Distortional Failure and DSM Design of Cold-Formed Steel S-Shaped Beams Under Uniform Bending

Barichello, Carolina; Landesmann, Alexandre; Camotim, Dinar

doi:10.1590/1679-78253616

Acessibilidade / Reportar erro

Brasil

Latin American Journal of Solids and Structures

Español English

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

Articles • Lat. Am. j. solids struct. 14 (12) • Dec 2017 • https://doi.org/10.1590/1679-78253616 copy

Distortional Failure and DSM Design of Cold-Formed Steel S-Shaped Beams Under Uniform Bending

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This work reports a numerical investigation on the distortional buckling/post-buckling behaviors, ultimate strength and Direct Strength Method (DSM) design of cold-formed steel S-beams, commonly used in industrial rack systems. The analyzed beams are single-span, under uniform bending, exhibiting two different end support conditions and 5 cross-sections dimensions. The post-buckling equilibrium paths and ultimate moments are obtained from shell finite element non-linear analysis through the software ANSYS. The reported results evidenced that current codified DSM distortional curve is unable to provide safely strength predictions for the selected beams.

Keywords:
Distortional failure; cold-formed steel beams; shell finite element

Cross-section		b _w	b _f	b _l	t	b _w /b _f	b _f /b _l	A	S
beam	shape	(mm)	(mm)	(mm)	(mm)	b _w /b _f	b _f /b _l	(cm² )	(cm³ )
S45-075		75	65	5	2.0	1.15	13	4.8	13.2
S45-090		90	75	6.25	1.8	1.2	12	5.1	16.5
S45-120		120	75	10	3.0	1.6	7.5	9.6	38.7
S45-140		140	100	10	2.5	1.4	10	10.0	48.6
S45-150		150	120	10	3.5	1.25	12	16.1	85.8
S90-075		75	65	5	2.0	1.15	13	5.6	13.0
S90-090		90	75	6.25	1.8	1.2	12	5.9	16.3
S90-120		120	75	10	3.0	1.6	7.5	10.9	38.2
S90-140		140	100	10	2.5	1.4	10	11.5	47.9
S90-150		150	120	10	3.5	1.25	12	18.6	84.6

Beam	F beams				P beams
	L _D	M _crD	$\frac{M_{b L}}{M_{c r D}}$	$\frac{M_{b G}}{M_{c r D}}$	L _D	M _crD	$\frac{M_{b L}}{M_{c r D}}$	$\frac{M_{b G}}{M_{c r D}}$
	(cm)	(kNcm)	$\frac{M_{b L}}{M_{c r D}}$	$\frac{M_{b G}}{M_{c r D}}$	(cm)	(kNcm)	$\frac{M_{b L}}{M_{c r D}}$	$\frac{M_{b G}}{M_{c r D}}$
S45-075	25	226.6	7.4	130.0	35	318.8	5.4	106.8
S45-090	35	210.9	4.8	123.8	50	301.5	3.5	96.2
S45-120	40	1310.5	4.5	46.4	60	1920.7	3.1	31.9
S45-140	50	725.5	4.0	105.7	80	1075.1	2.7	63.1
S45-150	40	1426.4	5.4	192.6	75	1995.3	4.0	88.8
S90-075	20	292.5	4.2	292.1	30	421.2	3.0	204.3
S90-090	25	280.3	3.1	330.1	40	408.5	2.2	200.5
S90-120	30	1744.9	3.3	95.4	50	2530.6	2.3	53.7
S90-140	40	982.0	2.8	201.7	65	1437.0	1.9	118.3
S90-150	40	1983.5	3.5	242.7	65	2659.6	2.7	156.7

Slenderness	Statistical Parameters	S45		S90
Slenderness	Statistical Parameters	F	P	F	P
Whole range	Average	1.60	1.24	1.61	1.03
	Standard Deviation	0.45	0.11	0.58	0.21
	Maximum	2.56	1.62	3.26	1.74
	Minimum	1.01	1.07	0.81	0.77
Low-to-moderate	Average	1.15	1.15	1.05	1.05
	Standard Deviation	0.08	0.04	0.11	0.04
	Maximum	1.25	1.21	1.17	1.11
	Minimum	1.01	1.07	0.81	0.98
Moderate-to-high	Average	1.85	1.29	1.92	1.02
	Standard Deviation	0.37	0.10	0.50	0.26
	Maximum	2.56	1.62	3.26	1.74
	Minimum	1.22	1.16	1.21	0.77

