2o6 Journal of Agricultural Research voi. vi. no.6 



verified ; and in order to carry the investigation farther, with slabs of longer 

 span than those previously investigated, the present series of tests was 

 undertaken at the Arlington Experimental Farm of the United States 

 Department of Agriculture. 



OBJECT OF INVESTIGATIONS 



The theory applied to the design of narrow rectangular reinforced- 

 concrete beams involves the assumption that the stress is constant 

 throughout the width of the beam. In a wide slab the stress distribu- 

 tion varies from a maximum at the point of application of the load to a 

 minimum at the extreme edges. Obviously then, if the rectangular- 

 beam theory were applied to the design of slabs under concentrated 

 loads, the width h used in the design formulas can not be taken as the 

 entire width of the slab. The rectangular-beam theory, however, could 

 be utilized in wide-slab design if it were known what width h should be 

 substituted in the design formulas, and it is the object of this paper to 

 explain tests for determining this width and to demonstrate the appli- 

 cation of the theory of narrow rectangular beams to the design of wide 

 slabs supported at two ends and subjected to concentrated loads. 



EFFECTIVE WIDTH 



The width of the slab that should be used in the rectangular-beam 

 formulas when applied to slab design will be termed the "effective width" 

 of the slab. It is that width over which, if the stress were constant and 

 equal to the maximum stress under actual conditions, the resisting 

 moment would equal the resisting moment of a slab of the same depth 

 and full width, but having varying stress distribution. If the straight- 

 line theory of stress distribution from neutral axis to upper fibers is 

 assumed to be applicable to slabs, the resisting moment of a given slab 

 is dependent on the total stress in the concrete or steel at the dangerous 

 section. The total stress in the concrete, however, is governed by the 

 stresses in the top fibers, and these stresses are proportional to the unit 

 deformations. If, then, there are two slabs of equal depth, one having 

 uniform distribution of deformations and the other a varying distribution, 

 but with their maximum deformations identical, they will likewise have 

 equal resisting moments if the summations of the deformations over their 

 respective widths are identical. 



In figure i , which represents a slab in position on two supports with a 

 concentrated load P, is illustrated the method of obtaining "effective 

 width." Strain-gauge readings are taken of the fiber deformations per- 

 pendicular to the supports, as indicated at eg. These concrete deforma- 

 tion values are plotted to scale, as, for instance, at fh, giving the deforma- 

 tion curve JHF, inclosing the area AJHFE. This curve shows the varia- 

 tion of stress from the center to each of the two free edges of the slab, and 

 the area under the curve is a function of the total concrete-resisting 



