Elsevier

Thin-Walled Structures

Volume 45, Issue 3, March 2007, Pages 301-306
Thin-Walled Structures

Ultimate strength of perforated steel plates under edge shear loading

https://doi.org/10.1016/j.tws.2007.02.013Get rights and content

Abstract

The aim of the present study is to investigate the ultimate strength characteristics of perforated steel plates under edge shear loading, which is a primary action type arising from cargo weight and water pressure in ships and ship-shaped offshore structures. The plates are considered to be simply supported along all (four) edges and kept straight. The cutout is circular and located at the center of the plate. A series of ANSYS nonlinear finite element analyses (FEA) are undertaken with varying the cutout size (diameter) as well as plate dimensions (plate aspect ratio and thickness). By the regression analysis of the FEA results obtained, a closed-form empirical formula for predicting the ultimate shear strength of perforated plates, which can be useful for first-cut strength estimations in reliability analyses or code calibrations, is derived. The accuracy of the ultimate strength formula developed is verified by a comparison with more refined nonlinear FEA results.

Introduction

In ships and ship-shaped offshore structures, cutouts are often located in plates to make a way of access or to lighten the structure. These perforations could reduce the ultimate strength of the plates. The cutouts are then needed to be included in the ultimate strength formulations as a parameter of influence where significant.

A number of useful studies related to buckling strength of perforated plates have of course previously been undertaken in the literature. Elastic buckling strength of perforated plates was studied by many investigators [1], [2], [3], [4], [5], [6], [7], [8].

Elastic buckling strength is often used as the basis of serviceability limit state (SLS) design for steel plates in ships and offshore structures [9], [10], [11] as well as other types of structures such as land-based structures. The previous studies related to elastic buckling of perforated steel plates are then useful for the SLS design purpose. On the other hand, it is important to realize that most moderately thick plates always involve plasticity to some degree until buckling takes place. The simple plasticity correction of elastic buckling strength is typically made to take into account the effect of plasticity using some approximate formulations such as the so-called Johnson–Ostenfeld formula. The elastic–plastic buckling strength so estimated is often termed the ‘critical’ buckling strength in maritime industry. In this regard, the elastic–plastic buckling of perforated steel plates has also been studied by many investigators [12], [13], [14], [15].

However, it is interesting to note that the critical or elastic–plastic buckling strength of perforated steel plates obtained by the above-mentioned plasticity correction of the corresponding plate elastic buckling strength can be greater than the ultimate limit state (ULS) strength (ultimate load-carrying capacity) in some cases, typically when the plates are moderately thick and/or the size of cutout is relatively large [9], [10], [11]. This is in contrast to perfect plates, i.e., without cutout, where the ‘critical’ buckling strength estimated by the plasticity correction of the elastic buckling strength is always smaller than the plate ultimate strength at pessimistic strength side. This means that the traditional method to estimate the critical buckling strength, i.e., by a simple plasticity correction is not valid for perforated plates.

Therefore, it is required to directly consider the plate ultimate strength for ULS design purpose as long as the plates have cutouts. The ultimate strength of perforated plates or plate girders used for land-based structures has then been studied in the literature [16], [17], [18]. Since the action characteristics of plate elements used for ships and ship-shaped offshore structures are quite different from those for land-based structures, similar studies are certainly necessary for perforated steel plates used for the former type of structures.

The aim of the present study is to investigate the ultimate shear strength characteristics of perforated steel plates used for ships and offshore structures. A series of ANSYS [19] elastic–plastic large deflection finite element analyses (FEA) are carried out with varying the cutout size as well as plate dimensions. By regression analysis of the FEA results, an empirical closed-form formula of perforated plate ultimate strength which can be useful for first-cut strength estimations in reliability analyses or code calibrations is derived.

Section snippets

Perforated steel plates and their structural modeling

For ships and ship-shaped offshore structures, cutouts are typically made in plates of ballast water tanks. In a continuous steel stiffened plate structure, a plate is surrounded by support members (stiffeners) which are typically designed so that they should not fail prior to the plate. In this regard, the plate in the present study considered to be simply supported at all (four) edges which are kept straight until the ultimate strength is reached. This boundary condition is usually adopted

Ultimate strength characteristics of perforated steel plates

Fig. 3 shows edge shear stress versus strain relations for a perforated plate with the aspect ratio of 3, with varying the cutout size (diameter), until and after the ultimate strength is reached. This plate is moderately thick because the plate slenderness ratio is 2.2. It is evident from Fig. 3 that the cutout significantly reduces the plate ultimate strength. For example, when the diameter of the cutout is 40% of the plate breadth, the plate ultimate strength is reduced by approximately 85%

Empirical ultimate strength formula for perforated plates

A closed-form empirical formula for the ultimate shear strength of perforated plates is now derived. Although the use of such empirical formula may be limited in terms of application range, ultimate strength-based reliability analyses and code calibrations which typically require first-cut strength estimates often need closed-form formula.

Based on the insights noted above, the plate ultimate reduction factor, Rτu, for edge shear may be empirically derived as a function of the cutout size and

Concluding remarks

The aim of the present paper has been to investigate the ultimate strength characteristics of perforated steel plates under edge shear loads. A series of ANSYS elastic–plastic large deflection FEA were then carried out with varying the cutout size as well as plate dimensions (aspect ratio and plate thickness).

It is confirmed that the cutout significantly reduces the plate ultimate strength. It is found that the plate aspect ratio affects the ultimate strength of perforated plates to some extent

Acknowledgment

The present study was undertaken at the Ship and Offshore Structural Mechanics Laboratory, Pusan National University, Korea, which is a National Research Laboratory funded by the Korea Ministry of Science and Technology (Grant no. M10600000239-06J0000-23910).

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      Paik and Thayamballi (2006) revealed that the ultimate limit state (ULS) approach was more useful than the traditional allowable stress method in design and safety evaluation, and they proposed the ULS design formula for various structural elements including the perforated plate. By Paik (2007) and Paik (2008), the limitations of the method of plasticity correction using the Johnson–Ostenfeld formula in determining the ultimate load of a perforated rectangular plate were disclosed, and a closed-form empirical formula that could easily predict the ultimate strength of a perforated steel plate was derived based on the finite element analysis results. All the preceding studies mentioned above made use of the assumption that all edges of the perforated steel plate were restrained by clamped supported or simply supported conditions, ignoring the effect of the interaction between the plate and the stiffener.

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