S45	λ _D	F beams					P beams
S45	λ _D	(\|δ\|/t) _lim	M _y	M _u	M _nD	M _u / M _crD	(\|δ\|/t) _lim	M _y	M _u	M _nD	M _u / M _crD
75	0.25	0.01	14.48	11.95	14.48	0.05	0.20	19.75	16.69	19.75	0.05
	0.50	0.07	56.62	46.52	56.62	0.21	0.29	80.32	66.86	80.32	0.21
	0.75	0.37	127.72	104.48	120.27	0.46	0.89	179.07	144.06	168.78	0.45
	1.00	1.30	226.47	169.40	176.69	0.75	2.00	318.63	232.14	248.57	0.73
	1.25	2.14	354.18	206.66	233.46	0.91	3.04	497.70	282.56	328.18	0.89
	1.50	3.34	509.55	222.25	289.96	0.98	6.65	717.58	339.30	408.13	1.06
	1.75	4.03	693.88	230.85	346.69	1.02	8.79	975.64	416.03	487.54	1.31
	2.00	5.88	907.18	240.18	403.57	1.06	9.94	1274.53	490.73	567.26	1.54
	2.25	5.80	1146.81	249.59	459.95	1.10	10.90	1614.22	558.05	647.19	1.75
	2.50	8.06	1416.72	260.10	516.77	1.15	11.75	1992.10	616.10	726.74	1.93
	2.75	8.96	1714.29	269.09	573.45	1.19	12.56	2410.80	667.95	806.49	2.10
	3.00	9.15	2039.50	277.27	630.00	1.22	13.46	2869.00	713.45	886.17	2.24
	3.25	10.37	2393.68	284.59	686.68	1.26	14.20	3366.70	753.95	965.81	2.37
	3.50	10.75	2776.83	290.65	743.44	1.28	15.07	3905.21	789.85	1045.58	2.48
90	0.25	0.01	13.19	10.84	13.19	0.05	0.13	18.14	15.58	18.14	0.05
	0.50	0.06	52.77	43.07	52.77	0.20	0.53	75.86	63.54	75.86	0.21
	0.75	0.28	118.74	96.31	111.85	0.46	0.85	169.86	137.22	159.96	0.46
	1.00	1.57	211.09	161.17	164.61	0.76	2.35	301.79	219.37	235.30	0.73
	1.25	3.19	329.82	198.69	217.36	0.94	3.84	471.64	266.59	310.75	0.88
	1.50	3.88	474.94	210.84	270.12	1.00	5.59	677.78	302.35	385.70	1.00
	1.75	5.68	646.45	219.81	322.87	1.04	12.37	923.50	372.87	461.31	1.24
	2.00	7.19	844.34	229.35	375.63	1.09	13.49	1205.50	433.07	536.51	1.44
	2.25	8.57	1068.62	239.46	428.38	1.14	13.96	1525.42	487.42	611.80	1.62
	2.50	9.25	1317.64	249.18	480.80	1.18	14.92	1884.93	540.15	687.49	1.79
	2.75	10.76	1594.69	258.27	533.59	1.22	15.93	2279.07	588.15	762.56	1.95
	3.00	12.00	1898.12	266.31	586.37	1.26	17.04	2712.78	631.85	838.00	2.10
	3.25	12.78	2227.94	273.83	639.14	1.30	18.08	3184.43	673.90	913.46	2.24
	3.50	14.82	2584.15	280.27	691.92	1.33	19.30	3692.35	711.85	988.71	2.36
120	0.25	0.01	81.27	67.27	81.27	0.05	0.85	119.97	105.36	119.97	0.05
	0.50	0.08	328.96	270.72	328.96	0.21	0.60	479.89	408.82	479.89	0.21
	0.75	0.33	735.32	602.20	693.34	0.46	1.37	1079.76	885.15	1017.54	0.46
	1.00	1.57	1311.96	1006.50	1022.92	0.77	3.31	1919.57	1403.90	1497.57	0.73
	1.25	3.19	2047.28	1252.90	1349.66	0.96	5.55	2999.32	1770.35	1977.61	0.92
	1.50	4.98	2949.01	1376.25	1677.57	1.05	7.30	4322.89	2048.05	2458.93	1.07
	1.75	6.24	4013.29	1474.20	2005.03	1.12	8.99	5882.54	2300.00	2938.77	1.20
