THEORY O! OIROIIMFERENTIAL REINFOROEMENT. If a ma terial is subjected to compression and restrained laterally, lateral com pressive stresses will be developed which tend to neutralize the principal compressive stresses and thus increase the resistance to rup ture. If the lateral stresses were equal to the principal stresses, there would be no rupture because there could be no shear. The effectiveness of the lateral restraint depends upon the ratio of the lateral to the longitudinal deformation of the material. This ratio is known as Poisson's ratio. Apparently the only experiments made to determine Poisson's ratio for concrete are those by Prof. A. N. Talbot, which gave values from 0.10 to 0.16 for a 1 : 2 : 4 concrete 60 days old at ordinary working loads, with values as high as 0.25 or 0.30 near the ultimate strength.* Knowing Poisson's ratio it is possible to deduce the relation between the lateral and the longitudinal stresses, and also the por tion of the longitudinal stress left unbalanced. Let u = Poisson's ratio, C = the total longitudinal unit stress, in lb. per sq. in., c = the excess of the longitudinal over the lateral compressive unit stress—the only portion of C that is significant, - the unit tensile stress in the steel, in lb. per sq. in., p — the ratio of the area of the steel to the total area of the column, the s;.eel being considered as a thin cylinder sur rounding the concrete, If there is no reinforcement p =0, and hence from equation 3, C = c. If p = 0.01 (1 per cent), and u be taken at 0.16 (its maximum value for working stresses) and n at 20 (its maximum), then C = 1.015c. In other words, under the most favorable circumstances, steel equivalent to 1 per cent of the area of the column increases the working strength of the concrete only 1.5 per cent; whereas 1 per cent of longitudinal reinforcement increased the strength 14 per cent (see § 486). From equation 4 it is seen that with the values assumed above, the unit stress in the steel is only 3.00 c, or say 3.00 X 500 = 1,500 lb. per sq. in. These examples are extreme cases chosen to show (1) that circumferential reinforcement is not nearly as efficient as the same amount of metal used as longitudinal reinforcement, and (2) that with circumferential reinforcement only comparatively small stresses can be developed in the steel with ordinary working stresses in the concrete. These conclusions are borne out by ex
periments. Tests made by Professor Talbot t show that with a 1 : 2 : 4 concrete 60 days old, a stress of 800 lb. per sq. in. in the concrete developed only 1,100 lb. per sq. in. in the steel.
However, although circumferential reinforcement adds but little to the safe working strength of a column, it adds materially to its ultimate strength. When the load on the column reaches the ultimate strength of the corresponding plain concrete column, the amount of shortening increases very rapidly and the lateral expan sion increases correspondingly rapidly. During this stage the elasticity of the reinforcement imparts to the column as a whole a considerable degree of elasticity. The shortening of the circum ferentially reinforced column at its maximum load is six to twelve times that of a plain concrete column at its maximum load. The effect of circumferential reinforcement on the ultimate strength of the column is two to three times as great as would be caused by the same amount of longitudinal reinforcement; but the exces sive amount of shortening and the liability to lateral deflection hake it doubtful whether this increase in strength can be utilized to any great extent in ordinary practice. Circumferentially rein forced columns exhibit a greater toughness near their maximum load than either plain or longitudinally-reinforced concrete columns, but do not have as great stiffness at working loads.
Empirical Formulas for Cicumferentially Reinforced Columns. The ultimate compressive strengt,h of a 1 :2 :4 concrete column reinforced with bands is expressed by the empirical formula C and p have the significance stated in § 488. The first term of the above equations is the unit ultimate strength of a 1:2 :4 plain concrete column; but the second terms are practically the same for a 1 : 1 : 3 or a 1 : 4 : 8 concrete. There is no material difference between mild and high-carbon reinforcement.