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  • 1. Challamel, Noel
    et al.
    Girhammar, Ulf Arne
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
    Lateral-torsional buckling of vertically layered composite beams with interlayer slip under uniform moment2012In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 34, p. 505-513Article in journal (Refereed)
    Abstract [en]

    The lateral-torsional stability of vertically layered composite beams with interlayer slip is investigated in this paper, based on a variational approach. Vertically layered elements are typically used in timber engineering but also in case of laminated glass elements. Both across-longitudinal or vertical slip due to rotation and longitudinal or horizontal slip due to lateral deflection are discussed. The theoretical framework of the lateral-torsional buckling problem is given, and some engineering closed-form solutions are presented for partially composite beams under uniform bending moment. Simplified kinematical relationships neglecting the axial and vertical displacements of the sub-elements give unrealistic values for the lateral-torsional buckling moment. Refined kinematical assumptions remove this peculiarity and render sound buckling moment results. Inclusion of the horizontal and vertical slips significantly affect the lateral-torsional buckling moment of these vertically laminated elements. A single lateral-torsional buckling formulae is derived, depending on both the horizontal and the vertical connection parameters. (C) 2011 Elsevier Ltd. All rights reserved.

  • 2. Challamel, Noel
    et al.
    Girhammar, Ulf Arne
    Umeå University, Faculty of Science and Technology.
    Variationally-based theories for buckling of partial composite beam-columns including shear and axial effects2011In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 33, no 8, p. 2297-2319Article in journal (Refereed)
    Abstract [en]

    This paper is focused on elastic stability problems of partial composite columns: the conditions for the axial load not to introduce any pre-bending effects in composite columns; the equivalence, similarities and differences between different sandwich and partial composite beam theories with and without the effect of shear, with and without the effect of axial extensibility, and also the effect of eccentric axial load application. The basic modelling of the composite beam-column uses the Euler-Bernoulli beam theory and a linear constitutive law for the slip. In the analysis of this reference model, a variational formulation is used in order to derive relevant boundary conditions. The specific loading associated with no pre-bending effects before buckling is geometrically characterized, leading to analytical buckling loads of the partial composite column. The equivalence between the Hoff theory for sandwich beam-columns, the composite action theory for beam-columns with interlayer slip and the corresponding Bickford-Reddy theory, is shown from the stability point of view. Special loading configurations including eccentric axial load applications and axial loading only on one of the sub-elements of the composite beam-column are investigated and the similarity of the behaviour to that of imperfect ordinary beam-columns is demonstrated. The effect of axial extensibility on kinematical relationships (according to the Reissner theory), is analytically quantified and compared to the classical solution of the problem. Finally, the effect of incorporating shear in the analysis of composite members using the Timoshenko theory is evaluated. By using a variational formulation, the buckling behaviour of partial composite columns is analysed with respect to both the Engesser and the Haringx theory. A simplified uniform shear theory (assuming equal shear deformations in each sub-element) for the partial composite beam-column is first presented, and then a refined differential shear theory (assuming individual shear deformations in each sub-element) is evaluated. The paper concludes with a discussion on this shear effect, the differences between the shear theories presented and when the shear effect can be neglected. 

  • 3.
    Girhammar, Ulf Arne
    et al.
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
    Källsner, Bo
    Elasto-plastic model for analysis of influence of imperfections on stiffness of fully anchored light-frame timber shear walls2009In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 31, no 9, p. 2182-2193Article in journal (Refereed)
    Abstract [en]

    In order to stabilize timber-framed buildings against lateral loads, the diaphragm action of roofs, floors and walls is often used. This paper deals with the influence of imperfections such as gaps and uplift on the stiffness and the horizontal displacement of fully anchored shear walls. The significance of analyzing the effects of imperfections is evident when evaluating the stiffness of shear walls; tests of walls show that the horizontal displacement is underestimated in calculations using the stiffness of sheathing-to-framing joints as obtained from experiments. Also, in real structures where hold-downs are used, the influence of gaps and uplift should be included in order to obtain realistic displacements in the serviceability limit state. The analytical model is based on ideal plastic behavior of the mechanical sheathing-to-timber joints with stresses parallel to the perimeter of the frame and on linear elastic behavior for stresses perpendicular to the bottom rail. Using this elasto-plastic model, the equations for the stiffness and the deflection versus the number of segments in the wall are derived. The fully anchored condition for the shear walls is simulated by applying a diagonal load to the shear wall. Three types of imperfections are evaluated: Walls with gaps at all studs, a gap only at the trailing stud, and gaps at all studs, except at the trailing stud. It is shown that the effect of imperfections on the stiffness of the wall in the initial stage is considerable. Depending on the distribution of the gaps and the number of segments included in the shear wall, the displacement of the shear wall is increased several times compared to that of a fully anchored wall diaphragm with no gaps; e.g. for a single segment wall more than four times. However, for walls with more than six segments the effect of imperfections can be neglected. Finally, the theoretical model is experimentally verified.

  • 4. Källsner, Bo
    et al.
    Girhammar, Ulf Arne
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
    Plastic models for analysis of fully anchored light-frame timber shear walls2009In: Engineering structures, ISSN 0141-0296, E-ISSN 1873-7323, Vol. 31, no 9, p. 2171-2181Article in journal (Refereed)
    Abstract [en]

    In order to stabilise timber-framed buildings against lateral loads, the diaphragm action of roofs, floors and walls is often used. This paper deals with plastic analysis models for fully anchored sheathed shear walls. The models are based on the assumption of plastic load-slip relations for the sheathing-to-framing joints. Only static loads are considered. The basic structural behaviour and assumptions for the plastic models are elucidated. Both upper and lower bound methods are applied. The load-bearing capacity and the deformation of the shear walls in the ultimate and serviceability limit states, respectively, are derived. Both a discrete point description and a continuous flow per unit length modelling of the fasteners are discussed. Also, the forces and displacements of the fasteners and sheathing are derived. The influence of flexible framing members and shear deformations in the sheets, and also the effect of vertical loads on the shear wall, both with respect to tilting and second order effects, on the horizontal load-bearing capacity and displacement are evaluated. The stress distribution and the reaction forces at the ends of the different framing members are derived. The elastic model is experimentally verified and an illustrative example is given. The main objective of this work is to contribute to a better understanding of the structural behaviour of these fully anchored walls and form the basis for establishing a new plastic design method for partially anchored shear walls, i.e. a design method capable of analysing the more practical conditions of no or partial anchorage of the studs and/or bottom rail in real structures.

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