Random Strength Parameters of Steel Corrugated Webs and Their Influence on the Resistance of Sin Plate Girders

Witold BASIŃSKI; Zbigniew KOWAL

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Random Strength Parameters of Steel Corrugated Webs and Their Influence on the Resistance of Sin Plate Girders

Witold BASIŃSKI

Zbigniew KOWAL

| 04 abr 2019

Architecture, Civil Engineering, Environment

Volumen 11 (2018): Edición 3 (September 2018)

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Publicado en línea: 04 abr 2019

Páginas: 65 - 77

Recibido: 28 sept 2017

Aceptado: 09 may 2018

DOI: https://doi.org/10.21307/acee-2018-039

Palabras clave
Corrugated web, Coefficients of variation, Normal distribution

© 2018 Witold Basiński et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Girders with corrugated webs, from which samples used in investigations into strength properties of corrugated webs were collected: a) with a flexible end stiffener; b) with a rigid end stiffener; c) cantilever girders

Girders at the test stand a) beam girder M 1.41 WTA 1250/300x15; b) cantilever girder M 152 WTA 1500/300x15

Girder M 1.41– box-marked site of sample collection from the girder along the fold for materials tests on the web strength

Dimensions of flat samples: a) sample from 2 mm thick web; b) sample from 2.5 mm thick web; c) sample from 3 mm thick web mm

Waveform shape – place of sample cutting out, along the fold, of samples from corrugated web

View of an exemplary 2.5 mm thick sample cut out of WTB girder web

Graph F – ΔL of tension of 3 mm thick steel sample cut out of the web of M 2.42 girder

Graph F – ΔL of tension of type 2 mm thick steel sample cut out of the web of M 1.32 girder

Normal distribution of yield strength Re for steel samples from corrugated webs cut out of girders: a) M 2.12 having the actual thickness of 2 mm; b) M 1.31 having the actual thickness of 2.6 mm

Factors of yield strength γm compared with the minimum value guaranteed by the steel mill γm235 and by the manufacturer γm215

Normal distribution of yield strength in all examined steel samples cut out of corrugated webs

Program of investigations

Girder	h_w × t_w [mm]	End Stiffener [mm]	L [mm]	Girder [mm]	h_w × t_w [mm]	End Stiffener [mm]	L [mm]
1	2	3	4	5	6	7	8
M 1.11	500x2	300x25	7825	M 1.12	500x2	300x25	6000
M 1.21	1000x2.5	300x25	7825	M 1.22	1000x2	300x25	6000
M 1.31	1000x2.5	300x25	7825	M 1.32	1000x2.5	300x25	6000
M 1.41	1250x2	300x25	7825	M 1.42	1250x2	300x25	6000
M 1.51	1500x2	300x25	7825	M 1.52	1500x2	300x25	6000
M 2.11	500x2.5	300x25	5825	M 2.12	500x2	300x25	3750
M 2.21	1000x2	300x25+tee bar	5825	M 2.22	1000x2	300x25	3750
M 2.31	1000x2.5	300x25+tee bar	5825	M 2.32	1000x2,5	300x25	3750
M 2.41	1000x3	300x25+tee bar	5825	M 2.42	1000x3	300x25	3750
M 2.51	1500x3	300x25+tee bar	5825	M 2.52	1500x2	300x25	3750

Steel yield strength that accounts for the impact of cold rolling acc. (6) [18]:

	web thickness 2 mm	web thickness 2.5 mm	web thickness 2 mm
Design yield strength f _y [MPa]	254.7	259.6	264.5

Parameters of normal distribution of geometric dimensions of steel samples from corrugated webs and of resistance obtained according to formulae (7) and (8)

Model	${\bar{b}}_{0}$	${\bar{a}}_{0}$	${\bar{S}}_{0}$	D² (A)	D(A)	V _A	D² (N)	D(N)	V _N
	mm	mm	mm²
1	2	3	4	5	6	7	8	8	9
Mean value for 2 mm samples	2.0	19.98	39.95	0.030	0.170	0.004	0.047	0.217	0.018
Mean value for 2.5 mm samples	2.57	19.92	51.18	1.111	1.054	0.021	0.209	0.457	0.030
Mean value for 3 mm samples	3.0	20.0	60.0	0.000	0.000	0.000	0.462	0.680	0.029

