Sample Solution from
Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Chapter 1
Problem 59RP
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Textbook Problem

In the marine crane shown, link CD is known to have a uniform cross section of 50 × 150 mm. For the loading shown, determine the normal stress in the central portion of that link.

Fig. P1.59

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Expert Solution
To determine

The normal stress in the centre portion of the link.

Answer

The normal stress in the centre portion of the link is 195.3MPa_

Explanation of Solution

Given information:

The uniform cross section is (50×150)mm.

Calculation:

Sketch the free body diagram of ABC as shown in Figure 1.

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Here, W is the weight of the loading.

Find the weight of the loading as follows:

W=mg (1)

Here, m is the mass of the loading and g is the acceleration due to gravity.

Substitute 80Mg for m and 9.81m/s2 in Equation (1).

W=80×9.81=784.8kN

Taking moment about A,

FCD×15W×28=015FCD28W=0FCD=2815W (2)

Substitute 784.8kN for W in Equation (2).

FCD=2815(784.8kN)=1,464.96=1,465kN

Find the area of the cross section using the relation:

A=bd (3)

Here, b is the width of the cross section and d is the depth of the cross section.

Substitute 50mm for b and 150mm for d in Equation (3).

A=50×150=7,500mm2(1m103mm)2=7.5×103m2

Determine the normal stress in the central portion of the link as follows:

σCD=FCDA (4)

Here, A is the area of the cross section and FCD is force in member CD.

Substitute 7.5×103m2 for A and 1,465kN for FCD in Equation (4).

σCD=1,4657.5×103=195.3×106Pa=195.3×106Pa×1Mpa106Pa=195.3Mpa

Thus, the normal stress in the centre portion of the link is 195.3MPa_.

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