Abstract
Formerly, the calculation formulas of the primary natural frequency of the both (A) all edges simply supported and (B) all edges clamped on the rectangular slabs have only been proposed. So Kojima(2012) had derived the calculation formulas of the primary natural frequency on the generalized support conditions of the rectangular flat slabs. The subjects of studies for support conditions on the rectangular flat slabs are (A) all edges simply supported, (B) all edges clamped, (C) two opposite edges simply supported and the other two edges clamped, (D) one edges simply supported and three edges clamped, (E) three edges simply supported and one edge clamped, (F) two adjacent edges simply supported and the other edges clamped, (G) all edges semi-clamped by Kojima(2012) between (A) all edges simply supported and (B) all edges clamped. Since the primary natural frequency of the ordinary flat slabs is intermediate between the simple support and the fix along edges, Kojima(2012) had defined restraints along edges of the flat slabs which are set to 1 by simple support along edges of the flat slabs and set to about 2 by fix along edges. Through the definition of the new restraints along edges, Kojima(2012) had estimated the primary natural frequency of the ordinary flat slabs is intermediate between all edges simply supported and clamped on the rectangular flat slabs, which are the numerical value is 1.5 times of all edges simply supported slabs. Kojima(2013a) had proposed the calculation formulas of the effective mass coefficient that the concentrated load affected the rectangular flat slabs. As the support conditions, Kojima(2013a) had calculated (A) all edges simply supported, (B) all edges clamped, (F) two adjacent edges simply supported and the other edges clamped and (G) all edges semi-clamped by Kojima(2012). Through a series of these processes, Kojima(2013b) had derived the calculation formulas of the maximum deflections from the concentrated load on the rectangular flat slabs. Timoshenko(1959) proposed the accurate solutions of the deflection on the rectangular flat slabs through both the all edges simply supported and clamped with the both the concentrated load and the uniformly distributed load. Kojima(2106) has proposed the following calculation formulas of the effective mass coefficients and the maximal deflection amount with the uniform load on the rectangular flat slabs. The support conditions on the rectangular flat slabs are the support conditions of (A) to (G).
It's said to a support conditions on flat slabs of real buildings is the (G) all edges semi-clamped by Kojima(2012) between (A) all edges simply supported and (B) all edges clamped. The calculation formulas of the maximum deflection with the uniform load under the support conditions of (A) to (F) was the solutions of the Fourier polynomial proposed by Timoshenko (1959).
This paper is the following calculation formulas of the maxim deflection with the uniform load on the rectangular flat slabs. The subjects of studies for support conditions on the rectangular flat slabs are (A) to (F) and (G) all edges semi-clamped by Kojima(2012). The support conditions on the flat slabs of the real buildings have been said to be (G) all edges semi-clamped between (A) all edges supported and (B) all edges clamped. The author has proposed the solutions incorporating the effective mass coefficient and the polynomial solutions of the function on the slenderness ratio λ by using the deflection amount at the center of the rectangular flat slabs with uniformed load under the various support conditions by Timoshenko(1959) and FEM analysis.
