20.6:
Bending of Material: Problem Solving
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.
20.6:
Bending of Material: Problem Solving
In this lesson, determine the ratio of the maximum bending moments applied to two metal pipes, given that both pipes can withstand a maximum stress of 100 MPa. Both pipes have an outer radius of 1.8 cm. Pipe A has an inner radius of 1.5 cm, and Pipe B has an inner radius of 1 cm. The ratio of the maximum bending moment applied to two metallic pipes, each with a different inner and outer radius, is determined by considering their dimensions. The inner radius of the first pipe is 1.5 cm, and for the second pipe, it is 1 cm.
The moment of inertia is given by the following equation. Using these values, calculate the moment of inertia for each pipe.
The maximum allowable bending moment for each pipe directly relates to the maximum stress, the moment of inertia, and the outer radius, which serves as the distance from the neutral axis to the extreme outer fiber of the pipe, as shown in the following equation:
Then, the maximum bending moment for each pipe will be determined using these calculated values. Finally, the ratio of these maximum bending moments for the two pipes is calculated. This ratio indicates each pipe's comparative torsional strength and resilience under maximum permissible stress. It also highlights the effect of the pipe's wall thickness on the maximum bending moment in this situation.