334 Methods For Analysis Of Statically Indeterminate Systems

For a statically indeterminate structure, equations of equilibrium alone are not sufficient to permit analysis (see Art. 3.28). For such systems, additional equations must be derived from requirements ensuring compatibility of deformations. The relationship between stress and strain affects compatibility requirements. In Arts. 3.35 to 3.39, linear elastic behavior is assumed; i.e., in all cases stress is assumed to be directly proportional to strain.

There are two basic approaches for analyzing statically indeterminate structures, force methods and displacement methods. In the force methods, forces are chosen as redundants to satisfy equilibrium. They are determined from compatibility conditions (see Art. 3.35). In the displacement methods, displacements are chosen as redundants to ensure geometric compatibility. They are also determined from equilibrium equations (see Art. 3.36). In both

FIGURE 3.73 Deflection calculations for a simple beam by unit load method. (a) Uniformly loaded beam. (b) Bending-moment diagram for the uniform load. (c) Unit load at midspan. (d) Bending-moment diagram for the unit load.

FIGURE 3.73 Deflection calculations for a simple beam by unit load method. (a) Uniformly loaded beam. (b) Bending-moment diagram for the uniform load. (c) Unit load at midspan. (d) Bending-moment diagram for the unit load.

methods, once the unknown redundants are determined, the structure can be analyzed by statics.

3.35 FORCE METHOD (METHOD OF CONSISTENT DEFLECTIONS)

For analysis of a statically indeterminate structure by the force method, the degree of indeterminacy (number of redundants) n should first be determined (see Art. 3.28). Next, the

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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