V. IS 800 2007 LSD - I Section - High Shear
Verify the design of an I section beam subject to high shear per the IS 800:2007 limit state method.
BIS. IS 800: General Construction in Steel - Code of Practice. 2007. Bureau of Indian Standards. New Delhi.
Details
- compression force of 100 kN at the "roller" end, and
- concentrated transverse loads of 350 kN at both of the one-third points acting along the minor axis of the section
The section used is a built-up I shape with 400 mm × 20 mm flanges, a web thickness of 8 mm, and an overall depth of 550 mm. The steel has a yield strength of 250 MPa, an ultimate tensile strength of 420 MPa, and a modulus of elasticity of 205×(10)3 MPa. The member is laterally supported along its length.
Validation
Section Properties
Depth of web, d = 550 - 2×20 = 510 mm
Cross-sectional area, Ax = 2(400 × 20) + 510 × 8 = 20,080 mm2 = 200.8 cm2
Moment of inertia about major axis,
Moment of inertia about minor axis,
Radius of gyration about major axis,
Radius of gyration about minor axis,
Elastic section modulus about major axis,
Elastic section modulus about minor axis,
Plastic section modulus about major axis,
Plastic section modulus about minor axis,
Constants
- γm0 = 1.1
- γm1 = 1.25
Section Classification
b = bf/2 = 200 mm
b / tf = 10 < 9.4ε = 9.4 and b / tf = 10 > 10.5ε = 10.5
Since the section is symmetric about both axes, the neutral axis is at mid-depth.
dw / tw = 63.75 < 84ε = 84
Hence, from Table 2 of IS 800:2007, the flange is compact and the web is plastic.
Therefore, the overall classification of the section is "compact".
h / bf = 1.375 > 1.2 and tf = 20 mm < 40 mm
Hence, from Table 10 of IS 800:2007, the buckling class about the major axis is "a" and the same about the minor axis is "b".
Check Slenderness Ratio
ky = kz = 1
The maximum allowable slenderness ratio is 180.
Slenderness ratio about the major axis, kzL / rz = 12.21 < 180
Slenderness ratio about the minor axis, kyL / ry = 29.10 < 180
So the slenderness is within the limit.
Axial Tension Capacity
Check for yielding of gross section:
Tdg = Ag × fy / γm0 = 4,564 kN
Check for rupture of critical section:
α = 0.8
Tdn = α × Anet × fu / γm1 = 5,398 kN
Block shear areas are not specified and therefore not checked.
No tension in the member, so critical ratio is 0.
Check Axial Compression
Axial compression capacity of major axis:
The non-dimensional slenderness ratio,
For buckling class "a", the imperfection factor, α = 0.21
So, as per Cl. 7.1.2.1 of IS 800:2007,
Therefore, axial compression capacity in the major axis: Pdz = Axfcdz = 4,564 kN
Axial compression capacity of minor axis:
The non-dimensional slenderness ratio,
For buckling class "b", the imperfection factor, α = 0.34
So, as per Cl. 7.1.2.1 of IS 800:2007,
Therefore, axial compression capacity in the minor axis: Pdy = Axfcdy = 4,360 kN, which governs.
The critical ratio for axial compression = 100 / 4,360 = 0.023
Check Shear Capacity
Major Axis
As per Cl. 8.4.1.1 of IS 800:2007, the shear area, Avz = 2×bftf = 16,000 mm2
So, as per Cl. 8.4.1,
Hence, shear capacity along major axis:
Minor Axis
As per Cl. 8.4.1.1 of IS 800:2007, the shear area, Avy = h×tw = 4,400 mm2
So, as per Cl. 8.4.1,
Hence, shear capacity along major axis:
As per Cl. 8.4.2, d / tw = 63.75 < 67ε, so resistance to shear buckling need not be checked.
No shear force along major axis (i.e., ratio = 0).
Critical shear ratio along minor axis: 350 / 577.4 = 0.606
Check Bending Capacity
Since the section has been classified as "compact", βb = 1.
Major Axis Bending
The actual shear force along the major axis, V = 350 kN > 0.6Vd = 346.4 kN. Thus, the section is subjected to high shear.
