Statics & Strength of Materials

Topic 4.12b - Problem Assignment 6 - Beam Deflection

The maximum deflection of various beams can be given by specific formulae. The following formulae work only for the specific stated beam configurations.

Beam simply supported at its end points with a point load at its midpoint. Maximum deflection occurs at the mid point and is:

y_max = FL³/(48EI)   

Beam simply supported at its end points with a uniformly distributed load. Total load is W. Maximum deflection occurs at the mid point and is:

y_max = 5FL³/(384EI)

Cantilever beam with a point load at the extreme end. Maximum deflection occurs at the free end and is:

y_max = FL³/(3EI)

Cantilever beam with a uniformly distributed load. Total load is W. Maximum deflection occurs at the free end and is:

y_max = FL³/(8EI)

In all of the above formulae, values are as shown below:

 For steel E = 30x10⁶ psi. and for Douglas fir or yellow pine E = 1.76x10⁶ psi.

1. Determine the deflection of the midpoint of a 14 foot long fir 2"x 10" beam which carries a uniformly distributed load of 75 pounds per foot. (.221")

2. Find the maximum deflection of a 4"x 6" pine cantilever beam 6 feet long that carries a load of 250 pounds per foot. (.552")

3. Find the maximum point load (acting at the end) that can be carried by a 16 foot long steel W14x38 cantilever beam if the beam end is limited to a maximum deflection of 1/4 inch. (3,270 lb)

4. Find the minimum moment of inertia necessary for a 20 foot long, simply supported, steel beam to deflect no more than 1/2 inch when a load of 20 tons is applied at the center of the beam. (768 in⁴)

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