What type of elevator... hoist type or hydraulic? Elevators generally have side rails for guidance and breaking. Can you find out from the elevator supplier what fastening is required? Some jurisdictions require a pit that may be 5'6" deep complete with illumination and a ladder. Is a drainage sump required? Lots of questions.

Dik

"detail the connection"... To What?

Mike McCann, PE, SE (WA)

Thank you Dik and Msquared48.
- It will probably be hoist type since it is for three-storey only.
A friend helped to make an assumption of 15kN load on each hook.
I didn't know how he got 15kN but I used that value plus floor load
to design four steel columns supporting the elevator at each corner.

- I am seeking for connection detail of hooks to columns (or beams)
and the elevator itself to hooks.

I will really appreciate if you correct me on anything that is not
compliant with actual construction and practice.

Ask the architect what manufacturer and model the elevator will be. Then call the elevator manufacturer and ask them for the design criteria. At least here in California we will get elevator shop drawings which provide forces on hoist beam, fall arrest beam, and guide rail columns for both typical usage and seismic forces.