Three identical boards are bolted together to form the...

Three identical boards are bolted together to form the built-up beam. If the wood has an allowable shear stress of $\tau_{\text {allow }}=450$ psi, determine the maximum allowable internal shear $\mathbf{V}$ that can act on the beam. Also, find the corresponding average shear stress in the $\frac{3}{8}$ in. diameter bolts which are spaced equally at $s=6$ in.

Key Concepts

Allowable Shear Stress

This is the maximum shear stress a material can safely withstand without experiencing failure. In design, it acts as a threshold to ensure that the material – whether wood, metal, or any other substance – will not deform or fracture under shear loading. It is determined from material properties and safety factors, and it governs the capacity of the beam to resist shear forces.

Built-Up Beam Action

A built-up beam is formed by combining several smaller, identical or different, members to act together as a single, larger beam. The composite behavior achieved enables the beam to have enhanced load-carrying capacity by sharing stresses among its components. This concept is vital in structural engineering as it allows for variations in materials and cross-sectional geometries to meet design requirements while making efficient use of resources.

Shear Transfer in Composite Members (Shear Flow)

In built-up beams, shear forces are transferred between the individual components through connection elements such as bolts or adhesives. The concept of shear flow describes the distribution of shear force along the interface between members. It is used to design and size the connectors so that they can safely transfer the internal shear forces without overstressing any single component.

Bolt Shear Stress

This concept pertains to the stress experienced by bolts when they are used as connectors in composite or built-up beams. Under shear forces, bolts are subjected to a shear load that must be distributed across their cross-sectional area. The average shear stress in a bolt is determined by dividing the applied shear force by the effective area resisting the shear, ensuring that the bolt operates within its safe stress range.

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