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If the Savage is too small dia. then why is remington's ok to chamber anything with a 1.062 shank. The actions are about the same thickness I think so I don't understand that statement.
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In the Remchester group of actions the peak pressure area of the barrel is ~1.200". The 1" or 1.062" x 16 tpi threads are inside the action and supported by same. The Savage barrel's breech end is 1.055" and the threads extend significantly forward out of the action to accommodate the headspace nut. Unless the Savage is breeched without the headspace nut it leaves you with ~ .250" wall thickness at your peak pressure location. (1" in front of the base of the seated bullet.) Likely this is OK with chrome moly or chrome vanadium steels. With 416R stainless combined with cold weather it is below minimum safety margins. If you use one of the 410 stainless blanks from Krieger you add some resilience in cold weather, however, it's pushing the edge of the envelope.