Bending Moment
Internal moment that causes a member to bend; basis of flexural design
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.
- 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)