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Elastic Flexural-Torsional Buckling
and IS:800-2007
Bhavin ShahAssociate Vice President VMS Engineering & Design Services (p) ltd.
Content of the presentation
1. What is Elastic Flexural Torsional Buckling ?2. IS:800-2007 (Simplified approach)3. Approach adopted in popular software4. Generalised equation for Mcr (Annexure-E of IS:800-
2007)5. Comparison of results with Simplified approach and the
Generalised equation6. Concluding Remarks7. Way Forward
What is Elastic Flexural Torsional Buckling ?
Bhavin Shah
What is Elastic Flexural Torsional Buckling ?
• Flexural-torsional buckling is an important limitstate that must be considered in structural steeldesign.
• Flexural-torsional buckling occurs when astructural member experiences significant out-of-plane bending and twisting.
• This type of failure occurs suddenly in memberswith a much greater in-plane bending stiffnessthan torsional or lateral bending stiffness.
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About US
Cantilever Beam
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www.steelconstruction.info
Beam with moments at End
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Warping
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IS:800-2007 (Simplified approach )
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C) When MCR is nearly 6 times more than (Zp * fy)
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Effective Length
Approach adopted in the popular software
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• Popular software (STAAD) uses this simplified concept for calculating Elastic Lateral
Torsional Buckling Moment.
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IS:800-2007 (Annexure E : Generalised equation )
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2
Also known as Three factor
formulae (depends on C1, C2 & C3)
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Difference between Simplified approach and the Generalised Equation
• Variation of moment across the span
• Height of application of load above shear centre
• Support conditions
• Non symmetry about major axis
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C1 : Moment Variation Factor
Variation of End Moments
Variation of Loading & Support Conditions
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C2 = Factor for Load application (height from shear center)
C2*yg• (Wherein yg= Distance between the point of application of the load
and the shear centre of the cross-section )
yg is positive when the load is acting towards the shear centre from the point ofapplication.
yg
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C3 : Factor for unsymmetry about major axis
• C3 = Applicable for sections which are notsymmetrical about major axis
• For doubly symmetric I sections, yj =0 andhence product C3*yj = 0.
• In our subsequent discussions, we will seeeffect of C1 and C2.
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Different boundary conditions
• K= effective length factors of the unsupported lengthaccounting for boundary conditions at the end lateralsupports. The effective length factor K varies from :
0.5 for complete restraint against rotation about weakaxis
1.0 for free rotate about weak axis0.7 for the case of one end fixed and other end free.
• Kw = warping restraint Factor. Unless specialprovisions to restrain warping of the section at the endlateral supports are made, Kw should be taken as 1.0.
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Extraction of results from Dissertation carried out by Anand Gajjar (D.D.U., Nadiad)
Guide : Bhavin Shah
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Variation of MCr : Moment gradient
K 1 Kw 1
Length E 1.1. Ψ = 1 Ψ = 0.75 Ψ = 0.5 Ψ = 0.25 Ψ = 0 Ψ = -0.25 Ψ = -0.5 Ψ = -0.75 Ψ = -1
3 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
4 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
5 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
6 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
7 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
8 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
9 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
10 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
11 1 1 1.12 1.29 1.53 1.84 2.23 2.64 2.86 2.75
12 1 1 1.14 1.32 1.56 1.88 2.28 2.71 2.93 2.75
K = 1.0 Kw = 1.0
Results for ISMB600 All Values of Mcr are normalised with respect to simplified approach.
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Variation of MCr : Moment gradient
Length E 1.1. Ψ = 1 Ψ = 0.75 Ψ = 0.5 Ψ = 0.25 Ψ = 0 Ψ = -0.25 Ψ = -0.5 Ψ = -0.75 Ψ = -1
3 1 0.63 0.83 0.96 1.13 1.36 1.65 1.96 1.96 1.99
4 1 0.69 0.91 1.05 1.24 1.49 1.81 2.15 2.15 2.18
5 1 0.75 0.97 1.13 1.34 1.61 1.95 2.31 2.31 2.35
6 1 0.79 1.03 1.20 1.41 1.70 2.06 2.45 2.45 2.49
7 1 0.83 1.08 1.25 1.48 1.78 2.16 2.56 2.56 2.60
8 1 0.85 1.12 1.29 1.53 1.84 2.23 2.64 2.64 2.69
9 1 0.88 1.15 1.33 1.57 1.89 2.29 2.71 2.71 2.76
10 1 0.90 1.17 1.36 1.60 1.93 2.34 2.77 2.77 2.82
11 1 0.89 1.16 1.35 1.59 1.91 2.32 2.75 2.75 2.80
12 1 0.92 1.20 1.40 1.65 1.98 2.41 2.85 2.85 2.90
K = 0.5 Kw = 1.0
Results for ISMB600 All Values of Mcr are normalised with respect to simplified approach.
