Shear Analysis of Non-Prismatic Concrete Beams

Due to the alteration in height, the centroidal axis of a non-prismatic beam has a non-linear layout when compared to a prismatic beam. Therefore, in case of a non-prismatic beam, the vertical cross-section cut, on which analysis from the codes are performed, is no longer perpendicular to the centroidal axis, unlike prismatic beam. Moreover, due to the geometry, these beams are prone to shear failure which is mainly due to the vertical component of the inclined cross-section forces. The main focus of this study is to compare the cross-section results obtained on inclined and vertical cut and also to validate the inclusion of the vertical component of the inclined forces in the shear capacity equation. Different approaches are proposed to calculate the cross-section results on an inclined cut, with the internal forces in the global (horizontal and vertical direction) as well as in the local direction (perpendicular and parallel direction of the cut). From the procedure it was seen that in a prismatic beam, subjected to four point bending test, the cross-section results remains the same irrespective of how the analysis is performed. However, in case of non-prismatic beams, the bending moment resistance obtained on an inclined cut, which is perpendicular to the centroidal axis with the forces in local direction, is greater than that obtained on a vertical cut. Therefore to be conservative it is recommended to perform cross-section analysis on a vertical cut in a non-prismatic beam. A procedure to calculate the shear capacity of non-prismatic beam is determined in this study. First, the shear resistance contributed by concrete and stirrups are calculated at the assumed critical section. Then the inclined internal forces are determined for each load case and the capacity of the beam is either reduced or increased by the vertical component. This capacity is compared with the applied loading and is checked for failure. Since the shear capacity is influenced by the applied loading, failure of the beam is defined as the load for which the determined capacity is lower than the applied loading. The results obtained from this procedure are in good agreement with the limited experimental data available. Therefore, it can be concluded that the vertical component of the inclined cross-section forces should be considered in the shear capacity equation. Finally non-prismatic bridge deck is also studied and different errors that engineers make in practice is further analyzed. Due to the non-linear layout of centroidal axis, engineers find it difficult to perform analysis on non-prismatic beams. Therefore, the cross-section of the deck is modified, such that the centroidal axis remains linear. The results determined on a modified deck is equal to that obtained on the original model. Another error engineers make is ignoring the inclination of internal forces, which leads to underestimation of the capacity. This study shows that the vertical component of the inclined cross-section forces, which is considered in the shear capacity, should be determined based on the bending moment obtained for the load combination where applied shear force is governing.