A beam consists of three planks connected as shown by steel...

A beam consists of three planks connected as shown by steel bolts with a longitudinal spacing of $225 \mathrm{mm}$. Knowing that the shear in the beam is vertical and equal to $6 \mathrm{kN}$ and that the allowable average shearing stress in each bolt is $60 \mathrm{MPa}$, determine the smallest permissible bolt diameter that can be used.

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Key Concepts

Cross-Sectional Area and Bolt Diameter

The cross-sectional area of a bolt, generally calculated using the formula for the area of a circle, plays a critical role in determining whether a bolt can safely transfer the shear load. The bolt diameter directly affects its area, and hence its resistance to shear stress under a given load.

Designing for Allowable Stress

Designing bolt connections involves comparing the actual shear stress with the allowable shear stress of the bolt material. This ensures that the bolts are not overstressed when subjected to the applied loads, thereby preventing failure and ensuring the integrity of the connection.

Shear Force

Shear force is a component of the overall load that acts parallel to the cross section of a structural member. It is critical in the design of connections, such as bolts, because it determines the force that must be resisted by each bolt in resisting lateral motion or disturbance.

Shear Stress

Shear stress is the stress component that results from an applied shear force acting on a specific area. In the context of bolted connections, it is essential to ensure that the shear stress imposed by the applied load does not exceed the material’s allowable limit, otherwise, failure can occur.

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