Cross$-$section For this problem, the beam is assumed to be loaded using a service $($unfactored$)$ load.

The beam shown below is assumed to be made using a homogeneous linear$-$elastic material.

a$.$ For the uniformly distributed service load, calculate the stresses at the top and bottom faces for

the section corresponding to maximum positive moment and maximum negative moment $($follow

common bending theory assumptions from strength of materials$).$

b$.$ Calculate the internal compressive and tensile resultant forces $($force couple$)$ for each of these

sections, and the distance of these force resultants taken from the neutral surface.

c$.$ Using the maximum absolute tensile stress calculated from the positive and negative moment

sections, determine if this beam is expected to crack if it is made of concrete with f$$c $=4000$ psi

$($Ref: Materials Handout; tensile strength of concrete is determined using the modulus of rupture

in that handout, fr$.$ The calculated stress in extreme tension fiber must not exceed fr for the beam

to remain uncracked$).$