• Structural Engineering and Mechanics
• /
• v.51 no.4
• /
• pp.601-625
• /
• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Journal of Korean Society of Steel Construction
• /
• v.26 no.3
• /
• pp.143-154
• /
• 2014

An improved method for evaluating effective buckling length of semi-rigid frame with inelastic behavior is newly proposed. Also, generalized exact tangential stiffness matrix with rotationally semi-rigid connections is adopted in previous studies. Therefore, the system buckling load of structure with inelastic behaviors can be exactly obtained by only one element per one straight member for inelastic problems. And the linearized elastic stiffness matrix and the geometric stiffness matrix of semi-rigid frame are utilized by taking into account 4th terms of taylor series from the exact tangent stiffness matrix. On the other hands, two inelastic analysis programs(M1, M2) are newly formulated. Where, M1 based on exact tangent stiffness matrix is programmed by iterative determinant search method and M2 is using linear algorithm with elastic and geometric matrices. Finally, in order to verify this present theory, various numerical examples are introduced and the effective buckling length of semi-rigid frames with inelastic materials are investigated.

• Structural Engineering and Mechanics
• /
• v.5 no.6
• /
• pp.785-801
• /
• 1997

Reinforced Concrete beams with tension and compression softening material constitutive laws are studied. Energy-based and non-local regularisation techniques are presented and applied to a R.C. element. The element characteristics (sectional tangent stiffness matrix, element tangent stiffness matrix restoring forces) are directly derived from their symbolic expressions through numerical integration. In this way the same spatial grid allows us to obtain a non-local strain estimate and also to sample the contributions to the element stiffness matrix. Three examples show the spurious behaviors due to the strain localization and the stabilization effects given by the regularisation techniques, both in the case of tension and compression softening. The possibility to overestimate the ultimate load level when the non-local strain measure is applied to a non softening material is shown.

• Journal of Korean Society of Steel Construction
• /
• v.20 no.1
• /
• pp.81-92
• /
• 2008

Generally the connection of members is defined as hinge or rigid. But, real joints on structure have to be considered semi-rigid connections because this permits relative rotation for members on joints. The purpose of this study is to derive a generalized tangential stiffness matrix of frames with semi-rigid connections and to develop a buckling analysis program. For the exact stiffness matrix, an accurate displacement field is introduced using an equilibrium equation for beam-columns under the bending and axial forces. Also, stability functions that consider sway deformation and force-displacement relations with rotational spring on ends were defined. In order to illustrate the accuracy of this study and the characteristics of semi-rigid for system buckling load, samples of angle-, portal- and 3-story frames with semi-rigid connections are presented, where the proposed approach is found to be in excellent agreement with other research results. Meanwhile, the application of codes such as Eurocode 3 and LRFD led to significant inaccuracies.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.31 no.1A
• /
• pp.9-18
• /
• 2011

Generally the connection of structural members is assumed as hinge, rigid and semi-rigid connections. The exact tangent stiffness matrix of a semi-rigid frame element is newly derived using the stability functions considering shear deformations. Also, linearized elastic- and geometric-stiffness matrices of shear deformable semi-rigid frame are newly proposed. For the exact stiffness matrix, an accurate displacement field is introduced by equilibrium equation for beam-column under the bending and the axial forces. Also, stability functions considering sway deformation and force-displacement relations with elastic rotational spring on ends are defined. In order to illustrate the accuracy of this study, various numerical examples are presented and compared with other researcher's results. Lastly, shear deformation and semi-rigid effects on buckling behaviors of structure are parametrically investigated.

• Journal of the Korean Society of Safety
• /
• v.29 no.3
• /
• pp.64-71
• /
• 2014

The generalized tangential stiffness matrix of semi-rigid frame element with shear deformations based on Haringx's shear theory is newly derived and compared with the previous study based on Engesser's shear theory. Also, linearized elastic and geometric stiffness matrices are newly presented from the exact tangential stiffness matrix. In oder to obtain the inelastic system buckling load of shear flexible semi-rigid frame structure, the Ef method by tangential modulus theory is adopted and the FE analysis programs are developed. Finally, the shear and semi-rigid effects of system bucking are investigated by two numerical examples.

• Structural Engineering and Mechanics
• /
• v.28 no.5
• /
• pp.587-601
• /
• 2008

In this study, a numerical procedure based on the finite element method for materially and geometrically nonlinear analysis of reinforced and prestressed concrete slender columns with arbitrary section subjected to combined biaxial bending and axial load is developed. In order to overcome the low computer efficiency of the conventional section integration method in which the reinforced concrete section is divided into a large number of small areas, an efficient section integration method is used to determine the section tangent stiffness. In this method, the arbitrary shaped cross section is divided into several concrete trapezoids according to boundary vertices, and the contribution of each trapezoid to section stiffness is determined by integrating directly the trapezoid. The space frame flexural theory is utilized to derive the element tangent stiffness matrix. The nonlinear full-range member response is traced by an updated normal plane arc-length solution method. The analytical results agree well with the experimental ones.

• Structural Engineering and Mechanics
• /
• v.11 no.4
• /
• pp.423-442
• /
• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• Steel and Composite Structures
• /
• v.41 no.6
• /
• pp.887-898
• /
• 2021

This paper presents a simplified model to capture the nonlinear behavior of steel frames depending on the spread of plasticity method. New interaction formulae were derived to evaluate the plastic strength for I-shaped steel sections under uniaxial bending moment and axial compression load. Also, new empirical formulae were derived to evaluate the tangent stiffness modulus of steel I-shaped cross-sections considering the effect of the residual stresses suggested by the specifications in European Convention for Construction Steelworks (ECCS). The secant stiffness which depends on the tangent modulus is used to evaluate the internal forces. Based on stiffness matrix method, a finite element analysis program was developed for the nonlinear analysis of space steel frames using the derived formulae. Comparison between the proposed model results with those given by the fiber model shows very good agreement. Numerical examples were introduced to verify, check the accuracy, and evaluate the efficiency of the proposed model. The analysis results show that the new proposed model is accurate and able to minimize the solution time.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2005.04a
• /
• pp.175-182
• /
• 2005

The present study is concerned with the application of dynamic relaxation method in the investigation of the large deflection behavior of spatial structures. This numerical algorithm do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using dynamic relaxation methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.