3: Bearing stress

3: Bearing Stress

Bearing stress arises in scenarios where one object presses against another, creating a localized compressive stress at the surface of contact. It is fundamentally a compressive stress, but its calculation and significance differ from the general compressive stress acting uniformly over a cross-section. Bearing stress specifically focuses on the stress at the interface where force is transferred from one component to another through direct contact.

Distinguishing Bearing Stress: Consider a bolt connecting two plates under tension. While the bolt shank experiences normal tensile stress, and the plates experience tension away from the hole, the critical point where the bolt head or nut presses against the plate (and similarly where the bolt shank presses against the inner surface of the hole in the plate) is subject to bearing stress. It's the stress that could cause localized yielding, crushing, or excessive deformation of the material at this contact surface.

Key Applications:

1. Connections (Bolts, Rivets, Pins): This is the most common context. The bearing stress is calculated at the interface between the fastener (bolt, rivet, pin) and the connected member (plate, gusset, lug). Failure occurs if this stress causes the hole in the plate to elongate (become oval) or the fastener to indent excessively into the plate material.

   • Formula: The average bearing stress ($\sigma_b$) is calculated as the force transmitted by the fastener ($P$) divided by the projected area of contact.
   • $\sigma_b = \frac{P}{d \times t}$
   • Where:
     • $d$ = Diameter of the fastener (bolt, rivet, pin)
     • $t$ = Thickness of the member against which the bearing force is applied (often the thinner plate in a lap joint).

2. Supports (Beams on Foundations, Truss Joints): Where a beam rests on a support (e.g., a steel beam on a concrete wall, a wooden beam on a masonry pier), bearing stress acts at the contact surface between the beam end and the support. Failure could involve crushing of the beam end or the support material.

   • Formula: $\sigma_b = \frac{P}{A_{contact}}$
   • Where:
     • $P$ = Reaction force at the support
     • $A_{contact}$ = Area of the contact surface (e.g., width of beam $\times$ length of bearing plate).

Important Considerations:

• Localized Effect: Bearing stress is highly localized to the immediate vicinity of the contact area. The stress distribution within this contact zone is rarely uniform; it peaks in the center and reduces towards the edges. However, the formula $\sigma_b = P / (d \times t)$ provides a valuable average bearing stress used for design and analysis.
• Material Properties: The allowable bearing stress ($\sigma_{b\_allow}$) depends on the strength of the weaker material in contact. It is often related to, but distinct from, the material's ultimate compressive strength ($\sigma_u$), typically using a formula like $\sigma_{b\_allow} = C \times \sigma_u$, where $C$ is a factor greater than 1 (e.g., 1.2-2.0) accounting for localized constraint. Always refer to design codes for specific values.
• Factor of Safety: As with other stresses, a factor of safety ($FS$) is applied to ensure the actual bearing stress ($\sigma_b$) does not exceed the allowable: $\sigma_b \leq \sigma_{b\_allow} = \sigma_{b\_ultimate} / FS$. The ultimate bearing stress ($\sigma_{b\_ultimate}$) is determined experimentally.
• Not Plate Compression: Crucially, bearing stress ($P/(d \times t)$) is not the compressive stress acting on the net cross-sectional area of the plate itself (which would be $P/((w - d) \times t)$ for a plate width $w$). It is specifically the contact stress between the fastener and the plate hole.