Effects of Key Factors on Hull Girder Ultimate Strength Estimation by Progressive Collapse Calculations

Ölmez, Hasan; Bayraktarkatal, Ertekin

doi:10.1590/1679-78252509

Hasan Ölmez

Karadeniz Technical University Trabzon, Turkey, hasanolmez@ktu.edu.tr

Ertekin Bayraktarkatal

İstanbul Technical University İstanbul, Turkey, bayrak@itu.edu.tr

Figures (13)
Tables (8)

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Figure 1
MOL Comfort - 313 m length container ship broke in two in June 2013 (Vesselfinder.com, 2013).

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Figure 2
Calculation flowchart for orthotropic panel historical P-du derivation.

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Figure 3
Definition sketch for the forced curvature principle in the case of pure bending (Özgüç, 2006Özgüç, Ö. (2006). Hull girder ultimate strength and fracture toughness of damaged marine structures, PhD Thesis, Universities of Glasgow and Strathclyde, UK.).

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Figure 4
Mid-ship cross sections of ten benchmark ships (1 - 4).

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Figure 4 Cont.
Mid-ship cross sections of ten benchmark ships (5 - 10).

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Figure 5
Component discretization of FRG, SHOT and CNT35 with HULT and IACS-CSR.

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Figure 6
Moment-curvature curves of model 1 to 6.

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Figure 6 Cont.
Moment-curvature curves of model 7 to 10.

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Figure 7
Moment-curvature curves of five benchmark ships.

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Figure 8
Typical 3,500 TEU double sided - double bottom container ship.

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Figure 9
Mid-ship section of considered container ship.

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Figure 10
Two different component discretization of the mid-ship section.

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Figure 11
(a) Effect of initial deflections (b) Effect of residual welding strength on ultimate strength of hull girder.

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Table 1
Progressive hull collapse analysis calculation table.

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Table 2
Considered ten benchmark typical ships.

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Table 3
Principal dimensions of the ten benchmark typical ship hull sections.

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Table 4
Summary of benchmark ship's ultimate bending moment results for all methods.

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Table 5
Summary of benchmark ship's ultimate bending moment results for all methods.

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Table 6
Progressive collapse analysis scenarios.

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Table 7
Geometrical and material specifications of longitudinal stiffener components.

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Table 8
Moment and curvature values at ultimate strength of container ship (CNT35).

	Instantaneous Curvature		κ_i	Instantaneous Neutral Axis Position		Z_Ti
Comp. No	z_ij	Δz_ij	ε_ij	du_ij	P_ij	M_ij
j: 1, 2, 3	z_ij	z_ij - z_Ti	ε_ij = κ_i × Δz_ij	ε_ij × L	From P-du curves	Pi × Δz_ij
	i: iteration number; j: component number				ΣP_i = 0	ΣM_i

No	Ship Type	Abbreviation	Reference
1	1/3 Scale Frigate	FRG	Dow, 1991Dow, R. S. (1991). Testing and analysis of a 1/3 scale welded steel frigate model, Proc. Int. Conf. on Advances in Marine Structures, ARE, 749-773.
2	Single Hull VLCC Oil Tanker (Energy Concentration)	SHOT	Rutherford and Calwell,1990Rutherford, S.E. and Caldwell, J.B. (1990). Ultimate longitudinal strength of ships: a case study, SNAME Transactions. 98: 441-471.
3	3,500 TEU Container	CNT35	ISSC, 2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.
4	47,326 DWT Double Hull Oil Tanker	DHOT1	Dalma, 2009Dalma, E. (2009). Ultimate hull girder strength assessment using semi-analytical and computational methods, PhD Thesis, National Technical University of Athens, Greece.
5	105,000 DWT Double Hull Oil Tanker	DHOT2	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.
6	313,000 DWT Double Hull Oil Tanker	DHOT3	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.
7	170,000 DWT Single Sided Bulk Carrier	SSBC	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.
8	169,000 DWT Double Sided Bulk Carrier	DSBC	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.
9	9,000 TEU Container	CNT90	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.
10	113,000 DWT Floating Production Storage and Offload	FPSO	Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.

