Remove all external loads on the basic determinate structure and apply an unknown value of redundant force/moment at the release end. Step 4: Deflection due to Unknown Redundant Force/Moment Here determine vertical displacement at C. Any analysis procedure for determinate structure as discussed in Module I may be followed. Step 3: Solution of Basis Determinate StructureĬalculate the magnitude of the displacement at the released end of the basic determinate structure. The basic determinate structure becomes a cantilever beam with concentrated load at mid-spanĪlternatively moment constraint at A may also be taken as Redundant. 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. Force method structural analysis examples software#Some drawbacks of standard software is that it can be inaccessible or expensive.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, This method is hands down the optimal and most common method to evaluate a structure with high precision and low calculation time. Sk圜iv Structural 3D is one such software which allows users to evaluate the effects of point loads, moments and distributed loads on a structure or design ( Sk圜iv S3D Documentation). There are a great number of Structural Analysis Software that can perform the accurate FEA calculations without the difficulty of having to manually set up the complex process. In saying this - FEA is an extremely powerful and accurate method of structural analysis and is the backbone of most Structural Analysis Software. It is common that an FEA model will comprise of matrices thousands of entries - making it pretty much impossible to be evaluated by human calculations. This can be an extremely difficult and time consuming process to set up and run. FEA requires that the structure is broken up into smaller parts (or elements) which can be evaluated individually for a more accurate estimate of the solution. It is a far more complicated, yet accurate method to run structural analysis compared to hand calculations. Finite Element Analysis (FEA) is a complex numerical method used to solve complicated problems which contain a number of variable inputs such as boundary conditions, applied loads and support types.
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