0.980 in. 0.25 in. t0.487 in. 2 in. L3 × 2 × 0.25 in. 3 in.

Problem 3 Conjugate Beam Method: For the given beam below, answer the questions. El = constant: P M=Pa B a a (a) Draw the conjugate beam (clearly show the supports of the conjugate beam and mark the important values). (b) Determine the slope angle at point B, 0B, of the real beam using the conjugate beam method. Determine the deflection at point B, Ag, of the real beam using the conjugate beam method.

Determine the moments of inertia Iu, Iυ and the product of inertia Iuυ for the rectangular area. The u and υ axes pass through the centroid C. Solve the above problem using Mohr’s circle. Hint: To solve, find the coordinates of the point P(Iu, Iuυ) on the circle, measured counterclockwise from the radial line OA. (See 10–19.) The point Q(Iυ, - Iuυ) is on the opposite side of the circle.

Using Castigliano's theorem, solve step by step the given frame.

Solve for maximum deflection using double method integration.

Determine the slope and deflection at point A of the beam shown in the figure.

2. By the moment-area method or conjugate-beam method, determine the deflection at the midspan (EIA) for the beam shown in figure below. All figures must be included and drawn straight. (Solve the deflection in terms of El, these two values of E and I are not given in the problem.) P, P2 1.0m B 3.0m 1.0m A 5.0m P2 N 976 676