A carbon steel ball with 27-mm diameter is pressed together with an aluminum ball with a 35-mm diameter by a force of 11 N.Determine the maximum shear stress and the depth at which it will occur for the aluminum ball. Assume the figure given below, whichis based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for thesematerials.Ratio of stress to Pmaσ. T1.00.80.60.40.20J₂, J₂0.5aσ₂Tmaxa2aDistance from contact surface1.5a2.5a3aThe maximum shear stress is determined to be 134.6ZMPa.The depth in the aluminum ball at which the maximum shear stress will occur is determined to be 0.0519 mm.

Carbon Diameter, dc = 27 mmAluminium Diameter, dA = 35 mmForce, F =11 NPoissons Ratio, 0.3…

A carbon steel ball with 27-mm diameter is pressed together with an aluminum ba Determine the maximum shear stress and the depth at which it will occur for the a is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at materials. σ. T 1.0

A carbon steel ball with 27-mm diameter is pressed together with an aluminum ba Determine the maximum shear stress and the depth at which it will occur for the a is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at materials. σ. T 1.0

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.2.4P: Solve the preceding problem if the internal pressure is 3,85 MPa, the diameter is 20 m, the yield...

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A carbon steel ball with 27-mm diameter is pressed together with an aluminum ball with a 35-mm diameter by a force of 11 N.
Determine the maximum shear stress and the depth at which it will occur for the aluminum ball. Assume the figure given below, which
is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these
materials.
Ratio of stress to Pma
σ. T
1.0
0.8
0.6
0.4
0.2
0
J₂, J₂
0.5a
σ₂
Tmax
a
2a
Distance from contact surface
1.5a
2.5a
3a
The maximum shear stress is determined to be 134.6
Z
MPa.
The depth in the aluminum ball at which the maximum shear stress will occur is determined to be 0.0519 mm.

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