THEORY OF LONGITUDINAL REINFOROEMINT. To compute the strength of a column having longitudinal reinforcement, let A = the total cross section of the column, A, = the cross section of the steel, / , = the unit working stress in the concrete, n = ratio of the modulus of elasticity of the steel to that of the concrete at a stress as determined from gross deforma tion P = the total safe strength of the column, p = the ratio of steel to total area = A, _ A.
Assuming that the steel and the concrete adhere together, the ratio of the unit stress in the steel to that in the concrete will be equal to the ratio of the coefficient of elasticity of the steel to that of the concrete for the stress as determined from gross deformations; and therefore the unit stress in the steel will be n and the total stress in the steel will be n A, = n f, pA. The area of the concrete is A — pA, and the total stress in the concrete is A (1—p). Con sequently the total strength of the column, The above equation shows that the strength of a reinforced concrete column varies as the unit stress in the concrete, but not directly, since the higher for any particular grade of concrete the lower and hence the lower n. A high grade concrete which will
permit the use of a higher value of will give a higher value of and hence a higher value of n.
The term (n-1)p shows the effect of the steel. For example, if n = 15 and p = 0.01, (n-1)p= 0.14, which shows that 1 per cent of reinforcement adds 14 per cent to the strength of the plain concrete column. The greatest relative effect of the steel occurs with poor concrete of low modulus. The unit stress in the steel = n h; and since n usually varies from 10 to 15, and from 300 to 500, the stress in the steel will vary from 3,000 to 7,500 lb. per sq. in., and consequently the stress in the steel reinforcement will always be relatively low.
Experiments show that there is no material difference in the strength of a column whether it is reinforced with plain, de formed, or Kahn bars; and also that there is practically no difference between weak and strong lateral connection between the longitudinal reinforcing bars.