Problem # 3 |

**You must use the method of integration** to find the equation for the deflection
of the shown beam at its center.

Consider as given : Length of beam : L Weight per unit length at the right end of beam : w _{o} Moment of inertia of cross-section : Young's modulus : E |

- Determine the equation for the support forces, R
_{1}and R_{2}. - Sketch of the relevant Free Body Diagram you are using to determine the equation for the internal shear force V(x).
- Integrate V(x) to find the equation for the internal momemt M(x).
- Integrate the equation E I y" = M(x) to find y(x).
- State the conditions from which to determine the integration constants and determine the integration constants.
- Determine the equation for the deflection at x=L/2 in terms of
**L, E, , and****w**_{o}.