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Dezi et. al (2010)
๐คพ
Projectile motion
This calculator determines the elastic critical moment for lateral torsional buckling of steel sections.
๐ This template has been written 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".
- (Non-contradictory Complementary Information) 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 is used here. The critical elastic moment (
๏ปฟ
) is an input into the buckling resistance moment (๏ปฟ
) which is crucial for assessing the capacity of a section in bending.Calculation
๐Technical notes
Inputs
Section Properties
๏ปฟ
๏ปฟ
๏ปฟSection size
:HE 700 Aโ๏ปฟ
๏ปฟ
๏ปฟ L
:5.00mโ๏ปฟ
Applied Load Type
๏ปฟ
๏ปฟ
๏ปฟApplied load type
:UDL (parabolic BM)โ๐กNote, 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:
๏ปฟ
๏ปฟ
๏ปฟSupport type
:Pinned/Pinnedโ๏ปฟ
๏ปฟ
๏ปฟLoad application
:Section centroidโSelected "Applied load type":
- End moments (linear BM)
Applicable user input:
๏ปฟ
๏ปฟ
๏ปฟฯ
:-0.268โOutputs
๏ปฟ
๏ปฟ
๏ปฟC1 factor
:1.127โ๏ปฟ
๏ปฟ
๏ปฟC2 factor
:0.454โ๏ปฟ
๏ปฟ
๏ปฟMcr
:4,437kN mโ๏ปฟ
Explanation
What 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:
๏ปฟ
๏ปฟ
What is the elastic critical moment?
The critical elastic moment,
๏ปฟ
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, ๏ปฟ
๏ปฟ
is a parameter in EC3 and serves as an input into the buckling resistance moment, ๏ปฟ
which is crucial for assessing the capacity of a section in bending.๏ปฟ๏ปฟ 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 Equations
Below are the parameters and equations as provided in NCCI SN003b, that are used in this calculator.
Elastic critical moment (๏ปฟ equation)
Load application point (๏ปฟ parameter)
Applied load type (๏ปฟ and ๏ปฟ parameters)
Ratio of end moments (๏ปฟ parameter)
๏ปฟ
Acknowledgements
This calculation was built in collaboration with Hakan Keskin. Learn more.
Related Resources
- Column Buckling Calculator
- Steel Section Designer to EC3
- Steel Beam and Column Designer to AS4100
- Steel Beam and Column Designer to AISC
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