Ultimate flexural capacity of steel reinforced concrete beams with rectangular section
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摘要:
采用JGJ 138—2016、СИ 3-78、YB 9082—2006、AISC 360-16、叶列平公式，计算了所收集的51个矩形截面型钢混凝土(SRC)梁试件的抗弯极限承载力，并将计算结果与试验值进行比较；分析了所收集试件的参数范围及现有计算方法出现计算误差的原因，讨论了现有计算方法在计算理论等方面存在的局限性，并进行理论推导，提出了矩形截面SRC梁抗弯极限承载力计算方法；采用所提出的计算方法，计算了所收集试件的抗弯极限承载力。分析结果表明：现有计算方法的计算值与试验值均存在一些偏差；СИ 3-78中的受压区高度取值不合理，且该方法的计算误差随混凝土强度提高而增大；JGJ 138—2016未考虑中性轴与型钢位置的相对关系对计算结果的影响，存在局限性；YB 9082—2006与AISC 360-16未考虑型钢与混凝土相互作用及型钢的布置方式等问题；叶列平公式计算结果较为保守；采用提出的抗弯极限承载力计算方法得到的计算值与试件试验值的比值均值为0.953，方差为0.015，计算值与试验值吻合较好；所收集SRC梁试件的含钢率为1.77%~5.77%，小于YB 9082—2006所建议的合理含钢率范围，因此，今后还需进一步开展高含钢率试件的补充试验，以便完善矩形截面SRC梁的抗弯极限承载力计算方法。
Abstract:JGJ 138—2016, СИ 3-78, YB 9082—2006, AISC 360-16, and YE Lie-ping's formulas were used to calculate the ultimate flexural capacities of 51 collected specimens of steel reinforced concrete (SRC) beams with rectangular sections. The calculated results were compared with the test values. The ranges of parameters of the collected specimens and the reasons for the calculation errors of the existing calculation methods were analyzed. The limitations of the existing calculation methods were discussed in terms of the calculation theory and other aspects. Theoretical derivations were performed, and a method for calculating the ultimate flexural capacities of SRC beams with rectangular sections was proposed, and the ultimate flexural capacities of the collected specimens were calculated by using the proposed method. Analysis results show that some deviations are found between the calculated values obtained by the existing calculation methods and the test values. The height value of the compression zone in СИ 3-78 is not appropriate, and the calculation error of this method increases with the increase in concrete strength. The impact of the relative relationship between the neutral axis and the position of the structural steel on the calculation results is not considered in JGJ 138—2016, and limitations exist. YB 9082—2006 and AISC 360-16 do not take into account the interaction between structural steel and concrete or the arrangement of the structural steel. The YE Lie-ping's formulas produce conservative results. The average ratio of the values calculated by the proposed method for the ultimate flexural capacity to the test values of specimens is 0.953, with a variance of 0.015. The calculated values agree well with the test values. The steel ratios of the collected SRC beam specimens range from 1.77% to 5.77%, which is smaller than the reasonable steel ratio range suggested by YB 9082—2006. Therefore, it is necessary to carry out further supplementary tests of specimens with high steel ratios in the future, so as to improve the calculation method for the ultimate flexural capacity of SRC beams with rectangular sections.
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图 6 现有计算方法与本文计算方法的计算值与试验值之比
Figure 6. Ratios of calculated values to test values for existing calculation methods and proposed calculation methods
图 7 JGJ 138—2016中型钢腹板的计算模型
Figure 7. Calculation model of structural steel web in JGJ 138—2016
图 10 不同混凝土强度下СИ 3-78计算值与试验值之比
Figure 10. Ratios of calculated values to test values of СИ 3-78 for different concrete strengths
