Jostein Hellesland

• Hellesland, Jostein (2023). Derivation of key characteristics of columns in frames with sway. WSEAS Transactions on Applied and Theoretical Mechanics. ISSN 1991-8747. 18, p. 255–269. doi: 10.37394/232011.2023.18.24. Full text in Research Archive Show summary

  The paper paper examines columns of elastic frames that are able to displace laterally under axial load. Columns on the same level (story) of such frames may contribute to lateral support (stability) or require lateral support (supported columns). In the former case, maximum moments will occur at column ends, but may occur between column ends in the latter case. The column response, including the formation of moments and shears, is often complicated, often calling for approximate analysis methods and information that presently may not be readily available. Main attention of the paper is paid to providing results that will be helpful in providing, in a rather simple manner, improved understanding of column mechanics, and that may be helpful also as a supplement to full second-order analyses. Towards this goal, the major objective of the paper is threefold: (i) to identify characteristic points, or behavioral“landmarks” in the axial load-moment solution space, through the study of rotationally restrained elastic columns and two-column panels with sidesway; (ii) to derive simple, novel, closed-form expressions for these, thereby providing a tool simplifying the establishment of the variation of end and maximum moments versus axial load; (iii) to identify to what extent isolated (single) column analyses may adequately represent horizontally interacting columns, and potential unwinding, in frames. Key-Words: - Structural mechanics, elasticity, second-order analysis, stability, framed column behavior, sidesway.

• Hellesland, Jostein (2020). New and extended design moment formulations for slender columns in frames with sway. Engineering structures. ISSN 0141-0296. 203. doi: 10.1016/j.engstruct.2019.109804. Full text in Research Archive Show summary

  Present first-order based design code formulations for slender columns in frames with sway, employ sway magnification factors (for global second-order effects) also as moment magnifiers for the individual columns of the frame (storey). This approach ignores differences in magnification of individual column moments caused by local second-order effects in the columns. This difference can be significant. Better understanding of this aspect will strengthen approximate first-order based elastic methods, for which the important superposition principle is valid. Towards this end, local second-order effects are considered for shears, end moments and maximum mo- ments, applicable over the full range of axial loads. Specifically, end moment and maximum moment expressions of columns with sway are derived. These represent novel contributions that are suitable in typical design code formats, and in practical design work. They will allow more rational column assessments, and will allow more economical designs than present structural code procedures. Proposals are verified by comparison with results from second-order in-plane elastic analyses of single restrained columns and columns in frame panels. Also, extensions to the general case of load combinations that include both gravity and sideways loading are briefly presented.

• Sollund, Håvar Andreas; Vedeld, Knut; Fyrileiv, Olav & Hellesland, Jostein (2016). Improved assessments of wave-induced fatigue for free spanning pipelines. Applied Ocean Research. ISSN 0141-1187. 61, p. 130–147. doi: 10.1016/j.apor.2016.10.004. Full text in Research Archive Show summary

  For subsea pipeline projects, the costs related to seabed correction and free span intervention are often considerable. Development of reliable methods for fatigue analyses of pipelines in free spans contributes to minimize costs without compromising pipeline integrity. Assessment of wave-induced fatigue damage on multi-span pipelines is investigated, and improved analysis methods are suggested in this paper. A time-domain (TD) algorithm is developed, which accounts for non-linear hydrodynamic loading and dynamic interaction between adjacent spans. The proposed TD approach is employed to evaluate linearized frequency-domain (FD) solutions from recognized design standards and to study the dynamic response of multi-span pipelines to direct wave loading. Differences between multi- and single-span analyses are described for the first time, and the common assumption that the main fatigue damage contribution comes from the fundamental mode is demonstrated not to hold for multi-spans. An improved FD solution capable of predicting multi-mode response is derived and demonstrated to give accurate fatigue life estimates for multi-span pipelines.

• Vedeld, Knut; Sollund, Håvar Andreas & Hellesland, Jostein (2015). Closed Analytical Expressions for Stress Distributions in Two-Layer Cylinders and Their Application to Offshore Lined and Clad Pipes. Journal of Offshore Mechanics and Arctic Engineering. ISSN 0892-7219. 137(2), p. 1–9. doi: 10.1115/1.4029357. Full text in Research Archive Show summary

  Closed-form analytical expressions are derived for the displacement field and corresponding stress state in two-layer cylinders subjected to pressure and thermal loading. Solutions are developed both for cylinders that are fully restrained axially (plane strain) and for cylinders that are axially loaded and spring-mounted. In the latter case, it is assumed that the combined two-layer cross section remains plane after deformation (generalized plane strain). The analytical solutions are verified by means of detailed three-dimensional finite element (FE) analyses, and they are easily implemented in, and suitable for, engineering applications. The chosen axial boundary conditions are demonstrated to be particularly relevant for pipeline and piping applications. By applying the exact solutions derived in the present study to typical offshore lined or clad pipelines, it is demonstrated that thermal expansion of the liner or clad layer may cause higher tensile hoop stresses in the pipe steel wall than accounted for in current engineering practice. It is shown that repeated cycles of start-up and shut-down phases for lined or clad pipelines cause significant plastic stress cycles in liners or claddings, which may pose a risk to the integrity of such pipelines.

• Brubak, Lars; Hareide, O. J. & Hellesland, Jostein (2014). Application of a Semi-Analytical Approach for Vibration Analysis of Irregularly Stiffened Plates. Trita-MEK. ISSN 0348-467X. p. 220–229. Full text in Research Archive Show summary

  Free vibration of irregularly stiffened plates is studied. The plates may be subjected to in-plane loads and the plate boundaries may be simply supported or rotationally restrained. The main objective is to demonstrate and validate the applicability of an approximate, semi- analytical computational model.

