The supporting wheel on a scaffold is held in place on the...

The supporting wheel on a scaffold is held in place on the leg using a 4 -mm-diameter pin. If the wheel is subjected to a normal force of $3 \mathrm{kN}$, determine the average shear stress in the pin. Assume the pin only supports the vertical 3-kN load.

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Key Concepts

Shear Stress

Shear stress is the force per unit area acting parallel to the cross-section of a material. It arises when forces are applied tangentially, leading to a sliding failure mode within the material. Understanding shear stress is critical for assessing the integrity of components under transverse loading.

Load Transmission

Load transmission refers to the manner in which external forces are transferred through a structure. In this context, the normal force acting on the wheel is transferred to the pin, making accurate analysis of how the force distributes across the fastener essential for ensuring safe design.

Cross-Sectional Area Calculation

The cross-sectional area of a pin, especially when circular, is computed using the formula A = (?/4) d², where d is the diameter. This calculation is fundamental in determining stress because the area over which the force is distributed directly impacts the magnitude of the resulting shear stress.

Material Strength Considerations

Understanding how materials resist applied stresses is crucial in mechanical design. The concepts of shear stress and load transmission are directly related to a material's ability to withstand shear forces without experiencing failure, which is essential in ensuring the safety and reliability of structural connections like pins.

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