17.2
Shearing Stress
Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones w…
A structure when subjected to transverse forces develops internal forces in the sectional plane between the points where the forces are applied.
The magnitude of these resultant forces is defined as the shear and the stress developed is called shearing stress.
Consider two plates connected by a bolt. When tension forces are applied to the plates, stresses will develop in the section of the bolt corresponding to the plane between the horizontal surfaces of the plates.
The stresses result in a single shear, equal to the applied tension forces. Shearing stress is not uniformly distributed and varies from zero at the surface of the member to a maximum value exceeding the average value.
The average shearing stress is computed by dividing the shear by the area of the cross-section.
When splice plates are used to connect two plates, shear occurs in each of the two planes of the bolt, which is referred to as double shear. The average shearing stress in each plane is determined by dividing the applied force by twice the cross-sectional area.
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Q1: What is shearing stress and how does it develop in a structure?
Shearing stress, denoted by tau (τ), develops when transverse forces act on a structure, creating internal forces within the sectional plane between applied force points. The magnitude of resultant internal forces is called shear, and the stress developed is shearing stress. This occurs commonly in connectors like bolts, pins, and rivets used to join structural members or machine components.
Q2: How is average shearing stress calculated?
Average shearing stress is computed by dividing the shear force by the cross-sectional area of the member. However, this represents only an average value, as actual shearing stress distribution varies across the section, ranging from zero at the surface to a maximum value that exceeds the average.
Q3: What is the difference between single shear and double shear?
Single shear occurs when shear develops in one plane, such as when tension forces are applied to two plates connected by a bolt. Double shear occurs when splice plates connect two plates, causing shear to develop in two planes of the bolt. Average shearing stress in double shear is calculated by dividing the applied force by twice the cross-sectional area.
Q4: Why is shearing stress not uniformly distributed across a cross-section?
Shearing stress distribution varies across a member's cross-section due to the nature of transverse force application and internal force redistribution. Stress ranges from zero at the surface to a maximum value that significantly exceeds the average, which is why engineers use average shearing stress calculations for design purposes rather than assuming uniform distribution.
Q5: What types of structural elements commonly experience shearing stress?
Bolts, pins, and rivets frequently experience shearing stresses as they connect machine components or structural members. When tension forces are applied to plates joined by these fasteners, shearing stresses develop in the fastener's section lying between the plates' surfaces, resulting in shear equal to the applied tension force.
Q6: How does shearing stress relate to general loading conditions?
Shearing stress is one type of internal stress that develops under stress general loading conditions when transverse forces act on a structure. Understanding how shearing stress develops and is distributed helps engineers analyze complex loading scenarios and design safe connections in mechanical systems.
Q7: What practical considerations apply when designing connections subject to shearing stress?
Designers must account for whether connections experience single or double shear, as this affects stress calculations and fastener sizing. Since shearing stress is non-uniform and peaks exceed average values, engineers apply safety factors and select appropriate fastener materials and dimensions to prevent failure under transverse loading.