The simply supported joist is used the construction of a floor for a building. In order to...

The simply supported joist is used the construction of a floor for a building. In order to keep the floor low with respect to the sill beams C and D, the ends of the joists are notched as shown. If the allowable shear stress for the wood is τallow = 350 psi and the allowable bending stress is σallow = 1700 psi, determine the smallest height h so that the beam will support a load of P = 600 lb. Also, will the entire joist safely support the load? Neglect the stress concentration at the notch.