• Vedeld, Knut; Sollund, Håvar Andreas; Hellesland, Jostein & Fyrileiv, Olav (2014). Effective axial forces in offshore lined and clad pipes. Engineering structures. ISSN 0141-0296. 66, p. 66–80. doi: 10.1016/j.engstruct.2014.01.051. Full text in Research Archive Show summary

  To protect pipelines from corrosion attacks, some offshore pipelines have corrosion resistant liners or cladding made from stainless steel. Stainless steels have higher temperature expansion coefficients and lower Poisson’s ratios than ordinary high strength carbon manganese steels. Due to the differences in material properties, liners and cladding have a non-trivial influence on the critical design parameter called the effective axial force in offshore pipelines. Current offshore design codes do not contain guid- ance on how to include the effects of liners and cladding on the effective axial force. In this paper, an exact analytical formula for the effective axial force in lined and clad pipes is deduced. A simplified approximate formula, which is more suitable for use in engineering contexts, is developed and its validity verified by comparisons to results of the complex exact one.

• Sollund, Håvar Andreas; Vedeld, Knut & Hellesland, Jostein (2014). Efficient analytical solutions for heated and pressurized multi-layer cylinders. Ocean Engineering. ISSN 0029-8018. 92, p. 285–295. doi: 10.1016/j.oceaneng.2014.10.003. Full text in Research Archive Show summary

  Two independent sets of analytical solutions have been derived for calculation of displacements and stresses in elastic multi-layer cylinders subjected to both pressure and thermal loading. The solutions are computationally efficient and easily implemented, and thus suitable for engineering applications. In particular, the novel solutions are relevant for offshore pipelines and risers, since the impact of internal and external coating layers on the stress state in the pipe wall often is disregarded or assessed by simplified methods in current pipeline engineering practice. Recursive solutions are obtained both for the case of uniform temperature in each cylinder layer and for the case of radially varying temperature in each cylinder layer. Both plane stress and plane strain conditions are considered. In addition, a recursive solution of the heat equation is derived for steady-state conditions. Applicability of the solutions is illustrated by using them on an offshore pipeline with a corrosion-resistant liner and multi-layered thermal insulation coating. It is demonstrated that coating layers, generally disregarded in conventional pipeline design, may have a non-negligible impact on hoop stresses and the true wall axial force.

• Sollund, Håvar Andreas; Vedeld, Knut; Hellesland, Jostein & Fyrileiv, Olav (2014). Dynamic response of multi-span offshore pipelines. Marine Structures. ISSN 0951-8339. 39, p. 174–197. doi: 10.1016/j.marstruc.2014.07.006. Full text in Research Archive
• Vedeld, Knut; Sollund, Håvar Andreas & Hellesland, Jostein (2013). Free vibrations of free spanning offshore pipelines. Engineering structures. ISSN 0141-0296. 56, p. 68–82. doi: 10.1016/j.engstruct.2013.04.013. Full text in Research Archive
• Challamel, Noël & Hellesland, Jostein (2013). Buckling of softening columns in a continuum damage mechanics perspective - Local versus non-local formulation. European Journal of Mechanics. A, Solids. ISSN 0997-7538. 39(May-June), p. 229–242. doi: 10.1016/j.euromechsol.2012.11.007. Full text in Research Archive Show summary

  This paper deals with the mathematical modelling of the buckling and post-buckling response of structural systems composed of quasi-brittle materials such as concrete (as found for instance inreinforced concrete columns). More specifically, columns with softening characteristics are of concern in this study. The moment-curvature constitutive law is based on continuum damage mechanics arguments (CDM theory). Then, the instability problem can be referred to as the Elastica problem for the case with a continuum damage mechanics constitutive law, or, for short, it may be referred to as the Continuum Damage Mechanica problem. It is numerically shown for the parameters of interest, that results from geometrically exact and second-order analyses for small rotations are almost equivalent. The instability of the imperfect softening system is associated with a limit load which decreases with the imperfection considered. Such columns are shown to be typically imperfection sensitive. Furthermore, a load-imperfection relationship is derived (similar to Koiter's power law), that can be useful in structural design contexts. An asymptotic expansion is performed to obtain a closed-form analytical solution of the limit load imperfection rule. A comparison with exact numerical values for the continuous column shows good agreement with the asymptotic expression results. The need for including non-locality formulations in a damage localization zone is finally discussed for post-buckling analysis in the presence of curvature softening. The adopted local bending-curvature constitutive law leads to the unloading Wood's paradox. To cover the propagation phenomenon of localization, some non-locality is included in a generalized formulation of the principle of virtual work. However, non-locality is not necessary for limit load calculations since limit loads occur for curvatures in the local hardening regime.

• Challamel, Noël; Kolvik, Gjermund & Hellesland, Jostein (2013). Plate buckling analysis using a general higher order shear deformation theory. International Journal of Structural Stability and Dynamics. ISSN 0219-4554. 13(5). doi: 10.1142/S0219455413500284. Full text in Research Archive Show summary

  The buckling of higher-order shear plates is studied in this paper with a unified formalism. It is shown that usual higher-order shear plate models can be classifed as gradient elasticity Mindlin plate models, by augmenting the constitutive law with the shear strain gradient. These equivalences are useful for a hierarchical classification of usual plate theories comprising Kirchhoff plate theory, Mindlin plate theory and third-order shear plate theories. The same conclusions were derived by Challamel(2011) for higher-order shear beam models. A consistent variational presentation is derived for all generic plate theories, leading to meaningful buckling solutions. In particular, the variationally-based boundary conditions are obtained for general loading configurations. The buckling of the isotropic or orthotropic composite plates is then investigated analytically for simply supported plates under uniaxial or hydrostatic in-plane loading. An analytical buckling formula is derived that is common to all higher-order shear plate models. It is shown that cubic-based interpolation models for the displacement field are kinematically equivalent, and lead to the same buckling load results. This conclusion concerns for instance the plate models of Reddy(1984) or the one of Shi(2007), even though these models are statically distinct (leading to different stress calculations along the cross section). Finally, a numerical sensitivity study is made.