	2.00	7.43	5240.10	1567.10	2332.22	1.20	11.05	7682.13	2549.40	3418.67	1.33
	2.25	8.86	6633.34	1650.35	2660.08	1.26	14.64	9721.67	2839.45	3898.59	1.48
	2.50	10.02	8189.11	1726.10	2987.64	1.32	16.36	12005.02	3138.40	4379.31	1.63
	2.75	11.21	9911.31	1790.40	3315.68	1.37	17.76	14524.45	3396.10	4859.20	1.77
	3.00	11.95	11796.04	1844.10	3643.45	1.41	18.79	17287.70	3611.20	5339.76	1.88
	3.25	13.00	13843.32	1885.95	3970.99	1.44	20.37	20287.02	3774.60	5819.64	1.97
	3.50	13.73	16053.14	1923.15	4298.37	1.47	21.85	23530.16	3885.55	6300.10	2.02
140	0.25	0.01	43.72	35.32	43.72	0.05	0.33	68.01	58.52	68.01	0.05
	0.50	0.06	179.75	144.18	179.75	0.20	0.68	267.20	224.33	267.20	0.21
	0.75	0.25	408.08	326.29	384.50	0.45	1.26	602.40	488.30	568.23	0.45
	1.00	1.67	723.86	557.05	565.06	0.77	3.35	1073.64	784.55	837.84	0.73
	1.25	2.88	1131.94	702.35	746.58	0.97	5.30	1680.90	979.95	1107.76	0.91
	1.50	4.40	1632.32	758.20	928.60	1.05	7.32	2419.33	1123.05	1376.22	1.04
	1.75	6.10	2220.15	801.55	1109.50	1.10	8.90	3293.79	1262.50	1645.24	1.17
	2.00	7.67	2900.28	848.55	1290.93	1.17	17.91	4299.42	1508.70	1913.40	1.40
	2.25	9.04	3672.72	898.10	1472.70	1.24	18.53	5441.07	1691.20	2182.05	1.57
	2.50	10.26	4532.61	945.00	1653.74	1.30	19.07	6718.75	1885.60	2451.06	1.75
	2.75	11.31	5484.79	989.60	1835.14	1.36	19.83	8132.46	2065.00	2720.32	1.92
	3.00	12.97	6529.28	1031.45	2016.80	1.42	21.37	9677.33	2234.10	2988.96	2.08
	3.25	13.72	7661.22	1070.35	2197.92	1.48	23.11	11353.38	2397.75	3257.13	2.23
	3.50	14.84	8885.46	1103.80	2379.30	1.52	23.71	13170.30	2533.90	3526.31	2.36
150	0.25	0.01	85.83	69.40	85.83	0.05	0.38	128.74	109.59	128.74	0.05
	0.50	0.05	360.48	288.84	360.48	0.20	0.46	497.81	415.26	497.81	0.21
	0.75	0.22	798.21	637.20	753.23	0.45	0.95	1124.37	905.65	1058.85	0.45
	1.00	0.89	1424.77	1054.50	1111.78	0.74	2.12	1991.24	1449.45	1554.31	0.73
	1.25	1.64	2231.56	1293.85	1470.33	0.91	3.63	3115.61	1795.50	2054.35	0.90
	1.50	2.97	3210.02	1376.05	1826.01	0.96	5.42	4488.88	2078.35	2553.81	1.04
	1.75	3.05	4368.72	1437.25	2182.51	1.01	11.33	6111.05	2523.20	3052.95	1.26
	2.00	5.45	5707.66	1503.90	2539.53	1.05	12.15	7982.13	2957.45	3551.88	1.48
	2.25	6.67	7218.25	1584.10	2894.97	1.11	12.34	10102.12	3354.70	4050.68	1.68
	2.50	7.52	8917.67	1666.65	3252.76	1.17	13.14	12471.01	3725.70	4549.38	1.87
	2.75	8.76	10788.76	1744.75	3609.12	1.22	14.05	15088.81	4062.10	5048.01	2.04
	3.00	9.96	12840.08	1816.65	3965.84	1.27	15.00	17955.51	4358.85	5546.59	2.18
	3.25	11.18	15063.06	1871.95	4321.52	1.31	15.94	21079.70	4624.20	6046.46	2.32
	3.50	11.04	17474.87	1913.60	4678.84	1.34	17.06	24444.21	4863.50	6544.87	2.44

