Deflection of Beam under continuous load, by integration.

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 : wo Moment of inertia of cross-section : Young's modulus : E

1. Determine the equation for the support forces, R₁ and R₂.
2. Sketch of the relevant Free Body Diagram you are using to determine the equation for the internal shear force V(x).
3. Integrate V(x) to find the equation for the internal momemt M(x).
4. Integrate the equation E I y" = M(x) to find y(x).
5. State the conditions from which to determine the integration constants and determine the integration constants.
6. Determine the equation for the deflection at x=L/2 in terms of L, E, , and w_o.