Fig shows a vertical stepped post A, B and C whose upper and lower post are of dia 30mm and 50mm respectively. A vertical load W1 = 12KN is applied at top post and additional load W2 is

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written 6.5 years ago by

teamques10 ★ 69k

• modified 5.4 years ago

uniformly applied around B. Calculate i)The normal stresses at the upper post ii) It is desire that stress in the upper and lower post is the same find W2

strength of materials

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written 6.5 years ago by

teamques10 ★ 69k

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$\sigma_1 =\frac{load}{area} = \frac{W_1}{A_1}\\ \sigma_2 =\frac{W_1 + W_2}{A2}$

$\textit{Case (i)}\hspace{0.05cm} \sigma = ? \hspace{0.05cm}\textit{for upper post}$

$\sigma_1 = \frac{P}{A} = \frac{12 \hspace{0.05cm}\times\hspace{0.05cm} 10^3}{\frac{\pi}{4}\hspace{0.05cm} \times\hspace{0.05cm} 30^2} \\ \hspace{0.25cm}= 16.97 \hspace{0.05cm}N/mm^2$

$\textit{Case (ii) It is given that} \hspace{0.05cm}\sigma_1 = \sigma_2\\ \frac{W1}{A1} = \frac{W1+W2}{A2}\\ 16.97 = \frac{12\hspace{0.05cm}\times\hspace{0.05cm}10^3 + W_2}{\frac{\pi}{4}\hspace{0.05cm}\times\hspace{0.05cm}50^2}\\ W_2 = 21.32\hspace{0.05cm}\times\hspace{0.05cm}10^3\hspace{0.05cm}N$

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