The change in the preload force after a bolt rod is subjected to an axial load can be explained as follows. Initially, one bolt is under a force Q0. When an additional axial force F is applied, the total resultant force becomes Q = F + Q0. In the bolted connection, this is represented as Q = F + Q0c, where Q0c denotes the residual preload. Due to mechanical principles, students often question why bolts stretch by K1 under working load F, and how the elastic deformation of the bolt is K1 + ΔK1, while the joint’s deformation is restored by K2 (where K2 = ΔK1). At that point, the elastic deformation of the connected member is K2 - ΔK1, and the residual preload reduces to Q0c.
Analyzing the spring forces and deformation of the rod, the resultant force on the bolt rod is given by Q = k1(K1 + ΔK1) (3), and the residual preload of the joint is Q0c = k2(K2 - ΔK2) (4). At this stage, the bolt rod experiences both the working load F and the residual preload force from the connected member, so Q = F + Q0c (5). From equation (4), if K2 = ΔK2, then Q0c = 0 and Q = F, meaning the initial preload Q0 has been fully released. Since Q0 = k2 × K2, when K2 becomes zero, the connected member is plastically deformed and no longer provides any elastic force, leading to the disappearance of the preload. The elastic deformation of the bolt rod, K1 + ΔK1, is independent of both the working load F and the original preload Q0.
The relationship between the initial preload Q0, the axial working load F, and the residual preload Q0c can be derived. From equation (3): Q = k1K1 + k1ΔK1. Substituting equation (1) gives Q = Q0 + k1ΔK1. Substituting into equation (5) yields: F + Q0c = Q0 + k1ΔK1 → ΔK1 = (F + Q0c - Q0)/k1 (6). From equation (4): Q0c = k2K2 - k2ΔK2 = Q0 - k2ΔK2 → ΔK2 = (Q0 - Q0c)/k2 (7). Combining equations (6) and (7), we get: Q0c = Q0 - (k2/(k1 + k2))F (8). Here, k1 and k2 are constants. So, for a fixed F, a higher Q0 results in a larger Q0c, and vice versa. For a fixed Q0, a larger F leads to a smaller Q0c.
In textbooks, the residual preload Q0c is typically related to the axial load F. For example, in sealed joints, Q0c is often taken as (1.5–1.8)F. To ensure this residual preload, the required initial preload Q0 can be calculated using equation (8): Q0 = (1.5–1.8)F + (k2/(k1 + k2))F (9). Here, k1 and k2 depend on the stiffness of the connected parts and the material properties.
From equation (9), the required initial preload Q0 can be determined based on the desired residual preload Q0c. In practical applications, bolted joints often include sealing gaskets. These gaskets have much lower stiffness compared to the joint itself, so the preload is mainly due to the bolt's elastic deformation, while the residual preload comes primarily from the gasket’s deformation.
As shown, during the teaching of preload and residual preload, students often raise questions about the mechanics involved, such as how preload arises and disappears. If students understand that preload is generated by the elastic deformation of the connected parts and the bolt, and that it vanishes once this deformation is gone, they can better grasp the concept of preload changes in bolted connections. This understanding helps clarify how preloads are generated, altered, and maintained in real-world scenarios.
Europe Type Scaffolding Casters
Europe Type Scaffolding Casters
Europe Type Scaffolding Casters
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