• Brubak, Lars; Hellesland, Jostein & Hareide, Ole J. (2013). Vibration analysis of plates with arbitrary stiffener arrangements using a semi-analytical approach, Computational Methods in Marine Engineering V. International Center for Numerical Methods in Engineering (CIMNE). ISSN 9788494140747. p. 320–331. doi: 10.1016/j.jcsr.2007.05.012. Full text in Research Archive
• Brubak, Lars; Andersen, Håkon S. & Hellesland, Jostein (2013). Ultimate strength prediction by semi-analytical analysis ofstiffened plates with various boundary conditions. Thin-walled structures. ISSN 0263-8231. 62(January), p. 28–36. doi: 10.1016/j.tws.2012.08.005. Full text in Research Archive Show summary

  Semi-analytical elastic methods for stiffened plate analysis are computationally very efficient. In addition to eigenvalue analysis,such methods may also offer a viable approach for the prediction of ultimate strength limits (USLs) of the plates when combined with appropriate strength criteria. In this paper,existing strength criteria are discussed,and extended criteria proposed for plates with various stiffener arrangements and boundary conditions such as full out-of-plane supports along all edges or plates with a free or partially stiffened edge.The extended criteria reflect in a simplified manner the effect of redistribution of stresses due to the formation of local plastic regions at stiffeners,supporting edges and in the plate interior.The equilibrium path is traced using large deflection theory and the Rayleigh–Ritz approach on an incremental form.The approach is able to account for the reserve strength of slender plates in the post buckling region. With the considered criteria included, good agreement is obtained with results from fully nonlinear finite element analyses for different support conditions and for a variety of plate and stiffener dimensions.

• Hellesland, Jostein (2012). Evaluation of effective length formulas and applications in system instability analysis. Engineering structures. ISSN 0141-0296. 45(12 (Dec)), p. 405–420. doi: 10.1016/j.engstruct.2012.06.028. Full text in Research Archive Show summary

  The paper deals with approximate effective length formulas, and how such formulas may be applied in system instability analysis of frames. End restraint assessments in a system instability perspective are discussed, and available formulas are reviewed. The overview is limited to the important class of compression members that are either completely unbraced (free-to-sway, zero shear) or fully braced against lateral translation of one end relative to the other. Whereas most approximate effective length formulas have been developed for positive end restraints, buckling modes of compression members in a frame can be associated with both positive and negative end restraints. It is a main concern of the study to identify the applicability of the various approximate formulas for a reasonable wide range of positive and negative restraint combinations. Extensive comparisons with exact effective length results have been carried out for isolated members, and applications in system instability analyses are demonstrated.

• Challamel, Noël & Hellesland, Jostein (2011). Simplified buckling analysis of imperfection sensitive reinforced concrete structures. In Freund, Jouni & Kouhia, Reijo (Ed.), Proceedings of the 24th Nordic Seminar on Computational Mechanics. Alto University publication series. ISSN 9789526043470. p. 141–144. Full text in Research Archive Show summary

  This paper is devoted to the buckling phenomenon of columns composed of a quasi-brittle material such as concrete. The constitutive law at the material or the structural scale is based on continuum damage mechanics arguments (CDM theory). We investigate, using a simple one-dimensional softening model based on continuum damage mechanics, how the buckling of reasonable slender reinforced concrete columns is associated with a limit load which decreases with the imperfection considered. The one-dimensional continuum problem is then analytically and numerically solved for an axially loaded cantilever column with some additional geometrical imperfection. The need of including some non-local properties is discussed for the post-buckling analysis. Though simplified, this column model will still give some qualitatively useful results for reinforced concrete columns.

• Brubak, Lars & Hellesland, Jostein (2011). Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge. Computers & structures. ISSN 0045-7949. 89(17-18), p. 1574–1585. doi: 10.1016/j.compstruc.2011.05.007. Full text in Research Archive Show summary

  A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.

• Andersen, Håkon s.; Hellesland, Jostein & Brubak, Lars (2010). Strength criterion for stiffened plates with a free or stiffened edge. Trita-MEK. ISSN 0348-467X. Full text in Research Archive Show summary

  Ultimate strengths of stiffened plates with a free or stiffened edge is considered. A large deflection, semi-analytical model for pre- and postbuckling calculations is used in combination with a proposed strength criterion. Strength estimates are compared with finite element analyses (FEA) results. Good agreement is found between the model and the FEA results.

• Brubak, Lars & Hellesland, Jostein (2010). Response propagation analysis of imperfect stiffened plates with a free or flexible edge using a semi-analytical method. Trita-MEK. ISSN 0348-467X. Full text in Research Archive Show summary

  A large deflection, semi-analytical method for response propagation analysis of stiffened plates with a free edge is presented. The formulations derived are implemented into a FORTRAN computer program, and numerical results are compared with fully nonlinear finite element analyses. Good agreement is obtained.

• Brubak, Lars; Hellesland, Jostein & Steen, Eivind (2009). Approximate postbuckling analysis of imperfect stiffened plates with a free edge. In Kvamsdal, T.; Pettersen, B.R.; Bergan, P.; Onate, E. & Garcia, J. (Ed.), Computational methods in marine engineering III. International Center for Numerical Methods in Engineering (CIMNE). ISSN 9788496736665. p. 336–338. Full text in Research Archive
• Hellesland, Jostein (2009). Second order approximate analysis of unbraced multistorey frames with single curvature regions. Engineering structures. ISSN 0141-0296. 31(8), p. 1734–1744. doi: 10.1016/j.engstruct.2009.02.015. Full text in Research Archive Show summary

  Present approximate second order methods for the analysis of unbraced multistorey frames may significantly underestimate moments in single curvature regions. To clarify reasons for this that may not be well understood, the mechanics of column interaction in single curvature regions are studied. Suitable tools for sidesway description are derived, including a nearly exact, explicit free sway effective length expression, that, when high accuracy is required, eliminates the need in many cases for cumbersome, iterative solutions of exact effective lengths from the transcendental instability equation. Two reasons for the underestimation are identified. One is related to the local second order effects, and the other to second order effects causing changes in rotational restraint stiffness at column ends due to vertical, inter-storey column interaction. A modified approximate storey magnifier approach is proposed that accounts for these local second order effects through two separate ``flexibility factors''. The approach is sufficiently simple to be viable in practical analyses, and predictions are found to compare well with more accurate results.

