An Introduction to Mechanical Engineering 1st. Edition by Michael Clifford | 9780340939963 | 340939966 | Holooly

Mechanical Engineering

An Introduction to Mechanical Engineering

71 SOLVED PROBLEMS

Question: 3.5

A solid circular shaft of diameter 50 mm and length 1000 mm is subjected to a torque, T. The shaft is made from an elastic–perfectly plastic material with τγ = 100 N/mm², G = 70 GN/m². Determine the magnitude of the torque required to cause yielding to occur at a radius of 15 mm (and greater) and ...

Verified Answer:

Equilibrium (moments about the axis)

T = \i...

Question: 3.6

A stepped circular shaft is built in at both ends; the two shaft segments are the same length, l. If the stepped shaft is made from an elastic–perfectly plastic material with τγ = 100N/mm², find the magnitude of the torque applied at the step to just cause yield in the smaller shaft. ...

Verified Answer:

Stress–strain behaviour Equilibrium

...

Question: 3.8

Shear stresses in a beam The section shown in Figure 3.87 is subjected to a vertical shear force, S = 50 kN, acting down the vertical centre line, i.e. the γ-axis. The second moment of area of the section, about the x-axis, which passes through the centroid of area, G, is Ixx = 2.31 × 10^6 mm^4. G ...

Verified Answer:

In the top flange Consider a position in the top f...

Question: 3.7

A hoist is constructed using two wooden bars (E = 12.4 GPa) as shown in Figure 3.70 and Figure 3.71. The allowable normal stress is 13.8 MPa. Determine the maximum permissible weight W that can be lifted using the hoist for the two cases: (a) L = 1.2 m; (b) L = 1.5 m. ...

Verified Answer:

By inspection, we see that member BC will be in co...

Question: 2.6

A particular coal has a mass analysis of 81% C, 5% H, 5% O, 9% ash. The volumetric analysis of the dry products is: 10% CO2, 1% CO, 8% O2, 81% N2 Determine the minimum air required for complete combustion of 1 kg of coal and the percentage of excess air required to produce the product gas ...

Verified Answer:

In this case it is useful to determine the require...

Question: 3.10

Shrink/interference fit A pair of mild steel cylinders (E = 200 GPa) of equal length have the following dimensions: (1) 40 mm bore and 80.06 mm outside diameter (2) 80 mm bore and 120 mm outside diameter i.e. there is a diametral interference of 0.06 mm. The larger cylinder is heated, placed around ...

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Conditions • After assembly, the radial interferen...

Question: 3.9

Thick cylinder with pistons A cylinder with 50 mm bore and 100 mm OD is subjected to an internal pressure of 400 bar. The end loads are supported by pistons which seal without restraint. Determine the distributions of stress across the cylinder wall. ...

Verified Answer:

p = 400 bar = 400 × 100 kPa = 40 × 1000 kPa = 40 N...

Question: 6.4

Find the steady-state response of each mass in the following two-degrees-offreedom system to a sinusoidal force of amplitude 10 N and frequency 6 Hz applied to the 1 kg mass. ...

Verified Answer:

Using the method presented in Section 6.2, the equ...

Question: 6.3

Use of the frequency response function Find the waveform of the steady-state vertical displacement of a reciprocating air compressor (mass, m = 4000 kg) that operates at a crank speed, Ω, of 300 rev/min. The machine is supported on a set of four resilient mounts that have an overall vertical ...

Verified Answer:

The compressor can be modelled as a rigid mass and...

Question: 5.2

Plot the root locus of a closed-loop system having the following open-loop transfer function:G(s) H(s) = K/(s² + 2s + 2)(s + 2) (5.171) ...

Verified Answer:

This can be expressed as

G(s)H(s) = \frac{K...

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