Abstract
The author has proposed the following calculation formulas on the rectangular flat slabs of the arbitrary width. Those are the primary natural frequency on the rectangular flat slabs, the new restraints along edges, the effective mass coefficient and the deflections of the live load.
Formerly, the calculation formulas of the primary natural frequency of the both all edges simply supported and all edges built-in 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 all edges simply supported, all edges built-in, two opposite edges simply supported and the other two edges clamped, one edges simply supported and three edges built-in, three edges simply supported and one edge built-in, two adjacent edges simply supported and the other edges clamped, all edges semi-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 built-in on the rectangular flat slabs, that is 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 the simply support along edges, the fixed support along edges, two adjacent edges simply supported and the other edges clamped, or all edges semi-clamped. 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 deflections on the rectangular flat slabs through both the all edges simply supported and built-in with the both the concentrated load and the uniformly distributed load. In this paper, the author has proposed the accurate solutions, the polynomial solutions and the solutions with arbitrary size incorporated effective load by Kojima on the deflections based by Timoshenko, s solutions on the rectangular flat slabs. Moreover, these solutions with arbitrary size incorporated effective load by Kojima(2013b) have been expanded not only the central concentrated load, but also the uniformly distributed load. The author compares and verifies among the accurate solutions, the polynomial solutions and the solutions with arbitrary size incorporated effective load by Kojima(2013b).
