Tiêu đề 8 Simple Stresses.pdf ✅

PSAD 8: Simple Stresses Determining the internal forces of members through static analysis is only one part of assessing whether the applied loads can be safely supported by a structure. Equally important is understanding how these forces are distributed across the entire cross section of the member. This distribution is often analyzed by considering the force intensity at any given point, which is calculated as force per unit area, commonly known as stress. 1. Axial Stress For a member under axial or normal loading, the corresponding stress it experiences is referred to as the axial or normal stress. The average value of the axial stress over the cross section is simply computed by dividing the axial force by the member cross-sectional area. Average Axial Stress σ = P A Where: P = axial force A = member cross-sectional area Note that the axial stress at a specific point in the cross section may vary, as the stress distribution is not always uniform. However, for simplicity in practice, it is often assumed that the distribution of axial stress is uniform, meaning the axial stress at any given point can be considered equal to the average axial stress. This assumption of uniform stress distribution by the average axial stress, holds true only if the axial force passes through the centroid of the cross-sectional area, a condition known as centric loading. 2. Shear Stress For a member experiencing shear force, or force that is parallel to the cross section, the corresponding stress it experiences is referred to as shear stress. The average value of the shear stress over the cross section is also computed by dividing the shear force by the member cross-sectional area.
Average Shear Stress τ௔௩௘ = V A Where: V = shear force As will be described in another discussion, the variation of shear stress along the member cross section is significant for certain member types and cannot be assumed to be uniform. However, for cases such as shear force experience by bolts, pins, rivets, and welds, the use of the average shear stress in analysis will be sufficient. This type of shear is also referred to as direct shear. 2.1 Single Shear In direct shear of fasteners (e.g., bolts, pins, and rivets), shear loading conditions will vary depending on the number of shear planes involved in the loading scenario. In single shear, the force is applied in such a way that it acts on a single shear plane. 2.2 Double Shear In double shear, the force is applied in a manner where the material experiences shear stress along two distinct shear planes. This is typically the case when a member connected using fasteners, is sandwiched between two other members or surfaces and the force is transferred to the middle member, causing shear in both directions. Single shear and double shear loading conditions can be verified by drawing the free body diagrams and performing static analysis. 3. Stresses on Inclined Planes In addition to causing axial stresses, an axial force can also induce shearing stresses when analyzing cross-sectional areas that are not perpendicular to the axis of the member. General Equation for Average Axial and Shear Stress on Inclined Planes σ = ௉ ஺ cosଶ θ τ = ௉ ଶ஺ sin 2θ Where: θ = inclination angle measured from the member cross section towards the inclined plane Note: From these general equations, the shear stress will be maximum when θ = 45° as the term sin 2θ is maximized (or equal to 1.0) at such inclination.