We have performed the stress analysis and provided guides for protecting the pumps to be used of various operations for an oil terminal. The loads are within allowables as per API 610 8th Edition.

The client is asking us to anchor rigidly the suction and discharge piping, close to the pump nozzles. Adding a new restriction (axial), which will not allow suction and discharge piping to expand from the fixed point, induces extremely high loads on the nozzles in the axial direction as the base of the pump is already anchored. So if You go for analysis it is a sure case of failure. How will we justify the anchor in analysis?

Client indicates that they had to anchor the suction and discharge piping, close to the nozzles, for a previous job, where they had some vibration problem with the pumps and for restricting the effects of the connecting piping system.

Also please advise, how critical are the nozzle loads for VT/Can pumps. Individual pump flow rate varies from 150m3/hr to 650m3/hr. Differential pressure varies from 8 to 14 bar. 2-3 pumps will be working in parallel discharging to a common header.

Anchoring the pumps near the nozzles, is a very critical decision, and should be based upon sound understanding of the consequences. Most of the Clients, insist to anchor the equipment(Pumps, Compressors, Vessels) near the nozzles, from the point of view of vibration isolation and maintenenace free longer life.
Under such circumstances, it is advisable to provide anchor upstream of the Y-strainer, and insert a Bellow Expansion Joint, flanged with the nozzle.
On the suction side this technique will work, but if the pump is building up high pressure like multistage pump, then on the discharge side, the required bellow may be very costly, or unavailable. Then under such circumstances other means of vibration isolation like snubbers type supports can be used to achieve the objective.
If you want detailed advice, send me the pump data, as well as piping configuration.

The vertical submerged pump used in many sulfuric acid plants has piping "anchor" recommmended by manufacturer, www.lewispump.com .
While their website does not show installation recommendations, you could request bulletin 185 that has figure 1. that shows 3 elbows from the pump discharge connection to "anchor" that is fixed to the grillage on top of typical tank. The structural support resembles a large "wobble" plate and has some lateral flexibility with the stiff plate axis oriented in the piping axis.
The actual stiffnesses of the "anchor" are much less than the CAESARII default stiffness value. Approximate stiffness could be 1E5 lb/inch , and less for lateral direction. This reduces the large calculated loads from anchor located near the pump. Their bulletin states "Proper installation of constraint will force all pipe expansion away from pump." That may be their intent, but with the CAESARII analysis there will be the large loads with two fixed points of the pump connection and anchor - if no flexibility is included for the anchor or equipment connection.
My opimion is that API 610 has much to say about horizontal pumps, but over-simplifies treatment of vertcal in-line pumps by just applying factor 2X for allowable forces and moments. Critical clearance areas (impellor, bearings) of vertical suspended pumps could be some feet distant from the nozzle loads that would possibly cause distortion of the casing, but API 610 considers vertically suspended pumps same as horizontal pumps in regard to allowable forces and moments. The appendix F of API 610 has examples for horizontal pumps and vertical in-line pumps, but does not have vertical suspended pump example. I would say vertical suspended double casing pump resembles a pendulum such that external loads are somewhat isolated from the loads on the nozzles.

I would suggest the following
a) Ask the person wanting the anchor to specify how accurately he can install it. He will say 1/16" for a fabrication, maybe a few thou for an adjustable support. (Points wear off bolts used as adjustable "legs" in about 10 minutes thus rendering the support useless). Use the thermal expansion if he insists that anchor can be installed with zero tolerance.
b) Prepare a simple textbook "built-in" cantilever calc with the the pipe size and nominal cantilever length. (A "guided cantilever" for those old enough to remember). Plug in the deflection to calculate the force.
c) Await the long face as the person realises the impracticality of what he has just asked for.

I can confirm from 1st hand experience that nozzles do fall off pumps with close coupled anchors !

Best Regards
Andrew