表 1 试件详细参数
Table 1. Detailed parameters of specimens
数据来源 试件编号 截面尺寸/mm 型钢 含钢率/% 受拉纵筋 f/MPa fy/MPa fcu/MPa 文献[10] SB-1 220×320 H200×100×5.5×8，居中 3.71 2Φ18 331.00 366.92 50.63 SB-2 220×400 H200×100×5.5×8，下偏40 mm 2.97 2Φ18 331.00 366.92 52.54 文献[11] C7 180×250 H100×100×6×8，居中 4.68 2Φ12 270.00 552.00 33.00 文献[12] SRCB-1 200×350 H200×100×5.5×8，上偏5 mm 3.73 2Φ14 305.00 365.00 50.60 SRCB-2 200×350 H200×100×5.5×8，上偏25 mm 3.73 2Φ14 305.00 365.00 50.60 SRCB-4 200×350 H200×100×5.5×8，上偏5 mm 3.73 2Φ20 305.00 390.00 50.60 SRCB-5 200×350 H200×100×5.5×8，上偏5 mm 3.73 2Φ14 305.00 365.00 56.00 SRCB-6 200×350 H200×100×5.5×8，上偏5 mm 3.73 2Φ14 305.00 365.00 66.20 文献[13] SRCL2-100%-1 d 200×300 H150×100×6×9，居中 4.32 3Φ16 356.05 399.75 52.21 SRCL4-100%-3 d 200×300 H150×100×6×9，居中 4.32 3Φ16 356.05 399.75 65.20 SRCL6-100%-7 d 200×300 H150×100×6×9，居中 4.32 3Φ16 356.05 399.75 72.73 SRCL7-100%-28 d 200×300 H150×100×6×9，居中 4.32 3Φ16 356.05 399.75 80.07 SRCL8-100%-90 d 200×300 H150×100×6×9，居中 4.32 3Φ16 356.05 399.75 85.23 文献[14] SL-1 200×250 I16，居中 5.17 2Φ10 340.60 348.10 21.36 SRC-1 200×260 I16，居中 4.97 2Φ18 340.60 433.02 27.56 SRCB-1a 200×200 I10，居中 3.54 2Φ12 365.00 401.00 30.10 SRCB-2b 200×200 I10，居中 3.54 2Φ12 365.00 401.00 30.10 SRCB-1b 200×250 I10，下偏50 mm 2.83 2Φ12 365.00 401.00 30.10 SRCB-2b 200×250 I10，下偏50 mm 2.83 2Φ12 365.00 401.00 30.10 SRCB-1c 200×300 I10，下偏100 mm 2.36 2Φ12 365.00 401.00 30.10 SRCB-2c 200×300 I10，下偏100 mm 2.36 2Φ12 365.00 401.00 30.10 SRCB-1d 200×350 I10，下偏150 mm 2.02 2Φ12 365.00 401.00 30.10 SRCB-2d 200×350 I10，下偏150 mm 2.02 2Φ12 365.00 401.00 30.10 BI-1 208×302 I20a，居中 5.60 2Φ16 280.00 256.00 24.30 BI-2 207×299 I20a，居中 5.69 2Φ16 280.00 256.00 24.20 BII-1 203×303 I20a，居中 5.72 2Φ12 280.00 435.00 22.50 BII-2 206×296 I20a，居中 5.77 2Φ12 280.00 435.00 21.70 文献[15] L1 200×400 I12，居中 1.77 2Φ16 315.00 360.00 47.20 L1a 200×400 I12，居中 1.77 3Φ18 315.00 376.00 47.20 L2 200×400 I20a，居中 4.90 2Φ16 315.00 360.00 47.20 L2a 200×400 I20a，居中 4.90 3Φ18 315.00 376.00 47.20 文献[16] 94 200×300 H200×100×6×6，居中 3.88 2Φ13 598.78 362.60 31.93 95 200×300 H200×100×6×6，居中 3.88 2Φ16 598.78 380.24 31.33 96 200×300 H200×100×6×6，居中 3.88 2Φ13 598.78 362.60 29.04 97 200×300 H200×100×6×6，居中 3.88 2Φ16 598.78 380.24 31.81 98 200×300 H200×100×6×9，居中 4.82 2Φ13 572.81 362.60 37.11 99 200×300 H200×100×6×9，居中 4.82 2Φ16 572.81 380.24 37.83 100 200×300 H200×100×6×9，居中 4.82 2Φ13 572.81 362.60 38.19 101 200×300 H200×100×6×9，居中 4.82 2Φ16 572.81 380.24 37.83 102 200×300 H100×100×6×6，居中 2.88 2Φ16 295.96 380.24 38.80 103 200×300 H100×100×6×6，居中 2.88 2Φ16 798.70 380.24 39.04 A1 200×300 H200×100×6×9，居中 4.82 2Φ10 572.81 364.56 37.35 A2 200×300 H200×100×6×6，居中 3.88 2Φ16 598.78 373.38 36.87 A3 200×300 H200×100×6×9，居中 4.82 2Φ16 572.81 373.38 41.08 A4 200×300 H200×100×6×12，居中 5.76 2Φ16 584.57 373.38 42.89 A5 200×300 H200×100×6×9，居中 4.82 2Φ16 572.81 373.38 44.70 A6 200×300 H200×100×6×9，居中 4.82 2Φ16 296.45 373.38 37.23 A7 200×300 H200×100×6×9，居中 4.82 2Φ16 471.87 373.38 43.86 A8 200×300 H200×100×6×9，居中 4.82 2Φ16 820.26 373.38 44.58 A9 200×300 H100×100×6×9，居中 3.82 2Φ10 572.81 364.56 45.30 A10 200×300 H100×100×6×9，下偏50 mm 3.82 2Φ10 572.81 364.56 49.16 
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