Hull Sec. Prop.		FRG	SHOT	CNT35	DHOT1	DHOT2	DHOT3	SSBC	DSBC	CNT90	FPSO
Length (m)		18	313	230	182.5	233	315	282	273	305	230.6
Breadth (m)		4.2	48.2	32.2	32.2	42	58	50	44.5	45.3	41.8
Depth (m)		2.8	25.2	21.5	18.1	21.3	30.3	26.7	23	27	22.9
Draft (m)		-	19	12.5	12.6	12.2	22	19.3	15	13.5	14.15
Cb		-	0.83	0.68	0.77	0.83	0.82	0.83	0.84	0.65	0.83
Cross Sec. Area (m²⁾		-	7.85	3.84	3.02	5.31	9.63	5.65	5.78	6.19	4.88
Neutral Axis (m)		1.42	12.1	8.50	7.68	9.18	12.97	11.18	10.05	11.61	10.21
I (Vertical) (m⁴⁾		0.06	863.7	237.5	164.8	359.5	1346.1	694.3	508.3	682.8	393.6
Z (m³⁾	Deck	0.03	66.30	18.33	13.81	29.68	77.24	44.35	39.27	44.37	31.04
	Bottom	0.04	70.95	27.23	18.72	39.13	103.77	62.06	50.54	58.78	38.52
σ_y MPa	Deck	245	315	355	245	315	315	390	355	355	315
	Bottom	245	315	315	315	315	315	315	315	315	315

