Determining average normal strain and average normal shear s

Determining average normal strain and average normal shear strain:

To determine the average normal strain and average shear strain in a known material based on a given load and geometry.

A flat plate ABCD distorts into the dashed shape AB\'C\'D shown after a load is applied with a = 121.0 mm , b = 55.0 mm , g = 8.0 mm , f = 20.0 mm , and e = 15.0 mm .

A) Determine the average normal strain (AC)avg along AC after the load has been applied.

B) Determine the average shear strain xy at A relative to the x and y axes.

C) Determine the average shear strain xy at point C relative to the x and y axes after deformation.

Solution

A) length of AC before alongation = (121^2+55^2)=132.91mm

Change in length along AC = (20^2+15^2) = 25 mm

Normal strain = {25}÷{132.91} = 0.188

B)shear strain at A = g÷ a = {8}÷{121} = 0.066

C) shear stress at c is same as shear stress at d . Reason is tan angle is same for c and d ={f}÷{a+e} =20÷235 =0.085