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Concrete Mix Design

Concrete is made from different proportions of cement, fine aggregate (sand), coarse aggregate, and water. Cement usually comes in 94 lb sacks, water is measured by gallons (volume), and coarse and fine aggregate by weight. These are all over the place.

There are two main methods of measuring concrete ingredients, the Absolute Volume Method, and a method using Proportion ratio of components

Absolute Volume

With Absolue Volume the components are measured out using their densities or specific gravities to calculate the volume that each ingredient will use in a given unit of concrete.

V_a = \dfrac{W}{G_s \gamma_{water}}

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Shear and Bending Stresses in Beams

Beams are one of the main design elements a structural engineer will work with. This is a loaded simply supported beam:

For the PE exam, a loaded beam has two main options for failure, shear and bending.

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