GATE2016-2-33

Question

A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is given by

$w=\dfrac{-Mx}{12EIL}(L-x)(x+c)$

where $E$ is the Young’s modulus, $I$ is the area moment of inertia and $c$ is a constant (to be determined) .

The slope at the center $x$ = $0$ is

• A. $ML/(2EI)$
• B. $ML/(3EI)$
• C. $ML/(6EI)$
• D. $ML/(12EI)$