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Deflection and Rotation of Simply Supported Beam with Concentrated Load


deflection-simply-supported-beam-force.png

Beam length - l = m

Load - F = kN

Second moment of area - I = cm4

Modulus of elasticity - E = GPa

Functions of rotation and deflection along the beam

EI = 0.01·E·I

d(x) = F/(4·EI)·((l2/4·xx3/3)·(xl/2) + (l2/4·(lx) – (lx)3/3)·(x > l/2))

φ(x) = F/(4·EI)·(l2/4 – x2)

$Plot{x | – d(x)·103 @ x ∈ [0; l]}

Maximum deflection

dmax = d(l/2)·103 mm

Maximum rotation

φmax = φ(0)·103 rad·10³

Calculate deflection at x = m

d(x)·103 mm


Substitute