Practice Question: Change in Beam Deflection with Length
NCEES Civil PE Specification IV.G.: Deflection
Problem
Two beams with equal section and material properties are both loaded at midpoint with load P. Given that Beam 2 deflects 2.5 inches, determine the deflection associated with Beam 1.
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Solution
Answer: A) 0.09 in
Maximum beam deflection for load P at midpoint:
$$ \delta=\frac{P\ast\ L^3}{48\ast\ E\ast\ I} $$
Deflection for Beam 1:
$$ \Delta_1=\frac{P\ast L_1^3}{48\ast E_1\ast I_1} $$
Where:
$$ L_1=8\ ft $$ Deflection for Beam 2:
$$ 2.5\ in=\frac{P\ast L_2^3}{48\ast E_2\ast I_2} $$
Where:
$$ L_2=24\ ft $$
Since section and material properties are equal:
$$ E_1=E_2 $$
$$ I_1=I_2 $$
Dividing deflection for Beam 1 by deflection for Beam 2:
$$ \frac{\Delta_1}{2.5\ in}=\frac{\left(8\ ft\right)^3}{\left(24\ ft\right)^3} $$
$$ \Delta_1=0.09\ in $$
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