Ch 4 – Axial Load (part 1 – sections 4.1 and 4.2 only) What is: Stress Strain Deformation Other topics: Thermal stress, statically indeterminate, stress concentrations. Figure: 04-00CO

Elastomer bearing

= 4.1 St. Venant’s Principle: St Venant’s: Figure: 04-01a St Venant’s: Stress profile, sufficiently removed from the local effect of loads will be uniform (i.e. = P/A) Stress and strain produced by statically equivalent load system will be the same.

St. Venant’s Principal: Figure: 04-01-01UN Note, def’m of grid uniform at middle, therefore strain and stress will be uniform.

4.2 Elastic Deformation of an Axial Member: Derive relationship between deformation, d, and Load, P Figure: 04-02a,b

Constant Load and Cross-Sectional Areas Figure: 04-03 Or, for multiple sections:

Example: Multiple sections Example: Multiple sections. Find total deformation of end A with respect to D. Area = 20 mm2. Material is steel w/ E = 200 GPa = 200 x 109 Pa: = 100 mm = 150 mm = 200 mm Figure: 04-05a

First, solve for internal loads: Figure: 04-05b

How would this answer change if aluminum instead of steel???? Figure: 04-05c How would this answer change if aluminum instead of steel????

Book example 4.1: Find dA/D Figure: 04-06aEx4.01

Find dC Figure: 04-07aEx4.02

Figure: 04-07bEx4.02

Statically indeterminate (you will cover this in 320) Problem 4.47 Equilibrium Compatibility