rod Compression and Bending

Verify the program-calculated design results for a 3 m long cantilever beam, subjected to axial compression and biaxial bending. The beam section used is a 50 mm diameter steel rod and is designed as per IS 800:2007 working stress design method.

## Details

The 3 m cantilever section is subject to a 10 kN axial compression load at the free end as well as 1 kN/m uniform loads along the length in both the "major" and "minor" axes. The cantilever is assumed to be laterally supported.

The steel yield stress is fy = 250 MPa, the specified minimum tensile strength is Fu = 420 MPa, and the modulus of elasticity is E = 205(10)3 MPa

## Validation

Section Properties

Gross area:

Moment of inertia:

Elastic section modulus:

Plastic section modulus:

Partial Safety Factors

Partial safety factor for failure in tension by yielding (per Table 5 of IS:800 2007), γm0 = 1.1.

Partial safety factor for failure at ultimate stress (per Table 5 of IS:800 2007), γm1 = 1.25.

Forces

Axial force,

Shear forces,

Moments,

Section Classification

Although Table 2 of IS800:2007 does not specify the classification for solid rod sections, the width to thickness ratio for a solid rod is 1.0. Hence, it is a Class 1 section (Plastic).

Check Slenderness Ratio

Ky = Kz = 1

The allowable slenderness ratio is 180.

Section fails in slenderness.

Check Axial Tension

The permissible stress in compression/tension due to yielding (per Section 11.2.1(a) ),

Assume that Anet = Ag and ɑ = 0.8, the design strength in rupture of critical section,

The permissible stress governed by rupture of the net section,

Check Axial Compression

Per section 11.3 of IS:800 2007.

The actual compression under service load,

Euler buckling stress,

Non-dimensional effective slenderness ratio,

The imperfection factor given in Table 7; for buckling class (as per Table 10 for solid sections), ɑ = 0.49.

$ϕ = 0.5 [ 1 + ɑ ( λ - 0.2 ) + λ 2 ] = 4.654$
$χ = 1 ϕ + ϕ 2 - λ 2 = 0.118$

The design compressive stress,

 (Cl. 7.1.2.1)
Design ratio in compression: $f c f ac = 5.102 16.10 = 0.317$ (for both local z and y axes)

Check for Shear

Per Cl 11.42 of IS: 800-2007

Per Cl. 8.4.1.1, the shear area is taken as the gross area of the solid round section; Av = Ag = 19.6 cm2.

The shear force used for design is taken as the resultant SRSS combination of the "major" and "minor" axes:

The plastic under pure shear is taken as the nominal shear strength,

The permissible shear stress at working load,

Design ratio in shear: $τ s τ ab = 2.165 100 = 0.022$

Check for Bending

Per Section 11.4 of IS: 800-2007

The bending moment used for design is taken as the resultant SRSS combination of the "major" and "minor" axes:

This is used as the "major" axis bending moment and the "minor" axis bending moment is taken as zero.

The actual bending stress,

The permissible bending stress at working load,

Design ratio in bending: $fbfab=518.2165=3.141$

Check for Combined Axial Force and Bending

As per Cl. 11.5.2(a) of IS: 800 2007.

$CmLT=0.9$
$KLT=−0.1(fcfac)CmLT−0.25=−0.1(0.317)0.9−0.25=−0.049$
$fcfac+0.6KyCmyfbcyfabcy+KLTfbcfabcz=0.317+0.6(1.254)(0.9)(0)−0.049(3.141)=0.163$
$fcfac+0.6KyCmyfbcyfabcy+KzCmzfbcfabcz=0.317+0.6(1.254)(0.9)(0)+1.254(0.9)(3.141)=3.862$

As per Cl. 11.5.2(b) of IS: 800 2007.

$fc0.6fy+fbcyfabcy+fbczfabcz=5.1020.6(250)+0165+3.141=3.175$

## Results

Table 1.
Slenderness ratio 239.7 239.71 negligible
Allowable stress in tension yielding on gross section (MPa) 150 150 none
Allowable stress in tension rupture on critical section (MPa) 185.5 185.472 negligible
Allowable stress in compression (MPa) 16.10 16.101 negligible
Critical ratio for axial compression 0.317 0.317 none
Allowable stress in shear (MPa) 100 100 none
Shear stress ratio 0.022 0.022 none
Allowable stress in bending (MPa) 165 165 none
Bending stress ratio 3.141 3.141 none
Interaction ratio for Cl. 11.5.2(a)(ii) 3.862 3.860 negligible
Interaction ratio for Cl. 11.5.2(b) 3.175 3.175 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\India\IS 800 2007 WSD - ROD - Compression and Bending.STD is typically installed with the program.

