Axial Compression Test and Bearing Capacity Design Method of Cold-Formed Steel with Unequal-Leg Lipped Angles
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摘要:
为研究轴心受压冷弯薄壁不等肢卷边角钢屈曲性能和承载力设计方法,采用试验和有限元程序分析其屈曲性能和极限承载力,并基于直接强度法提出承载力设计建议方法. 首先,开展32根不同截面、长细比和宽厚比的冷弯薄壁不等肢卷边角钢轴压试验;随后,采用ABAQUS有限元软件对冷弯薄壁不等肢卷边角钢在不同宽厚比、肢宽比、长细比等条件下的屈曲性能和承载力进行参数化分析;最后,基于试验和有限元分析结果提出轴心受压冷弯薄壁不等肢卷边角钢构件承载力计算的修正直接强度法公式. 结果表明:宽厚比较小,试件易发生弯扭屈曲,宽厚比较大,试件易发生局部屈曲(或弯扭)和局部相关屈曲;构件极限承载力随长细比增大而降低,随着宽厚比的增大,承载力增长趋势逐渐减缓;提出的修正直接强度法计算轴心受压冷弯薄壁不等肢卷边角钢构件承载力的可靠度指标均值均大于3.2,建议方法准确且安全可靠.
Abstract:To study the buckling performance and bearing capacity design method of the cold-formed thin-walled steel (CFTWS) with unequal-leg lipped angles under axial compression, the tests were conducted, and a finite element program was used to analyze the buckling performance and ultimate bearing capacity. Based on the direct strength method, the bearing capacity design method was presented. Firstly, the 32 CFTWS with unequal-leg lipped angles with different sections, slenderness ratios, and width-to-thickness ratios were tested under axial compression. Then, ABAQUS finite element software was used to perform parametric analysis on the buckling performance and bearing capacity of CFTWS with unequal-leg lipped angles with different width-to-thickness ratios, width ratios of legs, and slenderness ratios. Finally, the modified direct strength method for calculating the bearing capacity of CFTWS with unequal-leg lipped angles under axial compression was proposed based on the results of the test and finite element analysis. The results show that the specimens with a small width-to-thickness ratio are prone to flexural-torsional buckling, while the specimens with a large width-to-thickness ratio are prone to the local buckling or buckling related to flexural-torsional buckling and local buckling. The ultimate bearing capacity of the specimens decreases with the increase in the slenderness ratio, and the increase amplitude of the bearing capacity slows down with the increase in the width-to-thickness ratio. The reliability analysis shows that the reliability indexes of the bearing capacity of the CFTWS with unequal-leg lipped angles under axial compression calculated using the modified direct strength method are greater than 3.2, indicating that the proposed method is accurate and reliable.
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表 1 试件名义几何尺寸
Table 1. Nominal geometric dimension of specimens
试件编号 bl/mm b2/mm al/mm a2/mm t/mm b1/t b2/t LL4030 40 30 15 15 2 20 15 LL6040 60 40 20 20 2 30 20 LL9060 90 60 20 20 2 45 30 LL12080 120 80 24 24 2 60 40 表 2 试件实测几何尺寸
Table 2. Measured geometric dimensions of specimens