Parameters of yield strength and tensile strength tests on web samples

Girder number	${\bar{b}}_{0}$	${\bar{a}}_{0}$	${\bar{S}}_{0}$	${\bar{L}}_{0}$	${\bar{L}}_{u}$	${\bar{A}}_{10}$	${\bar{F}}_{eH}$	${\bar{F}}_{m}$	${\bar{R}}_{e}$	${\bar{R}}_{m}$	${\bar{R}}_{e} / {\bar{R}}_{m}$
Girder number	mm	mm	mm²	mm	mm	%	kN	kN	MPa	MPa
1	2	2	4	5	6	7	8	9	12	13	14
M 1.11	2.0	20.0	40.0	70.0	85.0	21.5	12.2	16.1	304.4	403.5	1.33
M 1.41	2.0	20.0	40.0	70.0	85.1	21.6	12.7	17.4	317.8	434.3	1.37
M 1.51 ^*	2.0	20.0	40.0	70.0	86.1	23.0	9.9	15.0	247.2	375.5	1.52
M 2.21	2.0	19.7	39.4	70.0	83.5	19.2	13.2	17.2	334.3	437.5	1.31
M 2.51	2.0	20.0	40.0	70.0	86.2	23.1	11.6	15.1	289.3	376.8	1.30
M 1.12	2.0	20.0	40.0	70.0	85.5	22.2	13.6	17.4	334.7	430.6	1.29
M 1.22	2.0	20.0	40.0	70.0	83.9	19.9	10.7	14.4	312.5	453.9	1.45
M 1.42 ^*	2.0	20.0	40.0	70.0	86.3	23.3	10.0	15.2	267.2	360.9	1.35
M 1.52	2.0	20.0	40.0	70.0	86.3	23.3	10.0	15.2	299.1	380.5	1.27
M 2.12	2.0	20.0	40.0	70.0	84.8	20.8	13.5	17.2	337.9	429.1	1.27
M 2.22	2.0	20.0	40.0	70.0	85.9	22.5	13.5	17.1	336.3	427.3	1.27
M 2.52	2.0	20.0	40.0	70.0	87.2	24.6	11.2	15.0	281.0	375.5	1.34
Mean value for 2 mm samples:									305.1	407.1	1.34
M 1.21 ^*	2.5	19.8	49.5	80.0	96.5	20.7	13.7	20.6	275.9	416.0	1.51
M 1.31 ^*	2.6	19.7	51.2	80.0	96.6	20.7	13.3	20.6	260.4	403.0	1.55
M 2.11	2.6	20.0	52.0	80.0	98.2	22.8	13.8	20.3	266.2	390.0	1.47
M 2.31	2.5	20.0	50.3	80.0	92.0	15.0	17.3	24.7	340.8	487.7	1.43
M 1.32 ^*	2.6	20.0	52.0	80.0	96.2	20.2	16.3	23.6	339.4	435.4	1.28
M 2.32	2.6	20.0	52.0	80.0	95.4	19.2	16.9	23.5	324.6	451.5	1.39
Mean value for ∼2.5mm samples:									301.2	430.6	1.44
M 2.41	3.0	20.0	60.0	90.0	107.9	19.9	19.5	25.3	325.5	422.0	422.0
M 2.42	3.0	20.0	60.0	90.0	103.2	14.6	26.8	32.6	445.9	544.1	1.22
Mean value for 3 mm samples:									385.7	483.0	1.26
Mean value for all samples:									310.2	419.2	1.36

Parameters of normal distribution of yield strength Re of steel samples of corrugated webs

