Numerical Method For Approximate Analysis of Building Slabs

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Title: Numerical Method For Approximate Analysis of Building Slabs

Author(s): Howard L. Furr

Publication: Journal Proceedings

Volume: 56

Issue: 12

Appears on pages(s): 511-542

Keywords: none

Date: 12/1/1959

Abstract:
A method for approximate elastic analysis of uniformly loaded slabs is developed. The method is applied to solid square and rectangular slabs, and to square slabs with square central openings. The slab is divided into a grid of orthogonal strips assumed to be equivalent to the original slab. The strips are treated as beams laying along the center lines of strips which are rigidly joined at their intersections. The uniform load is divided into so-called equivalent concentrated loads applied at beam intersections and the grid is deflected to an arbitrary position while carrying these loads. Joints are not permitted to rotate during deflection. Fixed-end moments developed by the deflection are distributed and vertical shears at each joint are computed. The ratio of summation of vertical shears at each joint to its applied load is computed and adjustments of the deflections are made until this ratio is constant throughout the grid. The deflected position under this condition is taken to be a solution condition and the distributed moments from such a position are divided by the constant ratio to give the bending moments in the beams due to the applied joint loads. Corrections are applied to account for the fact that the load is distributed rather than concentrated at joints. An attempt is made to account for plate action by considering both torque and bending in each strip of the grid. Elastic action and homogeneous material are assumed, and it is understood that the results are approximate due to these and other assumptions made in the development.