Elsevier

Thin-Walled Structures

Volume 40, Issue 1, January 2002, Pages 45-83
Thin-Walled Structures

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

https://doi.org/10.1016/S0263-8231(01)00043-XGet rights and content

Abstract

This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.

Introduction

A limit state is formally defined as a condition for which a particular structural member or an entire structure fails to perform the function that it has been designed beforehand for. From the special view point of a structural designer, four types of limit states are usually considered, namely serviceability limit state, ultimate limit state, fatigue limit state and accidental limit state. In design, these various types of limit states may be considered against different safety levels, the actual safety level to be attained for a particular type of limit state being a function of the perceived consequences to be accounted for and ease of recovery to be incorporated in design. Of concern in this paper is the ultimate limit state design of steel stiffened panels.

Theoretically, the primary modes of overall failure for a stiffened panel subject to predominantly compressive loads may be categorized into the following six groups, namely

  • Mode I: Overall collapse after overall buckling of the plating and stiffeners as a unit, see Fig. 1(a),

  • Mode II: Plate-induced failure by yielding at the corners of plating between stiffeners, see Fig. 1(b),

  • Mode III: Plate-induced failure by yielding of a plate–stiffener combination at mid-span, see Fig. 1(c),

  • Mode IV: Stiffener-induced failure by local buckling of stiffener web, see Fig. 1(d),

  • Mode V: Stiffener-induced failure by lateral–torsional buckling of stiffener, see Fig. 1(e), and

  • Mode VI: Gross yielding.

Mode I typically represents the collapse pattern when the stiffeners are relatively weak. In this case, the stiffeners can buckle together with plating, the overall buckling behavior remaining elastic. The stiffened panel can normally sustain further loading even after overall buckling in the elastic regime occurs and the ultimate strength is eventually reached by formation of a large yield region inside the panel and/or along the panel edges. In Mode I, the panel behaves as an ‘orthotropic plate’.

The other groups (i.e., Modes II–VI) normally take place when the stiffeners are relatively strong so that the stiffeners remain straight until the plating between stiffeners buckles or even collapses locally. The stiffened panel will eventually reach the ultimate limit state by failure of stiffeners together with associated plating. It is noted that the stiffened panel with weak stiffeners where failure of stiffeners occurs prior to buckling of plating normally follows Mode I, i.e., failure after overall buckling occurs in the elastic regime.

Mode II typically represents the collapse pattern wherein the panel collapses by yielding at the corners of plating between stiffeners, which is usually termed a plate-induced failure at ends. This type of collapse can also occur in some cases when the panel is predominantly subjected to biaxial compressive loads. Mode III indicates a failure pattern in which the ultimate strength is reached by column or beam-column type collapse of the plate–stiffener combination with the associated effective (reduced) plating. Mode III typically takes place by yielding of the plate–stiffener combination at mid-span, which is usually termed a plate-induced failure at mid-span.

Modes IV and V failures typically arise when the ratio of stiffener web height to stiffener web thickness is too large and/or when the type of the stiffener flange is inadequate to remain straight so that the stiffener web buckles or twists sideways. Mode IV represents a failure pattern in which the panel collapses by local buckling of stiffener web, while Mode V can occur when the ultimate strength is reached by lateral–torsional buckling (also called tripping) of stiffener.

Mode VI typically takes place when the panel slenderness is very small (i.e., the panel is very stocky or thick) and/or when the panel is predominantly subjected to the axial tensile loading so that neither local nor overall buckling occurs until the panel cross section yields entirely.

Calculation of the ultimate strength of the stiffened panel under combined loads taking into account all of the possible failure modes noted above is not straightforward, because of the interplay of the various factors previously mentioned such as geometric/material properties, loading, post-weld initial imperfections (i.e., initial deflection and residual stress) and boundary conditions. As an approximation, this paper considers that the collapse of stiffened panels occurs at the lowest value among the various ultimate loads calculated for each of the above collapse patterns. This leads to an easier alternative wherein one calculates the ultimate strengths for all collapse modes mentioned above separately and then compares them to find the minimum value, which is then taken to correspond to the real panel ultimate strength.

The behavior of steel stiffened panels normally depends on a variety of influential factors, namely geometric/material properties, loading characteristics, initial imperfections, boundary conditions and existing local damage related to corrosion, fatigue crack and denting. A number of studies on the ultimate strength for stiffened panels have been undertaken experimentally, numerically and theoretically. Comparisons between some of these methods have been performed by many investigators [1], [2], [3], [4].

