22.3 : 梁のせん断応力: 問題解決

A cantilever beam with a rectangular cross-section is subjected to distributed and point loads.

To calculate shearing stress in the beam, the loads acting upon it are first identified. Reactions at the fixed end are then calculated using equilibrium equations.

Vertical reaction is the sum of distributed and point loads, and the moment reaction is the sum of their moments.

The shear force distribution along the beam due to the loads is determined by drawing a shear force diagram starting from reaction forces at the fixed end, including the distributed load and the point load.

Shearing stress is calculated using a formula considering the shear force at that point, the first moment of the cross-section area about the neutral axis, and the cross-section's moment of inertia.

The shearing stress is calculated at various critical points along the beam, typically near the supports and at the point load location.

The maximum shearing stress should be compared with the material's allowable shear stress to determine if the beam is safe.