Testing of rectangular beams on a layered soil

Abstract

In a beam positioned on a soil bed, counteractive stresses, the determination of the distribution of which is a major concern for solution of the so-called contact problem of a beam on a continuous bed, develop under an external load and the weight of the beam itself. The stress distribution should satisfy equilibrium and compatibility conditions for the beam and the bed beneath it. At the present time, limitations associated with deformations of the system (plain strain, or axisymmetric problem) are assigned to the computational programs most frequently used, implying that the actual width of the beam is not used.Model tests were performed using a three-level concrete basin with various thicknesses of an "artificial soil" serving as the bed for the loaded rectangular beams (Fig. 1).We tested several compositions of a mixture with different contents of components from which the following optimal content with respect to strength was selected: 87% sand, 10% bentonite, 3% cement, and water in an amount of 400 wt. % of the bentonite. The mixture selected was retained in the liquid state in the testing basin for a period of 20 days after mixing (see Fig. 1, c).Immediately prior to testing, i.e., 20 days after the soil had been charged into the basin, specimens were removed for determination of their characteristics.Compressibility characteristics and the average compression modulus M s = 6,500 kN/m 2 were determined from oedometric tests using loaded circular plates 15 and 30 cm in diameter (see Fig. 1, d). The coefficient of cohesion c = 20 kN/m 2 , the angle of internal friction ϕ = 33 o , and the strength of the undrained soil as measured by a vane c u = 140 kN/m 2 . The artificial soil with the composition cited and the method employed for its preparation in the basin can be used for similar model experiments.A steel beam with a length L = 1.5 m, width b = 0.085 m, and height h = 0.050 m was used for the testing. The elastic modulus was determined in accordance with Fig. 2, a, and from the expression for the deflection of a beam on two supports, when a force acts halfway between them The paper describes model tests of a rectangular, transversely loaded flexible beam on an artificially prepared soil of different layers and variable thickness (mixture: sand, bentonite, cement, water). Settlements and bending moments (relative deformations of the beam) were determined along its length. Data relative to the model tests are compared.

Contact Problem of Combined Footing Resting on Elastic Base

“…n An Mx qp dd. (13) Accordingly, the boundary shear forces on the same section planes can be defined as integral sum of differential forces over the area of corresponding rigid footing () (, )( ,) ,…”

“…There are many publications considering various analytical and numerical methods and solutions for contact problems of simple-shaped foundations like flexible foundation beams, rigid or flexible plates of basic shapes. Some of them are reviewed and discussed in [4], [7] monographs [8], [9] and more related to the presented problem [10], [12] as well as their experimental verification [13]. But there is a lack of those deliberated to the more specific ones such as combined foundations, due to in-herent complexity of any thorough analysis of such problems due to lack of accurate, i. e. closed-form analytical solutions for any but the simplest foundation shapes.…”