Practice Question: Deflection in Simply Supported Beam with Uniformly Varying Load

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Solution

Maximum moment for a simple beam with a uniformly increasing load is given by:

\[{\Delta }_{max}=0.013\frac{WL^3}{EI}\]

where:

W = Total Load

L = Span of Beam

E = Modulus of Elasticity

I = Moment of Inertia

Total load based on triangular distribution:

\[W=\frac{1}{2}\times 30\times 4=60\ kip\]

Maximum Deflection:

\[{\Delta }_{max}=0.013\times \frac{60\times {(30\times 12)}^3}{3,600\times 9,261}\]

\[{\Delta }_{max}=1.1\ in\]

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