where E is the modulus of elasticity, or Young's modulus.

If a steel bar is stretched, the width of the bar will be reduced to account for the increase in length (Fig. 3.14a). Thus the normal strain in the x direction is accompanied by lateral strains of opposite sign. If ex is a tensile strain, for example, the lateral strains in the y and z directions are contractions. These strains are related to the normal strain and, in turn, to the normal stress by fx

where v is a constant called Poisson's ratio.

If an element is subjected to the action of simultaneous normal stresses /x, /y, and fz uniformly distributed over its sides, the corresponding strains in the three directions are

FIGURE 3.14 (a) Normal deformation. (b) Shear deformation.

FIGURE 3.14 (a) Normal deformation. (b) Shear deformation.

Similarly, shear strain y is linearly proportional to shear stress v

where the constant G is the shear modulus of elasticity, or modulus of rigidity. For an isotropic material such as steel, G is directly proportional to E:

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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