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Elastoplastic analysis of steel-concrete composite members and frames collapsed due to bending
Abstract
The beam element for three-dimensional pure steel frames proposed by the first author is extended for steelconcrete composite members. The authors call this approach the "fibered plastic hinge method". The stress-strain relation of a concrete fiber is modeled as an elastic-perfectly plastic type in this study. Comparisons with the authors' experimental results on RC beams strengthened by carbon fiber sheet and available test results on steel-concrete composite columns and frames show that the developed beam element has a sufficient accuracy for bending problem although there are some limitations. The element may be used to examine a performance of moment-resistant steelconcrete composite frames.
An accurate plastic hinge type beam elememt has been developed by the authors for three-dimensional (3-D) elastoplastic large deformation analysis of frames which contain all kinds of members: i.e. steel members, RC members, SRC members, CFT members, PC members, steel damper braces and tension braces. The element was originally proposed for pure steel frames by the first author (Shugyo 2003) and named Fibered Plastic Hinge Model (FPHM). The formulation procedure is a combination of the modified incremental stiffness method, the updated Lagrangian formulation, and numerical integration of fiber stiffnesses about the sections at the plastic hinges. The following assumptions are made to form the elastoplastic tangent stiffness matrix of the pure steel element: (1)members have thin walled closed or open sections, and cross sections remain plane and do not distort in the absence of cross-sectional warping, (2)deflection is large but elastic strain is small, (3)axial stress and the shear stress due to St. Venant torsion participate in yielding of fibers of members with closed sections, while only axial stress participates for members with open sections, (4)plastic deformation consists of only four components that correspond to axial force, biaxial bending moments, and torsional moment or bimoment, (5)there is no local buckling, (6)although an actual generalized plastic strain increments in a short element generally distribute nonlinearly, it is idealized as generalized plastic strain increments distribute linearly with the values at element nodes i and j, (7)incremental plastic deformations in the two half portions occur concentrically in the plastic hinge of zero length at element nodes i and j respectively. Because of the above mentioned assumption (6), the element requires at least four-element approximation for a frame member. This causes considerable increase of total degrees of freedom in the analysis of multi-bay multi-story frames.
In this paper a method to reduce the total degrees of freedom in frame analysis by the FPHM is presented. Introducing the plastic deformation reduction coefficient, the assumption (6) is modified as one-element approximation for a frame member has sufficient accuracy for practical use. The optimum value of the plastic deformation reduction coefficient is examined by using quasi-static analysis of four kinds of one-bay one-story plane portal frames, 3-D quasi-static analysis of two-bay four-story steel frame which contains composite beams and semirigid column bases, and 3-D quasi-static analysis of twenty-story eccentric steel frame with H-shaped steel columns.
The adequacy of the fibered plastic hinge model proposed by the authors for the three-dimensional collapse analysis of steel frames with H-columns under strong vertical loads is examined. Also a procedure is presented for evaluation of the strain of the member caused by three-dimensional elastoplastic deformation of a steel frame. The procedure realizes to obtain the strain of a member by a plastic hinge model, not a fiber model. Available test results for one-bay one-story three-dimensional steel frames subjected to eccentric horizontal load under a strong constant vertical load are used to examine the accuracy of the model.
The large deformation/post-peak behavior analysis method of concrete beams and columns considering bond-slip of reinforcement is developed. The analytical procedure is capable of predicting the response of concrete beams and columns under axial force and biaxial bending in the material and geometrical nonlinear domains, including post-peak behavior using the incremental arch length method. The paper gives an outline of the nonlinear analysis method which includes the effect of bond-slip of reinforcement to handle the large deformation region, and three numerical examples are given to illustrate the use of the proposed procedure.
RC structural members subjected to several axial loads(N) combined with transverse loads(S) were analyzed by 3-D FE model. From the results, the load-carrying capacities of RC members analyzed by the FE model taking account of riaxial behavior of concrete are larger than that analyzed by a fiber model taking account of uniaxial behavior of concrete. The peak compressive stresses of concrete both at a beam-column joint section and at a critical section are larger than the uniaxial compressive strength of concrete.
The purpose of this study is to investigate the relations of axial load ratio to deformation capacity of steel reinforced concrete columns. A total of 20 steel reinforced concrete columns were tested under a constant axial load and varied lateral loads. In designing the test work, the axial load level and the steel area ratio were chosen as main parameters. From the test results, inelastic behavior, maximum strength, deformation capacity, as well as the effects of axial load and steel area ratio on them are discussed. Elastic-plastic analyses on all specimens were carried out. The analytical results are in accordance with the test results well.
A beam element is presented for analysis of the elastoplastic large deflection of three-dimensional (3D) frames that have steel members with semirigid joints. A plastic hinge type formulation was employed, combining the "modified incremental stiffness method," the updated Lagrangian formulation, and numerical integration about the end sections of the element. The end sections of the element are discretized into small areas to estimate the plastic deformations of the element. The elastic and plastic deformations of the element are treated separately. The behavior of a semirigid joint is modeled as the element-end compliance. The method can treat comprehensively the plastic deformations due to torsion and warping. Considering the assumptions of the method, a four-element approximation for a member gives excellent results for a 3D analysis of semirigid and pin--connected steel frames as well as for rigid frames. The adequacy of the method is verified by comparing the results with experimental ones obtained by the writer. Some examples are presented to demonstrate the accuracy and efficiency of the method.