1. "The bridge had become inadequate to deal with the increase in road traffic which had taken place since its construction".
2. "The bridge had become inadequate to deal with the increase in road traffic since its construction".
They are both okay. The string "increase in road traffic since" asserts that the increase "had taken place" - that's clear - so you can omit the latter if you wish. Alternatively, you could replace it with "had occurred"
3. "The bridge had become inadequate to deal with the increase in road traffic which had occurred since its construction".