We have considered using a Yrod as a vertical support for piping system. This was modelled as a Y restraint with Zero friction,we calculate that the rod rotation is very small <0.1 deg and we think its justified that we have not considered friction as the rod angle has been kept to below 4 deg and we do not have a sliding contact surface for the piping load to act upon. Our client has challenged this approach and I'm struggling to find mathematical proof's of why at less than 4 deg then horizontal resistance to movement is not considered?
... Any ideas or references?? Thanks.

Matt,

Doesn't the 4 deg limitation is for slanting of hanger rod(or hanger itself)?
So rod length and x or z displacement are not supposed to exceed 8 deg(you can give initial slanting to the hanger for margin), i guess.
Assume rotation(deg) rx, rz, ry in displacement is not what you're looking for.