By James R. Newman
The area of arithmetic (4 volumes)
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Extra info for The World Of Mathematics [Vol 4]
The intermediate case p case of no prestress p =0 = V2 and the are shown by full and dashed- dotted lines respectively. For the intermediate case the change in slope corresponds to crackirig of the section. The curves for p = 0 have been simplified in neglecting the ten- sile strength of the concrete. A more exact analysis or an actual experimental observation may give somewhat different values from those shown in the figure. However, the order of magnitude as weIl as the trend should be weIl indicated.
15 as function of the dead load moment M(DL) for different prestressing ratios p. The latter is defined as the ratio of the prestressing moment M(Pr) to the dead and live load moment M(DL+LL) = - M(Pr)jM(DL+LL) p (13 ) The two ordinates of the figure are non-dimensionalized by appropriate values. The dead load moment is divided by the dead plus live load moment such that for the abscissa ° the dead load part is zero whereas for the abscissa 1 the live load part is zero. e. at the time of form work removal without the influence of creep.
16. It is assumed that the dead load moment M(DL) is equal to one third, the live load moment two thirds of the total moment M(DL+LL). Hence the dead load plus prestress deflections are given by the abscissa V3 in the graph of Fig; 15 and also Fig. 16. The live load deflections, taken as instantaneous without influence of creep, start from the dead load plus prestress deflections of this abscissa. Taking for example the case of no prestress, p = 0, at time t =0 the additional live load deflection will follow the dashed-dotted dead load deflection line up to the full value 2/3 for the live load moment.