I guess we discuss two different aspects. I am talking about classic Bourdon effect, which is about a partially flattened cross section tube that tend to become more circular due to internal pressure. As an effect of this, the angle will tend to increase. The formula of the bending moments applied at the ends is proportional of the internal pressure and the ovalization. If the ovalization is very low, the moments are also low.
This effect is not addressed by code.
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Dan