• Hellesland, Jostein (2009). Extended second order approximate analysis of frames with sway-braced column interaction. Journal of constructional steel research. ISSN 0143-974X. 65(5), p. 1075–1086. doi: 10.1016/j.jcsr.2008.08.008. Full text in Research Archive Show summary

  Present approximate second order methods for the analysis of frames with sway are not capable of reflecting the transition from sway to partially braced, and nearly fully braced behaviour of individual columns in the frames. The main aim of the paper is to extend the approximate storey magnifier approach to account for such a transition. The key to this is in the manner local second order effects are reflected. A high order shear relationship is proposed, an general sway magnifier, critical load and effective length formulations are presented both in terms of first order lateral storey stiffness and critical, free-sway column loads. Their interrelationship, and simplifications leading to existing approaches, and adaptions in present codes and standards, are discussed. Comparisons are made with exact critical loads, sway and moment magnifiers for nearly unbraced, partially braced and nearly fully braced systems. The proposed, extended approach provide predictions that generally are in very good agreement with exact results at all axial load levels. The more simplified approaches provide good agreement for low to moderate load levels for some column end restraint combinations, and up to relatively high load levels for other combinations.

• Brubak, Lars & Hellesland, Jostein (2008). Strength criteria in semi-analytical, large deflection analysis of stiffened plates in local and global bending. Thin-walled structures. ISSN 0263-8231. 46(12), p. 1382–1390. doi: 10.1016/j.tws.2008.03.013. Full text in Research Archive Show summary

  Various strength criteria that may be used in semi-analytical methods for ultimate strength prediction of arbitrarily stiffened plates are studied. The main objective is to evaluate the applicability of the criteria in ultimate strength predictions of in-plane loaded plates, both in local and global bending. The equilibrium path is traced using large deflection theory and the Rayleigh–Ritz approach on an incremental form. The approach is able to account for the reserve strength of slender plates in the postbuckling region. Results are compared with fully nonlinear finite element analyses for a variety of plate dimensions and stiffeners with regular and irregular arrangements. Good agreement is obtained with a combination of a plate and a stiffener criterion. With the considered criteria included, the method is computationally very efficient and gives rather high numerical accuracy.

• Steen, Eivind; Byklum, Eirik & Hellesland, Jostein (2008). Elastic postbuckling stiffness of biaxially compressed rectangular plates. Engineering structures. ISSN 0141-0296. 30(10), p. 2631–2643. doi: 10.1016/j.engstruct.2008.02.006. Full text in Research Archive Show summary

  The elastic buckling and postbuckling response of biaxially compressed plates is analysed with main focus on change of in-plane postbuckling stiffness under prescribed plate shortenings rather than the more normal load control. An analytical closed form single-degree-of-freedom solution is derived and compared with an analytical multi-degree-of-freedom model. Results for the analytical multi-degree-of-freedom-model are obtained by solving numerically the equilibrium equations using the perturbation expansion technique with arc length control in an incremental scheme. Both models are applied to specific plate examples and comparisons with results obtained using a commercial nonlinear finite element program are included.

• Hellesland, Jostein (2008). Mechanics and slenderness limits of sway-restricted reinforced concrete columns. Journal of Structural Engineering. ISSN 0733-9445. 134(8), p. 1300–1309. doi: 10.1061/8(1300. Full text in Research Archive Show summary

  Several aspects of nonslender (short) column limits are considered. Such limits, below which it is acceptable to ignore local second-order effects that may cause maximum moment to develop between member ends, are generally confined to columns of braced frames, but are relevant for sway-restricted columns of unbraced frames also. Local and global second-order effects are reviewed in this context, and the effect of global second-order effects (sway-modified moments) is discussed, and it is concluded that the end moment ratios of approximate moment magnifier expressions and slenderness limits should be expressed in terms of sway-modified end moments. The need for providing separate slenderness limits, such as in the ACI 318-05 code, for columns of nonsway and sway frames, is questioned. The ACI limits are critically reviewed and several inconsistencies pointed out with respect to their differences and different basis on which they were derived. They are compared with a more comprehensive limit, that may replace both of the ACI limits, and comparisons are also made with a summary of nonlinear analysis results

• Brubak, Lars & Hellesland, Jostein (2007). Semi-analytical postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending. Thin-walled structures. ISSN 0263-8231. 45(6 (June)), p. 620–633. doi: 10.1016/j.tws.2007.04.011. Full text in Research Archive Show summary

  A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh–Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises’ yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer program based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.

• Hellesland, Jostein (2007). Mechanics and Effective Lengths of Columns with Positive and Negative End Restraints. Engineering structures. ISSN 0141-0296. 29(12), p. 3464–3474. doi: 10.1016/j.engstruct.2007.08.021. Full text in Research Archive Show summary

  In approximate buckling analysis of frame structures, it is common practise to simplify by considering compression members in isolation with end restraints that supposedly reflect the interaction with the surrounding structure. Buckling modes and effective lengths of such members have traditionally been limited to modes that can be associated with positive end restraints. A wider range of realistic buckling modes, that also imply negative end restraints, are reviewed and discussed, and approximate formulas for effective lengths and inflection point locations are developed from simple physical models for unbraced and fully braced compression members. The formulas are expressed in in terms of convenient end fixity factors that allow for simple and elegant formulations. The range of applicability of the formulae are identified by comparisons with exact results for a reasonable wide range of positive and negative restraints, and applications to special structures are demonstrated.

