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EXAMPLE 2.11 The compound beam in Fig 2-3la is fixed at A. Determine the reactions at A, B, and C. Assume that the connection at B is a pin and C is a roller 15th Fig, 2-3 62 Free-Body Diagrams. The free-body diagram of each segment is shown in Fig. 2-31B. Why is this problem statically determinate? b- l0 t iS h Equations of Equilibrium. There are six unknowns Applying the six equations of equilibrium, using previously calculated results, we have Segment BC + Mc =0; -6000 + B,(15) = 0 B, =400 lb ARs Ans ARL c, 400 lb Segment AB MA-72.0k.ft Ay-8000 + 400-04,-7.60 k Ani Ant ARs +1xF,-0; 63
This structure is statically determinate because the number of unknown reactions are equal to the number of equilibrium equations.
The solution is already complete because all the unknown reactions Ax, Ay, Ma, Bx,By,Cx and Cy have already been found out.
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