• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.147-161
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• 2012

This paper presents a curvature method for analysis of beam-columns with different materials and arbitrary cross-section shapes and subjected to combined biaxial moments and axial load. Both material and geometric nonlinearities (the p-delta effect in this case) were incorporated. The proposed method considers biaxial curvatures and uniform normal strains of discrete cross-sections of beam-columns as basic unknowns, and seeks for a solution of the column deflection curve that satisfies force equilibrium conditions. A piecewise representation of the beam-column deflection curve is constructed based on the curvatures and angles of rotation of the segmented cross-sections. The resulting bending moments were evaluated based on the deformed column shape and the axial load. The moment curvature relationship and the beam-column deflection calculation are presented in matrix form and the Newton-Raphson method is employed to ensure fast and stable convergence. Comparison with results of analytic solutions and eccentric compression tests of wood beam-columns implies that this method is reliable and effective for beam-columns subjected to eccentric compression load, lateral bracings and complex boundary conditions.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.519-537
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• 2005

A new generalized Bernoulli/Timoshenko beam-column element on a two-parameter elastic foundation is presented herein. This element is based on the exact solution of the differential equation which describes the deflection of the axially loaded beam resting on a two-parameter elastic foundation, and can take into account shear deformations, semi - rigid connections, and rigid offsets. The equations of equilibrium are formulated for the deformed configuration, so as to account for axial force effects. Apart from the stiffness matrix, load vectors for uniform load and non-uniform temperature variation are also formulated. The efficiency and usefulness of the new element in reinforced concrete or steel structures analysis is demonstrated by two examples.

• Steel and Composite Structures
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• v.22 no.3
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• pp.663-675
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• 2016

The effects of slenderness ratio, eccentricity and column slope on the load-carrying capacities and failure modes of variable and uniform concrete filled steel tubular (CFST) latticed columns under axial and eccentric compression were investigated and compared in this study. The results clearly show that all the CFST latticed columns with variable cross section exhibit an overall failure, which is similar to that of CFST latticed columns with a uniform cross section. The load-carrying capacity decreases with the increase of the slenderness ratio or the eccentricity. For 2-m specimens with a slenderness ratio of 9, the ultimate load-carrying capacity is increased by 3% and 5% for variable CFST latticed columns with a slope of 1:40 and 1:20 as compared with that of uniform CFST latticed columns, respectively. For the eccentrically compressed variable CFST latticed columns, the strain of the columns at the loading side, as well as the difference in the strain, increases from the bottom to the cap, and a more significant increase in strain is observed in the cross section closer to the column cap.

• Structural Engineering and Mechanics
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• v.37 no.1
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• pp.111-129
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• 2011

This paper presents a nonlinear analysis of reinforced concrete column with lap splice confined by FRP wrapping in the critical hinging zone. The steel stress-slip model derived from the tri-uniform bond stress model presented in the companion paper is included in the nonlinear frame analysis to simulate the response of reinforced concrete columns subjected to cyclic displacement reversals. The nonlinear modeling is based on a fiber discretization of an RC column section. Each fiber is modeled as either nonlinear concrete or steel spring, whose load-deformation characteristics are calculated from the section of fiber and material properties. The steel spring that models the reinforcing bars consists of three sub-springs, i.e., steel bar sub-spring, lap splice spring, and anchorage bond-slip spring connected in series from top to bottom. By combining the steel stress versus slip of the lap splice, the stress-deformation of steel bar and the steel stress-slip of bars anchored into the footing, the nonlinear steel spring model is derived. The analytical responses are found to be close to experimental ones. The analysis without lap splice springs included may result in an erroneous overestimation in the strength and ductility of columns.

• Journal of Korean Society of Steel Construction
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• v.24 no.1
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• pp.109-117
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• 2012

This study seeks to devise a design application for a beam structure with partially restrained composite connection to a CFT column. A cost-efficient and stable component is applied by adjusting the stiffness ratio of the column connection through partially restrained composite connection. Based on a review of the structure's stability, it was confirmed that in the case of a low-rise building as a moment frame, resistance without bracing is feasible because stiffness increased by virtue of the partial restrained composite connection by composite action. In the case of a high-rise building, lateral resistance load of moment frame was approximately 10% when proper partial restrained rate was at around 60%. With considerations related to economic efficiency, the partial restriction effect of the beam component was significantly activated by the uniform load, but that of the beam activated by concentrated load was not significantly indicative. The analysis indicated that 60% partial restrained girder at the connection was the most economical in the case of uniform load. It also showed that end moments can be reduced by approximately 25%.

• Journal of KSNVE
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• v.7 no.1
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• pp.91-97
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• 1997

An analysis is presented on the stability of an elastic cantilever column having the elastic restraints at its free end, carrying an added tip mass, and subjected to uniformly distributed follower forces. The elastic restraints are formed by both a translational spring and a rotatory spring. For this purpose, the governing equations and boundary conditions are derived by using Hamilton's principle, and the critical flutter loads and frequencies are obtained from the numerical evaluation of the eigenvalue functions of this elastic system. The added tip mass increases as a whole the critical flutter load of the elastic cantilever column, but the presence of its moment of inertia of mass has a destabilizing effect. The existence of the translational and rotatory springs at the free end increases the critical flutter load of the elastic cantilever column. Nevertheless, their effects on the critical flutter load are not uniform because of their coupling. The translational spring restraining the free end of the cantilever column decreases the critical flutter load by coupling with a large value of tip mass, while by coupling with the moment of inertia of tip pass its effect on the critical flutter load is contrary. The rotatory spring restraining the free end of the cantilever column increases the critical flutter load by coupling with the tip mass, but decreases it by coupling with the moment of inertia of the tip mass.

