Final answer:
To solve for the deflection of the beam using the Superposition Method, consider each load acting separately and sum up the individual deflections. Start with the point load P and calculate the deflection using the formula (P L^3) / (48 E I). Then, consider the distributed load w and calculate the deflection using the formula (w L^4) / (8 E I). Plug in the given values and sum up the individual deflections to get the total deflection of the beam.
Step-by-step explanation:
To solve for the deflection of the beam using the Superposition Method, we need to consider each load acting separately and then sum up the individual deflections. Let's start with the point load P. The deflection caused by a point load at the center of a simply supported beam can be calculated using the formula δ = (P L^3) / (48 E I), where δ is the deflection, P is the point load, L is the span length, E is the Young's modulus, and I is the moment of inertia.
Next, we consider the distributed load w. The deflection caused by a uniformly distributed load on a simply supported beam can be calculated using the formula δ = (w L^4) / (8 E I), where δ is the deflection, w is the load per unit length, L is the span length, E is the Young's modulus, and I is the moment of inertia.
Now, we can plug in the given values: P = 31, w = 8, L = 7, b = 423, h = 522, and E = 20. Using the formulas mentioned earlier, we can calculate the deflection caused by each load and then sum them up to get the total deflection of the beam.