Problem: The rigid bar DEC is welded at point C to the rolled-steel beam AB (E = 29 x 106 psi). For the loading shown, determine:
a) the slope at point A
b) the deflection at point C
Solution: Here's the free body with the 4 kip force at D moved to C and an appropriate moment shown as a result. If you look at the original free body (before moving the force), you will see that the forces and reactions are symmetrically located, so that the reactions are equal (4 kip each). Or you can do a sum of the moments and a sum of the forces and compute the reactions.
The slope is unknown at all points on the beam, so I integrate again...
At x = 0, y = 0, so C2 = 0. At x = 6, y = 0, so
Now I can find the slope and deflection at the points requested:
1 This is a variation on problem 9.44 in Beer & Johnston's Mechanics of Materials, 2nd Edition.