# Numerical Study on the Bending Performance of Steel-Ribbed Composite Slabs for Substations
## 5 Bidirectional Bending Performance of Composite Slabs
### Triple-Spliced Composite Bidirectional Slab  
Figure 17a,c,e,g show the deflection of the double-spliced composite bidirectional slab, the distribution of cracks on the bottom surface, and the stress in the prestressing steel at the cracking load of 51.374 kN/m\({}^{2}\). The mid-span deflection is 1.181 mm. Cracks initially appear at the center of the slab and extend in the transverse direction parallel to the long edge of the slab. The stress in the prestressed steel is approximately 1030 MPa with a uniform distribution. The stress in the transverse rebars demonstrates a concentration at the joints at the third-point locations, with a maximum value of 45.82 MPa. Figure 17b,d,f,h depict the corresponding behaviors at the failure load of 96.555 kN/m\({}^{2}\), slightly lower than that of the double-spliced composite bidirectional slab. The mid-span deflection at failure, which is 14.88 mm, is comparable to that of the double-spliced composite bidirectional slab. The crack distribution on the bottom surface is similar to that of the double-spliced composite bidirectional slab, with a checkerboard pattern near the mid-span and extending  
Figure 16: Load–stress curves for reinforcement at the center of the slab: (**a**) Prestressing steel; (**b**) Joint-connecting rebar.  
Figure 15: Analysis results of double-spliced composite bidirectional slab: (**a**) Deflection at cracking; (**b**) Deflection at failure; (**c**) Initial bottom cracks at cracking; (**d**) Distribution of bottom cracks at failure; (**e**) Stress in prestressing steel at cracking; (**f**) Stress in prestressing steel at failure; (**g**) Stress of transverse rebar stress at cracking; (**h**) Stress of transverse rebar stress at failure.  
diagonally toward the corners. The prestressing steel near the center of the slab has yielded, resulting in the failure of the slab. The maximum stress of the transverse rebars occurs in the full-length rebars crossing the joints at the third-point joint locations, measuring 304.4 MPa. The other short rebars in the precast slab are at lower stress levels, most below 200 MPa.  
Figure 17: Analysis results of triple-spliced composite bidirectional slab: (**a**) Deflection at cracking; (**b**) Deflection at failure; (**c**) Initial bottom cracks at cracking; (**d**) Distribution of bottom cracks at failure; (**e**) Stress in prestressing steel at cracking; (**f**) Stress in prestressing steel at failure; (**g**) Stress of transverse rebar stress at cracking; (**h**) Stress of transverse rebar stress at failure.  
Figure 18a,b illustrate the load-stress curves of the prestressed steel and the joint-connecting rebar at the center of the slab. When the load reaches about 50 kN/m\({}^{2}\), the stress in the prestressing steel begins to develop rapidly due to concrete cracking in the transverse direction, which is consistent with the double-spliced composite slab. In contrast, for the joint-connecting rebars, the load-stress curve shows a turning point at 65 kN/m\({}^{2}\), significantly higher than that observed in the double-spliced composite bidirectional slab. Furthermore, the maximum stress of the transverse joint-connecting rebars is much lower at the center of the slab, which is only about 130 MPa. This is attributed to the monolithic nature of the concrete at the slab's center, indicating that joint position is critical to the stress distribution of the transverse reinforcement.