Girder number	E(R _e) [Mpa]	R _ek [Mpa]	D ²(R _e)	D(R _e)	f _y [Mpa]	V _Re	V _Re235	V _Re215	γ _m	γ _m235	γ _m215
1	2	3	4	5	6	7	8	9	10	11	12
M 1.11	304.4	299.15	10.13	3.1826	294.69	0.0105	0.1390	0.1791	1.0151	0.7974	0.7296
M 1.41	317.8	307.57	38.76	6.2258	298.85	0.0196	0.1589	0.1972	1.0292	0.7863	0.7194
M 1.51^*	247.2	243.12	6.04	2.4576	239.68	0.0099	0.0301	0.0794	1.0144	0.9805	0.8970
M 2.21	334.3	321.48	61.41	7.8365	310.50	0.0234	0.1811	0.2176	1.0354	0.7568	0.6924
M 2.51	289.3	278.64	42.39	6.5108	269.53	0.0225	0.1144	0.1566	1.0338	0.8719	0.7977
M 1.12	334.7	328.38	15.00	3.8730	322.96	0.0116	0.1816	0.2181	1.0168	0.7276	0.6657
M 1.22	339.4	334.82	7.85	2.8018	330.90	0.0083	0.1876	0.2235	1.0118	0.7102	0.6497
M 1.42^*	267.2	257.21	36.78	6.0647	248.72	0.0227	0.0735	0.1191	1.0341	0.9448	0.8644
M 1.52	299.1	291.99	18.65	4.3186	285.95	0.0144	0.1307	0.1714	1.0211	0.8218	0.7519
M 2.12	337.9	333.88	6.03	2.4556	330.44	0.0073	0.1857	0.2218	1.0104	0.7112	0.6506
M 2.22	336.3	325.33	44.91	6.7015	315.95	0.0199	0.1837	0.2199	1.0297	0.7438	0.6805
M 2.52	281	273.17	23.02	4.7979	266.45	0.0171	0.0998	0.1432	1.0252	0.8820	0.8069
Average values 2 mm	307.4	299.6	25.91	5.0906	292.90	0.0166	0.1388	0.1789	1.0231	0.8112	0.7422
M 1.21^*	275.9	266.26	34.65	5.8864	258.02	0.0213	0.0904	0.1346	1.0319	0.9108	0.8333
M 1.31^*	260.4	250.70	34.91	5.9085	242.43	0.0227	0.0595	0.1063	1.0341	0.9694	0.8869
M 2.11	266.2	260.28	13.13	3.6235	255.21	0.0136	0.0715	0.1173	1.0199	0.9208	0.8424
M 2.31	340.8	326.04	81.16	9.0089	313.43	0.0264	0.1893	0.2251	1.0402	0.7498	0.6860
M 1.32^*	312.5	303.33	30.95	5.5633	295.54	0.0178	0.1512	0.1902	1.0264	0.7952	0.7275
M 2.32	324.6	310.44	74.97	8.6585	298.32	0.0267	0.1683	0.2059	1.0406	0.7877	0.7207
Average values 2.5 mm	296.7	286.2	44.96	6.7053	277.20	0.1217	0.1217	0.1632	1.0322	0.8556	0.7828
M 2.41	325.5	312.86	59.11	7.6883	302.09	0.0236	0.1695	0.2070	1.0357	0.7779	0.7117
M 2.42	445.9	422.88	197.6	14.0570	403.20	0.0315	0.1884	0.3157	1.0488	0.5828	0.5332
Average values 3 mm	385.7	367.9	128.36	11.3296	352.70	0.0294	0.2290	0.2614	1.0422	0.6804	0.6225
Average values for all samples	312.0	302.4	41.87	6.4707	294.1	0.0207	0.1427	0.1825	1.0277	0.8237	0.7536

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Random Strength Parameters of Steel Corrugated Webs and Their Influence on the Resistance of Sin Plate Girders

Publicado en línea: 04 abr 2019

Páginas: 65 - 77

Recibido: 28 sept 2017

Aceptado: 09 may 2018

DOI: https://doi.org/10.21307/acee-2018-039

Palabras clave
Corrugated web, Coefficients of variation, Normal distribution

© 2018 Witold Basiński et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 6.

Figure 5.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Program of investigations

Steel yield strength that accounts for the impact of cold rolling acc. (6) [18]:

Parameters of normal distribution of geometric dimensions of steel samples from corrugated webs and of resistance obtained according to formulae (7) and (8)

Parameters of yield strength and tensile strength tests on web samples

Parameters of normal distribution of yield strength Re of steel samples of corrugated webs

Random Strength Parameters of Steel Corrugated Webs and Their Influence on the Resistance of Sin Plate Girders

Publicado en línea: 04 abr 2019

Páginas: 65 - 77

Recibido: 28 sept 2017

Aceptado: 09 may 2018

DOI: https://doi.org/10.21307/acee-2018-039

Palabras claveCorrugated web, Coefficients of variation, Normal distribution

© 2018 Witold Basiński et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 6.

Figure 5.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Program of investigations

Steel yield strength that accounts for the impact of cold rolling acc. (6) [18]:

Parameters of normal distribution of geometric dimensions of steel samples from corrugated webs and of resistance obtained according to formulae (7) and (8)

Parameters of yield strength and tensile strength tests on web samples

Parameters of normal distribution of yield strength Re of steel samples of corrugated webs

Palabras clave
Corrugated web, Coefficients of variation, Normal distribution