As Mr. Lee mentioned well, there are so many factors for the welding contraction. Even though you can find some articles for the welding contraction in several journals for welding, the application may be limited because the condition may not be the same as your need completely.
I remember a case below when I was working in pressure vessel manufacturing shop before.
; When we made multi cans (girth seam) for the whole shell section of the pressure, we used 1.5 to 3.0 mm weld gap between shell cans. After final welding of the girth seams, the gap length was almost disappeared due to the contraction even if it the contraction rates were slightly different according to thickness, shell diameter, shell length, materials, and welding process.
Here are some information (see attachment as well), but they are a very small part of all cases.
http://internet.ktu.lt/lt/mokslas/zurnalai/medz/pdf/medz0_73/03%20Audronio%20str%20(169-173).pdf
J. M. J. McDill, A. S. Oddy, J. A. Goldak, and S. Bennison, , Finite element analysis of weld distortion in carbon and stainless steels, The Journal of Strain Analysis for Engineering Design, Volume 25, Number 1 / 1990, Professional Engineering Publishing
일반적인 탄소강은 응고수축과 변태에 의한 수축 두가지를 경험하게 됩니다.
TWI등의 자료에 의하면 각각 3%dhk 7%의 수축이 발생한다고 되어 있지요
그러나, 실무에서는 이런 자료가 별로 도움이 안됩니다.
그 보다 훨씬 더 많은 변수(용접입열, Pass 수, 냉각속도, Deposit Thickness Per pass등)가 작용하기 때문에 대부분 현장의 실무자가 느끼는 감이 훨씬 더 정화한 경우를 많이 보게 됩니다.