Determine the required diameter of the pins at A and B to...

Determine the required diameter of the pins at $A$ and $B$ to the nearest $\frac{1}{16}$ in. if the allowable shear stress for the material is $\tau_{\text {allow }}=6 \mathrm{ksi} .$ Pin $A$ is subjected to double shear, whereas pin $B$ is subjected to single shear.

Key Concepts

Dimensional Tolerancing and Rounding

In engineering design, dimensions are often rounded to standard increments, such as the nearest 1/16 inch. This practice ensures that components conform to manufacturing capabilities and maintain consistency in assembly and performance.

Shear Stress

Shear stress is the force per unit area acting parallel to the cross-section of a material. It is a fundamental concept in mechanics of materials used to determine whether a structural component or material will fail under applied loads.

Single Shear vs. Double Shear

In single shear, the loading causes a failure along one plane, whereas in double shear, the load is distributed over two planes. Understanding the difference is critical for properly assessing the stresses and sizing components since the same load divides across more than one shear plane in double shear, reducing the stress per plane.

Allowable Shear Stress

Allowable shear stress is a material property that represents the maximum shear stress a component can sustain safely. In design, it serves as a limit to prevent failure, ensuring that the applied shear force does not exceed a fraction of the material’s inherent strength.

Pin Diameter Calculation

Determining the required pin diameter involves calculating the cross-sectional area necessary to resist the applied shear load while not exceeding the material's allowable shear stress. Once the required area is known, geometric relationships — such as those for the area of a circle — are used to solve for the diameter.

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