S90	λ _D	F beams					P beams
S90	λ _D	(\|δ\|/t) _lim	M _y	M _u	M _nD	M _u / M _crD	(\|δ\|/t) _lim	M _y	M _u	M _nD	M _u / M _crD
75	0.25	0.05	18.22	15.82	18.22	0.05	0.30	26.03	25.63	26.03	0.06
	0.50	0.09	72.90	62.63	72.90	0.21	0.78	105.44	98.65	105.44	0.23
	0.75	0.53	164.02	138.32	154.68	0.47	1.03	236.92	205.82	223.23	0.49
	1.00	1.02	292.89	226.23	228.33	0.77	2.23	421.76	317.40	328.82	0.75
	1.25	1.76	456.91	278.72	301.21	0.95	7.88	658.68	425.14	434.06	1.01
	1.50	2.79	657.38	303.85	374.13	1.04	9.56	947.66	579.30	539.13	1.38
	1.75	4.11	895.60	321.13	447.44	1.10	10.98	1290.02	746.50	644.47	1.77
	2.00	4.97	1170.26	343.17	520.68	1.17	12.09	1684.45	917.85	749.66	2.18
	2.25	6.05	1480.07	368.86	593.58	1.26	13.00	2132.25	1086.80	855.03	2.58
	2.50	7.28	1827.64	393.05	666.76	1.34	13.58	2632.11	1247.95	960.27	2.96
	2.75	7.45	2211.65	409.59	739.90	1.40	14.13	3185.35	1396.95	1065.65	3.32
	3.00	7.54	2632.11	418.84	813.03	1.43	14.74	3790.66	1533.05	1170.93	3.64
	3.25	7.02	3089.02	420.34	886.13	1.44	15.00	4449.34	1650.05	1276.31	3.92
	3.50	8.45	3582.38	432.49	959.22	1.48	15.01	5160.09	1737.75	1381.61	4.13
90	0.25	0.06	17.90	15.56	17.90	0.06	0.37	26.03	26.02	26.03	0.06
	0.50	0.10	69.95	60.07	69.95	0.21	0.88	102.49	96.33	102.49	0.24
	0.75	0.76	157.80	133.65	148.65	0.48	1.41	229.39	200.40	216.24	0.49
	1.00	1.52	279.82	216.94	218.39	0.77	2.44	408.34	312.42	318.56	0.76
	1.25	1.97	437.62	265.30	288.57	0.95	3.58	637.73	379.08	420.54	0.93
	1.50	3.36	631.22	284.48	358.96	1.01	11.95	919.17	548.40	522.91	1.34
	1.75	3.88	858.98	299.49	429.01	1.07	13.44	1251.05	698.50	625.02	1.71
	2.00	5.41	1120.90	314.71	498.85	1.12	14.51	1633.36	847.15	726.99	2.07
	2.25	7.00	1418.61	333.27	568.91	1.19	15.35	2067.73	995.25	829.21	2.44
	2.50	7.93	1752.12	351.91	639.12	1.26	16.24	2552.53	1133.15	931.28	2.77
	2.75	8.32	2119.79	369.59	709.15	1.32	17.12	3089.39	1262.50	1033.55	3.09
	3.00	7.96	2523.25	380.90	779.31	1.36	17.92	3676.68	1383.45	1135.69	3.39
	3.25	8.54	2960.87	383.95	849.33	1.37	18.52	4314.41	1493.40	1237.73	3.66
	3.50	7.87	3434.28	387.09	919.46	1.38	19.25	5004.19	1592.55	1339.92	3.90
120	0.25	0.01	110.77	97.55	110.77	0.06	0.82	156.60	160.35	156.60	0.06
	0.50	0.05	435.42	381.15	435.42	0.22	1.48	634.04	608.35	634.04	0.24
	0.75	0.60	981.61	846.75	924.86	0.49	1.63	1424.67	1252.15	1342.02	0.49
	1.00	1.48	1745.51	1362.15	1361.32	0.78	3.33	2532.33	1960.05	1974.72	0.77
	1.25	2.60	2727.12	1698.25	1797.53	0.97	4.82	3953.18	2439.90	2606.15	0.96
	1.50	3.80	3926.44	1847.15	2233.60	1.06	5.96	5694.87	2801.10	3239.49	1.11
	1.75	4.96	5343.48	1976.75	2669.61	1.13	14.05	7749.76	3840.50	3871.74	1.52
	2.00	4.15	6978.22	1997.60	3105.56	1.14	15.08	10121.67	4487.75	4504.26	1.77
