Question #115086

A series connected composite member ABCD consists of a brass rod BC, 50mm in diameter and 200mm long, to the ends of which are concentrically welded steel rods of 20mm diameter and 100mm in length. The member is supported at A and D as shown in figure 4. When an axially aligned force is applied at D in the positive x direction, point D moves 0.15mm. (i) The axial movement of points B and C (ii) The axial stress in each part of the composite member

Expert's answer

As per the given question,

For the section BC,

The diameter of the brass "=50mm"

Length =200mm

For the section AB and CD,

diameter =20mm

and length =100mm

force is applied at D, then elongation in the total length

"\\Delta l=0.15mm"

"\\Delta l=2\\Delta l_1+\\Delta l_2"

"\\Rightarrow 0.15 mm =2\\Delta l_1+\\Delta l_2"

We know that,

"Y=\\dfrac{Fl}{A\\Delta l}"

"\\Delta l=\\dfrac{Fl}{AY}"

Now, substituting the values,

"0.15mm=\\dfrac{F\\times 200mm}{\\pi 25^2Y}+2\\times \\dfrac{F\\times 100mm}{\\pi 10^2Y}"

the diagram mentioning in the question is not available, so situation and values are not clear.

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