Sample Problem $4\mathrm{.}3$

The cantilever beam in

Fig.$($a$)$ carries a triangular

load. The intensity of

which varies from zero at

the left end to $360l\frac{b}{f}t$ at

the right end. In addition, $a^1$

$1000-$lb upward vertical

load acts at the free end of

the beam. $(1)$ Derive the

shear force and bending

moment equations. And

$(2)$ draw the shear force

and bending moment

diagrams. Neglect the

weight of the beam.

Solution

Note that the triangular load has been

replaced by is resultant, which is the

force $0\mathrm{.}5(12)(360)=2160lb($area

under the loading diagram$)$ acting at

the centroid of the loading diagram.