	2.25	4.15	8834.50	1997.60	3542.34	1.14	15.26	12810.59	5000.00	5136.97	1.98
	2.50	4.15	10904.66	1997.60	3978.16	1.14	13.39	15816.54	5000.00	5769.80	1.98
	2.75	4.15	13196.36	1997.60	4414.68	1.14	12.62	19135.68	5000.00	6402.03	1.98
	3.00	4.15	15705.77	1997.60	4851.08	1.14	12.37	22775.66	5000.00	7035.08	1.98
	3.25	4.15	18429.07	1997.60	5286.80	1.14	12.25	26728.84	5000.00	7667.58	1.98
	3.50	4.15	21373.91	1997.60	5723.09	1.14	12.23	30999.04	5000.00	8300.21	1.98
140	0.25	0.00	62.23	53.76	62.23	0.05	1.35	90.96	92.25	90.96	0.06
	0.50	0.08	244.15	209.47	244.15	0.21	1.37	359.05	342.07	359.05	0.24
	0.75	0.85	550.54	470.82	519.23	0.48	2.01	809.05	708.70	762.10	0.49
	1.00	1.51	981.39	771.25	765.65	0.79	3.10	1436.18	1107.05	1120.45	0.77
	1.25	2.72	1536.72	957.30	1012.39	0.97	4.51	2245.23	1351.60	1480.07	0.94
	1.50	3.79	2211.72	1025.35	1257.70	1.04	5.58	3231.41	1528.90	1838.74	1.06
	1.75	4.74	3006.41	1087.10	1502.18	1.11	15.05	4399.51	2309.85	2198.23	1.61
	2.00	5.77	3925.57	1146.80	1747.34	1.17	16.33	5749.52	2758.25	2558.23	1.92
	2.25	6.69	4969.20	1207.60	1992.97	1.23	17.52	7276.67	3188.45	2917.51	2.22
	2.50	7.63	6137.29	1260.65	2238.91	1.28	18.70	8980.94	3600.40	3276.28	2.51
	2.75	8.47	7425.07	1308.00	2484.21	1.33	19.80	10867.13	3987.20	3635.56	2.77
	3.00	8.79	8837.32	1343.70	2729.83	1.37	20.77	12935.23	4336.90	3995.21	3.02
	3.25	8.84	10374.04	1352.60	2975.70	1.38	21.68	15180.47	4649.60	4354.42	3.24
	3.50	10.22	12030.44	1363.30	3221.08	1.39	22.59	17602.83	5000.00	4713.28	3.48
150	0.25	0.01	126.94	152.63	126.94	0.08	0.79	169.25	169.02	169.25	0.06
	0.50	0.17	499.28	614.20	499.28	0.31	1.14	668.53	631.90	668.53	0.24
	0.75	0.83	1117.03	1297.10	1052.12	0.65	1.31	1497.84	1305.65	1410.79	0.49
	1.00	1.88	1980.19	1763.30	1545.47	0.89	2.21	2657.18	2032.70	2073.27	0.76
	1.25	3.19	3097.22	1945.40	2042.19	0.98	3.42	4155.02	2507.85	2739.14	0.94
	1.50	2.75	4459.66	1997.60	2537.79	1.01	11.17	5982.89	3589.20	3403.88	1.35
	1.75	2.75	6075.97	1997.60	3035.16	1.01	12.40	8140.79	4572.90	4067.97	1.72
	2.00	2.75	7937.69	1997.60	3531.53	1.01	10.28	10637.18	5000.00	4733.77	1.88
	2.25	2.75	10044.82	1997.60	4027.22	1.01	9.25	13463.61	5000.00	5398.84	1.88
	2.50	2.75	12397.35	1997.60	4522.44	1.01	8.68	16620.07	5000.00	6063.39	1.88
	2.75	2.75	15003.76	1997.60	5018.86	1.01	8.48	20115.02	5000.00	6729.10	1.88
	3.00	2.75	17847.11	1997.60	5513.36	1.01	8.40	23940.01	5000.00	7394.27	1.88
	3.25	2.75	20952.80	1997.60	6010.28	1.01	8.36	28095.03	5000.00	8059.03	1.88
	3.50	2.75	24295.43	1997.60	6505.48	1.01	8.36	32580.07	5000.00	8723.46	1.88

Individual owner www.lajss.org - São Paulo - SP - Brazil
E-mail: lajsssecretary@gmsie.usp.br

Acompanhe os números deste periódico no seu leitor de RSS

[1] * Corresponding author