Analyses of One-Way Floor and Roof Systems

The ACI 318 Building Code permits an approximate analysis for continuous systems in ordinary building if:
Components are not prestressed.
Beams and one-way slabs are continuous over two or more spans.
In successive spans, the ratio of the larger span to the smaller does not exceed 1.20.
The spans carry only uniform loads.
The ratio of live to dead service load(s) (not factored) does not exceed 3. Members are prismatic.
This analysis determines the maximum moments and shears at faces of supports and the midspan moments representing envelope values for the respective loading combinations. In this method, factored moments are computed from

integrally with their supports should be taken as the clear span plus the depth of slab or beam but need not exceed the distance between centers of supports. For spans of continuous frames, spans should be taken as the distance between centers of supports. For solid or ribbed slabs with clear spans not exceeding 10 ft, if built integrally with their supports, spans may be taken as the clear distance between supports.
If an elastic analysis is performed for continuous flexural members for each loading combination expected, calculated factored moments may be redistributed if the ratio p of tension-reinforcement area to effective concrete area or ratio of   p – p’, where p’ is the compression-reinforcement ratio, to the balanced-reinforcement ratio b, lie within the limits given in the ACI 318 Building Code. Positive factored moments should be increased by a percentage  and negative factored moments decreased by  to reflect the moment redistribution property of underreinforced concrete in flexure. When p or p’   is not more than 0.5pb, the percentage is given by

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