Practice Question: Calculating Moment of Inertia for a Given Deflection Limit

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Solution

For a uniform distributed load (UDL) on a simple span, the maximum elastic deflection is given by:

\[{\Delta }_{max}=\frac{5wL^4}{384\ EI}\le \ \frac{L}{360}\]

where the moment of inertia “I” is determined by:

\[I=\frac{1800wL^3}{384\ E}\]

 

By using consistent units:

\(w = 5\ k/ft = 0.416\ k/in;\ L = 40\ ft = 480\ in;\ E = 29,000\ k/in^2\)

\[I > 7448\ in^4\]

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