1 Introduction
2 Background
2.1 Effective Slab Width
Codes/existing studies | Equations for \({{\varvec{B}}}_{{\varvec{e}}{\varvec{f}}{\varvec{f}}}\) | Parameters | Beam reinforcement |
---|---|---|---|
ACI 318 (2019) | b + Min (16ts, L0, Ln/4) | b, ts, L0, Ln | Normal-strength steel |
Eurocode 8 (1996) | b + 4ts | b, ts | |
SNiP code (1997) | Min (L/6, b + 12ts) | b, ts, L | |
Durrani and Zerbe (1987) | b + 2 h | b, h | |
Pantazopoulou et al. (1988) | b + 6d | b, d | |
Zhen et al. (2009) | b + 4 h | b, h | |
Qi et al. (2010) | b + Min (Max(L/5, 3 h), L0/2) | b, h, L, L0 | |
Ning et al. (2016) | b + 5.4 h | b, h |
2.2 Review of RC Structures with High-Strength Steel
3 Description of Analitical Study
3.1 Study Parameters
Beam reinforcement | Type | Slab thickness, ts (mm) | Beam height/Beam span, h/L (mm/mm) | ||
---|---|---|---|---|---|
Grade | Yield strength (MPa) | Reinforcement ratio, ρ (%) | |||
60 | 420 | 1.5 | Type I (with a clear yielding point) | 100 | 500/5000 |
80 | 593 | 1 | 150 | 600/6000 | |
100 | 690 | 0.85 | Type II (without a clear yielding point) | 200 | 700/7000 |
120 | 830 | 0.7 |
3.2 Model Development
Elements | Beam | Slab | ||
---|---|---|---|---|
Properties | Horizontal truss | Diagonal truss | Horizontal truss | Diagonal truss |
Cross-sectional area (mm2) | 3923 | 1298 | 1800 | 196 |
Young’s modulus (GPa) | 29.5 | 132.55 | 25.72 | 355.01 |
3.3 Model Validation
4 Analytical Results
4.1 Effects of Beam Reinforcement Grade
4.2 Effect of Slab Thickness
4.3 Effect of Height and Span Length of Beam
5 Design Recommendations
6 Conclusions
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The slab reinforcement can contribute to the beam flexural strength in the negative moment region. The contribution reduces as moving far from the center of the beam due to the shear lag effect, though.
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When the grade of the beam reinforcement increases, the behavior of beam-column-slab assemblage becomes more flexible under lateral loads. This higher flexibility results in a larger drift ratio at the point when the concrete in the beam reaches ultimate compression strain. The larger drift ratio at this point increases the stress/strain in the slab reinforcement, resulting in a wider effective slab width for the cases with HSS.
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The effective slab width increases with the increase of the drift ratio since the strain penetrates into more slab reinforcement. At large drift ratios, the effective slab width is insensitive to the beam reinforcement grade. However, at low drift ratios, this width increases as the beam reinforcement grade increases, particularly at the point where the unconfined concrete reaches ultimate compression strain.
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The effective slab width for the negative moment is insensitive to the slab thickness since the concrete has cracked. On the other hand, the height/span length of the beam influences the effective slab width. However, its effect is independent of the one from the beam reinforcement grade.
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In general, design code provisions tend to have a lower effective slab width and underestimate the contribution of the slab reinforcement. The simulation results obtained from this paper as well as those from existing studies show a much higher effective slab width. The results from this paper indicate an effect of the beam reinforcement grade on the effective slab width.
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Based on the parametric study results, a modification coefficient was derived to incorporate the effect of the beam reinforcement grade on the effective slab width. This coefficient was applied to the design equation developed by Zhen et al. (2009) which shows a similar result for the case with normal-strength reinforcement.
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The proposed simple expression with the modification coefficient can reasonably capture the effective slab width obtained from the simulations, and it can be applied for the reinforced concrete T-beam configured with HSS in negative moment regions to estimate the beam nominal flexural strength with contributions of slab reinforcement.