Connection Timeout Expired. The timeout period elapsed while attempting to consume the pre-login handshake acknowledgement.

Error Message : Connection Timeout Expired. The timeout period elapsed while attempting to consume the pre-login handshake acknowledgement. This could be because the pre-login handshake failed or the server was unable to respond back in time. The duration spent while attempting to connect to this server was – [Pre-Login] initialization=13477; handshake=14506; 

Error comes when try to connect sql server instance from another machine

Solution:

Enable port 1433 in firewall.