# Braced Cantilever

**Mechanics Corner**

A Journal of Applied Mechanics and Mathematics by DrD, # 32

© Machinery Dynamics Research, LLC, 2015

**Braced Cantilever**

**Introduction**

Anyone who has actually gotten into machine design is familiar with this difficulty. Consider the situation where a project is well advanced, many plans have been made, and it is all based on the assumption of the adequacy of one particular part. When you finally get to the detailed analysis of that part, the calculations show that it is not adequate. What can you do?

To make the problem much more concrete, consider the cantilever beam shown in Figure 1. It supports a weight W at the free end, and when someone finally makes the calculation, the tip deflection, δ, is unacceptably large. The whole system design has been developed on the assumed adequacy of that cantilever, and there is no room to put in a beam with a larger section to give more stiffness. What can be done?

Any of countless machine design texts, mechanics of materials texts, etc., give the formula for the end deflection,

δ=(WL³)/(3EI)

where

E= Young's modulus for the beam material

I= area moment of inertia for the beam cross section

L= length of the beam

W= tip load value

While we can argue that someone should have checked this earlier, finger-pointing does not fix the problem.

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