# Numerical Study on the Bending Performance of Steel-Ribbed Composite Slabs for Substations
## 4 Unidirectional Bending Performance of Composite Slabs
### Discussion of Results  
Figure 14 shows the load-deflection curves for composite slabs A and B, and both present typical two-stage load-bearing characteristics with the point of concrete cracking as the turning point. Before cracking, the composite slab is in the elastic stage, and the load-deflection curve is approximately a straight line. After cracking, the curves show a turning point, indicating a significant reduction in the slab's stiffness. As the load increases and cracks develop, the post-crack stiffness of the composite slab remains relatively stable until failure. Throughout this entire process, the composite slab exhibits commendable ductility. The stiffness and ultimate capacity of composite slab A are slightly greater than those of composite slab B, due to a marginally higher prestressing steel ratio in composite slab A compared with composite slab B.  
The theoretical results of the flexural capacity using the codes [22; 25] were also calculated here for reference and double-checked for the rationality of the numerical analysis. Composite slab A was taken as an example, with the calculation process outlined as follows:  
The width and thickness of composite slab A is \(b=1650\) mm, \(H=130\) mm. The number of the prestressing steel is \(n=22\) with the diameter \(d=5\) mm and the yielding strength \(f_{py}=1570\) MPa. The concrete cover of the prestressing steel is \(c=23\) mm. The calculation span is \(l_{0}=2500\,-\,50\,\times\,2=2400\) mm.  
Figure 13: Analysis results of composite slab B under unidirectional loading: (**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.  
The effective depth of the section is  
\[h_{0}=H-c-d/2=130-23-5/2=104.5\;\mathrm{mm}. \tag{1}\]  
The area of reinforcement is  
\[A_{p}=(n\pi d^{2})/4=(22\times\pi\times 5^{2})/4=431.969\;\mathrm{mm}^{2}. \tag{2}\]  
The relative height of the compression zone is  
\[\xi=(A_{p}f_{py})/(f_{c}^{\prime}bh_{0})=(431.969\times 1570)/(26.8\times 1650 \times 104.5)=0.147. \tag{3}\]  
The section resistance moment coefficient is  
\[\alpha_{s}=(1-(1-\xi)^{2})/2=(1-(1-0.147)^{2})/2=0.136. \tag{4}\]  
The bending capacity of the section is  
\[M=\alpha_{s}f_{c}^{\prime}bh_{0}{}^{2}=0.136\times 26.8\times 1650\times 104.5^{ 2}=6.567\times 10^{7}\;\mathrm{N\cdot mm}. \tag{5}\]  
The external uniformly distributed load is  
\[q=(8\times M)/({bl_{0}}^{2})=(8\times 6.567\times 10^{7})/(1650\times 2400^{2} )=55.278\;\mathrm{kN/m}^{2} \tag{6}\]  
Similarly, the external uniformly distributed load of composite slab B can be obtained as \(52.955\;\mathrm{kN/m}^{2}\). The errors between the theoretical calculations and the simulation results for slabs A and B are \(-5.13\%\) and \(-7.76\%\), respectively. The theoretical calculations yield slightly lower values than those obtained from the FE models. This is likely due to the omission of the contribution from the steel ribs in the theoretical calculations. Overall, the FE analysis demonstrates a relatively high level of accuracy and can be reliably utilized for subsequent static analyses of bidirectional slabs.