To calculate the flexural-shear resistance of prestressed concrete members without shear reinforcement, a method based on Critical Shear Crack Theory (CSCT) has been presented for the new Eurocode (prEN1992). Two alternatives provided in draft 7/2020 (prEN1, prEN2) are the starting point given, and two other alternatives are proposed for analysis by this thesis (prEN3, prEN4). These alternatives and other design codes were evaluated based on the concepts involved, assumptions made, and the results obtained compared with experimental results.

The research started by compiling basic concepts handled by empirical (ACI318-19 or EC2), MCFT-based (AASHTO-LRFD), and CSCT-based (prEN1992) approaches for the calculation of the flexural-shear resistance of members without shear reinforcement. Experimental results of slender prestressed concrete beams without shear reinforcement were collected from the ACI-DAfStb-PC/2015 database, and these tests were classified into subsets according to the relevant criteria used in the different design codes such as type of shear failure or cross-section shape. Subset 1 groups rectangular and I/T shaped beams with flexural-shear failure. Subset 2 retains the rectangular beams from subset 1, and subset 3 filters the tests from subset 2, applying conditions checking for anchorage or flexural failures. In addition, different critical locations were assumed, some according to design code suggestions (x_r=d or x_r=a-d), and others according to an assumption based on test results (x_r=0.65a).

The comparative evaluation results of the flexural-shear strength estimated by the different design codes with the experimental results were made for the 3 subsets and 3 critical locations defined. From this data set, the critical location x_r=a-d was chosen as the appropriate based on a general evaluation of the precision acquired by the approaches and the higher flexural stresses present. Then the data for the 3 subsets at this location are captured and presented in a range from lowest to highest from here on.

Based on the results, it was concluded that AASHTO-LRFD and prEN1 are the most precise approaches with COV less than 0.25. However, AASHTO-LRFD tends to obtain very conservative results. ACI318-19M has the worst performance in terms of precision with COV in the range of 0.29 to 0.45, its approximate method tends to get results below the desired level of safety, and its detailed method tends to be more conservative. EC2 achieves a regular precision with COV between 0.28 and 0.31, the linearized alternative for the new Eurocode (prEN2) obtains similar COV values ending up with a regular precision as well, and both approaches have a good level of safety.

To improve prEN2, new alternatives (prEN3 and prEN4) were derived based on the linearization of the main failure criterion of the CSCT. Of the alternatives, prEN4 was the most precise (COV=0.25-0.26) with a good level of safety, recognizing that this alternative correctly applies the concept of prestressing as preload and incorporates the effect of the normal loads on the shear strength with a direct relationship dependent on the ratio d/a_cs, where a_cs=|M_Ed/V_Ed |. Finally, all approaches were tested in terms of usability in design cases for simply supported and continuous slab decks, concluding that prEN4 has a significant advantage in usability since it is an expression similar to the one used in the current EC2, and also obtains results that are on the safe side compared with a more precise approach like prEN1.
Alternative 4 (prEN4) is an approach with good accuracy and safety level, and can incorporate the effect of prestress on shear resistance straightforwardly and consistently, complying with the main assumptions of the CSCT and the assumption of prestressing as a preload indicated for the Eurocodes, thus incorporating only the influence of normal loads applied to the neutral axis to contribute to the shear resistance. prEN4 is also an approach that has been shown to capture the influence of all parameters considered to obtain a reliable estimation of the flexural-shear resistance; therefore, it is recommended to consider it as a potential alternative for a handy and reliable calculation of the flexural-shear resistance of beams without shear reinforcement.