• Brubak, Lars; Hellesland, Jostein & Steen, Eivind (2007). Closure to discussion by O. Bedair of 'Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements'. Journal of constructional steel research. ISSN 0143-974X. 63(12), p. 1618–1620. doi: 10.1016/j.jcsr.2007.05.012. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2007). Approximate buckling strength analysis of arbitrarily stiffened, stepped plates. Engineering structures. ISSN 0141-0296. 29(9), p. 2321–2333. doi: 10.1016/j.engstruct.2006.12.002. Full text in Research Archive Show summary

  A computationally efficient method for the elastic buckling and buckling strength analysis of in-plane biaxial and shear loaded stiffened plates with varying, stepwise constant thickness is presented. The main focus is on biaxial loading cases. The stiffeners may be sniped or end-loaded (continuous), and their orientations may be arbitrary. Both global and local plate buckling modes are captured. The method is semi-analytical and makes use of simplified displacement computations that involve the elastic buckling load (eigenvalue), determined using a Rayleigh–Ritz approach, and finally stress computations using large deflection theory in combination with strength assessment using von Mises’ yield criterion as applied to membrane stresses. The displacements are represented by trigonometric functions, defined over the entire plate. The method is implemented into a Fortran computer program, and numerical results, obtained by the method for a variety of plate and stiffener geometries, are compared with corresponding fully nonlinear finite element analysis results. An extension to strength analysis that also includes lateral loading is discussed.

• Brubak, Lars; Hellesland, Jostein & Steen, Eivind (2007). Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements. Journal of constructional steel research. ISSN 0143-974X. 63(4), p. 532–543. doi: 10.1016/j.jcsr.2006.06.002. Full text in Research Archive Show summary

  Buckling of plates with arbitrarily oriented, sniped stiffeners is studied. The main objective is to present and validate an approximate, semi-analytical computational model for such plates subjected to in-plane loading. Estimation of the buckling strength is made using the von Mises’ yield criterion for the membrane stress as the strength limit. The formulations derived are implemented in a Fortran computer code, and numerical results are obtained for a variety of plate and stiffener geometries. The model may handle complex plate geometries, by using inclined stiffeners to enclose irregular plate shapes. The method allows for a very efficient analysis. Relatively high numerical accuracy is achieved with low computational efforts. The results are, in most cases, found to be conservative compared to fully nonlinear finite element analysis results.

• Brubak, Lars & Hellesland, Jostein (2007). Strength criteria in stiffened plate analysis using semi-analytical, large deflection methods. In Onate, E.; Garcia, J.; Bergan, P. & Kvamsdal, T. (Ed.), Computational Methods in Marine Engineering II. International Center for Numerical Methods in Engineering (CIMNE). ISSN 9788496736191. p. 71–74. Full text in Research Archive
• Hellesland, Jostein (2005). Nonslender Column Limits for Braced and Unbraced Reinforced Concrete Members. ACI Structural Journal. ISSN 0889-3241. 102(1), p. 12–21. Full text in Research Archive
• Mari, Antonio R. & Hellesland, Jostein (2005). Lower slenderness limits for rectangular reinforced concrete columns. Journal of Structural Engineering. ISSN 0733-9445. 131(1). Full text in Research Archive
• Hellesland, Jostein (2000). An improved K-factor formula. Discussion, Journal of Structural Engineering. ISSN 0733-9445. 126(5). Full text in Research Archive

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• Hellesland, Jostein (2023). Historiske opptegnelser om Skudeneshavn og omegn (1800-1950) av Telegrafbestyrer Johannes Hellesland. Skudenes Historielag. ISBN 9788283350968. 212 p. Full text in Research Archive
• Casandjian, Charles; Challamel, Noël; Lanos, Christophe & Hellesland, Jostein (2013). R. C. Beams, Columns and Frames - Mechanics and Design. John Wiley & Sons. ISBN 9781848214828. 320 p. Full text in Research Archive
• Hellesland, Jostein; Challamel, Noël; Casandjian, Charles & Lanos, Christophe (2013). R. C. Beams, Columns and Frames - Section and Slender Member Analysis. John Wiley & Sons. ISBN 9781848215696. 320 p. Full text in Research Archive

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• Hellesland, Jostein (2019). 2. ordens beregninger av staver og rammer -- Generelt og etter Eurokode 2 (NS-EN 1992-1-1). Full text in Research Archive
• Hellesland, Jostein (2017). 2. ordens beregninger av staver og rammer - Generelt og etter Eurokode 2 (NS-EN 1992). Full text in Research Archive
• Hellesland, Jostein (2016). Second order structural analysis of members and systems -- Revised proposal for EC2-5.8 (CEN Document TG6/N107). Full text in Research Archive
• Hellesland, Jostein (2016). Preliminary global stiffness proposal (for second order global system analysis) (Doc. TG6/N77). Full text in Research Archive
• Hellesland, Jostein (2016). Second order analysis of members and systems -- Revised and updated proposal for EC2-5.8 (Doc.TG6/N82). Full text in Research Archive
• Hellesland, Jostein (2015). Comments on EI-values in the moment-magnifier procedure of EC2, and in Dutch rules (Doc.TG6/N48). Full text in Research Archive
• Hellesland, Jostein (2015). Flexural stiffness for slender columns -- A collection of published research (Doc. TG6/N61). Full text in Research Archive
• Brubak, Lars; Hareide, O. J. & Hellesland, Jostein (2014). On Application of a Semi-Analytical Approach for Vibration Analysis of Irregularly Stiffened Plates. Full text in Research Archive
• Hellesland, Jostein (2014). Second order analysis of members and systems -- Proposal for EC2-5.8 (doc.CEN/TC250/SC2/WG1/TG6 N14). Full text in Research Archive
• Hellesland, Jostein (2014). Discussion of proposal for Second order structural analysis of members and systems (doc. TG6/14). Full text in Research Archive
• Hellesland, Jostein (2014). Principles and basis for nominal stiffness and curvature (doc. TG6/N37). Full text in Research Archive
• Hellesland, Jostein (2013). Second order structural analysis of members and systems -- Preliminary comments towards revising EC2:2004-sect.5.8. Full text in Research Archive
• Brubak, Lars; Hellesland, Jostein & Hareide, Ole J. (2013). Vibration analysis of plates with arbitrary stiffener arrangement using a semi-analytical approach. Full text in Research Archive
• Challamel, Noël & Hellesland, Jostein (2012). Post-buckling and post-failure of CDM structural systems. Full text in Research Archive
• Challamel, Noël & Hellesland, Jostein (2012). Buckling of Imperfect CDM Structural Systems. Full text in Research Archive
• Hareide, Ole J.; Brubak, Lars; Steen, Eivind & Hellesland, Jostein (2012). Approximate buckling model for steel-elastomer sandwich plates. Full text in Research Archive Show summary

