After Adding Addition Web server in F5 load balancer I'm getting Session time out issue.
Which type of session time-out issue? Is it immediate or after some amount of time. Is it every time you start with a fresh browser session and try to connect, or intermittent?
If you are load balancing between multiple web servers, you will need to enable Sticky sessions, or equivalent. Essentially, a single individual browser session cannot be served from multiple different web servers.