Question

An aluminum sphere 20 mm in diameter, is pressed with a load of 300 N against a hard-plastic sphere 40 mm in diameter. The elastic modulus of aluminum is 69 GPa and that of the plastic is 82 GPa. The Poisson’s ratios for aluminum and plastic are respectively 0.33 and 0.206; Determine

A) The contact circle diameter, B) Maximum contact pressure, C) Maximum shear stress in the wheel using stress curves for contacting spheres

Answer #1

**ANSWER:--**

**SHEAR STRESS:---Shear Stress. Shear Stress (t) is a
measure of the force of friction from a fluid acting on a body in
the path of that fluid.**

Two spheres are pressed together with a force of 800 N. Each
sphere is 25.4 mm in diameter and made of a material having a
Young’s modulus of 220 MN/M^2, and a Poisson’s ratio of 0.275.
Determine: Contact area dimensions, maximum pressure, and principal
stresses.

Hertzian Contact streess
A ball and socket joint used at the end of an automotive rocker
arm has a hardened steel spherical surface 20 mm in diameter
fitting in a hard–bronze alloy spherical seat 20.2 mm in diameter.
Determine the maximum contact stress resulting from a load of 2,000
N.
The hardened steel rocker arm material properties:
Poisson’s ratio ?steel = 0.3, modulus of elasticity Esteel = 207
GPa
The hard–bronze alloy spherical seat material properties:
Poisson’s ratio ?bronze =...

A hollow circular steel column 2m long and outer diameter 200
mm carries an axial load of 325 kN. If the compressive stress is
150 MPa, lateral strain for external diameter is is 0.000325 and
Poisson’s ratio is 0.3, find the minimum wall thickness required
for the column. Also calculate the shear modulus for the material
of the column. Take E = 210 GPa.

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