Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 8, Problem 8.2.1P

A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.

Expert Solution & Answer
Check Mark
To determine

Maximum permissible pressure in the balloon.

Answer to Problem 8.2.1P

Maximum permissible pressure is pmax=1.442 psi

Explanation of Solution

Given Information:

Outer diameter D=20 in

Thickness t=0.012 in

Tensile stress σ=1 ksi

Shear stress τ=0.3 ksi

We know for inner diameter d=D2t=202×0.012=19.976 in ,

Tensile stress,

  σ=pr2tσ=p×d/22t1000=p×19.976/22×0.012p=2.403 psi

Shear stress,

  τ=pr4tτ=p×d/24t0.3×1000=p×19.976/24×0.012p=1.442 psi

From above we can see that the maximum permissible pressure is pmax=1.442 psi

Conclusion:

Hence we get,

Maximum permissible pressure is pmax=1.442 psi

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Chapter 8 Solutions

Mechanics of Materials (MindTap Course List)

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