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Variation of MCr : Loading & Support condition
Length E 1.1. Case 1 Case 2 Case 3 Case 4 Case 5
3 1 1.13 2.49 1.37 3.03 1.05
4 1 1.13 2.41 1.37 2.94 1.05
5 1 1.13 2.33 1.37 2.84 1.05
6 1 1.13 2.27 1.37 2.76 1.05
7 1 1.13 2.21 1.37 2.69 1.05
8 1 1.13 2.15 1.37 2.62 1.05
9 1 1.13 2.11 1.37 2.57 1.05
10 1 1.13 2.07 1.37 2.53 1.05
11 1 1.11 2.00 1.34 2.43 1.02
12 1 1.13 2.02 1.37 2.46 1.05
Case 1
Case 2
Case 3
Case 4
Case 5
Yg = 0 mm K = 1.0 Kw = 1.0
Results for ISMB600 All Values of Mcr are normalised with respect to simplified approach.
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Variation of MCr : Load and Support conditions
Length E 1.1. Case 1 Case 2 Case 3 Case 4 Case 5
3 1 0.75 0.74 0.84 1.08 0.71
4 1 0.77 0.74 0.86 1.08 0.73
5 1 0.79 0.75 0.89 1.08 0.75
6 1 0.81 0.76 0.92 1.09 0.77
7 1 0.84 0.77 0.95 1.11 0.79
8 1 0.85 0.79 0.97 1.12 0.80
9 1 0.87 0.81 1.00 1.15 0.82
10 1 0.89 0.83 1.02 1.17 0.83
11 1 0.88 0.83 1.02 1.17 0.83
12 1 0.92 0.87 1.06 1.22 0.86
Yg = 300mm K = 1.0 Kw = 1.0
Results for ISMB600
Case 1
Case 2
Case 3
Case 4
Case 5
All Values of Mcr are normalised with respect to simplified approach.
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Variation of MCr : Load and Support conditions
Length E 1.1. Case 1 Case 2 Case 3 Case 4 Case 5
3 1 0.40 0.31 0.37 0.38 0.36
4 1 0.47 0.35 0.44 0.43 0.43
5 1 0.53 0.39 0.51 0.48 0.49
6 1 0.58 0.43 0.57 0.53 0.55
7 1 0.63 0.47 0.63 0.59 0.60
8 1 0.67 0.51 0.67 0.63 0.64
9 1 0.70 0.54 0.71 0.68 0.68
10 1 0.73 0.57 0.74 0.72 0.71
11 1 0.73 0.58 0.75 0.74 0.72
12 1 0.77 0.62 0.80 0.79 0.76
Results for ISMB600
Yg = 300mm K = 0.5 Kw = 1.0 Case 1
Case 2
Case 3
Case 4
Case 5
All Values of Mcr are normalised with respect to simplified approach.
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Variation of MCr : Load and Support conditions
Length E 1.1. Case 1 Case 2 Case 3 Case 4 Case 5
3 1 0.62 0.79 0.68 1.05 0.64
4 1 0.67 0.83 0.74 1.09 0.70
5 1 0.73 0.86 0.80 1.13 0.75
6 1 0.80 0.88 0.85 1.17 0.80
7 1 0.80 0.91 0.88 1.19 0.83
8 1 0.83 0.92 0.91 1.22 0.86
9 1 0.85 0.94 0.94 1.24 0.89
10 1 0.87 0.95 0.96 1.25 0.90
11 1 0.87 0.94 0.95 1.23 0.90
12 1 0.90 0.97 0.99 1.27 0.93
Results for ISMB600
Yg = 0 mm K = 0.5 Kw = 1.0 Case 1
Case 2
Case 3
Case 4
Case 5
All Values of Mcr are normalised with respect to simplified approach.
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Concluding Remarks
Flexural-torsional buckling is an important limit statethat must be considered in structural steel design.
Popular software adopts simplified approach forcalculation of elastic critical moment (Mcr).
In the simplified approach, effect of moment variationacross the span, height of loading from shear centreand different supporting conditions are notconsidered.
There can be substantial variation in the value of Mcr(between simplified vs generalised equation as perAnnexure-E of IS:800-2007).
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Way Forward As a part of the road map of IAStructE for 2014-16, it has
been decided to form the separate professional committee,
named as BIS-CODAL Committee, IAStructE.
Main aim of the committee shall be to bridge the gap between
practicing engineers / academicians and BIS Technical
Committee (CED). For details of the committee, pl visit
: http://iaseguj.org/forum/topic/33
We have initiated the activities with IS:800-2007. All the
collated queries / comments (received from across the
country) will be sent to BIS for further action.
You may send your queries related to IS:800-2007 vide e-mail
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References :• IS:800-2007 – General construction in steel
• A Parametric Study of Elastic Critical Moments in StructuralDesignSoftware by MARTIN AHNLÉN JONAS WESTLUND
• Lateral-Torsional Buckling of Steel Beams with Open Cross Section by HERMANN ÞÓR HAUKSSON JÓN BJÖRN VILHJÁLMSSON
• Stability of Steel beams and columns by TATA Steel
