Calculate the support reactions in the continuous beam ABC due to loading as shown in Fig.1.1 Assume EI to be constant throughout.
Select two reactions vise, at B(R1 ) and C(R2 ) as redundant, since the given beam is statically indeterminate to second degree. In this case the primary structure is a cantilever beam AC. The primary structure with a given loading is shown in Fig. 1.2
In the present case, the deflections (? L)1 and (? L) 2 of the released structure at B and C can be readily calculated by moment-area method. Thus
(? L) 1 = ? 819.16 / EI
(? L) 2 = ? 2311.875/ EI (1)
For the present problem the flexibility matrix is,
a11= 125/3EI ,a21= 625/6EI
a12= 625/6EI , a22 = 1000/3EI (2)
In the actual problem the displacements at B and Care zero. Thus the
compatibility conditions for the problem may be written as, a11 R1+ a12 R2 + (? L) 1 = 0
a21 R1+ a22 R2+ (? L) 2 = 0(3)
Substituting the value of E and I in the above equation,
R1 = 10.609 KN and R2 = 3.620 KN
Using equations of static equilibrium, R3 = 0.771 KN m and R4 = ?0.755KN m
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