试件编号 bl/mm b2/mm al/mm a2/mm t/mm 长度 L/mm 长细比 λ LL4030-400-1 42.13 31.43 15.97 15.54 1.98 400.00 39.19 LL4030-400-2 41.51 31.45 15.56 16.34 1.98 399.27 39.88 LL4030-900-1 42.00 31.61 15.96 14.84 1.99 900.00 87.28 LL4030-900-2 42.25 31.05 15.14 15.79 2.00 900.00 89.45 LL4030-1500-1 41.98 31.48 15.99 15.28 1.97 1498.37 147.14 LL4030-1500-2 41.93 31.42 15.93 15.95 2.00 1499.33 146.65 LL4030-2100-1 42.07 31.32 15.60 15.96 1.98 2101.17 206.51 LL4030-2100-2 42.20 31.59 15.52 15.66 1.98 2101.27 206.93 LL6040-400-1 61.68 41.48 21.63 19.48 1.98 400.00 29.54 LL6040-400-2 61.35 41.52 21.17 21.00 1.97 399.00 29.40 LL6040-900-1 62.05 41.60 21.45 19.37 1.98 900.00 66.46 LL6040-900-2 62.16 41.63 21.54 19.61 2.09 900.00 68.25 LL6040-1500-1 62.10 41.64 21.06 20.48 1.99 1499.43 110.40 LL6040-1500-2 61.80 41.76 21.35 20.98 2.07 1499.27 111.54 LL6040-2100-1 62.24 41.37 21.32 19.86 1.91 2101.10 152.65 LL6040-2100-2 61.44 41.91 20.92 20.47 1.98 2100.00 154.12 LL9060-400-1 91.80 61.41 20.25 20.02 1.97 400.00 22.15 LL9060-400-2 91.92 61.31 20.12 20.50 1.97 399.50 22.16 LL9060-900-1 91.51 61.43 19.90 21.05 1.99 900.00 49.79 LL9060-900-2 91.90 61.89 20.67 20.19 2.00 900.00 49.39 LL9060-1500-1 91.50 62.59 20.51 20.88 2.00 1498.90 81.56 LL9060-1500-2 91.43 62.42 21.08 19.88 1.97 1499.10 81.69 LL9060-2100-1 92.07 61.52 20.99 19.69 1.98 2100.00 115.66 LL9060-2100-2 91.60 61.94 21.83 21.01 2.00 2101.03 113.94 LL12080-400-1 121.53 81.77 24.92 23.98 1.98 400.00 16.95 LL12080-400-2 121.30 81.82 24.19 24.22 1.98 399.27 17.00 LL12080-900-1 122.30 81.71 25.11 24.05 1.97 900.00 38.10 LL12080-900-2 121.87 81.95 23.68 24.90 1.97 900.00 38.23 LL12080-1500-1 121.97 82.20 24.71 24.17 2.00 1498.22 63.34 LL12080-1500-2 122.48 81.87 24.95 24.70 1.97 1499.13 63.33 LL12080-2100-1 122.79 81.89 23.76 24.03 1.98 2101.17 89.38 LL12080-2100-2 121.04 82.24 24.71 24.49 1.97 2100.14 88.61 表 3 试验和有限元分析角钢屈曲模式和承载力对比
Table 3. Comparisons of buckling modes and bearing capacities of steel angles between test and finite element analysis
试件编号 屈曲模式 ΔLmax ΔGmax Pt PFE PD PMD PY Pt/PY Pt/ PFE Pt/ PD Pt/PMD 试验 有限元 一阶模态 LL4030-400-1 FT FT F 0.49 0.28 79.66 83.17 83.77 74.38 72.51 1.0986 0.9578 0.9509 1.0710 LL4030-400-2 FT FT F 0.41 0.34 79.38 82.66 83.67 73.51 73.41 1.0813 0.9603 0.9488 1.0799 LL4030-900-1 FT FT F 1.30 0.83 50.68 53.93 56.47 50.71 27.68 1.8312 0.9397 0.8974 0.9995 LL4030-900-2 FT FT F 1.54 0.77 52.72 54.70 56.90 50.97 27.97 1.8852 0.9638 0.9265 1.0342 LL4030-1500-1 FT FT F 1.30 0.38 40.70 40.93 40.36 42.15 23.01 1.7689 0.9944 1.0085 0.9655 LL4030-1500-2 FT FT F 1.14 0.17 40.98 41.52 41.89 43.75 23.88 1.7159 0.9869 0.9783 0.9366 LL4030-2100-1 FT FT F 1.84 0.08 30.52 31.19 24.48 25.57 13.96 2.1867 0.9786 1.2467 1.1936 LL4030-2100-2 FT FT F 1.10 0.09 29.26 31.35 24.50 25.59 13.97 2.0948 0.9335 1.2343 1.1434 LL6040-400-1 L L L 0.67 0.46 103.70 105.82 102.94 95.81 119.12 0.8706 0.9800 1.0074 1.0824 LL6040-400-2 L L L 0.75 0.31 102.46 105.26 105.33 96.41 121.73 0.8417 0.9734 0.9728 1.0628 LL6040-900-1 FT FT F 1.08 0.63 83.69 85.39 94.17 76.27 52.34 1.5989 0.9800 0.9886 1.0973 LL6040-900-2 FT FT F 1.17 0.74 83.62 84.70 98.45 80.28 54.25 1.5414 0.9872 0.9494 1.0416 LL6040-1500-1 FT FT F 