Question

a beam of square cross section, 100 mm x 100 mm carries an uniformly distributed load of 250 n/m over the whole span. find the maximum bending stresses at mid-span and at three-quarter span points.

Answer 1

The maximum bending stresses at the mid-span and three-quarter span points of the beam are 1500 N/m² and 1125 N/m², respectively.

Step-by-step explanation:

To find the maximum bending stresses at mid-span and three-quarter span points, we can use the formula for bending stress:

Stress = (6 * Load * Length) / (Width^2 * Depth)

For the mid-span point:

Length = Width = Depth

= 100 mm

= 0.1 m

Load = 250 N/m

Substituting these values into the formula, we get:

Stress = (6 * 250 * 0.1) / (0.1^2 * 0.1)

= 1500 N/m²

For the three-quarter span point, the length will be reduced to 0.75 of the total span length:

Length = 0.75 * 0.1 m = 0.075 m

Substituting the new length and the same values for the other variables into the formula, we get:

Stress = (6 * 250 * 0.075) / (0.1^2 * 0.1)

= 1125 N/m²