Bending: shear force and bending moment diagrams is a core Mechanical Engineering (ME) concept in Engineering. This guide explains what it is, walks through a fully worked example, and lists the key equations you need — with a short quiz to test yourself.

Key equations and worked example

A 4 m cantilever beam with E·I = 2×10⁶ N·m² carrying 40 kN at its tip deflects δ = P·L³/(3EI) = 40000×64/(3×2×10⁶) ≈ 0.43 m. Double the span to 8 m and deflection grows 8× — deflection scales with L³. Move the load slider and watch the tip sag.

• <code>Bending stress: σ = M·y / I</code>
• <code>Cantilever tip deflection: δ = P·L³ / (3EI)</code>
• <code>Simply-supported centre deflection: δ = P·L³ / (48EI)</code>
• <code>Stiffness scales with I (second moment of area)</code>

Bending: shear force and bending moment diagrams in detail

Bending: shear force and bending moment diagrams is one of the central ideas in Mechanical Engineering (ME), and it appears in Engineering curricula under Strength of Materials. It is worth learning deeply because it connects to so many other topics in this section.

Beams bend because load creates internal bending moment, resisted by stresses across the section (σ = M·y/I). Stiffer sections (larger I) and shorter spans deflect less. A cantilever is fixed at one end; a simply-supported beam rests on two piers. Engineers keep deflection within limits like span/360.

For exams, the pattern is predictable: first a definition or statement of the result, then a direct numerical application of one of the equations above, then a "why" question — why the formula takes that form, or what changes when a variable is doubled or halved. The worked example and quiz below cover exactly that progression.

Quick self-check:

• Q: How does doubling a cantilever&#39;s span change its tip deflection?<br />A: It increases 8× — deflection ∝ L³.
• Q: Why are I-beams shaped like an I?<br />A: Material placed far from the neutral axis maximises I, giving the most stiffness per kilogram.
• Q: Where is bending stress maximum in a beam?<br />A: At the outermost fibres (top and bottom surfaces), farthest from the neutral axis.