JCT - Is the contractor liable to carryout and complete the design in D&B contract?

If the Contractor is taken the responsibility of carrying out and complete the design in D&B Jct contract is it okay? and what are the consequences of taking this responsibility?

The design responsibility in this scenario is exactly the same as any other obligation to carry out work. Therefore yes it is ok, though most contractors will want to appoint a specialist designer depending on the size and complexity of the work. The key consequence to ensure is that the design obligation is based on skill and care (which is insurable) not fitness for purpose whi8ch is the general standard for the construction activities (and is not readily insurable).