What's the software you want to creat it in? A lot of non-linear engineering software packages allow rigid connection by rigid links or rigid surfaces (so called tied mesh).

What software are you using?

I'm using ABAQUS, and I did select General contact, but still doesn't work as supposed to be. 

I've attached the input file above. 

I prefer the first step is direct contact.

What kind of contact you want to simulate?

I agree with DR Mohannad

 Thanks Dr. Al-Sherrawi,

What do you mean by "Direct contact"? I haven't seen this option in ABAQUS. 

Thanks Dr. Ali A. Abdulhameed,

Between Steel & Concrete, and Concrete-Concrete. 

Dear Qusay..I agree with Dr, alsherrawi answer..Alsherrawi indicate that you can use direct contact between the steel and concrete (fully bonded) the option is existed in ABAQOUS..regards

To keep you updated, General contact works for me. 

Does anyone have an idea to solve this issue?

(The general contact domain for modeling contact interactions in Abaqus/Standard has double-sided facets. Initial contact adjustments for resolving gaps and overclosures when a surface with double-sided facets is paired with any surface having double-sided facets may be incorrect. Similarly, adjustments for double-sided surfaces crossing each other may be incorrect and no additional warnings or error messages will be issued. In all these cases, we recommend using single-sided surfaces under *CONTACT INITIALIZATION ASSIGNMENT to handle initial adjustments more precisely and avoid possible convergence problems.)

I'm modeling steel tube filled with concrete and I see there is a tiny gab when I assemble them together. I tried to set up (CONTACT INITIALIZATION ASSIGNMENT) with default settings but it doesn't work. making finer mesh gives me another error (Distortion error)