A 2 × 12 floor joist spans 16′-6″ and rests on its  in edge. It carries a uniformly distri...

A 2 × 12 floor joist spans 16′-6″ and rests on its  in edge. It carries a uniformly distributed load of 67 lb/ft across its entire length.

(a) One end of the joist rests on the 3i-in surface of a 2 × 4 plate. Determine the bearing stress that develops on the plate.

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(b) The other end of the joist is attached to a joist header and this assembly rests on a sill plate. The assembly is constructed so that only 2 in of the joist end is bearing on the sill plate. Determine the bearing stress that develops on the sill plate.