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.
