## Chapter 7

## Q. 7.3

A cantilever of length 2 metre fails when a load of 2 kN is applied at the free end. If the section of the beam is 40 mm × 60 mm, find the stress at the failure.

## Step-by-Step

## Verified Solution

Given :

Length, L = 2 m = 2 × 10³ mm

Load, W = 2 kN = 2000 N

Section of beam is 40 mm × 60 mm.

∴ Width of beam, b = 40 mm

Depth of beam, d = 60 mm

Fig. 7.10 (a) shows the section of the beam.

Section modulus of a rectangular section is given by equation (7.7).

∴ Z=\frac{b d^2}{6}=\frac{40 \times 60^2}{6}=24000 mm ^3

Maximum bending moment for a cantilever shown in Fig. 7.10 is at the fixed end.

∴ M=W \times L=2000 \times 2 \times 10^3=4 \times 10^6 Nmm

Let σ_{\max} = Stress at the failure

Using equation (7.6), we get

M=\sigma_{\max } . Z

∴ \sigma_{\max }=\frac{M}{Z}=\frac{4 \times 10^6}{24000}= \pmb{1 6 6 . 6 7 N / m m ^2.}