• Structural Engineering and Mechanics
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• v.63 no.3
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• pp.385-400
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• 2017

This paper presents an experimental study on the behavior of axially-loaded steel RHS (rectangular hollow section) compression members that are partially reinforced along their lengths with welded steel plates. 28 slender column tests were carried out to investigate the effects of the slenderness ratio of the unreinforced member and the ratio of the reinforced length of the member to its entire length. In addition to the slender column tests, 14 stub-column tests were conducted to determine the basic mechanical properties of the test specimens under uniform compression. Test results show that both the compressive strength and stiffness of an RHS member can be increased significantly compared to its unreinforced counterpart even when only the central quarter of the member is reinforced. Based on the limited test data, it can be concluded that partial reinforcement is, in general, more effective in members with larger slenderness ratios. A simple design expression is also proposed to predict the compressive strength of RHS columns partially reinforced along their length with welded steel plates by modifying the provisions of AISC 360-10 to account for the partial reinforcement.

• Earthquakes and Structures
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• v.16 no.2
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• pp.235-251
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• 2019

Corrosion of reinforcement is the greatest threat to the safety of existing reinforced concrete (RC) structures. Most of the olden structures are gravity load designed (GLD) and are seismically deficient. In present study, investigations are carried out on corrosion damaged GLD beam-column sub-assemblages under reverse cyclic loading, in order to evaluate their seismic performance. Five GLD beam-column sub-assemblage specimens comprising of i) One uncorroded ii) Two corroded iii) One uncorroded strengthened with steel bracket and haunch iv) One corroded strengthened with steel bracket and haunch, are tested under reverse cyclic loading. The performances of these specimens are assessed in terms of hysteretic behaviour, energy dissipation and strength degradation. It is noted that the nature of corrosion i.e. uniform or pitting corrosion and its location have significant influence on the behaviour of corrosion damaged GLD beam-column sub-assemblages. The corroded specimens with localised corrosion pits showed in-cyclic strength degradation. The study also reveals that external strengthening which provides an alternate force path but depends on the strength of the existing reinforcement bars, is able to mitigate the seismic risk of corroded GLD beam-column sub-assemblages to the level of control uncorroded GLD specimen.

• Advances in concrete construction
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• v.16 no.1
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• pp.21-34
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• 2023

This work presents a complete optimal model for trapezoidal combined footings that support a concentric load and moments around of the "X" and "Y" axes in each column to obtain the minimum area and the minimum cost. The model presented in this article considers a pressure diagram that has a linear variation (real pressure) and the equations are not limited to some cases. The classic model takes into account a concentric load and the moment around of the "X" axis (transverse axis) that is applied due to each column, i.e., the resultant force is located at the geometric center of the footing on the "Y" axis (longitudinal axis), and when the concentric load and moments around of the "X" and "Y" axes act on the footing is considered the uniform pressure applied on the contact surface of the footing, and it is the maximum pressure. Four numerical problems are presented to find the optimal design of a trapezoidal combined footing under a concentric load and moments around of the "X" and "Y" axes due to the columns: Case 1 not limited in the direction of the Y axis; Case 2 limited in the direction of the Y axis in column 1; Case 3 limited in the direction of the Y axis in column 2; Case 4 limited in the direction of the Y axis in columns 1 an 2. The complete optimal design in terms of cost optimization for the trapezoidal combined footings can be used for the rectangular combined footings considering the uniform width of the footing in the transversal direction, and also for different reinforced concrete design codes, simply by modifying the resisting capacity equations for moment, for bending shear, and for the punching shear, according to each of the codes.

• International Journal of Concrete Structures and Materials
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• v.8 no.2
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• pp.99-116
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• 2014

The American Concrete Institute (ACI) 318-11 permits the use of the moment magnifier method for computing the design ultimate strength of slender reinforced concrete columns that are part of braced frames. This computed strength is influenced by the column effective length factor K, the equivalent uniform bending moment diagram factor $C_m$ and the effective flexural stiffness EI among other factors. For this study, 2,960 simple braced frames subjected to short-term loads were simulated to investigate the effect of using different methods of calculating the effective length factor K when computing the strength of columns in these frames. The theoretically computed column ultimate strengths were compared to the ultimate strengths of the same columns computed from the ACI moment magnifier method using different combinations of equations for K and EI. This study shows that for computing the column ultimate strength, the current practice of using the Jackson-Moreland Alignment Chart is the most accurate method for determining the effective length factor. The study also shows that for computing the column ultimate strength, the accuracy of the moment magnifier method can be further improved by replacing the current ACI equation for EI with a nonlinear equation for EI that includes variables affecting the column stiffness and proposed in an earlier investigation.