Suponga que, si el esfuerzo de corte en el acero supera...

Suponga que, si el esfuerzo de corte en el acero supera aproximadamente $4.00 \times 10^8 \mathrm{~N} / \mathrm{m}^2$, el acero se rompe. Determine la fuerza de corte necesaria para a) cortar un tornillo de acero de 1.00 cm de diámetro y b) perforar un agujero de 1.00 cm de diámetro en una placa de acero de 0.500 cm de grueso.

Key Concepts

Calculation of Shear Area

Determining the appropriate area over which shear stress acts is crucial. For a solid cylindrical object, such as a screw, the area is typically the cross-sectional area of the circle. For processes like drilling a hole in a plate, the shearing occurs along the cylindrical surface surrounding the hole; therefore, the shear area is calculated as the product of the hole's perimeter (circumference) and the thickness of the plate.

Shear Stress

Shear stress is the force per unit area acting parallel to the plane of interest. It is a critical material property that defines the maximum stress a material can withstand before failure along a plane, and is especially important in processes like cutting or shearing where the applied force must not exceed this threshold.

Force and Stress Relationship

In mechanics of materials, the force causing shear (shear force) can be determined by multiplying the shear stress by the area over which it is applied. This relationship, expressed as F = ? × A, is fundamental when estimating the force needed to break or cut through a material.

Circular Geometry

Problems involving cylindrical objects require the use of circle geometry. The cross-sectional area is derived from the formula A = ?r², and the circumference (used to calculate the lateral surface area in shearing) is given by C = 2?r. These formulas are essential for correctly determining the areas involved in shear failure scenarios.

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