Question

A rectangular beam of 10cm wide, is subjected to a maximum shear force of 50kN and the corresponding maximum shear stress is 3MPa. The depth of beam is

Answer 1

Given:

Breadth = 10 cm

Maximum sheer force = 50 kN

Maximum sheer stress = 3 MPa

To find:

The depth.

Solution:

By formula,

Sheer stress = 3 * Force / 2 * Breadth * Depth

Substituting,

We get,

3 = 3 * 50 / 2 * 0.1 * Depth

Depth = 3 * 50 / 2 * 0.1 * 3

Hence, Depth = 250 mm

Answer 2

we know, maximum shear stress = 3 × shearing force/2 {area of rectangular beam}

Given,
maximum shear stress = 3MPa = 3 × 10^6 Pa
shearing force = 50kN = 50 × 10³ N
breadth of rectangular beam = 10cm = 0.1 m
Let depth of beam is D

then, 3 × 10^6 = 3 × 50 × 10³/2 × 0.1 × D
3 × 10³ = 150/0.2D
3 × 10³ = 750/D
D = 750/3 × 10³
D = 250 × 10^-3 m = 250 mm

hence, depth of beam = 250mm