Elastic Critical Moment Calculator for Lateral Torsional Buckling to EC3

This calculator determines the elastic critical moment for lateral torsional buckling of steel sections.
All calculations are performed in accordance with:
EN 1993-1-1:2005 Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings. This code is typically referred to as "EC3". 
NCCI SN003b-EN-EU: Elastic critical moment for lateral torsional buckling 
EC3 does not include a formula for the elastic critical moment and hence the NCCI (Non-contradictory Complementary Information) is used here. The critical elastic moment (﻿Mcr​
) is an input into the buckling resistance moment (﻿Mb,Rd​
) which is crucial for assessing the capacity of a section in bending.
Calculation📃Technical notes
InputsSection Properties
﻿﻿Section size
:HE 700 A​
﻿
﻿﻿ L
:5.00m​
﻿
﻿
Applied Load Type
﻿﻿Applied load type
:UDL (parabolic BM)​
﻿
💡Note, the below inputs are applicable based on your selected "Applied load type". Otherwise, they will not affect the calculation.
Selected "Applied load type":
UDL (parabolic BM) or Point load at midspan (triangular BM)
Applicable user input:
﻿﻿Support type
:Pinned/Pinned​
﻿
﻿﻿Load application
:Section centroid​
﻿
Selected "Applied load type":
End moments (linear BM)
Applicable user input:
﻿﻿ψ
:-0.268​
﻿
Outputs﻿﻿C1 factor
:1.127​
﻿
﻿﻿C2 factor
:0.454​
﻿
﻿﻿Mcr
:4,437kN m​
﻿
﻿
ExplanationWhat is lateral torsional buckling?Lateral torsional buckling occurs in members in bending. It is where the beam bends in it's minor axis and twists, as this behavior is the least stiff bending failure.
Lateral torsional buckling is particularly relevant in beams that are slender, have a significant length between supports or are not laterally supported along their length. These conditions make the beam more susceptible to twisting and lateral displacement when subjected to bending moments.
This is what lateral torsional buckling looks like:
﻿
﻿
﻿
﻿
What is the elastic critical moment?The critical elastic moment, ﻿Mcr​
 is the critical bending moment that leads to the onset of elastic lateral torsional buckling (LTB) in a beam. It is analogous to how the Euler buckling concept identifies the critical compression causing a column to succumb to elastic flexural buckling, 
﻿﻿Mcr​
 is a parameter in EC3 and serves as an input into the buckling resistance moment, ﻿Mb,Rd​
 which is crucial for assessing the capacity of a section in bending.
﻿﻿Mcr​
 in Eurocode 3
The engineer's role is to design a beam that has an adequate bending strength to resist applied moments without experiencing LTB. This involves selecting a beam size and positioning lateral supports such that the bending stresses are within acceptable limits.
NCCI Parameters and EquationsBelow are the parameters and equations as provided in NCCI SN003b, that are used in this calculator.
Elastic critical moment (﻿Mcr​
 equation)
Load application point (﻿zg​
 parameter)
Applied load type (﻿C1​
 and ﻿C2​
 parameters)
Ratio of end moments (﻿ψ
 parameter)
﻿
AcknowledgementsThis calculation was built in collaboration with Hakan Keskin. Learn more.
Related ResourcesColumn Buckling Calculator
Steel Section Designer to EC3
Steel Beam and Column Designer to AS4100
Steel Beam and Column Designer to AISC
Check out our full library of CalcTree templates here!
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Elastic Critical Moment Calculator for Lateral Torsional Buckling to EC3

Calculation

📃Technical notes

Inputs

Section Properties

Applied Load Type

Outputs

Explanation

What is lateral torsional buckling?

What is the elastic critical moment?

$M_{cr}$
in Eurocode 3

NCCI Parameters and Equations

Elastic critical moment (

$M_{cr}$
equation)

Load application point (

$z_{g}$
parameter)

Applied load type (

$C_{1}$
and

$C_{2}$
parameters)

Ratio of end moments (

$ψ$
parameter)

Acknowledgements

Related Resources

Elastic Critical Moment Calculator for Lateral Torsional Buckling to EC3

Calculation

📃Technical notes

Inputs

Section Properties

Applied Load Type

Outputs

Explanation

What is lateral torsional buckling?

What is the elastic critical moment?

﻿﻿Mcr​ in Eurocode 3

NCCI Parameters and Equations

Elastic critical moment (﻿Mcr​ equation)

Load application point (﻿zg​ parameter)

Applied load type (﻿C1​ and ﻿C2​ parameters)

Ratio of end moments (﻿ψ parameter)

Acknowledgements

Related Resources

$M_{cr}$
in Eurocode 3

Elastic critical moment (

$M_{cr}$
equation)

Load application point (

$z_{g}$
parameter)

Applied load type (

$C_{1}$
and

$C_{2}$
parameters)

Ratio of end moments (

$ψ$
parameter)