Mechanics of Materials Solved Problems

Stress

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1.1 - Determine the normal stress in the member under tension.

Mechanics of Materials Stress Solved Example Problem

Solution

1.2 - Determine the normal stress in this hollow circular member in tension.

Solution

1.3 - This member of varying cross sectional area is in tension. Determine the normal stress in each region.

Solution

1.4 - The bolt passes through a drilled hole in two plates, which are subjected to equal and opposite applied forces. Determine the average shearing stress in the bolt.

Mechanics of Materials Single Shear Stress Solved Example Problem

Solution

1.5 - The pin connection shown creates double shear in the pin, reducing the average shearing stress compared to a single shear connection. Determine the average shearing stress in the pin.

Mechanics of Materials Double Shear Stress Solved Example Problem

Solution

1.6 - 14kN is applied to the rod. Determine the bearing stress on the block.

Mechanics of Materials Bearing Stress Solved Example Problem

Solution

1.7 - The rod is in single shear. Determine the maximum allowable load that can be applied.

Solution

1.8 - The aluminum members are joined with epoxy on their overlapping surfaces. Determine the maximum allowable load that can be applied with a factor of safety of 3.3.

Mechanics of Materials Allowable Load Solved Example Problem 1

Mechanics of Materials Allowable Load Solved Example Problem 2

Mechanics of Materials Allowable Load Solved Example Problem 3

Solution

Strain

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2.1 - The aluminum rod is fixed to a wall and subjected to an axial load. Determine the displacement of the free end of the rod, and also calculate the strain in the member.

Mechanics of Materials Strain Displacement Solved Example Problem

Solution

2.2 - A steel member with varying cross sectional area is fixed to a wall and subjected to an axial load. Determine the displacement of the free end of the member.

Solution

2.3 - A rigid bar is supported by a steel cable of diameter 6mm and subjected to a downward load. Determine the elongation of the cable.

Solution

2.4 - A rigid bar is suspended by two steel members and subjected to load P. Determine the deflection of point E.

Solution

2.5 - A composite member with a rigid end cap is subjected to an axial load P. Determine the total displacement, and the stress in each material. Each section is of equal width (10mm).

Solution

2.6 - The member below is statically indeterminate. Use the method of superposition to find the reaction forces.

Mechanics of Materials Statically Indeterminate Strain Solved Example Problem

Solution

2.7 - The aluminum member is 2.5m long at 20°C. Determine the elongation (thermal expansion or contraction) of the member when its temperature is 45°C, and also -45°C.

Mechanics of Materials Thermal Strain Solved Example Problem

Solution

2.8 - The steel member is confined to a length of 4m at which is unstressed. Use the method of superposition to determine the axial stress that develops when its temperature rises by 60°C.

Solution

2.9 - There is initially a 0.5mm gap between the aluminum member and the wall. Determine the internal axial stress in the member after its temperature increases by 90°C.

Mechanics of Materials Thermal Expansion Solved Example Problem

Solution

2.10 - A slender member is measured to have the following deflections when in subjected to the tensile load. Use this information to determine Poisson's ratio, and modulus of elasticity of the material.

Mechanics of Materials Poisson's Ratio Solved Example Problem

Solution

Torsion

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3.1 - Determine the angle of twist of the free end of the solid steel rod when a 2kNm torque is applied.

Solution

3.2 - Determine the angle of twist of the free end of the hollow steel rod when a 1.1kNm torque is applied.

Solution

3.3 - The solid steel shaft has two distinct sections with different diameters. Determine the angle of twist of the free end when a 100Nm torque is applied.

Solution

3.4 - Determine the maximum shearing strain and maximum shearing stress that develop in the solid solid steel rod when a 2kNm torque is applied.

Solution

3.5 - Determine the maximum shearing strain & shearing stress and minimum shearing strain & stress that develop in the hollow solid steel rod when a 6kNm torque is applied.

Solution

3.6 - Determine the minimum diameter of the solid steel rod so that the allowable shear stress is not exceeded when a 4kNm torque is applied.

Solution

3.7 - Determine the maximum torque that can be applied to the hollow steel rod.

Solution

3.8 - Determine the minimum thickness of the hollow steel shaft so that the allowable shear stress will not be exceeded when a 6.8kNm torque is applied.

Solution

Pure Bending

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4.1 - Determine the moment of inertia, maximum allowable moment, and radius of curvature for this rectangular beam in pure bending.

Solution

4.2 - The beam from the previous problem is rotated 90°. Determine the new moment of inertia, maximum allowable moment, and radius of curvature and compare it to the previous problem.

Solution

4.3 - Determine the moment of inertia, maximum allowable moment, and radius of curvature for this wide flange beam in pure bending.

Solution

4.4 - Determine the moment of inertia, maximum allowable moment, and radius of curvature for this T-beam in pure bending.

Solution

4.5 - Determine the moment of inertia, maximum allowable moment, and radius of curvature for this C-channel beam in pure bending.

Solution

Pure Bending of Composite Materials

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5.1 - Determine the maximum stress that develops in each material of this composite member in pure bending when a 2.1kNm moment is applied.

Solution

5.2 - Determine the maximum stress that develops in each material of this composite member in pure bending when a 1.8kNm moment is applied.

Solution

5.3 - Determine the maximum stress that develops in each material of this reinforced concrete beam in pure bending when a 25kNm moment is applied.

Solution

Energy Methods

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