A steel pipe of 12 -in. outer diameter is fabricated from (1)/(4) -in.-thick plate by welding al

step 1 In this question we have to determine the largest torque that can be applied to the pipe. So her

A steel pipe of 12 -in. outer diameter is fabricated from...

A steel pipe of 12 -in. outer diameter is fabricated from $\frac{1}{4}$ -in.-thick plate by welding along a helix that forms an angle of $45^{\circ}$ with a plane parallel to the axis of the pipe. Knowing that the maximum allowable tensile stress in the weld is 12 ksi, determine the largest torque that can be applied to the pipe.

Key Concepts

Allowable Tensile Stress

Allowable tensile stress is a design parameter that represents the maximum stress a material or weld can safely withstand before failure occurs. It is a critical concept in structural design, ensuring that the components operate well within safe limits. In welded joints, particularly in applications where complex loading is present, the allowable tensile stress serves as a benchmark against which calculated stresses must be compared to ensure the integrity and reliability of the structure.

Helical Weld Geometry

This concept involves understanding how a weld can follow a helical (spiral) path around a cylindrical object. The geometry of a helix means that the weld is inclined relative to both the axis and the circumference of the pipe. Analyzing a helical weld requires decomposing the effects of load along the axis of the pipe and around its circumference, which in turn affects the distribution of stresses along the weld’s length.

Stress Analysis in Welded Joints

This concept includes evaluating the stress distribution in a weld when it is subjected to forces, especially under complex loading conditions such as tension, compression, and torsion. Key to this analysis is determining how applied loads convert into stresses along the weld, ensuring that the stress does not exceed the material's maximum allowable limit. Understanding the transformation of forces because of the weld’s orientation is essential for designing safe and effective welded connections.

Torque Transmission in Cylindrical Structures

Torque transmission in cylindrical structures, such as pipes, involves the application of a twisting force that generates shear stresses within the material. When a weld constructed along a helical path is used, the relationship between the applied torque and the induced tensile or shear stresses must be carefully analyzed. The geometry of the weld, including its inclination, directly influences its capacity to resist the applied torque while keeping stresses within allowable limits.

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