Calculation Method of Axial Compression Capacity for Rectangular Short Reinforced Concrete Columns Confined with Innovative Five-Spiral Stirrups
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摘要:
螺旋箍筋应用于钢筋混凝土柱能明显提高柱的承载力及延性，为了研究五螺箍矩形混凝土短柱在轴心受压荷载作用下的力学性能和轴压承载力计算方法，首先，结合已有文献中的试验建立有限元模型，并将有限元分析结果与试验结果进行对比，以验证有限元模型的正确性；其次，基于材料用量相等的原则，设计了4种不同配箍形式的矩形截面柱，基于已验证了的有限元模型开展了不同混凝土强度对上述4种柱的轴压承载力和延性的影响研究；最后，通过对五螺箍柱进行参数分析，提出了基于体积配箍率的轴压承载力计算方法. 研究结果表明：五螺箍较五环箍、矩形箍和矩形螺旋箍柱构件承载力均值分别提高0.78%、6.70%和13.73%，延性系数均值分别提高2.00%、10.32%和10.41%，说明五螺箍柱有较高的承载力和延性；与各国规范提出的公式进行对比，本文建议的轴压承载力计算方法较为简便，且与试验值的误差均值仅为2.83%.
Abstract:Application of spiral stirrups can obviously improve the axial bearing capacity and ductility of reinforced concrete (RC) columns. This paper aims to study the mechanical properties of rectangular short RC columns confined with five-spiral stirrups under axial compression and to present a calculation method for the axial compression bearing capacity by finite element analysis of a number of concrete short column specimens under axial compressive loading. Firstly, a finite element model is established on the basis of experiments available in the literature, and the finite element analytical results are compared with experimental values to verify the correctness of the finite element model. Subsequently, the finite element model is used in a parametric analysis to study the likely influence of concrete strength on the axial bearing capacity and ductility of rectangular short columns with 4 different stirrup configurations which are designed in a principle of equal material consumption. Finally, through analysis of influencing factors for the rectangular short RC columns confined with five-spiral stirrups, a calculation method of axial compression bearing capacity based on volume-stirrup ratio is proposed. The analysis results show that compared with those of RC columns with five-hoop stirrups, rectangular stirrups and rectangular-spiral stirrups, the average bearing capacity of the RC columns with the five-spiral stirrups is increased by 0.78%, 6.70%, and 13.73%, respectively; and the average ductility coefficient is increased by 2.00%, 10.32%, and 10.41%, respectively. It demonstrats that the five-spiral stirrup columns have higher bearing capacity and ductility. In addition, compared to the formulas recommended by codes of different countries, the calculation method of axial compression bearing capacity proposed in this paper is relatively simple, and the average error between calculation and experimental values is only 2.83%.
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图 2 4种不同配箍形式矩形截面柱
Figure 2. Four types of rectangular columns with different stirrup configurations
图 7 约束作用系数-体积配箍率关系
Figure 7. Relationship between confinement coefficients and volume-stirrup ratios
表 1 试验和有限元计算结果对比
Table 1. Comparison of experiment and finite element calculation results
