Lateral‑torsional buckling (LTB) is a stability phenomenon that occurs in slender, unbraced beams when the compression flange tends to lift and twist under bending. The critical moment at which this instability initiates depends on the beam’s flexural stiffness about the strong axis (Iy), the stiffness about the weak axis (Iz), the warping constant (Cw), and the effective unbraced length.
The governing expression for the elastic critical moment Mcr for a simply supported beam is derived from the differential equation of equilibrium and incorporates both flexural‑torsional and warping effects. Material properties – Young’s modulus (E) and shear modulus (G) – also influence the buckling resistance because they control the beam’s ability to resist torsional deformation and warping.
In practice, engineers compare the applied bending moment (M) to Mcr. If M exceeds Mcr, additional lateral bracing or a redesign is required to prevent sudden loss of load‑carrying capacity.
E = Young’s modulus (MPa)
G = shear modulus (MPa)
I_{y} = strong‑axis moment of inertia (cm⁴)
I_{z} = weak‑axis moment of inertia (cm⁴)
C_{w} = warping constant (cm⁶)
L_{b} = effective unbraced length (m)
What is lateral-torsional buckling?
How do I calculate the critical moment for lateral-torsional buckling?
What factors affect lateral-torsional buckling in beams?
When is lateral-torsional buckling a concern in beam design?
Can this calculator be used for any type of beam?
Results are for informational purposes only and do not constitute professional advice.