Problem: a rectangular beam made out of $4000$ psi normal weight concrete is simply supported over a $20$ ft clear span.

How much load at the center of the beam, that it will carry without cracking.

Part a$)$ Use gross section properties to estimate $M_{cr}$

Part b$)$ Use transformed Section properties to estimate $M_{cr}$

Part c$)$ If $12-$kip load is applied at the center of the beam, find the stresses in steel rebar and concrete at the top.

Given: Concrete Strength $=4000$

Beam width $(b)=12$ in$.$; beam depth $(h)=24$ in$.$ Beam effective depth $(d)=20in.$

Beam span $(L)=20ft$

Principle: To crack the beam, the moment caused by the external load has to be

equal to the cracking moment of the beam.