1.15 0.60 59.96 61.98 74.21 61.37 42.31 1.4172 0.9673 0.9480 0.9769 LL6040-1500-2 FT FT F 1.42 0.43 60.82 63.31 78.23 64.30 44.60 1.3638 0.9607 0.9775 0.9459 LL6040-2100-1 FT FT F 1.17 0.24 48.66 50.69 41.59 43.44 23.71 2.0519 0.9600 1.1699 1.1201 LL6040-2100-2 FT FT F 1.42 1.08 49.94 50.96 42.99 44.90 24.51 2.0376 0.9800 1.1617 1.1122 LL9060-400-1 L L L 0.99 0.35 126.76 129.35 104.56 124.03 153.51 0.8257 0.9800 1.2123 1.0220 LL9060-400-2 L L L 0.57 0.57 125.71 129.60 106.03 124.39 155.32 0.8094 0.9700 1.1855 1.0106 LL9060-900-1 FT + L FT + L L 1.12 0.71 94.42 96.00 108.68 101.84 68.10 1.3865 0.9835 0.9688 0.9271 LL9060-900-2 FT + L FT + L L 1.02 0.92 95.60 97.20 107.99 102.07 67.07 1.4253 0.9835 0.9853 0.9366 LL9060-1500-1 FT + L FT + L L 0.79 0.71 77.34 80.36 90.86 94.90 51.80 1.4929 0.9625 0.9512 0.8149 LL9060-1500-2 FT + L FT + L L 0.88 0.83 77.04 78.87 85.54 89.34 48.77 1.5797 0.9768 0.9006 0.8623 LL9060-2100-1 D D F 1.22 0.90 59.95 61.37 48.74 50.90 27.79 2.1574 0.9768 1.2300 1.1776 LL9060-2100-2 D D F 1.08 0.77 61.51 63.42 54.77 57.20 31.22 1.9701 0.9700 1.2232 1.0754 LL12080-400-1 L L L 0.59 0.22 147.54 150.67 117.71 146.76 224.28 0.6578 0.9792 1.2535 1.0053 LL12080-400-2 L L L 0.58 0.14 146.78 150.41 117.29 146.49 223.06 0.6580 0.9759 1.2515 1.0020 LL12080-900-1 FT + L FT + L L 1.20 0.56 136.59 138.37 117.55 118.57 105.70 1.2923 0.9872 1.1620 1.1520 LL12080-900-2 FT + L FT + L L 1.52 1.11 131.36 138.86 118.35 118.60 106.10 1.2380 0.9460 1.1099 1.1075 LL12080-1500-1 FT + L FT + L L 1.20 1.56 97.14 98.99 116.57 104.35 81.31 1.1948 0.9813 0.8334 0.9309 LL12080-1500-2 FT + L FT + L L 1.52 1.11 98.56 98.19 116.67 102.58 83.41 1.1817 1.0038 0.8447 0.9608 LL12080-2100-1 FT + L FT + L L 1.44 1.42 85.43 85.91 73.43 76.89 41.97 2.0354 0.9948 1.2634 1.1110 LL12080-2100-2 FT + L FT + L L 1.45 1.54 85.82 86.48 76.31 80.96 44.19 1.9419 0.9926 1.2246 1.0600 均 值 1.4760 0.9741 1.1246 1.0318 方 差 0.2060 0.0002 0.0227 0.0077 变异系数 0.1395 0.0002 0.0201 0.0074 表 4 冷弯薄壁型不等肢卷边角钢轴压构件可靠指标
Table 4. Reliability indexes of CFTWS with unequal-leg lipped angles under axial compression
类型 ρ2 组合形式 ρ1=0.5 ρ1=1.0 ρ1=2.0 ρ1=3.0 可靠指标平均值 办公楼 0 1.3G + 1.5L1 4.518 4.467 4.442 4.403 4.457 0.5 1.3G + 0.9 × 1.5(L1 + W) 4.306 4.298 4.253 4.198 4.264 1.0 1.3G + 0.9 × 1.5(L1 + W) 4.178 4.161 4.102 4.087 4.132 2.0 1.3G + 0.9 × 1.5(L1 + W) 4.096 4.011 3.918 3.824 3.962 3.0 1.3G + 0.9 × 1.5(L1 + W) 3.954 3.898 3.837 3.763 3.863 4.0 1.3G + 0.9 × 1.5(L1 + W) 3.781 3.675 3.621 3.601 3.670 住宅 0 1.3G + 1.5L2 4.924 4.869 4.841 4.799 4.858 0.5 1.3G + 0.9 × 1.5(L2 + W) 4.693 4.684 4.635 4.575 4.647 1.0 1.3G + 0.9 × 1.5(L2 + W) 4.554 4.535 4.471 4.454 4.503 2.0 1.3G + 0.9 × 1.5(L2 + W) 4.464 4.372 4.270 4.168 4.318 3.0 1.3G + 0.9 × 1.5(L2 + W) 4.309 4.248 4.182 4.101 4.210 4.0 1.3G + 0.9 × 1.5(L2 + W) 4.121 4.005 3.947 3.925 3.999 注:ρ1 为活荷载标准值与风荷载标准值之和与恒荷载标准值的比值,ρ2 为风荷载标准值与活荷载标准值的比值. -
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