Flexural behavior of steel deep beams prestressed with externally unbonded straight multi-tendons

External prestressing is one of the most powerful techniques to retrofit and strengthen the existing beams and columns. In this paper, the flexural behavior of deep beam prestressed with multi-tendons is investigated under concentrated forces for both post- and pre- tensioning processes. Solutions for displacements and stresses are achieved based on Timoshenko beam theory. Besides, a statically indeterminate system was established, and a compatibility condition between the beam and tendons was founded to solve the increase in tendon force in loading period in pre-tensioning. Verifications were performed in tables by applying Finite element analysis. Finally, parameter studies were carried out to examine the effects of tendon force and eccentricity on the flexure of beams. Numerical results were summarized into a series of curves indicating the distribution of warping stresses on flanges and the increases in sub-tendon forces.