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フーチング下の半無期限弾性基盤内に生ずる応力に関する研究Studies on the Stresses Produced in a Semi-infinite Elastic Foundation by a Footing酒井, 信一Theories of subgrade reaction in which a spring is substituted for an elastic foundation have been widely used for the analysis of problems involved in a footing on an elastic foundation. This method can be applied to a wide range of footing by varying the way of spring connection and taking a viscous shear layer into consideration, thus giving satisfactory results to stress and deflection in a footing and contact pressure on the basis of footing. However, it is not suitably applied to that footing in which deformation is called in question and is of no use for the calculation of stress is a foundation. Exact solutions in view of the theory of elasticity include a number of analytical solutions to footings which are made of rigid plates and some analytical solutions to footings which are made of elastic plates and placed under most limited loading. However, they are actually applicable to only limited cases. In the present study, these problems are treated as problems of two-dimensional elasticity with basic equations derived on the following premises: (1) The foundation is an isotropic and homogeneous semi-infinite elastic solid with level surface, to which Boussinesq's equation on stress and strain applies. (2) A differential equation of fourth order on an elastic line applies with respect to deflection in a beam. (3) The distribution of subgrade reaction is expressed by a cubic polynomial. (4) Load is considered to consist of vertical load and bending moment, which are expressed by a step function. (5) Unknown numbers are determined by the equilibrium condition ∑V=0 and ∑M=0 and the condition on which the beam is brought into close contact with the surface of the foundation. For obtaining stresses produced in a semi-infinite elastic foundation by a footing the auther has introduced, in Chapter 3 and Chapter 4, fundamental formula for contact pressure produced in a foundation by a beam and for vertical, horizontal, and shearing stresses in it, using a general differential equation of th elastic curve of a beam and the Boussinesq's theory on stress and strain. In Chapter 5, in the first place, he introduced the coefficient of contact pressure in the formula of contact pressure calculation, for various cases of loading. In the next place, he introduced formula for horizontal, vertical and shearing stresses produced in a foundation, using the Boussinesq's stress formula and replacing the contact pressure obtained in the preceding section with the load beared by the surface of a semi-infinite elastic foundation. Since the introduced formula are rather complicated and not preferable for practical usage, they are simplified for easier calculation, and, at the same time, the foundation was latticed and calculated values of the cofficient in the formula at the lattice points are listed. By utilizing these appended lists, stresses produced in a semi-infinite elastic foundation by any load laid upon a beam lying on it are easily obtained by a very simple four rules calculation. If a load is combination of loads, it is only required to add the values of the coefficient of contact pressure or values of stresses for the respective loads algebraically because the principle of superposition holds in these cases.Article信州大学農学部紀要 8(1): 1-115(1971)信州大学農学部1971-07-30jpndepartmental bulletin paperhttp://hdl.handle.net/10091/2265https://soar-ir.repo.nii.ac.jp/records/108530583-0621AN00121352信州大学農学部紀要811115https://soar-ir.repo.nii.ac.jp/record/10853/files/Agriculture08-01-01.pdfapplication/pdf5.1 MB2015-09-25