The following design parameters are used:
• The lateral support condition is specified by LAT 1
• The cantilever member is specified by CAN 1
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 12-Jan-2021
ENGINEER NAME TK
END JOB INFORMATION
*****************************************************************************
*This problem has been created to validate the program calculated design
*results of rod section subjected to axial Compression and biaxial bending
*using IS 800 2007 (WSD)
*****************************************************************************
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 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 DUTCH
1 TABLE ST RD50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FX -10
1 UNI GY -1
1 UNI GZ -1
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE IS800 WSD
LAT 1 ALL
CAN 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - IS-800-2007-WSD (V2.1)
****************************************************
|----------------------------------------------------------------------------------|
|*  Member Number:      1                                                          |
|  Member Section:  ST   RD50                  (DUTCH SECTIONS)                    |
|  Status: FAIL  Ratio:   3.860  Critical Load Case:     1  Location:       0.00   |
|  Critical Condition: Sec. 11.5.2(a)                                              |
|  Critical Design Forces:  (Unit: KN    METE)                                     |
|      FX:      10.000E+00 C     FY:       3.000E+00      FZ:       3.000E+00      |
|      MX:       0.000E+00       MY:      -4.500E+00      MZ:       4.500E+00      |
|----------------------------------------------------------------------------------|
|  Section Properties:    (Unit:  CM  )                                            |
|  AXX:      19.600E+00          IZZ:      30.700E+00          RZZ:       1.252E+00|
|  AYY:      19.600E+00          IYY:      30.700E+00          RYY:       1.252E+00|
|  AZZ:      19.600E+00          IXX:      61.400E+00           CW:       0.000E+00|
|  ZEZ:      12.280E+00          ZPZ:      20.833E+00                              |
|  ZEY:      12.280E+00          ZPY:      20.833E+00                              |
|----------------------------------------------------------------------------------|
|  Slenderness Check:    (Unit:  KN    METE)                                       |
|  Actual Length:        3.000E+00                                                 |
|  Parameters:     LZ:        3.000E+00  LY:        3.000E+00                      |
|                  KZ:            1.000  KY:            1.000                      |
|  Actual Ratio: 239.71 Allowable Ratio: 180.00  LOAD:     1                       |
|----------------------------------------------------------------------------------|
|  Section Class:      Plastic; Flange Class:      Plastic; Web Class:      Plastic|
|----------------------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - IS-800-2007-WSD (V2.1)
****************************************************
|----------------------------------------------------------------------------------|
|  Member Number:      1                                                           |
|  Member Section:  ST   RD50                  (DUTCH SECTIONS)                    |
|----------------------------------------------------------------------------------|
|  Tension:    (Unit:  KN    METE)                                                 |
|  Parameters:     FYLD:      250.000E+03       FU:      420.000E+03               |
|                   NSF:            1.000    ALPHA:            0.800               |
|  Yielding   :  Actual Stress:           0.000E+00    LC:     0                   |
|                Allowable Stress:      150.000E+03    As per:  Sec. 11.2.1(a)     |
|  Rupture    :  Actual Stress:           0.000E+00    LC:     0                   |
|                Allowable Stress:      185.472E+03    As per:  Sec. 11.2.1(b)     |
|----------------------------------------------------------------------------------|
|  Compression:    (Unit:  KN    METE)                                             |
|  Buckling Class:   Major: c    Minor: c    As per:Cl. 7.1.2.2                    |
|  Major Axis:   Actual Stress:           5.102E+03    LC:     1  Loc:     0.000   |
|                Allowable Stress:       16.101E+03    As per:  Sec. 11.3.1        |
|  Minor Axis:   Actual Stress:           5.102E+03    LC:     1  Loc:     0.000   |
|                Allowable Stress:       16.101E+03    As per:  Sec. 11.3.1        |
|----------------------------------------------------------------------------------|
|  Shear:    (Unit:  KN    METE)                                                   |
|  Major Axis:   Actual Stress:           0.000E+00    LC:     0  Loc:     0.000   |
|                Allowable Stress:      100.000E+03    As per:  Sec. 11.4.2        |
|  Minor Axis:   Actual Stress:           2.165E+03    LC:     1  Loc:     0.000   |
|                Allowable Stress:      100.000E+03    As per:  Sec. 11.4.2        |
|----------------------------------------------------------------------------------|
|  Bending:    (Unit:  KN    METE)                                                 |
|  Parameters:   Laterally Supported      KX:   1.00  LX:   3.000E+00  Cantilever  |
|  Major Axis:                                                                     |
|  Actual Stress:  fbc:    518.238E+03  fbt:    518.238E+03  LC:     1  Loc:     0.|00
|  Allowable Stress:  Fbc/Fbt:    165.000E+03    As per:  Sec. 11.4.1(a)           |
|  Minor Axis:                                                                     |
|  Actual Stress:  fbc:      0.000E+00  fbt:      0.000E+00  LC:     0  Loc:     0.|00
|  Allowable Stress:  Fbc/Fbt:    165.000E+03    As per:  Sec. 11.4.1(a)           |
|----------------------------------------------------------------------------------|
|  Combined Interaction:                                                           |
|  Parameters:  PSI: 1.00   CMX:    0.900   CMY:    0.900   CMZ:    0.900          |
|  Member Stability (Bending+Compression):                                         |
|  Equation 2:        Ratio:     3.860    As per:  Sec. 11.5.2(a)   Ky :   1.2535  |
|                     LC:            1    Loc:       0.000          Kz :   1.2535  |
|  Member Strength (Bending+Compression):                                          |
|                     Ratio:     3.175    As per:Sec. 11.5.2(b)                    |
|                     LC:            1    Loc:       0.000                         |
|----------------------------------------------------------------------------------|
|  Checks               Ratio   Load Case No.      Location from Start( METE)      |
|                                                                                  |
|  Tension                0.000       0                       0.000E+00            |
|  Compression            0.317       1                       0.000E+00            |
|  Shear Major            0.000       0                       0.000E+00            |
|  Shear Minor            0.022       1                       0.000E+00            |
|  Bend Ten Major         3.141       1                       0.000E+00            |
|  Bend Comp Major        3.141       1                       0.000E+00            |
|  Bend Ten Minor         0.000       0                       0.000E+00            |
|  Bend Comp Minor        0.000       0                       0.000E+00            |
|                (i)      0.000       0                       0.000E+00            |
|  Sec. 11.5.2(a)(ii)     3.860       1                       0.000E+00            |
|  Sec. 11.5.2(b)         3.175       1                       0.000E+00            |
|----------------------------------------------------------------------------------|