  The paper describes the development of a semi-analytic buckling model for steel-elastomer sandwich plates using the Rayleigh-Ritz method. The model includes transverse shear deformations which are important in this type of plate. The unknowns - the deflections and cross-sectional rotations -are approximated by Fourier series. All combinations of in-plane tensile, compressive and shear loads are allowed. Pre-stressing of the plate and elastic springs on the boundary are also included. The model has been implemented in a FORTRAN programme and the results have been compared with results from the finite element programme ABAQUS.

• Brubak, Lars & Hellesland, Jostein (2010). On response propagation analysis of imperfect stiffened plates with a free or flexible edge using a semi-analytical method. Full text in Research Archive
• Andersen, Håkon S.; Hellesland, Jostein & Brubak, Lars (2010). On strength criteria for stiffened plates with a free or stiffened edge. Full text in Research Archive
• Hellesland, Jostein (2009). Closure to "Mechanics and Slenderness Limits of Sway-Restricted Reinforced Concrete Columns" by Jostein Hellesland. Journal of Structural Engineering. ISSN 0733-9445. 135(11), p. 1431–1433. Full text in Research Archive
• Hellesland, Jostein (2009). Lineære og ikke-lineære beregningsmetoder -- 2. ordens virkninger. Full text in Research Archive
• Hellesland, Jostein (2009). Lineære og ikke-lineære beregningsmetoder -- 2. ordens virkninger. Full text in Research Archive
• Hellesland, Jostein (2009). Lineære og ikke-linære beregningsmetoder-- 2. ordens lastvirkninger. Full text in Research Archive
• Hellesland, Jostein (2009). Lineære og ikke-lineære beregningsmetoder -- 2. ordens virkninger. Full text in Research Archive
• Brubak, Lars; Hellesland, Jostein & Steen, Eivind (2009). Approximate postbuckling analysis of imperfect stiffened plates with a free edge. Full text in Research Archive
• Hellesland, Jostein (2008). NS-EN 1992 Lineære og ikke-lineære beregningsmetoder - 2. ordens lastvirkninger. Full text in Research Archive
• Hellesland, Jostein (2008). NS-EN 1992, Eurokode-2 -- Lineære og ikke-lineære beregningsmetoder; 2. ordens lastvirkninger. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2007). Strength criteria in stiffened plate analysis using semi-analytical, large deflection methods. Full text in Research Archive
• Hellesland, Jostein (2005). Buckling of plates, slenderness limits of columns, etc. -- Research overview. Full text in Research Archive
• Hellesland, Jostein & Brubak, Lars (2005). Stability of Stiffened Orthotropic Plates: Performance Based Design. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2005). Computational buckling strength analysis of stiffened plates with varying thickness. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2004). Knekningsanalyse av plater med vilkårlig orienterte stivere. Full text in Research Archive
• Osnes, Harald & Hellesland, Jostein (2004). Faststoff-/konstruksjonsmekanikk ved UiO. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2004). Approximate buckling strength analysis of plates with arbitrarily oriented stiffeners. Full text in Research Archive
• Andersen, Alfred; Osnes, Harald & Hellesland, Jostein (2000). Computational analysis of computational joints. Full text in Research Archive
• Hellesland, Jostein (1999). Slanke konstruksjonsdeler. Full text in Research Archive
• Hellesland, Jostein (1999). Bridge design and construction in Norway. Full text in Research Archive
• Hellesland, Jostein (1999). Slanke konstruksjonsdeler. Full text in Research Archive
• Hellesland, Jostein (1999). Structural engineering for the largest petroleum exploration structure in the North Sea, Full text in Research Archive
• Hellesland, Jostein (1998). Slanke trykkstaver etter NS 3473, Full text in Research Archive
• Hellesland, Jostein (1998). Dimensjoneringshjelpemidler for slanke trykkstaver, Full text in Research Archive
• Hellesland, Jostein (1998). Trykkstaver i rammesystem--Knekklengder, Full text in Research Archive
• Hellesland, Jostein (2019). Approximate end and maximum moment formulations for slender columns in frames with sway. Universitetet i Oslo. Full text in Research Archive Show summary

  Based on a study of isolated restrained columns, and two-column panel frames, the often complicated mechanics of moment formations in the members are studdied using elastic second-order theory for the purpose of establishing a base on which procedures for moments due to sidesway can be evaluated. A distinction is made between moment developments in “supporting (bracing) sway columns” and “supported (braced) sway columns”. The primary objective is to derive improved slender column design expressions that are suitable in approximate design code formats. Both shear, end moments and maximum moments, applicable over the full range of axial loads, are considered. Proposals are presented that will allow more economical designs of framed columns with sway. Extended application to load combinations that include both gravity and sideways loading are also suggested.

• Hellesland, Jostein (2019). Mechanics of columns in sway frames -- Derivation of key characteristics. Universitetet i Oslo. Full text in Research Archive Show summary

  Columns in sway frames may be divided into laterally ``supporting (bracing) sway columns'', which can resist applied lateral shears, and ``supported (braced) sway columns'', which must have negative shears from the rest of the frame to support them. The supported sway column acts like a braced column with an initial displacement of one end relative to the other. The maximum moment will occur at the end of a supporting sway column, but may occur between the ends of a supported sway column. Mechanics of such columns, single or part of panels, are studied using elastic second-order theory. The main objective is to establish simple, explicit expressions for characteristic points in the moment versus axial load space. Such results may be useful in teaching, in design practice to assist in the assessment of the often complicated column response, and also useful as a supplement to full, second-order structural analyses.

