Question

(20) The square beam AB, of length, L, and helght, h, in Fig. P3 is made of steel with an elastic modulus of E. Beam AB has an area moment of inertia, 1. A distributed load, w, is applied along the entire length. Note: The length is very large compared to the cross-sectional dimensions of the beam. Thus, assume bending loadings dominate Logically walk through the steps as requested in parts at that would be used to determine the reaction force at the pin B (F) in terms of E, I. L and w using Castigliano's Theorem. Use the given reference frame. a. In the box provided next to Fig. P3, draw an FBD for the entire beam. Show only nonzero reactions b. This structure is (Circle the correct answer.) 1. statically determinate statically indeterminate c. On Fig. P3. clearly show where cut(s) should be made to find the internal moments, e.g. Mix), and any other internal forces that are required to keep the beam in equilibrium when cut. d. On the facing page, draw the respective FBD for each cut needed to find the contributions to the STAR equation, and specify the limits for each cut. e. Write the boundary condition that will be the basis for determining F. 1. Derive the associated M(x) equations and any other equations and their derivatives that would be substituted into the STAR equation. 9. Circle the option that would be used to determine the rotation at B (Co): Add a dummy vertical force at B (Fs) and solve for au - il Use the reaction force Fs and solve for au Add a dummy moment at B (Ms) and solve for as WL w Nm)

please do all the parts clearly and accurately

Answer 1

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Date Page tx f 2اميه 8. fyou 1 %wt xt х (Sf) zul won BM) XX 3w1.X- willin 8 (B,M) z wln - wx2 o to I limits at B 9 Do = dos tu add a dunny moment & solce 24 - JM

Date Page No By om wet 3 wl 8 using eq 0 - ܨܘ وميا Ay: sul M + 3 wl. la wez using eq. 16 wp2 z w12 M A we fi- 3] - we (4-3 w12 8 A @ free body diagram A will الس ومم 11 Static indeterminacy Re- 3 It is statically indeterminate structure - 4-3= 1