In the context of structural mechanics and material stress calculations, understanding applied shear force is fundamental. Applied shear force is essentially the force component that acts parallel to a surface or cross-section, attempting to cause that section to slide or shear relative to another section.
Based on the provided information regarding the calculation of shear stress, the applied shear force is defined as the force denoted by 'F' in the formula for average shear stress.
Understanding Applied Shear Force ('F')
The reference states that in calculations, shear stress ($\tau$) is related to an applied force ('F') and the cross-sectional area ('A'). The formula given is:
$\tau = \frac{F}{A}$
Here, 'F' is the applied force on the member that causes the shear stress. This 'F' is what we refer to as the applied shear force in this context. It is the specific force component that acts parallel to the area 'A' across which the shear is occurring.
What Does 'F' Represent?
- Source: This force 'F' typically originates from external loads or reactions applied to a structural member or component.
- Direction: For it to be a shear force, 'F' must act parallel to the surface or area of interest. Forces perpendicular to the surface cause normal stress (tension or compression), not shear stress.
- Effect: When applied, this force 'F' tries to slide one part of the material or component past an adjacent part.
Finding the Value of 'F'
While the formula $\tau = F/A$ shows how applied shear force relates to shear stress and area, it doesn't directly tell you how to find the value of 'F' itself in a complex structural system. Determining the applied shear force ('F') on a specific section of a member or component requires analyzing the external forces and reactions acting on the overall structure.
Methods to determine 'F' in various engineering scenarios include:
- Direct Application: Sometimes, 'F' is a simple external force applied directly, such as the force trying to shear a bolt in a joint.
- Structural Analysis: For beams, columns, or more complex structures, the internal shear force 'F' at any given cross-section is calculated using principles of statics (sum of forces) by considering the external loads and reactions acting on the part of the structure to one side of the section. This often involves creating shear force diagrams.
Key Components in Shear Calculation
The relationship between applied shear force, area, and shear stress can be summarized in a table:
| Symbol | Meaning | Description | Common Units |
|---|---|---|---|
| $F$ | Applied Shear Force | The force component parallel to the cross-sectional area | Newtons (N), Pounds (lb) |
| $A$ | Cross-sectional Area | The area over which the shear force acts | $m^2$, $in^2$ |
| $\tau$ | Average Shear Stress | The average stress distributed over the area 'A' | Pascals (Pa), psi |
Practical Insight: Simple Shear Example
Consider a simple bolted connection where two plates are held together by a single bolt, and a force is applied to pull the plates in opposite directions parallel to the bolt's shank.
- The applied shear force ('F') on the bolt is the force transmitted through the joint, trying to shear the bolt through its cross-section. If the force pulling the plates is 1000 N, and the bolt resists this force by developing internal shear stresses, the applied shear force on the bolt's cross-section is 1000 N.
- The cross-sectional area ('A') is the area of the bolt's circular shaft where the shearing occurs ($\pi r^2$).
- The average shear stress ($\tau$) in the bolt is then calculated using $\tau = F/A$.
In this example, the applied shear force 'F' is the 1000 N force that the bolt is subjected to, acting parallel to its circular cross-section.
To "calculate" applied shear force generally means identifying and quantifying the specific force component that is acting parallel to a relevant area within a system. It's the 'F' you input into the shear stress formula $\tau = F/A$.
