Design of partially prestressed concrete beams based on the cracking control provisions

In the technical literature the combination of conventional steel reinforcement and prestressing steel as strength reinforcement in a flexural concrete member is usually implied by the term partial prestressed element. Partially prestressed elements are used in the practice and their design is based on rational analysis, on the satisfaction of the requirements of both serviceability and ultimate strength limitations and finally on the engineering judgment. In the present work the estimation of the required partial prestressing based mainly on the crack control of concrete is proposed. First, based on the allowable crack width as it is stated by the codes (ACI 318 or Eurocode 2), the stress of the non-prestressed reinforcement is estimated. Then the depth of compression zone is derived using a cubic equation formed for this purpose. Further the required effective pre-strain of the prestressing steel and henceforth the required prestress force are calculated. Design charts and three numerical paradigms are also presented and commented herein.