A thin-walled pipe system is shown in Fig. P. 14.35...

A thin-walled pipe system is shown in Fig. P. 14.35 supporting a force $P$. If $P$ is 5000 lb , what should the thickness $t$ be for a tensile yield stress of 50,000 pai and a safety factor of 17 Use the octahedral shear criterion. Do not consider weight of the pipe. Figure P. 14.35 .

Key Concepts

Stress Analysis in Pipe Structures

In the context of pipe structures under load, stress analysis involves determining how an applied force is distributed within the geometry of the pipe. This includes converting applied loads into stresses using the geometry of the thin-walled section, ensuring that the design remains within the allowable stress limits dictated by the material properties and safety considerations.

Octahedral Shear Criterion

The octahedral shear criterion is a yield theory used for ductile materials, which posits that yielding begins when the octahedral (or shear) stress reaches a critical value. This criterion provides a method for combining the effects of the three principal stresses into a single scalar measure, enabling a more comprehensive evaluation of complex, multi-axial stress states.

Thin-Walled Structure Assumption

This concept assumes that the wall thickness of a structure, such as a pipe, is small compared to its other dimensions, which allows for the assumption of uniform stress distribution across the thickness. This simplification makes the stress analysis more straightforward by neglecting any through-thickness gradients, which is common in preliminary design calculations for hollow circular sections.

Tensile Yield Stress

Tensile yield stress is the maximum tensile stress a material can withstand before it begins to deform plastically. It sets the fundamental limit for design, as any applied stress must be kept below this value (usually divided by a safety factor) to prevent permanent deformation or failure of the material.

Safety Factor

The safety factor is a design guideline that introduces a margin of error by dividing the material's yield strength by a prescribed value. This ensures that the operating stresses remain well below the yield limit, accounting for uncertainties in loading, material properties, and potential imperfections in the system.

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