Deflection of the free end of cantilever having point load at the mid span is

This question was previously asked in

MPSC AE CE Mains 2018 Official (Paper 1)

Option 3 : \(\frac{{5w{l^3}}}{{48EI}}\)

ST 1: Logical reasoning

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20 Questions
20 Marks
20 Mins

**Calculation:**

The deflection of a free end cantilever is given below fig.

\(\Delta _{B}=\Delta _{C}+\Theta _{C}\times \frac{L}{2}\)

\(=\frac{w(\frac{L}{2})^{3}}{3EI}+\frac{w(\frac{L}{2})^{2}}{2EI}\times\frac{L}{2}\)

\(=\frac{wL^{3}}{24EI}+\frac{wL^{3}}{16EI}\)

\(=\frac{wL^{3}}{EI}\left ( \frac{1}{24}+\frac{1}{16} \right )\)

\(=\frac{5wL^{3}}{48EI}\)