For the same STRESS, LENGTH and YOUNG'S MODULUS of both strands, then yes, the elongation will be same for different strand areas.
Look at your elongation equation, substitute P/A for STRESS, and you are left with:
Δ = σ L / E
Intuitively, if you stress a tension members (with the same E) to the same level of stress, then the strain will be the same. If both members are of the same length then their elongations will be the same. Δ = ε L
I notice in your calc sheet that you are using E = 199,000 MPa. For 7-wire strand the E is usually a bit less than that. Check the test value from your strand mill certificate. Usually in the range of 195-197,000 MPa.
Also, don't get too carried away with reporting theoretical elongation to 2 decimal places. 902.79 mm should be presented as 903, or even better to round to the closest 5 mm, so 905 mm. Your field guys will appreciate it - they are not using a micrometer to measure the strand elongation on a 145m long bed.
Finally, I am curious - your calcs show a strand UTS of fpu = 1770 MPa. Is this the common grade of strand you use in Bahrain? In the USA (and many other countries) 270 ksi or 1860 MPa is more common.
For elongation, I have to format the cell in excel to show no decimal. I was in a hurry.
Our company is buying strands from a Chinese company. They are supplying 9.3 strand with 1770 Mpa and 12.7mm strand with 1860. Yes its common here. Bahrain follow BS more. I am trying to reduce the prestressing force as its a Chinese strand(lol).
