• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.4
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• pp.1-9
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• 2009

This paper investigates inelastic lateral-torsional buckling of stepped beams subjected to uniformly distributed load and end moments. A three-dimensional finite-element program ABAQUS (2007) and a regression program MINITAB(2006) were used to analytically develop new design equation for singly and doubly stepped beams with simple boundary condition. The flanges of the smaller cross-section in the stepped beams were fixed at 30.48 by 2.54 cm, whereas the width and thickness of the flanges of the larger cross-section varied. The web thickness and height of the beams were kept at 1.65 cm and 88.9 cm, respectively. The ratios of the flange thickness, flange width, and stepped length of beam are considered with analytical parameters. Two groups of 27 cases and 36 cases, respectively, were analyzed for doubly and singly stepped beams in the inelastic buckling range. The combined effects of residual stresses and geometrical imperfection on inelastic lateral-torsional buckling of beams are considered. The distributions of residual stress of the cross-section is same as shown in Pi and Trahair (1995) and the initial geometric imperfection of the beam is set by central displacement equal to 0.1% of the unbraced length of beam. The comparisons between results from proposed equations and the results from finite element analyses were presented in this paper. The maximum differences of two results are of 13% for the doubly stepped beam and 10% for the singly stepped beam. The proposed equations definitely improve current design methods for the inelastic lateral-torsional buckling problem and increase efficiency in building and bridge design.

• Journal of Korean Society of Steel Construction
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• v.20 no.2
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• pp.237-246
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• 2008

The cross-sections of continuous multi-span beams sometimes suddenly increase, or become stepped, at the interior supports of continuous beams to resist high negative moments. The three-dimensional finite-element program ABAQUS (2006) was used to analytically investigate the inelastic lateral-torsional buckling behavior of stepped beams subjected to pure bending moment and resulted in the development of design equations. The flanges of the smaller cross-section were fixed at 30.48 by 2.54 cm, whereas the width and/or thickness of the flanges of the larger cross-section varied. The web thickness and height of beam was kept at 1.65 cm and 88.9 cm, respectively. The ratios of the flange thickness, flange width, and stepped length of beams are considered analytical parameters. Two groups of 27 cases and 35 cases, respectively, were analyzed for double and single stepped beams. The combined effects of residual stresses and geometrical imperfection on inelastic lateral-torsional buckling of beams are considered. First, the distributions of residual stress of the cross-section is same as shown in Pi, etc (1995), and the initial geometric imperfection of the beam is set by central displacement equal to 0.1% of the unbraced length of beam. The new proposed equations definitely improve current design methods for the inelastic LTB problem and increase efficiency in building and bridge design. The proposed solutions can be easily used to develop new design equation for inelastic LTB resistance of stepped beams subjected to general loading condition such as a concentrated load, a series of concentrated loads or uniformly distributed load.

• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.1-12
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• 2010

According to the capacity design concept which forms the basis of the current steel seismic codes, the braces in concentrically braced frames (CBFs) should dissipate seismic energy through cyclic tension yielding and cyclic compression buckling while the beams and the columns should remain elastic. Brace buckling in inverted V-braced frames induces unbalanced vertical forces which, in turn, impose the additional beam moments and column axial forces. However, due to difficulty in predicting the location of buckling stories, the most conservative approach implied in the design code is to estimate the column axial forces by adding all the unbalanced vertical forces in the upper stories. One alternative approach, less conservative and recommended by the current code, is to estimate the column axial forces based on the amplified seismic load expected at the mechanism-level response. Both are either too conservative or lacking technical foundation. In this paper, three combination rules for a rational estimation of the column axial forces were proposed. The idea central to the three methods is to detect the stories of high buckling potential based on pushover analysis and dynamic behavior. The unbalanced vertical forces in the stories detected as high buckling potential are summed in a linear manner while those in other stories are combined by following the SRSS(square root of sum of squares) rule. The accuracy and design advantage of the three methods were validated by comparing extensive inelastic dynamic analysis results. The mode-shape based method(MSBM), which is both simple and accurate, is recommended as the method of choice for practicing engineers among the three.

• The korean journal of orthodontics
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• v.25 no.5 s.52
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• pp.525-541
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• 1995

This study was designed to investigate force systems and tooth movements produced by retraction archwire during retraction of four maxillary incisors after the maxillary canine retraction into the maxillary first premolar extraction space using the computer-aided three-dimensional finite element method. A three-dimensional finite element model, consisting of 2248 elements and 3194 nodes, was constructed. The model consisted of maxillary teeth and surrounding periodontal membranes, .022'$\times$.028'-slot brackets, and 5 types of retraction archwires(.019'$\times$.025' stainless steel archwire) modeled using the beam elements. The contact between the wire and the bracket slot was modeled using the gap elements because of the non-linear elastic behaviors of the contact between them. The forces and moments, End displacements produced by retraction archwire were measured at various conditions to investigate the difference according to types of loops, magnitudes of activation force, gable angle, and anterior lingual root torque. The results were expressed quantitative and visual ways in the three-dimensional method. The following conclusions can be drawn from this study.1. When the tear-drop loop archwire was activated, the mesio-distal and lingual translational movements of the teeth helped to close the extraction space, but unwanted movements of the teeth including intrusions and extrusions, and rotational movements in each direction occurred. 2. Activation of T-loop archwire compared with those of other types of retraction archwires produced the least translational movements of the teeth helped to space closure and also the least unwanted movements of the teeth. 3. Increasing amount of activation in the tear-drop archwire led not only to increase of translational movements of the teeth helped to space closure, but also to increase of unwanted movements of the teeth. 4. Addition of gable bend in the tear-drop archwire helped anterior teeth to translational movements in the mesio-distal direction, but increased unwanted movements of the teeth 5. Addition of anterior lingual root torque in the tear-drop archwire helped central and lateral incisor to improve their facio-lingual inclination, but increased unwanted movements of the teeth.