试件编号 材料强度/MPa 钢筋配置/mm 轴压承载力/kN 混凝土 纵筋 大螺箍 小螺箍 纵筋 大螺箍 小螺箍 试验值 模拟值 误差/% C2-1 39.4 420 280 280 D25 D13@50 D13@50 21670 22378 3.26 C2-3 40.3 D16@70 D13@70 20411 22109 8.32 C2-4 40.3 D13@60 D13@60 19336 21749 12.47 C2-5 39.4 D10@50 D10@50 18181 20128 10.70 
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表 2 有限元模型主要参数
Table 2. Main parameters of finite element models
编号 螺旋箍筋
间距/mm螺旋箍筋
强度/MPa混凝土
强度/MPa大（小）螺箍
直径/mm体积配箍率/% 峰值荷载/kN DI M-1 45 335 26.8 10(6) 2.15 11020.60 1.84 M-2 50 335 26.8 10(6) 1.93 10779.40 1.78 M-3 55 335 26.8 10(6) 1.76 10613.50 1.76 M-4 50 335 23.4 10(6) 1.93 9979.90 1.97 M-5 50 335 29.6 10(6) 1.93 11472.50 1.75 M-6 50 400 26.8 10(6) 1.93 11163.90 1.94 M-7 50 500 26.8 10(6) 1.93 11744.80 2.16 M-8 50 335 26.8 10(8) 2.45 11078.90 2.13 M-9 50 335 26.8 12(8) 3.01 11756.80 2.27
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表 3 9个模型的轴压承载力计算
Table 3. Axial compression bearing capacity calculation of nine models
编号 模拟值 Nue/kN 计算值/kN 相对误差/% ${N_{{\text{u1}}}}$ ${N_{{\text{u2}}}}$ ${N_{{\text{u3}}}}$ ${N_{{\text{u4}}}}$ ${N_{{\text{u5}}}}$ ${\delta _{\text{1}}}$ $ {\delta _{\text{2}}} $ ${\delta _{\text{3}}}$ ${\delta _{\text{4}}}$ ${\delta _{\text{5}}}$ M-1 11020.60 10024.25 10459.24 6543.56 7871.88 11039.23 −9.04 −5.09 −40.62 −28.57 0.17 M-2 10779.40 9601.01 10019.12 6543.56 7871.88 10675.10 −10.93 −7.05 −39.30 −26.97 −0.97 M-3 10613.50 9258.53 9656.58 6543.56 7871.88 10373.72 −12.77 −9.02 −38.35 −25.83 −2.26 M-4 9979.90 9001.25 9362.72 6002.76 7162.57 9610.15 −9.81 −6.18 −39.85 −28.23 −3.70 M-5 11472.50 10094.93 10555.22 6988.93 8456.03 11552.11 −12.01 −8.00 −39.08 −26.29 0.69 M-6 11163.90 10104.07 10515.16 6543.56 7871.88 11386.56 −9.49 −5.81 −41.39 −29.49 1.99 M-7 11744.80 10878.01 11257.04 6543.56 7871.88 12481.12 −7.38 −4.15 −44.29 −32.98 6.27 M-8 11078.90 10056.88 10453.68 6543.56 7871.88 11110.52 −9.22 −5.64 −40.94 −28.95 0.29 M-9 11756.80 10962.58 11334.17 6543.56 7871.88 11579.44 −6.76 −3.59 −44.34 −33.04 −1.51 绝对值均值 9.71 6.06 40.91 28.93 1.98 标准差 0.0197 0.0175 0.0215 0.0261 0.0195
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表 4 4个试验构件的轴压承载力
Table 4. Axial compression bearing capacity calculation of four test members
编号 试验值[16]/kN 计算值/kN 相对误差/% ${N_{{\text{u1}}}} $ ${N_{{\text{u2}}}} $ ${N_{{\text{u3}}}} $ ${N_{{\text{u4}}}} $ ${N_{{\text{u5}}}} $ ${\delta _{\text{1}}} $ ${\delta _{\text{2}}} $ ${\delta _{\text{3}}} $ ${\delta _{\text{4}}} $ ${\delta _{\text{5}}} $ C2-1 21672.00 20569.22 21094.45 12090.38 11518.40 22156.09 −5.09 −2.66 −44.21 −46.85 2.23 C2-2 20412.00 19005.14 19508.17 12291.21 11706.16 20390.35 −6.89 −4.43 −39.78 −42.65 −0.11 C2-4 19332.00 19334.76 19871.39 12291.21 11706.16 20319.01 0.01 2.79 −36.42 −39.45 5.11 C2-5 18181.00 17305.58 17781.27 12090.38 11518.40 18883.65 −4.82 −2.20 −33.50 −36.65 3.86 绝对值均值 4.20 3.02 38.48 41.40 2.83 标准差 0.029 4 0.009 7 0.046 0 0.043 9 0.021 6
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