• Brubak, Lars & Hellesland, Jostein (2010). Semi-analytical large displacement analysis of stiffened imperfect plates with a free or stiffened edge. Universitetet i Oslo. Full text in Research Archive
• Hellesland, Jostein (2009). Todimensjonal elastisitetsteori for tynne plater--Introduksjon. Avd. for mekanikk, Matematisk instittt. Full text in Research Archive
• Hellesland, Jostein (2009). Konstruksjonsmekanikk MEK3500/4500--Ekasamensoppgaver med løsningsforslag. Avd. for mekanikk, Matematisk institutt. Full text in Research Archive
• Hellesland, Jostein (2008). Extended second order approximate sway and critical load analysis of frames with sway-braced column interaction. Universitetet i Oslo. Full text in Research Archive Show summary

  Present approximate second order methods for the analysis of frames with sway are not capable of reflecting the transition from sway to partly braced, and nearly fully braced behaviour of individual columns in the frames. The main aim of the paper is to extend the approximate storey magnifier approach to account for such a transition. The key to this is in the manner local second order effects are reflected. A high order shear relationship is proposed, and general sway magnifier, critical load and effective length formulations are presented both in terms of first order lateral storey stiffness and critical, free-sway column loads. Their interrelationship, and simplifications leading to existing approaches, and adaptions in present codes and standards, are discussed. Comparisons are made with exact critical loads, sway and moment magnifiers for nearly unbraced, partly braced and nearly fully braced systems.

• Hellesland, Jostein (2008). Approximate second order analysis of unbraced frames reflecting inter-storey interaction in single curvature regions. Universitetet i Oslo. Full text in Research Archive Show summary

  Present approximate second order methods for the analysis of unbraced multistorey frames may significantly underestimate moments in single curvature regions. To clarify reasons for this that may not be well understood, the mechanics of column interaction in single curvature regions are studied. Suitable tools for sidesway description are derived, including a nearly exact, explicit free-sway effective length expression, that, when high accuracy is required, eliminates the need for cumbersome, iterative solutions of exact effective lengths from the transcendental instability equation. Two reasons for the underestimation are identified. One is related to the local second order "N-delta" effects, and the other to second order effects causing changes in rotational restraint stiffness at column ends due to vertical, inter-storey column interaction. A modified approximate storey magnifier approach is proposed that accounts for these local second order effects through two separate "flexibility factors". The approach is sufficiently simple to be viable in practical analyses, and predictions are found to compare well with more accurate results.

• Hellesland, Jostein (2007). Mechanics and Slenderness Limits of Sway-Restricted R.C. Columns. Universitetet i Oslo. Full text in Research Archive Show summary

  Several aspects of nonslender (short) column limits are considered. Such limits, below which it is acceptable to ignore local second-order effects that may cause maximum moment to develop between member ends, are generally confined to columns of braced frames, but are relevant for sway-restricted columns of unbraced frames also. Local and global second-order effects are reviewed in this context, and the effect of global second-order effects (sway-modified moments) is discussed, and it is concluded that the end moment ratios of approximate moment magnifier expressions and slenderness limits should be expressed in terms of sway-modified end moments. The need for providing separate slenderness limits, such as in the ACI 318-02 code, for columns of nonsway and sway frames, is questioned. The ACI limits are critically reviewed and several inconsistencies pointed out with respect to their differences and different basis on which they were derived. They are compared with a more comprehensive limit, that may replace both of the ACI limits, and comparisons are also made with a summary of nonlinear analysis results.

• Brubak, Lars & Hellesland, Jostein (2007). Strength criteria in local and global semi-analytical, large deflection analysis of arbitrarily stiffened plates. Universitetet i Oslo. Full text in Research Archive Show summary

  Various strength criteria that may be used in semi-analytical methods for ultimate strength prediction of arbitrarily stiffened plates are studied. The main objective is to evaluate the applicability of the criteria in ultimate strength predictions of in-plane loaded plates, both in local and global bending. The equilibrium path is traced using large deflection theory and the Rayleigh-Ritz approach on an incremental form. The approach is able to account for the reserve strength of slender plates in the postbuckling region. Results are compared with fully nonlinear finite element analyses for a variety of plate dimensions and stiffeners with regular and irregular arrangements. Good agreement is obtained with a combination of a plate and a stiffener criterion. With the considered criteria included, the method is computationally very efficient and gives rather high numerical accuracy.

• Brubak, Lars & Hellesland, Jostein (2006). Approximate buckling strength analysis of arbitrarily stiffened, stepped plates. Universitetet i Oslo. Full text in Research Archive Show summary

  A computationally efficient method for elastic buckling and buckling strength analysis of biaxially loaded, stiffened plates with varying, stepwise constant thickness, are presented. The stiffeners may be sniped or end-loaded (continuous), and their orientations may be arbitrary. Both global and local plate buckling modes are captured. The method is semi-analytical and makes use of simplified displacement computations that involve the elastic buckling load (eigenvalue), determined using a Rayleigh-Ritz approach, and finally stress computations using large deflection theory in combination with strength assessment using von Mises' yield criterion applied to membrane stresses. The displacements are represented by trigonometric functions, defined over the entire plate. The method is implemented into a Fortran computer code, and numerical results, obtained for a variety of plate and stiffener geometries, are compared to fully nonlinear finite element analysis results.

• Brubak, Lars & Hellesland, Jostein (2006). Semi-analytical buckling strength analysis of arbitrarily stiffened plates with varying thickness. Universitetet i Oslo. Full text in Research Archive
• Brubak, Lars & Hellesland, Jostein (2006). Computational postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending. Universitetet i Oslo. Full text in Research Archive Show summary

  A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh-Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises' yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer code based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.

