Learning Goal:

The method of virtual work can be applied to beams and frames. The displacement $$ of a specific point on a beam caused by external loading can be determined using the virtual work equation $1*={\displaystyle \underset{0}{\overset{L}{}}}\frac{mM}{EI}dx,$ where $1$ is the external virtual unit load acting on the beam in the directions of the deflection, $m$ is the internal virtual moment in the beam, expressed as a function of $x$ and caused by the external virtual unit load, $M$ is the internal moment in the beam, expressed as a function of $x$ and caused by real loads, $L$ is the member's length, $E$ is the modulus of elasticity, and I is the moment of inertia of the beam's cross$-$sectional area. The slope angle $$ can also be determined usina the method of virtual work. Instead of a unit load, a unit

Figure

$2$ of $3$

Part A

For the beam shown in $($Figure $2),$ determine the displacement at $C.$ Use the method of virtual work and assume $A$ is pinned, $B$ is a roller, and $El$ is constant. Assume a positive displacement acts downward.

Express your answer in terms of some or all of the variables $P,d,E,$ and I.

Vlew Avallable Hint$($s$)$

Part B

For the beam shown in $($Figure $2),$ determine the slope at $A.$ Use the method of virtual work and assume $A$ is pinned, $B$ is a roller, and $El$ is constant. Let a positive angle be measured counterclockwise from the horizontal.

Express your answer in terms of some or all of the variables $P,d,E,$ and I.

Vlew Avallable Hint$($s$)$