20 | Elasticity

At the end of this section you should be able to:

Use singularity function (Macaulay bracket) to create internal moment equation
Use double-integral method to find slope and deflection across span of beam
Find the slope and deflection of a statically-determinate or indeterminate beam at an arbitrary location
Find location and value of maximum deflection and slope

Statically Determinate Beams

Hibbeler 9e 12.32: Deflection in bearing-bearing shaft

Hibbeler 9e 12.42: Deflection in pin-roller beam with distributed load

Hibbeler 9e 12.74: Finding maximum deflection in beam

Statically Indeterminate Beams

Hibbeler 9e 12.101: Deflection in pin-roller-roller beam

Hibbeler 9e 12.124: Deflection in beam with gap

Hibbeler 9e 12.104: Deflection in cantilever-roller beam

Code

Python Files

Matlab File for Deflection Plots

Mathematica File

Beam Tables

Statically Determinate Beams

Hibbeler 9e 12.32: Deflection in bearing-bearing shaft

Python Solution

Hibbeler 9e 12.42: Deflection in pin-roller beam with distributed load

Python Solution

Hibbeler 9e 12.74: Finding maximum deflection in beam

Python Solution

Statically Indeterminate Beams

Hibbeler 9e 12.101: Deflection in pin-roller-roller beam

Wolfram Alpha solution

Python Solution

Hibbeler 9e 12.124: Deflection in beam with gap

Wolfram Alpha solution

Python Solution

Hibbeler 9e 12.104: Deflection in cantilever-roller beam

Wolfram Alpha solution

Python Solution

Code

Python Files

Google Drive

Matlab File for Deflection Plots

Mathematica File

Beam Tables

An alternative to deriving the elastic equation for every beam, beam tables can be used to reference the general formula for different scenarios. For more complicated loading or boundary conditions, equations can be superimposed to match the situation.