Calculation of Elastic Shortening Losses

[asixth]

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.

 

[EdR]

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.

 

[asixth]

Thanks Ed.R,

I went through the steps you provided and it checks out.