The simply supported beam of length 5m is applied point load of 6kn at the middle of beam and having cross section of 30mm width 50mm height. What is the maximum bending stress?

The simply supported beam of length 5m is applied point load of 6kn at the middle of beam and having cross section of 30mm width 50mm height. What is the maximum bending stress?

Solution

In this question, W=6kN, b=30mm, d==50mm, L=5m.

Bending stress can be calculated using the formula sigma=My/I

where M is the maximum bending moment

y is the distance between neutral axis and place where the stress has to be determined

I is the moment of inertia of the section

M= maximum bending moment for simply supported beam carrying point load at its center = WL/4 = 6 x 5/4 =7.5 kNm

y= maximum bending stress occurs at extreme fiber of the section = d/2 =0.05/2 = 0.025m

I = for rectangular section = bd^3/12 = 0.03 x 0.05^3/12 = 3.125x10^-7 mm^4

so, the bending stress = 600000 kN/sq.m