2fi

modulus of elasticity of the material moment of inertia of the beam span fixed-end moment at A fixed-end moment at B

Use of these equations for each member in a structure plus equations for equilibrium at the member connections is adequate for determination of member displacements. These displacements can then be substituted into the equations to determine the end moments.

FIGURE 3.76 Fixed-end moments in beams.

As an example, the beam in Fig. 3.75a will be analyzed by employing the slope-deflection equations [Eqs. (3.135a and b)]. From Fig. 3.76, the fixed-end moments in span AB are

The fixed-end moments in BC are

FIGURE 3.77 (a) Member of a continuous beam. (b) Elastic curve of the member for end moment and displacement of an end.
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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