• Hellesland, Jostein (2005). Review and Discussion of Proposed Changes to ACI 318-02 Slender Column Provisions. Universitetet i Oslo. Full text in Research Archive Show summary

  ACI Committee 318 (Standard Building Code) established some time ago a Slender Column Task Group that was charged with formulating code provisions, to streamline, and if possible, to simplify the current requirements on slender column design in the ACI 318-02 code. Proposed revisions by the Task Group were presented in documents labeled CTG3.1 and CTG3.2. The Task Group has made a considerable revision effort, both with regard to layout and reduction in the volume of provisions, and also with regard to technical content. A major change is the proposed combination into one of the two currently separate sections on moment magnification for the nonsway and sway cases. This change simplifies the presentation and make the provisions easier to comprehend. The stiffness provisions would seem to have become more complex, on the other hand. It is further proposed to adopt a moment magnifier expression of an earlier code version. Other revision proposals concern effects of sustained loading, safety aspects through the stiffness reduction factors, and lower slenderness limits. In the present report, a review is made of, and comments are provided to, major items in the revision proposal. The rationality of some of the proposed changes are questioned.

• Brubak, Lars; Hellesland, Jostein & Steen, Eivind (2005). Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements. Universitetet i Oslo. Full text in Research Archive Show summary

  Buckling of plates with arbitrarily oriented, sniped stiffeners are studied. The main objective is to present and validate an approximate, semi-analytical computational model for such plates subjected to in-plane loading. Estimation of the buckling strength is made using the von Mises' yield criterion for the membrane stress as the strength limit. The formulations derived are implemented in a Fortran computer code, and numerical results are obtained for a variety of plate and stiffener geometries. The model may handle complex plate geometries, by using inclined stiffeners to enclose irregular plate shapes. The method allows for a very efficient analysis. Relatively high numerical accuracy is achieved with low computational efforts. The results are, in most cases, found to be conservative compared to fully nonlinear finite element analysis results.

• Hellesland, Jostein (2005). Comments to Proposed Changes to ACI 318-02 Slender Column Provisions. Universitetet i Oslo. Full text in Research Archive
• Hellesland, Jostein (2005). Analysis of second order effects with axial loads, EN 1992-1-1-2004 (E), 5.8 -- Nasjonalt tillegg (NA). Avd. for mekanikk. Full text in Research Archive
• Hellesland, Jostein (2003). Non-slender RC Column Limits. Universitetet i Oslo. ISSN 9788255313892. Full text in Research Archive Show summary

  Structural frame systems may be analyzed and designed based on forces from conventional first order theory when second order effects of axial forces on displacements in the compression members of the system are negligible. This is often the case. Slenderness limits at which this is the case are studied in this paper. Existing limits are reviewed and major factors that affect such limits are investigated. A new slenderness measure, labeled normalized slenderness, is defined based on a reduced stiffness concept. In addition to the geometrical slenderness, the normalized slenderness is a function of axial force and reinforcement. Slenderness limit predictions are obtained from numerical nonlinear analyses for unbraced (sway) members and for transversely loaded braced members. For such members, new slenderness limits are proposed and verified against the nonlinear results. They are generally found to be more reliable than existing lower limit formulations. Braced compression members subjected to end moments only are dealt with in a separate paper.

• Hellesland, Jostein (2003). Non-slender Column Limits for Braced, End-loaded Members. Universitetet i Oslo. ISSN 9788255313908. Full text in Research Archive Show summary

  Structural frame systems may be analyzed and designed based on forces from conventional first order theory when second order effects of axial forces on displacements in the compression members of the system are negligible. This is often the case. Extensive nonlinear analysis results are presented to document slenderness limits below which this is so for braced, end moment loaded compression members with various end restraints. Major factors that affect lower slenderness limit predictions of such members are investigated and a new lower slenderness limit is proposed and verified against the nonlinear results. Slenderness is defined in terms of a socalled normalized slenderness that, in addition to the geometrical slenderness, is a function of axial force and reinforcement. The limit itself is a function of the first order end moment ratio. The formulation is rational and the proposed limits are generally found to be more reliable than existing lower limit formulations.

• Mari, Antonio & Hellesland, Jostein (2003). When can second order effects in columns be neglected? Department of Construction Engineering, Universitat Politecnica de Catalunya,. ISSN 9788487691270. Full text in Research Archive
• Hellesland, Jostein (2002). Lower slenderness limits for braced, end loaded r.c. compression members. Universitetet i Oslo. ISSN 9788255313564. Full text in Research Archive Show summary

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• Hellesland, Jostein (2002). Lower slenderness limits for unbraced and transversely loaded braced r.c. compression members. Universitetet i Oslo. ISSN 9788255313557. Full text in Research Archive Show summary

  Effects of axial forces on the displacements in compression members, generally termed second order effects, are small and can be neglected in a great many structures. In recognition of this, most design codes and standards for reinforced concrete structures give lower slenderness limits for compression members, and allow structures to be designed for forces obtained by conventional first order theory when these limits are not exceeded. The paper studies such limits for unbraced (sway) members and for transversely loaded braced members. Existing limits are reviewed, major factors that affect lower limits are investigated and slenderness limit predictions are obtained from numerical nonlinear analyses. Finally, a new lower slenderness limit formulation is presented. The slenderness is defined in terms of a so-called normalised slenderness. In addition to the geometrical slenderness, it is a function of axial force and reinforcement. The formulation is rational and may replace, or used as an alternative to, existing lower limit formulations.

• Hellesland, Jostein; Osnes, Harald; Skeie, Geir & Grue, John (2000). Proceedings of the 13TH NORDIC SEMINAR ON COMPUTATIONAL MECHANICS (NSCM-13) Oslo, 20-21 October, 2000. Universitetet i Oslo. ISSN 9788255312574. Full text in Research Archive Show summary

  These proceedings contain the papers presented at the 13th Nordic Seminar on Computational Mechanics (20-21 October, 2000). The seminars are organized annually under sponsorship of the Nordic Association for Computational Mechanics (NoACM), whose member countries are the Nordic and the Baltic countries. The papers cover a wide range of subjects within computational mechanics.

• Hellesland, Jostein (1999). On column slenderness limits. Universitetet i Oslo. Full text in Research Archive

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