冷弯不等肢卷边角钢轴压试验及承载力设计方法

姚行友; 胡成立; 刘亚菲; 郭彦利

doi:10.3969/j.issn.0258-2724.20230010

冷弯不等肢卷边角钢轴压试验及承载力设计方法

doi: 10.3969/j.issn.0258-2724.20230010

1.
南昌工程学院土木与建筑工程学院，江西南昌 330099
2.
南昌工程学院江西省水利土木工程基础设施安全重点实验室，江西南昌 330099

基金项目: 国家自然科学基金项目（51868049）；江西省自然科学基金重点项目（20242BAB26074）

详细信息

作者简介:
姚行友（1978—），男，教授，研究方向为冷弯型钢结构，E-mail：yaoxingyoujd@163.com

中图分类号: TU392.1
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出版历程
- 收稿日期: 2022-10-10
- 修回日期: 2023-05-09
- 网络出版日期: 2024-08-05
- 刊出日期: 2023-07-07

Axial Compression Test and Bearing Capacity Design Method of Cold-Formed Steel with Unequal-Leg Lipped Angles

1.
School of Civil and Architectural Engineering, Nanchang Institute of Technology, Nanchang 330099, China
2.
Jiangxi Provincial Key Laboratory of Hydraulic & Civil Engineering Infrastructure Security, Nanchang Institute of Technology, Nanchang 330099, China

摘要

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.
- 冷弯薄壁型钢 /
- 不等肢卷边角钢 /
- 宽厚比 /
- 长细比 /
- 局部屈曲
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.
- cold-formed thin-walled steel /
- steel with unequal-leg lipped angles /
- width-to-thickness ratio /
- slenderness ratio /
- local buckling

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图 1 不等肢卷边角钢截面

Figure 1. Section of steel with unequal-leg lipped angles

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图 2 应力-应变曲线

Figure 2. Stress-strain curves

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图 3 纵向初始缺陷量测位置

Figure 3. Measuring locations of longitudinal initial defect

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图 4 试件初始缺陷

Figure 4. Initial defect of specimens

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图 5 试验装置

Figure 5. Test setup

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图 6 位移计布置

Figure 6. Layout of displacement meters

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图 7 长度为400 mm的角钢柱屈曲模式

Figure 7. Buckling mode of steel angle with length of 400 mm

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图 8 长度为900、1500 mm的角钢柱屈曲模式

Figure 8. Buckling mode of steel angle with lengths of 900 mm and 1 500 mm

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图 9 长度为2100 mm的角钢柱屈曲模式

Figure 9. Buckling mode of steel angle with length of 2 100 mm

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图 10 荷载-位移曲线

Figure 10. Load-displacement curves

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图 11 有限元分析模型

Figure 11. Finite element analysis model

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图 12 有限元分析一阶屈曲模态

Figure 12. First-order buckling mode of finite element analysis

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图 13 试验与有限元分析屈曲模式对比

Figure 13. Comparison of buckling modes between test and finite element analysis

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图 14 试验与有限元分析荷载-位移曲线对比

Figure 14. Comparison of load-displacement curves between test and finite element analysis

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图 15 极限承载力和长细比关系曲线

Figure 15. Relationship between ultimate bearing capacity and slenderness ratio

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图 16 试验和有限元分析角钢屈曲模式和承载力对比

Figure 16. Comparisons of buckling modes and bearing capacities of steel angles between test and finite element analysis

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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	b_l/mm	b₂/mm	a_l/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

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表 2 试件实测几何尺寸

Table 2. Measured geometric dimensions of specimens

试件编号	b_l/mm	b₂/mm	a_l/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

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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			Δ_Lmax/ mm	Δ_Gmax/ mm	P_t/kN	P_FE/kN	P_D/kN	P_MD/kN	P_Y/kN	P_t/P_Y	P_t/ P_FE	P_t/ P_D	P_t/P_MD
试件编号	试验	有限元	一阶模态	Δ_Lmax/ mm	Δ_Gmax/ mm	P_t/kN	P_FE/kN	P_D/kN	P_MD/kN	P_Y/kN	P_t/P_Y	P_t/ P_FE	P_t/ P_D	P_t/P_MD
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

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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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冷弯不等肢卷边角钢轴压试验及承载力设计方法

doi: 10.3969/j.issn.0258-2724.20230010

作者简介: 姚行友（1978—），男，教授，研究方向为冷弯型钢结构，E-mail：yaoxingyoujd@163.com

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Axial Compression Test and Bearing Capacity Design Method of Cold-Formed Steel with Unequal-Leg Lipped Angles

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作者简介:
姚行友（1978—），男，教授，研究方向为冷弯型钢结构，E-mail：yaoxingyoujd@163.com