difference in tendon extension of same tendon being stressed in two stage (50% first stage,50% second stage)

Question:
There is difference in elongation of tendon in stage one and stage 2 line T1 in stage one with 50% prestress is approx 61mm but T1 in stage 2 with rest 50% jacking force  elongation is 70mm why??


Answer:
Let's say we take anchorage loss as zero (just for better understanding of things).

When we prestress 50% of T1 tendon at CS1, the prestress value is 728.19 N/mm2 at stressing end and 662.81N/mm2 at other end due to immediate losses. The elongation value is calculated due to stresses just after immediate losses (friction losses).

Because of friction losses, there will be different prestressing stress value (f) in tendon at each end of the element. Moreover, for sake of convenience, we assume that length of tendon (L) = length of element.

So, total elongation of tendon for that element = Avg. stress * L  / E(tendon)
where, E(tendon) = Elastic Modulus of tendon.
Total elongation for T1 at CS1 comes out to be 61.66 mm.(Calculation shown in Excel Sheet)

Now, for CS2, stress in tendon (before applying further 50% stressing) will be stresses after all losses at the end of CS1 stage.

So, actual stress will be less. So, prestressing end stress is less than 728.19N/mm2 which will 0.9798*728.19 = 713.5N/mm2.

So, when we apply remaining 50% prestressing, our final stress at prestressing end should be = 728.19 + 728.19 = 1456.38 N/mm2. 
So net stress applied will be 1456.38 - 713.5 = 742.7 N/mm2. 

Thus, elongation calculated will be more.(Calculation shown in Excel Sheet)
Calculations has been shown in excel sheet which has been attached for further review.
Creation date: 5/27/2021 11:28 AM (jatin2010)      Updated: 5/27/2021 12:08 PM (jatin2010)
Files   
Systra.xlsx
16.3 KB
TRANSVERSE PT PASSED NON DEVIATOR.mcb
353.1 KB