(Cl 8.2.1.1) |
Per Cl 9.2.2(a) for "compact" sections:
The plastic section modulus excluding shear area,
Plastic design strength of cross-section area excluding shear area,
Mdvz = Mdz - β(Mdz - Mfdz) = 1,082 - 0.045×(1,082 - 944.4) = 1,076 kN·m | (Cl. 8.2.1.3) |
So, the governing bending strength with respect to the major axis is Mdz = Mdvz = 1,076 kN·m
Actual bending moment about the major axis is Mz = 350 kN·m.
The critical bending ratio in the major axis is 350 / 1,076 = 0.325
Minor Axis Bending
There is no shear along the minor axis.
So, the governing bending strength with respect to the minor axis is Mdy = 290.9 kN·m
No bending moment about the minor axis in beam, so critical ratio is 0.
Check Combined Interaction of Axial Compression and Bending
Section strength calculation as per Cl. 9.3.1:
n = N / Nd = 0.022 < 0.2
Hence, from Table 17:
α1 = max(5n , 1) = 1
α2 = 2
Mndy = Mdy = 290.9 kN·m | (Cl. 9.3.1.2(c) ) |
1.11·Mdz·(1 - n) = 1,168 kN·m > Mdz
Mndz = Mdz = 1,076 kN·m
Overall member strength in bending and axial compression
ny = Fx / Pdy = 0.023
nz = Fx / Pdz = 0.022
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Slenderness ratio | 29.1 | 29.10 | none | |
Tension capacity, gross yielding (kN) | 4,564 | 4,564 | none | |
Tension capacity, rupture of critical section (kN) | 5,398 | 5,398 | none | |
Ratio for tension | 0 | 0 | none | |
Axial compression capacity about major axis (kN) | 4,564 | 4,564 | none | |
Axial compression capacity about minor axis (kN) | 4,360 | 4,360 | none | |
Ratio for compression | 0.023 | 0.023 | none | |
Shear capacity in major axis (kN) | 2,099 | 2,099 | none | |
Ratio for shear in major axis | 0 | 0 | none | |
Shear capacity in minor axis (kN) | 577.4 | 577.35 | negligible | |
Ratio for shear in minor axis | 0.606 | 0.606 | none | |
Bending capacity about major axis (kN·m) | 1,076 | 1,077 | negligible | |
Ratio for bending about major axis | 0.325 | 0.325 | none | |
Bending capacity about minor axis (kN·m) | 290.9 | 209.939 | negligible | |
Ratio for bending about minor axis | 0 | 0 | none | |
Ratio per Cl. 9.3.1.1 | 0.106 | 0.106 | none | |
Ratio per Eq.2 of Cl. 9.3.2.2 | 0.314 | 0.314 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\India\IS 800 2007 LSD - I Section - High Shear.STD is typically installed with the program.
The following design parameters are used:
- The default value of ALPHA is used.
- The default values of KY and KZ are used.
- The default value of the maximum allowable slenderness ratio, MAIN, of 180 is used.
- The beam type is simply supported, specified by CAN 2
- The beam is laterally supported, specified by LAT 1
- The default values of CMX, CMY, and CMZ of 0.9 are used.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 23-Jun-19
END JOB INFORMATION
*****************************************************************************
*This problem has been created to validate the program calculated design
*results of laterally supported I section subjected to high shear force due to
*applied axial compression and
*biaxial bending, designed using IS 800 2007 (LSD)
*****************************************************************************
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 AMERICAN
1 TAPERED 0.55 0.008 0.55 0.4 0.02
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -350 1
1 CON GY -350 2
JOINT LOAD
2 FX -100
PERFORM ANALYSIS
SECTION 0.33 0.66
PRINT ANALYSIS RESULTS
PRINT MEMBER SECTION FORCES
PARAMETER 1
CODE IS800 LSD
CAN 2 ALL
FYLD 250000 ALL
TRACK 2 ALL
