Question

A cantilever beam of length l is subjected to a moment m at the free end. The moment of inertia of the beam cross section about the neutral axis is i and the young's modulus is e. The magnitude of the maximum deflection is

Answer 1

Answer:

Explanation:

answer is a

Answer 2

Given that,

Length = l

Moment = m

Moment of inertia = I

Young's modulus = e

We need to calculate the magnitude of the maximum deflection

Using equation of deflection

$El\dfrac{d^2y}{dx^2}=M$

On integration

$El\dfrac{dy}{dx}=Mx+C_{1}$

At x = o. slope $\dfrac{dy}{dx}=0$

Put the value into the formula

$C_{1}=0$

So, the equation of deflection is

$El\dfrac{dy}{dx}=Mx$

Again integration,

$Ely=\dfrac{Mx^2}{2}+C_{2}$

At x = 0 , deflection is zero

So, $C_{2}=0$

The equation of deflection at free end

$Ely=\dfrac{Mx^2}{2}$

$y=\dfrac{Mx^2}{2El}$

Hence, The magnitude of the maximum deflection is $\dfrac{Mx^2}{2El}$