Practice Question: Calculating Deflection in Simple Beam

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Solution

Deflection at "x" distance from support in a simple beam is given by:

\[{\Delta }_x=\frac{wx}{24EI}(L^3-2Lx^2+x^3)\]

 

\(w = 3\ kip/ft = 0.25\ kip/in\)
\(L = 30\ ft = 360\ in\)
\(x = 10\ ft = 120\ in\)
\(E = 3,600\ ksi\)
\(I = 17,280\ in^4\)

 

\[{\Delta }_{10ft}=\frac{0.25\ \times 120\ }{24\times 3,600\ ksi\ \times 17,280\ {in}^4}\left({360}^3-2\times 360\times {120}^2+\ {120}^3\right)\]

 

\[{\Delta }_{10ft}=0.764\ in\]

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