Smith [5] presents a series of tests on full scale welded steel grillages subjected to a combination of axial compression and lateral pressure. Efforts on experimental investigation for stiffened panel collapse behavior are made by Tanaka and Endo [6], Hu et al. [7] and Hopperstad et al. [8], among others. Smith and his colleagues [9], [10], [11], [12] provide an extensive contribution to the ultimate strength design for ship stiffened panels under combined in-plane and lateral pressure loads. The panel ultimate strength formulation based on column or beam-column type collapse pattern is typically based on the so-called Perry–Robertson formula [13], [14], [15], [16], [17], [18], [19]. Local buckling of stiffener webs is studied by Paik et al. [20]. Many researchers have studied tripping of stiffeners theoretically, numerically and experimentally. Earlier work that used classical theory of thin-walled bars has been summarized and expanded by Bleich [21]. During the 1970s and 1980s, further studies have been undertaken by Faulkner et al. [22], [23], [24], [25] and Adamchak [26]. Hughes [15] has reviewed and summarized some of these studies. During the 1990s, in addition to the tripping problem under axial compression alone [27], [28], [29], [30], the effect of combined axial compression and lateral loads has been studied by Hughes and Ma [31], [32] and Hu et al. [33].

While the previous studies being useful for prediction of the stiffened panel ultimate strength, most studies are based on one or two collapse patterns. As previously noted, various failure modes can potentially involve in collapse of a stiffened panel and the panel ultimate strength formulation should accommodate all these potential collapse patterns mentioned above. The stiffened panel in ships is generally subjected to combined in-plane and lateral pressure loads. In-plane loads include axial load and in-plane bending, which are mainly induced by overall hull girder bending. Lateral pressure is due to water pressure and cargo. These load components are not always applied simultaneously, but more than one normally exist and interact. Thus it is of crucial importance to evaluate the panel ultimate strength taking into account the effect of combined loading. Since the post-weld initial imperfections in the form of initial deflections and residual stresses exist in ship stiffened panels and can affect (reduce) significantly the ultimate strength, such welding induced initial imperfections should be included in the strength calculations as parameters of influence.

The aim of the present paper is to develop an advanced, yet design-oriented method for evaluating the ultimate limit state of stiffened panels under combined axial load, in-plane bending and lateral pressure. It is considered that the collapse of stiffened panels occurs at the lowest value among the various ultimate loads calculated for each of the six collapse patterns mentioned above. The panel ultimate strengths for all collapse modes are calculated separately and then compare them to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections are included as parameters of influence. To test the validity of the developed method, verification examples are studied by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with the Det Norske Veritas design guideline for marine stiffened plate structures.

Section snippets

Modeling of steel stiffened panels

Fig. 2 shows a typical steel stiffened plate structure. Its response can be studied at three levels, namely the entire structure level, the stiffened panel level and the bare plate level. This paper is primarily concerned with the second level (i.e., the stiffened panel level) in which a panel is supported by girders along longitudinal edges and by frames (or floors) along transverse edges. In the following, some basic idealizations made for development of the panel ultimate strength

Panel ultimate strength formulations

This paper calculates the panel ultimate strengths for various collapse modes separately. The real panel ultimate strength is then considered to be the lowest value among the various ultimate loads calculated for each of the collapse patterns. In a sense, contribution of the present paper is integration of past efforts which have been separately made for individual collapse patterns. Since a more elaborate description for panel ultimate strength formulations of all collapse modes considered may

Verification examples

To test the validity of the panel ultimate strength formulations, verification examples are now considered. In these examples, the ultimate strength formulations are compared with experimental, numerical and theoretical results. Predictions from the design oriented procedures proposed in this paper were automated using a computer program called ALPS/ULSAP which stands for Analysis of Large Plated Structures/ULtimate Strength Analysis of Panels.

The nonlinear FEM computes the elastic-plastic

Concluding remarks

The aim of the present study has been to develop an advanced, yet design-oriented method for predicting the ultimate strength of steel stiffened panels under combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups, namely overall grillage collapse, yielding at the corners of plating between stiffeners, yielding of the plate–stiffener combination at mid-span, local buckling of stiffener web, lateral–torsional buckling

Acknowledgements

The present study was undertaken under financial support from the Research Institute of Marine Systems Engineering of the Seoul National University, Seoul, Korea (Director: Prof. Hang S. Choi) who is thanked for this support. The authors are grateful to Dr. A.K. Thayamballi of Chevron Shipping and Dr. E. Steen of Det Norske Veritas for their valuable comments.

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