The rolled-steel beam shown has been reinforced by attaching...

The rolled-steel beam shown has been reinforced by attaching to it two $12 \times 175$ -mm plates, using 18 -mm-diameter bolts spaced longitudinally every $125 \mathrm{mm}$. Knowing that the average allowable shearing stress in the bolts is 85 MPa, determine the largest permissible vertical shearing force.

Key Concepts

Shear Stress

Shear stress is the internal force per unit area that acts parallel to the cross-section of a material. It is a key parameter in determining whether a component, like a bolt or a plate in a structural connection, can safely resist applied loads without failure.

Bolt Cross?Sectional Area

The cross?sectional area of a bolt, typically calculated using its diameter for circular sections, is fundamental in assessing its resistance to shear. A larger cross?sectional area allows the bolt to carry greater loads, as the shear load is distributed over this area.

Load Distribution in Bolt Groups

In a bolt group, the applied load is shared among the individual bolts according to their positions, spacing, and the load path. Properly understanding and estimating this load distribution is crucial to designing a connection that avoids overloading any single bolt.

Calculation of Shear Capacity

Calculating the shear capacity of a connection entails determining the allowable load each bolt can withstand (using the bolt’s cross?sectional area and the allowable shear stress) and summing the contributions of all bolts in the connection. This calculation ensures that the connection can safely support the imposed shear forces.

Bolted Connection Design

Designing bolted connections involves selecting appropriate bolts, determining their spacing, and ensuring that the collective capacity of the bolts meets or exceeds the applied loads. This process ensures that structural elements are securely joined and that load transfer between them is effective.

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