Solution to Problem 639 | Deflection of Cantilever Beams

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Problem 639
The downward distributed load and an upward concentrated force act on the cantilever beam in Fig. P-639. Find the amount the free end deflects upward or downward if E = 1.5 × 106 psi and I = 60 in4.
 

Cantilever beam with uniform downward load and concentrated upward load

 

Solution 639

 

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Re: Solution to Problem 639 | Deflection of Cantilever Beams

The 123 is a conversion from ft3 to in3. The product "area of moment diagram × distance" has unit of lb·ft3. Take for example the triangular area in the moment diagram.

(1/2)(6 ft)(5400 lb·ft)(6 ft) = 97 200 lb·ft3

We need to convert it into lb·in3 to make it consistent with the unit of E which is psi (or lb/in2) and unit of I which is in4.

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