# Numerical Study on the Bending Performance of Steel-Ribbed Composite Slabs for Substations
## 5 Bidirectional Bending Performance of Composite Slabs
### Discussion of Results  
Figure 21 presents the load-deflection curves for the double-spliced composite slab, triple-spliced composite slab, and the cast-in-place monolithic slab under bidirectional loading. The loading behavior of the slabs can be categorized into five distinct stages: the decompression state, elastic state, incipient cracking state, diagonal cracking state, and fully cracked state. In the initial decompression stage, the camber effect induced by prestressing is completely counteracted, bringing the deflection of the slabs to a condition equivalent to the starting state of non-prestressed members. Subsequently, as the load increases, the slabs transition into the elastic stage, exhibiting high stiffness with no damage. It can be seen that all the slabs demonstrate comparable stiffness during the elastic phase prior to cracking. Upon reaching the incipient cracking stage, transverse cracks begin to form perpendicular to the direction of the prestressed steel, leading to a gradual reduction in stiffness. The cracking loads of the double-spliced composite slab, the triple-spliced composite slab, and the cast-in-place monolithic slab are at similar levels, 53.701, 51.374, and 52.538 kN/m\({}^{2}\), respectively. As diagonal cracks initiate and propagate, the stiffness further diminishes, eventually stabilizing in the final, fully cracked state. Compared with unidirectional loading conditions, the cracking load and bearing capacity of the double-spliced and triple-spliced bidirectional composite slabs both have great improvements, by more than 60%. The double-spliced composite slab and the cast-in-place monolithic slab exhibit a similar response and failure load. However, there are some differences in the crack propagation and post-crack stiffness between the composite and monolithic slabs. Due to the existence of the splicing joints in composite slabs, the overall integrity is reduced and the diagonal cracking is slightly delayed compared with the monolithic slab. Therefore, the post-crack stiffness of the double-spliced composite slab is slightly lower than that of the monolithic slab during the early stage of cracking, but the difference diminishes after cracks have fully developed. For the triple-spliced composite slab, its response is softer as a result of a marginally lower ratio of the prestressing steel, with decreases of 3.24% and 4.68% for failure load compared with the cast-in-place slab and double-spliced composite slab, respectively. In terms of ultimate mid-span deflection, the double-spliced and triple-spliced composite slabs exhibit values of 14.85 mm and 14.88 mm, respectively. These deflections are 7.53% and 7.75% greater than that of the cast-in-place slab, which measures 13.81 mm. This indicates that the presence of splicing joints slightly reduces the overall structural integrity of the slabs; however, the arrangement of the joints has a negligible impact on serviceability. Overall, all three bidirectional slabs demonstrate excellent ductility throughout the loading process. Figure 20: Load–stress curves for reinforcement at the center of the slab: (**a**) Prestressing steel; (**b**) Joint-connecting rebar. The failure of all three slabs is initiated by the yielding of the longitudinal prestressing steel oriented parallel to the short edge of the bidirectional loading slab. To incorporate more failure modes and investigate the influence of major factors, parametric analysis was conducted regarding the ratio of prestressing steel, concrete strength, strength, and diameter of the joint-connecting rebars. The thickness and space of the steel ribs were not involved in the parametric analysis because previous studies [26] have shown that the steel ribs mainly enhance the stiffness during construction and have a very limited contribution after composition.