![]() ![]() Here vertical reaction C y is the redundant force. Redundant forces/moment should be chosen such that the remaining structure is stable and statically determinate.įor the given propped cantilever beam, the basic determinate structure may be obtained by removing the prop at C (Figure 8.5). This force/moment is called redundant force/moment. Each release is made by removing an external or an internal force/moment. The static indeterminacy of the propped cantilever beam is one.Ī number of releases equal to the degree of indeterminacy is introduced. Step 1: Determine the Degree of Static Indeterminacy The steps involved in method of consistent deformation are as follows, It is an indeterminate structure with degree of static indeterminacy one. Ĭonsider a propped cantilever beam subjected to a concentrated load at its mid-span as shown in Figure 8.4. If δ 1 and δ 2 are the deflection due to P 1 and P 2 respectively, linearity implies, P 1/P 2 = δ 1/ δ 2. If δ 1, δ 2, and δ 3 are the deflection at mid-span respectively due to P 1, P 2, and P 3 when they act separately, principle of superposition states,įor a linear elastic structure, load, P and deflection, δ, are related through stiffness, K, as P = Kδ. For instance, suppose d be the deflection at mid-span of a simply supported beam subjected to three concentrated load P 1, P 2 and P 3 (Figure 8.3a). The second condition implies that the relative rotation at B is zero.įor the rigid frame shown in Figure 8.2, displacement compatibility conditions at B are,įor a linear elastic structure, the deflection caused by two or more loads acting simultaneously is the sum of deflections caused by each load separately. It is the condition which ensures the integrability or continuity of different members or components of a loaded structure while being deformed.įor the continuous beam shown in Figure 8.1, displacement compatibility conditions at B are, ![]()
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