20.6 : 材料弯曲：解决问题

Consider two metallic pipes having an inner radii of 1.5 cm and 1 cm, respectively, and an outer radii of 1.8 cm. If both pipes can withstand a maximum stress of 100 megapascals, then what will be the ratio of the maximum value of the couple that can be applied to each pipe?

Here, the moment of inertia of the pipe is proportional to the difference between the outer radius raised to the fourth power and the inner radius raised to the fourth power. The moment of inertia for each pipe is calculated by substituting the given radii.

The required maximum allowed couple moment is related to the maximum allowed stress via the moment of inertia and the perpendicular distance between the outmost element of the pipe to the neutral axis, which is the outer radii for each pipe.

Substituting the known values, the maximum allowed couple for each pipe can be calculated.

Dividing the maximum couple moments for each pipe gives the required ratio.