A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0 X 105 N is applied to each of the four sides, parallel to the side. (b) Find the displacement x in centimeters.
Solution 36E Shear modulus (S) for the square steel plate is the ratio of shear stress to shear strain . S = shear stre=s F IA shear strain x/h where,Shear stress is the force acting tangent to the surface divided by the area A on which it acts; shear strain is the ratio of the displacement x to the transverse dimension h. Step 1 of 2: 5 Now, The area on which the force(9 × 10 N ) is acting tangent to the surface is A= 2 (0.100 × 0.5 × 10 ) m , h= 0.1 m Shear strain = FI/A S = 7.5 × 10 Pa for steel S FI = AS (9×10 ) = ( (0.100×0.5×10 )×(7.5×10)) Shear strain = 2.4× 10 2