Hydraulic Ram and Compound Cylinder Analysis

Stress Analysis of Hydraulic Ram

The cylinder of a hydraulic ram has 200 mm inner diameter and 50 mm thickness (Fig.Q1). When the fluid pressure inside the cylinder is 12 MN/m2,

a. Find the general expressions for radial and hoop stress.

b. Find the maximum and minimum hoop stresses in the material.

c. Find the radial and hoop stress at a point in the barrel 22 mm from the inner surface.

d. Show by means of a diagram how both hoop and radial stress vary over the thickness.

Figure Q2 shows a pin jointed frame arrangement. The Young’s modulus for each element is E=200 kN/mm2, the cross-sectional area of the inclined member is 5000 mm2, while the cross-sectional area of the horizontal member is 18000 mm2. A load of 500 kN is applied at node 2 in vertical direction.

Determine the global stiffness matrix for each member.

Determine the global finite element equation for the whole structure.

Identify all known boundary conditions for force and displacement.

Find the horizontal and vertical displacement of node 2.

A compound cylinder of 220 mm external diameter and 160 mm internal diameter is made by shrinking one tube onto another. After cooling, a radial stress of 20 MPa is produced at the common surface which is of diameter 190 mm. Calculate:

i. The shrinkage hoop stresses at the inner and outer diameters of inner cylinder.

ii. The shrinkage hoop stresses at the inner and outer diameters of outer cylinder.

iii. The shrinkage allowance.