Remarks		FRG		SHOT		CNT35		DHOT1		DHOT2
		Hog.	Sag.	Hog.	Sag.	Hog.	Sag.	Hog.	Sag.	Hog.	Sag.
Multimate (x10³ kNm for model FRG & x10⁶ kNm for models SHOT to DHOT2)	Chen [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.49	9.54	20.23	18.54	6.56	5.47	-	-	-	-
	Cho [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	11.32	9.48	20.09	16.75	6.69	5.13	-	-	-	-
	Masaoka [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.49	11.50	20.01	19.00	8.07	7.95	-	-	-	-
	Rigo(1) [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	13.26	9.47	18.46	17.90	7.60	6.51	-	-	-	-
	Rigo(2) [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.12	9.88	17.54	17.10	7.20	6.91	-	-	-	-
	Yao [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	10.90	8.58	19.03	16.84	6.72	6.72	-	-	-	-
	ALPS/HULL [Paik,2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.]	10.45	9.94	16.77	15.83	6.92	6.64	-	-	8.49	6.90
	Paik-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	9.62	17.36	16.18	6.97	6.95	-	-	-	-
	Mod. P-M [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	18.70	17.83	6.4	7.08	-	-	-	-
	Benson [2011Benson, S. (2011). Progressive collapse assessment of lightweight ship structures, Ph.D. Thesis, Newcastle University, UK.]	-	10.20	-	-	-	-	-	-	-	-
	Dalma [2009Dalma, E. (2009). Ultimate hull girder strength assessment using semi-analytical and computational methods, PhD Thesis, National Technical University of Athens, Greece.]	-	-	-	-	-	-	-	3.09	-	-
	ISR-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	21.2	20.2	7.49	7.18	-	-	-	-
	CR-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	21.86	20.63	7.66	7.63	-	-	-	-
	Özgüç [2006Özgüç, Ö. (2006). Hull girder ultimate strength and fracture toughness of damaged marine structures, PhD Thesis, Universities of Glasgow and Strathclyde, UK.]	12.01	9.60	17.89	16.45	6.79	6.70	-	-	-	-
	Tayyar [2011Tayyar, G. T. (2011). Determination of ultimate strength of the ship girder, PhD Thesis, İstanbul Technical University, İstanbul-Turkey.]	-	9.74	17.02	-	-	-	-	-	-	-
	Dow [1991Dow, R. S. (1991). Testing and analysis of a 1/3 scale welded steel frigate model, Proc. Int. Conf. on Advances in Marine Structures, ARE, 749-773.]	11.39	9.64	18.80	-	-	-	-	-	-	-
	Ruth-Caldwell [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	-	-	17.94	-	-	-	-	-	-	-
	CSR-CR [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	20.71	18.59	7.88	7.59	-	-
	CSR-PNU [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	20.10	18.71	7.76	6.85	-	-
	Rina Rules [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	19.84	18.47	6.86	5.90	-	-
	CSR-FSB [Andric et al., ,2014Andric, J., Kitarovic, S., Bicak, M. (2014). IACS incremental - iterative method in progressive collapse analysis of various hull girder structures, Brodogradnja/Shıpbuıldıng 65/1: 65-78.]	-	-	19.41	18.30	7.58	6.82	-	-
	CSR-KTU [Ölmez,2014Ölmez, H. (2014). Ultimate strength estimation of ship hull girders by progressive collapse analysis approach, PhD Thesis, Karadeniz Technical University, Trabzon-Turkey.]	12.11	10.25	19.30	18.03	7.25	6.65	4.88	2.97	8.75	6.95
	HULT	12.18	9.53	17.66	16.95	7.34	6.68	5.26	3.25	8.61	7.08
Mean / All Methods		11.86	9.784	19.04	17.91	7.21	6.74	5.07	3.10	8.62	6.98
St.Dv. / All Methods		0.841	0.633	1.416	1.314	0.492	0.702	0.269	0.140	0.13	0.09
COV / All Methods		0.071	0.065	0.074	0.073	0.068	0.104	0.053	0.045	0.013	0.018
COV / Smith Based		0.060	0.087	0.062	0.049	0.069	0.115	0.053	0.064	0.014	0.013
Remarks		DHOT3		SSBC		DSBC		CNT90		FPSO
		Hog.	Sag.	Hog.	Sag.	Hog.	Sag.	Hog.	Sag.	Hog.	Sag.
Multimate (x10⁶ kNm for models DHOT3 to FPSO)	Chen [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	27.40	24.33	19.06	15.20	-	-	-	-	-	-
	Cho [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	28.66	20.80	18.99	13.69	-	-	-	-	-	-
	Masaoka [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	30.59	26.59	18.56	16.02	-	-	-	-	-	-
	Rigo(1) [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	28.32	19.57	18.71	14.34	-	-	-	-	-	-
	Rigo(2) [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	25.61	24.07	17.06	14.34	-	-	-	-	-	-
	Yao [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	28.88	20.42	17.36	14.45	-	-	-	-	-	-
	ALPS/HULL [Paik et al., 2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.]	23.59	19.57	16.60	15.38	12.03	12.2	13.08	16.60	8.76	7.28
	Paik-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	27.34	22.50	17.50	15.80	-	-	-	-	-	-
	Mod. P-M [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	25.67	22.39	16.58	14.8	-	-	-	-	-	-
	Benson [2011Benson, S. (2011). Progressive collapse assessment of lightweight ship structures, Ph.D. Thesis, Newcastle University, UK.]	-	-	-	-	-	-	-	-	-	-
	Dalma [2009Dalma, E. (2009). Ultimate hull girder strength assessment using semi-analytical and computational methods, PhD Thesis, National Technical University of Athens, Greece.]	-	-	-	-	-	-	-	-	-	-
	ISR-FEM [ISSC,2012Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	30.11	28.18	18.33	17.73	-	-	-	-	-	-
	CR-FEM [ISSC,2012Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	31.00	25.00	18.40	16.86	-	-	-	-	-	-
	Özgüç [2006Özgüç, Ö. (2006). Hull girder ultimate strength and fracture toughness of damaged marine structures, PhD Thesis, Universities of Glasgow and Strathclyde, UK.]	27.45	21.15	17.34	14.19	-	-	-	-	-	-
	Tayyar [2011Tayyar, G. T. (2011). Determination of ultimate strength of the ship girder, PhD Thesis, İstanbul Technical University, İstanbul-Turkey.]	-	-	-	-	-	-	-	-	-	-
	Dow [1991Dow, R. S. (1991). Testing and analysis of a 1/3 scale welded steel frigate model, Proc. Int. Conf. on Advances in Marine Structures, ARE, 749-773.]	-	-	-	-	-	-	-	-	-	-
	Ruth.-Caldwell [ISSC, 2000Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	-	-	-	-	-	-	-	-
	CSR-CR [ISSC,2012Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	29.85	25.01	18.34	14.92	-	-	-	-	-	-
	CSR-PNU [ISSC,2012Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	28.42	22.13	18.36	14.50	-	-	-	-	-	-
	Rina Rules [ISSC,2012Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	28.20	21.67	17.48	13.95	-	-	-	-	-	-
	CSR-FSB [Andric et al., 2014Andric, J., Kitarovic, S., Bicak, M. (2014). IACS incremental - iterative method in progressive collapse analysis of various hull girder structures, Brodogradnja/Shıpbuıldıng 65/1: 65-78.]	28.43	21.16	17.87	14.19	-	-	-	-	-	-
	CSR-KTU [Ölmez,2014Ölmez, H. (2014). Ultimate strength estimation of ship hull girders by progressive collapse analysis approach, PhD Thesis, Karadeniz Technical University, Trabzon-Turkey.]	28.11	20.58	18.05	14.65	12.28	12.88	14.35	16.18	9.55	7.74
	HULT	24.59	21.55	17.45	15.12	11.76	12.69	13.88	16.74	9.30	7.46
Mean / All Methods		28.01	22.62	17.89	15.01	12.02	12.25	13.77	16.51	9.202	7.491
St.Dv. / All Methods		1.798	2.426	0.758	1.044	0.260	0.410	0.642	0.291	0.402	0.234
COV / All Methods		0.064	0.107	0.042	0.069	0.022	0.034	0.047	0.018	0.041	0.032
COV / Smith Based		0.056	0.101	0.037	0.042	0.031	0.047	0.024	0.020	0.018	0.019

