The ground stress condition under the strip load of semi-infinite length

Abstract

Uneven pressure on the strip foundations of building extensions due to the influence of their free ends often leads to the setting extensions aside from the main building, and uneven pressure on the ground of bridge abutments from adjoining embankments can cause the abutments slope in the direction of the embankments. This took place in Dneprodzerzhinsk (Ukraine) on railway and highway bridges, and abutments slope nearly caused the breaking-down of the bridge superstructures. The plane problem solution of the theory of elasticity for a loaded strip of an infinite length used in calculating is inefficient. The presented solution of the spatial problem for a semi-infinite length strip load specifies the ground stress condition at the free ends of the strip foundation, and also in foundation grounds of the bridge abutments from the pressure of adjoining embankments. The components of even load stress and triangular load stress σ_z are obtained by integration of stress values for the elementary concentrated force over the area of the strip. The other components of triangular load stresses, according to the known solution defining stresses, were under the rectangular foundation of the same load. The solution: central point of coordinates moves along the y-axis from the center of the foundation to its end; the target stress components are of stress components under a rectangular foundation by defining the limit of these stresses, when l → ∞. The obtained solutions satisfy the conditions on infinity; the normal stresses σ_z , σ_x and the shear stresses τ_zx change to the known solutions for the plane strain when - ∞ ← y → ∞ . The stresses τ_xy and τ_yz are damped approximately on the distance of y = 2,5b from the strip end, and the stress σ_y becomes permanent and is not taken into account when calculating. Subtracting from the solution corresponding to the strip of a semi-infinite length with the central point of coordinates of x = 0, y = 0 , the same solution with the central point of coordinates of x = 0, y = l for even stress and respectively x = -b / 2, y = 0 and x = -b / 2, y = l for the triangular load we get an easier solution compared to the known one which determine the stress components at the rectangular foundation ground. So that, knowing the solution for any kind of strip load it is possible to find the solutions for rectangular foundation and vice versa. The obtained formulas allow solving plasto-elastic tasks. Here, b and l are the width and the length of the strip.