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
Statically Determinate Beams
Hibbeler 9e 12.32: Deflection in bearing-bearing shaft
Hibbeler 9e 12.32: Deflection in bearing-bearing shaft
Hibbeler 9e 12.42: Deflection in pin-roller beam with distributed load
Hibbeler 9e 12.42: Deflection in pin-roller beam with distributed load
Hibbeler 9e 12.74: Finding maximum deflection in beam
Hibbeler 9e 12.74: Finding maximum deflection in beam
Statically Indeterminate Beams
Statically Indeterminate Beams
Hibbeler 9e 12.101: Deflection in pin-roller-roller beam
Hibbeler 9e 12.101: Deflection in pin-roller-roller beam
Hibbeler 9e 12.124: Deflection in beam with gap
Hibbeler 9e 12.124: Deflection in beam with gap
Hibbeler 9e 12.104: Deflection in cantilever-roller beam
Hibbeler 9e 12.104: Deflection in cantilever-roller beam
Code
Code
Python Files
Python Files
Matlab File for Deflection Plots
Matlab File for Deflection Plots
Mathematica File
Mathematica File
Beam Tables
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.