Remarks		FRG		SHOT		CNT35		DHOT2		SSBC
		Hog	Sag	Hog	Sag	Hog	Sag	Hog	Sag	Hog	Sag
Multimate (x10³ kNm for model FRG & x10⁶ kNm for models SHOT to SSBC)	Chen [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.49	9.54	20.23	18.54	6.56	5.47	-	-	19.06	15.20
	Cho [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	11.32	9.48	20.09	16.75	6.69	5.13	-	-	18.99	13.69
	Masaoka [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.49	11.5	20.01	19.00	8.07	7.95	-	-	18.56	16.02
	Rigo (2) [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	12.12	9.88	17.54	17.10	7.20	6.91	-	-	17.06	14.34
	Yao [ISSC,2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	10.90	8.58	19.03	16.84	6.72	6.72	-	-	17.36	14.45
	ALPS/HULL [Paik et al.,2002Paik, J. K., Wang, G., Kim, B. J., Thayamballi, A. K. (2002). Ultimate limit state design of ship hulls, SNAME Transactions 110: 85-114.]	10.45	9.94	16.77	15.83	6.92	6.64	8.49	6.90	16.60	14.28
	Paik-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	9.62	17.36	16.18	6.97	6.95	-	-	17.50	15.80
	Modified P-M [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	18.70	17.83	6.4	7.08	-	-	16.58	14.8
	ISR-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	21.2	20.2	7.49	7.18	-	-	17.06	14.34
	CR-FEM [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	21.86	20.63	7.66	7.63	-	-	17.36	14.45
	Ozguc [2006Özgüç, Ö. (2006). Hull girder ultimate strength and fracture toughness of damaged marine structures, PhD Thesis, Universities of Glasgow and Strathclyde, UK.]	12.01	9.60	17.89	16.45	6.79	6.70	-	-	16.60	15.38
	Tayyar [2011Tayyar, G. T. (2011). Determination of ultimate strength of the ship girder, PhD Thesis, İstanbul Technical University, İstanbul-Turkey.]	-	9.74	17.02	-	-	-	-	-	17.50	15.80
	Dow [1991Dow, R. S. (1991). Testing and analysis of a 1/3 scale welded steel frigate model, Proc. Int. Conf. on Advances in Marine Structures, ARE, 749-773.]	11.39	9.64	18.80	-	-	-	-	-	16.58	14.8
	Ruth.-Caldwell [ISSC, 2000Technical Committee VI.2 (2000). Ultimate hull girder strength, Proceedings of the 14th International Ship and Offshore Structures Congress 2 Nagasaki.]	-	-	17.94	-	-	-	-	-	17.06	14.34
	CSR-CR [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	20.71	18.59	7.88	7.59	-	-	17.36	14.45
	CSR-PNU [ISSC,2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	20.10	18.71	7.76	6.85	-	-	16.60	15.38
	Rina Rules [ISSC, 2012Technical Committee III.1. (2012). Ultimate strength, Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock 1.]	-	-	19.84	18.47	6.86	5.90	-	-	17.50	15.80
	CSR-FSB [Andric et al.,2014Andric, J., Kitarovic, S., Bicak, M. (2014). IACS incremental - iterative method in progressive collapse analysis of various hull girder structures, Brodogradnja/Shıpbuıldıng 65/1: 65-78.]	-	-	19.41	18.30	7.58	6.82	-	-	16.58	14.8
	CSR-KTU [Olmez, 2014Ölmez, H. (2014). Ultimate strength estimation of ship hull girders by progressive collapse analysis approach, PhD Thesis, Karadeniz Technical University, Trabzon-Turkey.]	12.11	10.2	19.30	18.03	7.25	6.65	8.75	6.95	17.06	14.34
	HULT- Model I	12.35	9.61	18.09	17.15	7.47	6.85	8.79	7.21	17.88	15.68
	HULT-Model II	12.05	9.46	17.38	16.80	7.29	6.55	8.25	6.84	16.75	14.73
	HULT-Model III	12.18	9.53	17.66	16.95	7.34	6.68	8.61	7.08	17.45	15.12
	Mean	11.82	9.737	18.95	17.81	7.205	6.750	8.578	6.99	17.32	14.91
	St.Dv.	0.656	0.621	1.435	1.311	0.473	0.682	0.218	0.14	0.743	0.642
	COV	0.055	0.064	0.076	0.074	0.066	0.101	0.025	0.02	0.043	0.043

