Problem $2$:

A $1$ m $-$long plain concrete beam with a circular cross section having a diameter equal to $200$

mm is simply supported and subjected to a downward uniformly distributed load along its

entire length, w$,$ as shown in the figure below. Determine the minimum uniform load $"$w$"$

that will cause the beam to crack if the compressive strength of concrete is $f_c^{\text{'}}=35$MPa

$(=23k\frac{N}{m^3}).$ Consider flexure and ignore shear and do not ignore the weight of the beam.