## 344

FIGURE 3.48 Shears, moments, and deformations for load at midspan of a fixed-end beam.

FIGURE 3.49 Diagrams for concentrated load on a fixed-end beam.

• The shear at a section is the algebraic sum of all forces on either side of the section.

• The bending moment at a section is the algebraic sum of the moments about the section of all forces and applied moments on either side of the section.

• A maximum bending moment occurs where the shear or slope of the bending-moment diagram is zero.

• Bending moment is zero where the slope of the elastic curve is at maximum or minimum.

• Where there is no distributed load along a span, the shear diagram is a horizontal line. (Shear is a constant, which may be zero.)

• The shear diagram changes sharply at the point of application of a concentrated load.

• The differences between the bending moments at two sections of a beam equals the area under the shear diagram between the two sections.

• The difference between the shears at two sections of a beam equals the area under the distributed load diagram between those sections.

## 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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