Deflection and Slope derivation Use the idealized set-up shown on the previous page to: a. Derive an expression (in terms of P, L, a and EI ) for the theoretical midpoint deflection of a simply supported beam under two equal symmetrically-placed con- centrated loads. b. Derive an expression for the slope at the left support. c. Derive an expression for the deflection under the spreader beam roller (distance a from the left support). 2. Theoretical Deflection For the aluminum specimen, using the given value of E and the expression derive in 1.a., calculate the theoretical midpoint deflection for each loading. Record these values on you datasheet. In your discussion: Discuss any discrepancies in theoretical and experimental deflection. 3. Plot Values Make a plot of deflection versus load for both experimental and theoretical values at the midpoint location. 4. Experimental E Using the displacement expression found in step 1.a. and the slope from the experimental values plot in step 3, determine the experimental modulus of elasticity, Eexp. In your discussion: Discuss any discrepancies in theoretical and experimental values