Scenario No	w₀	σ_rcx	tcomponent
1	0.025 × β² × t_p	-0.15 × σ_Yp	t_cor-ABS
2	0.1 × β² × t_p	-0.15 × σ_Yp	t_cor-ABS
3	0.3 × β² × t_p	-0.15 × σ_Yp	t_cor-ABS
4	0.1 × β² × t_p	-0.05 × σ_Yp	t_cor-ABS
2	0.1 × β² × t_p	-0.15 × σ_Yp	t_cor-ABS
5	0.1 × β² × t_p	-0.3 × σ_Yp	t_cor-ABS

Stf. No	Web mm	Flange mm	Stif. Type	Mat. Yield MPa	Stf. No	Web mm	Flange mm	Stif. Type	Mat. Yield MPa
1	300 x 38		Flat	352.8	9	230 x 10		Flat	313.6
2	300 x 28		Flat	313.6	10	300 x 13	90 x 17	L	313.6
3	250 x 10	90 x 15	L	313.6	11	150 x 12	90 x 12	L	313.6
4	250 x 12	90 x 16	L	313.6	12	250 x 12	90 x 15	L	313.6
5	300 x 11	90 x 16	L	313.6	13	150 x 12		Flat	313.6
6	300 x 13	90 x 17	L	313.6	14	150 x 9	90 x 9	L	313.6
7	350 x 12	100 x 17	L	313.6	15	150 x 10		Flat	313.6
8	400 x 11.5	100 x 16	L	313.6	16	300 x 11	90 x 16	L	313.6

		IACS-CSR	Chen	ALPS/HULL	FEM	Rina Rules	Rigo-2	Yao	HULT
(Sagging)	Mu x10⁶ kN.m	6.81	5.47	6.64	6.95	5.89	6.91	6.72	6.68
	κ_u	1.65x10^-4	1.13x10^-4	1.5x10^-4	2.7x10^-4	2.09x10^-4	1.58x10^-4	1.41x10^-4	1.52x10^-4
(Hogging)	Mu x10⁶ kN.m	6.65	6.56	6.92	6.97	6.86	7.20	6.72	6.83
	κ_u	1.94x10^-4	2.49x10^-4	1.87x10^-4	2.17x10^-4	2.49x10^-4	1.62x10^-4	1.63x10^-4	1.57x10^-4

Brasil

Brasil

Effects of Key Factors on Hull Girder Ultimate Strength Estimation by Progressive Collapse Calculations

Abstract