A cast iron pipe of external diameter 300 mm has walls 10 mm thick and is required to carry water to a maximum of half its internal depth. If the failure stress in tension of cast iron is $138 N / mm ^{2}$ calculate the maximum allowable simply supported span the pipe can have. Take the density of cast iron as $72.3 kN / m ^{3}$ and ignore the negligibly small shear stresses.
Ans. 27.0 m.

Question

A cast iron pipe of external diameter 300 mm has walls 10 mm thick and is required to carry water to a maximum of half its internal depth. If the failure stress in tension of cast iron is [latex]138 N / mm ^{2}[/latex] calculate the maximum allowable simply supported span the pipe can have. Take the density of cast iron as [latex]72.3 kN / m ^{3}[/latex] and ignore the negligibly small shear stresses.
Ans. 27.0 m.

Accepted Answer

The cross sectional area of the pipe is

[latex]A=\pi\left(300^{2}-280^{2} ight) / 4=9110.6 mm ^{2}[/latex]

and its weight/m length is

[latex] ext { weight } / m =72.3 imes 9110.6 imes 1 / 10^{6}=0.66 kN[/latex]

The volume of water in 1 m length of pipe is

[latex]vol / m =\frac{\pi imes 280^{2} imes 1}{2 imes 4 imes 10^{6}}=0.03 m ^{3}[/latex]

So that the weight/m of water in the pipe is

[latex] ext { weight } / m =0.03 imes 100^{3}=20 kg =0.29 kN[/latex]

The pipe therefore carries a uniformly distributed load of 0.66 + 0.29 = 0.95 kN/m.
The maximum bending moment occurs at the mid-span of the pipe and is

[latex] ext { B.M }_{\max }=\frac{0.95 imes L^{2}}{8}=0.12 L^{2} kNm[/latex] (L is in m)

The direct tensile stress due to bending is given by Eq. (9.9)

[latex]\sigma_{x}=-\frac{M y}{I}[/latex] (9.9)

and is

[latex]\sigma=-\frac{0.12 L^{2} imes 10^{6} imes(-150)}{\pi\left(300^{4}-280^{4} ight) / 64}=0.19 L^{2} N / mm ^{2}[/latex]

This stress is the major principal stress, [latex]\sigma_{I}[/latex], so that Eq. (14.57) applies.

[latex]\sigma_{ I }=\sigma_{ Y } \quad( ext { tension })[/latex] (14.57)

Then

[latex]0.19 L^{2}=138[/latex]

from which
L = 27.0 m

Question 14.P.26: A cast iron pipe of external diameter 300 mm has walls 10 mm...

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