LAT 1 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - IS-800-2007-LSD (V2.2) **************************************************** |----------------------------------------------------------------------------------| | Member Number: 1 | | Member Section: TAPERED (AISC SECTIONS) | | Status: PASS Ratio: 0.606 Critical Load Case: 1 Location: 0.00 | | Critical Condition: Sec. 8.4 | | Critical Design Forces: (Unit: KN METE) | | FX: 100.000E+00 C FY: 350.000E+00 FZ: 0.000E+00 | | MX: 0.000E+00 MY: 0.000E+00 MZ: 0.000E+00 | |----------------------------------------------------------------------------------| | Section Properties: (Unit: CM ) | | AXX: 200.800E+00 IZZ: 121.257E+03 RZZ: 24.574E+00| | AYY: 44.000E+00 IYY: 21.336E+03 RYY: 10.308E+00| | AZZ: 160.000E+00 IXX: 222.037E+00 CW: 14.981E+06| | ZEZ: 4.409E+03 ZPZ: 4.760E+03 | | ZEY: 1.067E+03 ZPY: 1.608E+03 | |----------------------------------------------------------------------------------| | 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: 29.10 Allowable Ratio: 180.00 LOAD: 1 | |----------------------------------------------------------------------------------| | Section Class: Compact; Flange Class: Compact; Web Class: Plastic| |----------------------------------------------------------------------------------| STAAD PLANE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - IS-800-2007-LSD (V2.2) **************************************************** |----------------------------------------------------------------------------------| | Member Number: 1 | | Member Section: TAPERED (AISC SECTIONS) | |----------------------------------------------------------------------------------| | Tension: (Unit: KN METE) | | Parameters: FYLD: 250.000E+03 FU: 420.000E+03 | | NSF: 1.000 ALPHA: 0.800 | | Yielding : Design Force: 0.000E+00 LC: 0 | | Capacity: 4.564E+03 As per: Sec. 6.2 | | Rupture : Design Force: 0.000E+00 LC: 0 | | Capacity: 5.398E+03 As per: Sec. 6.3 | |----------------------------------------------------------------------------------| | Compression: (Unit: KN METE) | | Buckling Class: Major: a Minor: b As per:Cl. 7.1.2.2 | | Major Axis: Design Force: 100.000E+00 LC: 1 Loc: 0.000 | | Capacity: 4.564E+03 As per: Sec. 7.1.2 | | Minor Axis: Design Force: 100.000E+00 LC: 1 Loc: 0.000 | | Capacity: 4.360E+03 As per: Sec. 7.1.2 | |----------------------------------------------------------------------------------| | Shear: (Unit: KN ) | | Major Axis: Design Force: 0.000E+00 LC: 0 Loc: 0.000 | | Capacity: 2.099E+03 As per: Sec. 8.4 | | Minor Axis: Design Force: 350.000E+00 LC: 1 Loc: 0.000 | | Capacity: 577.350E+00 As per: Sec. 8.4 | |----------------------------------------------------------------------------------| | Bending: (Unit: KN METE) | | Parameters: Laterally Supported KX: 1.00 LX: 3.000E+00 Simp Suppr | | Major Axis: Design Force: -350.000E+00 LC: 1 Loc: 1.000 | | Capacity: 1.077E+03 As per: Sec. 9.2.2(a | | Minor Axis: Design Force: 0.000E+00 LC: 0 Loc: 0.000 | | Capacity: 290.939E+00 As per: Sec. 8.2.1.2 | |----------------------------------------------------------------------------------| | Combined Interaction: | | Parameters: PSI: 1.00 CMX: 0.900 CMY: 0.900 CMZ: 0.900 | | Section Strength: Ratio: 0.106 As per: Sec. 9.3.1.1 | | LC: 1 Loc: 1.000 | | Overall Member Strength (Bending+Compression): | | Equation 2: Ratio: 0.314 As per: Sec. 9.3.2.2 Ky : 1.0028 | | LC: 1 Loc: 1.000 Kz : 0.9986 | |----------------------------------------------------------------------------------| | Checks Ratio Load Case No. Location from Start( METE) | | | | Tension 0.000 0 0.000E+00 | | Compression 0.023 1 0.000E+00 | | Shear Major 0.000 0 0.000E+00 | | Shear Minor 0.606 1 0.000E+00 | | Bend Major 0.325 1 1.000E+00 | | Bend Minor 0.000 0 0.000E+00 | | Sec. 9.3.1.1 0.106 1 1.000E+00 | | Sec. 9.3.2.2(ii) 0.314 1 1.000E+00 | |----------------------------------------------------------------------------------|