The boards are glued together to form the built-up beam. If...

The boards are glued together to form the built-up beam. If the wood has an allowable shear stress of $\tau_{\text {allow }}=$ $3 \mathrm{MPa}$, and the glue seam at $D$ can withstand a maximum shear stress of $1.5 \mathrm{MPa}$, determine the maximum allowable shear $\mathbf{V}$ that can be developed in the beam.

Key Concepts

Built-Up Beams

Built-up beams are structural elements composed of multiple layers or components that are assembled together to act as a single unit under load. By combining materials such as wood boards with proper adhesives and fasteners, the resultant beam can achieve improved strength and stiffness compared to its individual components, provided the connection between layers is adequately designed.

Shear Stress in Beams

Shear stress is the internal stress that develops within a beam when an external shear force is applied, causing layers of the beam to slide relative to one another. In beam analysis, understanding shear stress distribution helps in determining how the internal forces are resisted and is crucial for ensuring the structure does not fail due to shear overload.

Allowable Shear Stress

Allowable shear stress is the maximum shear stress that a material can safely experience under load conditions without incurring failure. This parameter is determined based on the material properties and safety factors, and it guides engineers in designing beams and other structures to ensure reliability and safety.

Adhesive Joint in Composite Beams

In composite or built-up beams, the adhesive joint (or glue seam) plays a critical role in transferring shear forces between the individual components. The strength of this joint is pivotal because if the adhesive fails, the beam may lose its composite action, leading to premature or catastrophic failure even if the primary material's allowable shear stress has not been exceeded.

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