calculation of elastic shortening losses

huangyhg

calculation of elastic shortening losses
hi guys,
i have a pretensioned girder and was backchecking the assumptions of prestress losses. i have looked at texts and they state that the stress change in the tendon due to elastic shortening can be calculated by:
delta_fs=es/ec*fc
where delta_fs is the loss of stress in the tendons, es/ec is the modular ratio and fc is the concrete stress at the level of the prestressing tendon (not the characteristic compressive strength of concrete in this example).
logically, i feel the stress loss in the prestressing tendon should be related to the ratio of (es*as)/(ec/ac), where as and ac is the cross-sectional area of steel and concrete respectivley.
what are others opinion on the topic.

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asixth:
consider a set of bars: delta=f l/(a e) = (sig) l/e
then equating delta for concrete and steel gives
deltac/deltas = 1 = sigc/ec = sigs/es or
sigs=es/ec sigc
i.e. the area is included by considering the stresses....
ed.r.
thanks ed.r,
i went through the steps you provided and it checks out.