STRESS SOLUTION OF GROUP PILES FOR STRUCTURAL ANALYSIS UNDER THE CONDITION SUBJECTED TO LATERAL LOAD.

Abstract

The conventional way of the design of a structure having pile foundations subjected to lateral load is the method which piles are divided from the super-structure then it is assumed that the super-structure is supported on the footings and does not subside. And the stress of pile is obtained by Chang's equation based on the assumptions that pile's length is infinite, pile is treated as a beam supported elastically and the behavier of pile and soil under lateral loading is in the range of elasticity. But it is well-known that there is obvious disagreement between the stress and deformation of pile top and those of super-structure which are obtained by the method descrived above. Therefore, with the view that the stress of super-structure and piles must be solved in one, in this paper, stress solution of group piles for structural analysis under the condition subjected to lateral load is derived. The solution starts from the transformation of Chang's equation due to convenience of the theoretical development. And new ideas that the horizontal movement and the rotation of footing are restricted by beams which connect footings each other are introduced into the theory. It is considered that the real condition of pile top embeded in footing is different from the condition that is rigid or freely rotative in Chang's equation. The coefficient which expresses the connective condition between pile top and footing is named "connective ratio at pile top" and is symbolized by "α". The concept of "α" is explained using fig.3 and 4 (fig.4 is called "α-line figure"). The value of α in the lateral loading experiment of a pile embeded in the concreate basement can be obtained with the following method. δ^^・ denotes the rotative component of horizontal displacement at free end of a pile and Q_0 is the lateral load (see fig.6). Q_0〜δ^^・ curve is superposed on the α-line figure, then α can be read. The solutions of group piles considering the rotative angle of footing and the connective ratio α at pile top are derived as (46), (47) and (48) equations. In the stress analysis of the structure supported on pile's foundation, the equation of pile top moment is expressed by the theory of group piles and the equation of bending moment of super-structure is expressed by the slop deflection method. And two equations of moment are suited through the rotative angle of footing, then the stiffness matrix is derived from the coefficients of equations. The rotative angles of footing and the other unknowns can be obtained by solving the stiffness matrix as simultaneous equations. The stress value which are calcurated by substituting the unknowns into (47), (48) equation and the equation of bending moment of super-structure are called "theoretical value". The results of stress analysis using a structural model and varying pile's diameter, structural rigidity, etc., are summarized as follows. (1) Part of stress values of structure obtained by the theoretical method excluding the equation of subsidence at footing is smaller than the theoretical values. (2) Stress of structure which has no piles and whose footing do not subside is called "stress of supported type". Stress of supported type is approximately equl to the theoretical valu at α=0. But α increases, then so dose the theoretical value of structural stress. For example, at α=1.0. the bending moment M_G at the exterior end of beams which connect footing each other, increases by 1.7〜1.9 times stress of supprted type. (3) _TI_E denotes the inertia moment of area of piles in the footing which locates in the corner of the structural frame and _TI_C denotes the others. The ratio of _TI_C to _TI_E (_TI_C/_TI_E) increaes, then so does the moment of pile top M_h in the corner footing. And M_h at _TI_C/_TI_E=3.0 is approximately 1.2 times MF which is the bending moment of

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