"The adaptability of the classical slope-deflection method analysis to the analysis of uniformly loaded building slab is the subject of this study. The paper demonstrates the use of slope-deflection in computing deflections and bending moments in uniformly loaded square building slabs both with and without central square openings. The results obtained are compared with results of other methods found by other investigators.
Numerous methods have been proposed for use in solving plate or slab problems. The exact solution in the form of a fourth order partial differential equation has proved to be of value in relatively few cases where boundary conditions are simple. Approximate methods have been developed but few of these have received general acceptance because of their complex nature. The development of slope-deflection equations offers the possibility of yielding good results in an approximate analysis of solid slabs and of slabs with openings. Openings in building slab are common, yet no generally accepted method exists for analyzing such slabs.
Modem electronic digital computers provides a means for reducing the time required for the long and tedious calculation that are frequently encountered in approximate analysis of slabs. With good computational facilities, then, the analyst can give more effort to develop a system of analysis that will yield results closer to the theoretical - or so called exact results.
In this paper, LGP-30 computer programming using floating point interpretive system 24.2 is used to solve the simultaneous equations developed in the analysis. The results have been compared to these obtained from theoretical computation introduced by Timoshenko and Wojtaszak.
The technique followed here is to divide the slab into an arbitrary number of orthogonal strips that are considered to be exactly equivalent to the slab. These strips are considered to be beams of the analogous gridwork formed by the orthogonal strips. The uniform load is divided up into a number of concentrated loads called panel or joint load. The joint loads are then applied at panel points of the grid causing the grid to deflect. The slopes, deflections and moments in the grid are assumed to be identical with those of the slab at corresponding points. These slopes, deflections and moments are the unknowns that must be evaluated in order to arrive at a solution. The number of unknowns, and hence the number of simultaneous equations required for solution, are dependent on the number of the strips that approximate the slab. Symmetry can greatly reduce the number of unknowns and, as a result, simplify the problem"--Introduction, pages 1-2.
Carlton, E. W.
Stites, Wilbur D.
Lee, Ralph E., 1921-2010
Schaefer, Rodney A., 1926-2002
Roberts, J. Kent, 1922-2014
Civil, Architectural and Environmental Engineering
M.S. in Civil Engineering
Missouri School of Mines and Metallurgy
vii, 116 pages
© 1961 Wu Ping-Yung, All rights reserved.
Thesis - Open Access
Concrete slabs -- Testing
Strength of materials -- Mathematical models
Print OCLC #
Electronic OCLC #
Link to Catalog Record
Ping-Yung, Wu, "Deformations and bending moments for a building slab with a central opening" (1961). Masters Theses. 2761.