Which of the two Ibeam sections will provide the least amoun

Which of the two I-beam sections will provide the least amount of stress for the beam loading shown below? What is that stress?

Solution

For the bending of beams, the equation is M/I = f/y

where M is the bending moment on the beam section

I is the Moment of Inertia of the cross section of the beam

f is the stress developed at a distance of y from the neutral axis of the beam.

here f = M. y/ I

Now for two beams with sections shown in a and b, the moment f Inertia of section b is more than that of section a.

Hence, the amount of stress in the beam with section b is least.

The stress is tensile at the top layer and in the portion above the neutral axis. The stress is compressive in the bottom layer and in the portion below the neutral axis of the beam.