The deflection(? L 1 )and(? L 2 )of the released structure can be evaluated from unit load method. The positive directions of the selected redundant are shown in Fig.8.3b. Let ( L ) be the transverse deflection at1 B and( L 2 bethe slope at B due to external loading. Now, calculate deflection at B duetoonly applied loading.
The R1 is assumed to positive in the upward direction and R2 is assumed to be positive in the counterclockwise direction. The primary structure in this case is acantilever beam which could be obtained by releasing the redundant R1 andR2. Select vertical reaction (R1)and the support moment(R2) at B as the redundant. Draw Shear force and bending moment diagrams by force method.įig 1.3 Fixed Beam with R1 and R2 as Redundant Using equations of static equilibrium, R3 = 0.771 KN m and R4 = ?0.755 KN mĪ Fixed beam AB of constant flexural rigidity is shown in Fig.1.3 The beam is subjected to auniform distributed load of w moment M= wL 2 kN.m. Substituting the value of E and I in the above equation, Thus theĬompatibility conditions for the problem may be written as, a11 R1+ a12 R2 + (? L) 1 = 0 In the actual problem the displacements at B and Care zero. Thusįor the present problem the flexibility matrix is,
In the pre sent case, the deflections (? L)1 and (? L) 2 of the released structure at B and C can be readily calculated by moment-area method. The primary structure with a given loading is shown in Fig.
In this case the primary structure is a cantilever beam AC. Select two reactions vise, at B(R1 ) and C(R2 ) as redundant, since the given beam is statically indeterminate to second degree. Calculate the support reactions in the continuous beam ABC due to loading as shown in Fig.1.1 Assume EI to be constant throughout.
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