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Deflection

Deflection is how much the beam bends under load. It depends strongly on the length ( $L^3$ ) and on the section stiffness $EI$ : a beam twice as long deflects eight times as much. Large $I$ values, as in I-beams, keep the deflection small.

\delta = \dfrac{PL^3}{48EI}

simply supported beam, point load at midspan

Symbols

$\delta$	deflection	m
$E$	modulus of elasticity	Pa
$I$	second moment of area	m⁴

Example

Doubling $L$ makes $\delta$ 8 times as large,

because $\delta \propto L^3$ and everything else is unchanged.

Deflection is very length-sensitive – halving the span reduces it the most.

Practise bending of beams for free →

← Maximum moment · Cross-section and I-beam →

Part of Statics and Dynamics: Bending of beams.