A simply supported beam of a span, L is subjected to a point load
A simply supported beam of a span, L is subjected to a point load, P at its mid-span. The maximum deflection induced will be:
Where EI is flexural rigidity
A. <span class="math-tex">\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{96{\rm{EI}}}}\)</span>
B. <span class="math-tex">\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{24{\rm{EI}}}}\)</span>
C. <span class="math-tex">\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{48{\rm{EI}}}}\)</span>
D. <span class="math-tex">\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{8{\rm{EI}}}}\)</span>
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Right Answer is: C
SOLUTION
Explanation:
The maximum deflection of a simply supported beam of span L carrying an isolated load at the center of the span, flexural rigidity being EI is given by:
\(\delta ~=~\frac{{{\rm{P}}{{\rm{L}}^3}}}{{48{\rm{EI}}}}\)
where P = point load acting at centre, EI = flexural rigidity, L = length of beam.
The deflection value for different conditions are as tabulated below:
