Final answer:
To solve for the deflection of the beam using the Area Moment Method, calculate the area moment of inertia, I, for the rectangular beam using the given values for width and height. Then calculate the bending moment, M, and finally use the formula for deflection, δ, substituting the given values for distributed load, modulus of elasticity, length, and moment of inertia.
Step-by-step explanation:
To solve for the deflection of the beam using the Area Moment Method, we first need to calculate the area moment of inertia, I, for the rectangular beam. The formula for I can be given by I = (1/12) * b * h^3, where b is the width of the beam and h is its height. We substitute the given values, b = 423 mm and h = 522 mm, into the formula to find I.
Next, we can calculate the bending moment, M, which is given by M = P * L, where P is the applied load and L is the length of the beam. Substituting the given values, P = 31 kN and L = 7 m, we can find M.
Finally, we can calculate the deflection, δ, using the formula δ = (5/384) * (w * L^4) / (E * I), where w is the distributed load, E is the modulus of elasticity, and I is the moment of inertia. Substituting the given values, w = 8 kN/m and E = 20 GPa, along with the previously calculated values of L and I, we can find the deflection.