Question

A hollow right circular cylinder is made of cast iron and has an outside diameter of 75 mm and an inside diameter of 60 mm. If the cylinder is loaded by an axial compressive force of 50 KN, determine the total shortening (in mm) in a 600-mm length. Take the modulus of elasticity to be 100 GPa and neglect any possibility of lateral buckling of the cylinder.

show the solution

Answer 1

the stress of cylinder is given by the hooke's law

where is a normal stress ( F is the axial force acting on the cylinder,and A is the cross-sectional area of the cylinder), E is the modulus of elasticity, and

is the strain of the cylinder.

the cross sectional area of the cylinder is given by

where, Do = outer circle diameter, Di = inner circle diameter

normal stress of the cylinder ,

=

= 31 Mpa

the strain of the cylinder,

i.e,

therefore the answer is 0.19 mm