Problem $2$: Elastic Bending and Shear Theory

a$.$ Draw the shear and monent diagrams for the beam.

b$.$ Draw the internal shear and bending stresses at section A$-$A$.$

c$.$ Find the force couple equivalent to the bending stresses at sfition A$-$A$.$

d$.$ Find the principal stresses at Point $1$ in the beam. Point $1$ is located half$-$way between the neutral axis and the bottom fiber of the beam. Include a sketch of the beam element and its stresses, and the transformed beam element with its principal stresses. Note: Ok to assume an average shear stress distribution of $=\frac{V}{A}.$