ماشین حساب خمش تیر

Beam bending occurs when a transverse load is applied to a structural member, causing it to deflect. The beam develops internal bending moments and shear forces. Bending stress varies linearly across the section — zero at the neutral axis and maximum at the extreme fibers.

A simply supported beam rests on two supports at its ends and is free to rotate at those points. A cantilever beam is rigidly fixed at one end and free at the other.

Cantilevers have larger deflections and moments at the fixed support than equivalently loaded simply supported beams.

Deflection depends on load type, span length (L), elastic modulus (E), and moment of inertia (I):

• SS center point load: δ = PL³/(48EI)
• SS UDL: δ = 5wL⁴/(384EI)
• Cantilever tip load: δ = PL³/(3EI)

The second moment of area (I) is a geometric property that measures the cross-section's resistance to bending. Larger I means less deflection and stress for the same load. For a rectangle: I = bh³/12. For a circle: I = πd⁴/64.

Common limits per building codes:

• L/360 — Floor beams (live load)
• L/240 — Total load
• L/180 — Roof beams
• L/500 — Precision machinery supports

Always check applicable design standards.