Solve Prob. 7–18 using the conjugate-beam method.

Data from Prob. 7–18

Determine the slope at D and the displacement at the end A of the beam. EI is constant. Use the moment-area theorems.

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7.5 CONJUGATE-BEAM METHOD The conjugate-beam method was formulated by H. Müller-Breslau. Essentially, it requires the same amount of calculation as the moment-area theorems to determine a beam's slope or deflection; however, this method relies only on the principles of statics, and hence its application will be more familiar. The basis for the method comes from the similarity of Eq. 4-1 (dv/dx = w) and Eq. 4-2 (dM/dx = V) to Eq. 7-2 and Eq. 7-4. To show this, we can write these equations as follows: Or after integrating, V 1 dV dx do dx = fw dx 0 = = W = M = [(21) d ΕΙ dx M ΕΙ d²M dx² d²v I dx² M = = W V= = = /[[wax]dx M ΕΙ [[/(M) dx] ΕΙ dx