STRUCTURAL

Bending Moment

Internal moment that causes a member to bend; basis of flexural design

Also calledbmbending moment diagrambmdmoment
Related on InfraLens
Definition

Bending moment is the internal reaction induced in a structural element when an external force or moment makes the element bend. At any section it equals the algebraic sum of moments of all forces on one side of that section, expressed in kN·m. The bending moment diagram (BMD) plots this along the member's length — its peak governs the flexural design of beams and slabs.

For a simply supported beam of span L under a uniformly distributed load w, the maximum bending moment is wL²/8 at mid-span. For a fixed beam it is wL²/12 at the supports and wL²/24 at mid-span. Continuous beams are usually analysed by moment-distribution, the IS 456 Cl. 22.5 moment-coefficient method, or software. The design moment Mu (factored) must not exceed the section's moment of resistance, Mu,lim = 0.36 fck b xu,max (d − 0.42 xu,max) for a singly reinforced section per IS 456 Annex G.

Where used
  • Flexural design of RCC beams + slabs (IS 456 Annex G)
  • Steel beam design (IS 800 limit state)
  • Bridge girder design (IRC 112)
  • Retaining-wall stem + footing design
  • Determining main reinforcement area Ast = Mu / (0.87 fy z)
Acceptance / threshold
Factored design moment Mu ≤ moment of resistance of the section. For singly reinforced beams keep xu ≤ xu,max (0.48d for Fe 415, 0.46d for Fe 500) so the section is under-reinforced and fails ductile.
Frequently asked
What is the maximum bending moment in a simply supported beam?
For a uniformly distributed load w over span L, Mmax = wL²/8 at mid-span. For a central point load P, Mmax = PL/4 at mid-span.
How is bending moment related to reinforcement?
The factored bending moment Mu determines the tension steel area: Ast ≈ Mu / (0.87 × fy × z), where z (lever arm) ≈ 0.9d for preliminary design. Higher moment → more steel or a deeper section.
Related terms