## A

Figure 7.31B. Concept of secondary momentsâ€”example 2B, compatibility method: (a) two-span continuous beam; (b) equivalent loads; (c) upward deflection Aj due to Wp (d) downward deflection A2 due to a load of 66.15 kips at center span; (e) load Ps corresponding to Aj - A2; (f) secondary moments.

B. (If continuity were established, their magnitudes would have been the same as calculated in the previous example).

In determining the equivalent loads, we have not considered the effect of continuity at support B. Therefore, the beam has a tendency to move away from the support due to the upward-acting equivalent loads. Because the beam, by compatibility requirements, stays attached to support B, another set of reactions is needed to keep the beam in contact with support B. These are the secondary reactions, and the resulting moments are the secondary moments. Of the loads shown in Fig 7.31B(b), only the upward load Wp = 1.225 kip-ft and the downward reaction RB = 66.15 kips influence the vertical deflection at B. The upward deflection of the beam at B due to Wp is given by the standard formula

5wl4

In our case, w = Wp = 1.225 kip-ft, l = 2 x 54 = 108 ft. Therefore, 5 x 1.225 x 1084

384E7 2,170,050 E7

T upward

The downward deflection at B due to reaction RB is given by RL3

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