• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.27-34
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• 1998

We introduce ${\delta}$-frames, strong ${\delta}$-frames and completely distributive lattices, and investigate some relationships among those frames.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.43-56
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• 1997

In this paper, we introduce a new class of ${\delta}$-frames and study its properties. To do so, we introduce ${\delta}$-filters, almost Lindel$\ddot{o}$f frames and Lindel$\ddot{o}$f frames. First, we show that a complete chain or a complete Boolean algebra is a ${\delta}$-frame. Next, we show that a ${\delta}$-frame L is almost Lindel$\ddot{o}$f iff for any ${\delta}$-filter F in L, ${\vee}\{x^*\;:\;x{\in}F\}{\neq}e$. Last, we show that every regular Lindelof ${\delta}$-frame is normal and a Lindel$\ddot{o}$f ${\delta}$-frame is preserved under a ${\delta}$-isomorphism which is dense and codense.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.3
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• pp.97-103
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• 2004

Most of the columns in centrally braced steel frame buildings are usually designed as the gravity columns to reduce connection cost. For a rational seismic performance evaluation of centrally braced steel frame buildings, it is important to properly incorporate in the analysis  the P-${\Delta}$ effects arising from the gravity columns. An effective scheme for the P-${\Delta}$ effects modeling due to the gravity columns was illustrated based on the concept of fictitious leaning column. Seismic performance evaluation of inverted V braced steel frames with or without P-${\Delta}$ effects modeling was conducted by following the FEMA 273 NSP (Nonlinear Static Procedure). The problem in estimating dynamic P-${\Delta}$ modification factor (C3) in FEMA 273 was discussed. The results of this study indicated that the P-${\Delta}$ effects should be included in the seismic performance evaluation of centrally braced steel frames. This study also showed that the inverted V braced frames, retrofitted by applying the tie bars to redistribute the inelastic demand over the height of the building, exhibit significantly improved seismic performance.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.45-52
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• 2010

Generalizing $Lindel{\ddot{o}}f$ frames and almost compact frames, we introduce a concept of almost $Lindel{\ddot{o}}f$ frames. Using a concept of ${\delta}$-filters on frames, we characterize almost $Lindel{\ddot{o}}f$ frames and then have their permanence properties. We also show that almost $Lindel{\ddot{o}}f$ regular $D({\aleph}_1)$ frames are exactly $Lindel{\ddot{o}}f$ frames. Finally we construct an almost $Lindel{\ddot{o}}fication$ of a frame L via the simple extension of L associated with the set of all ${\delta}$-filters F on L with ${\bigvee}\{x^*{\mid}x{\in}F\}=e$.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.43-52
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• 1999

In this paper, we introduce sub-${\delta}$-frames and simple extensions on a ${\delta}$-frame, and study their properties.

• Journal of Korean Society of Steel Construction
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• v.13 no.4
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• pp.363-372
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• 2001

The objective of this study is to evaluate the $P-{\Delta}$ effect in the case of weak beam unbraced frames by experimental approach. To evaluate $P-{\Delta}$ effect, four specimens were tested under monotonic loading condition. The parameters of tests are the stiffness of column and the axial load ratio. The results show that the value of axial load affects frame stability because $P-{\Delta}$ effects promote the yielding of beam. The maximum lateral load increases in proportion to the increment of column stiffness and rotational stiffness of supports, The collapse mechanism of weak beam unbraced frames is stably formed in the condition of low axial load ratio. The $B_2$ factor of limit state design code does not properly consider the $P-{\Delta}$ effect in inelastic region.

• International Journal of High-Rise Buildings
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• v.2 no.4
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• pp.355-365
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• 2013

The paper reports results of recent studies on the effects of column support conditions on the lateral displacements of moment frames at incipient collapse. The article presents a number of exercises in the plastic theory of structures that lead to useful design formulae. It has been shown that Drift Shifting (DS) is caused due to differences in the stiffnesses of adjoining columns, and that changes in drift ratios are more pronounced at first level column joints in both fixed as well as pinned base frames. In well proportioned moment frames, DS in the upper levels could be minimized, even reduced to zero. It has been demonstrated that DS can be eliminated in properly designed fixed and grade beam supported (GBS) moment frames. Several examples, including symbolic P-delta effects, have been provided to demonstrate the validity and the applications of the proposed ideas to the design and drift control of moment frames. The proposed methodology is exact within the bounds of the theoretical assumptions and is well suited for preliminary design and teaching purposes.

• Journal of Korean Society of Steel Construction
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• v.15 no.4 s.65
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• pp.457-466
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• 2003

This study aimed to evaluate the stability of steel frames with weak column-strong beam and consider P-effect using the experimental approach. Towards this end, three specimens were tested under monotonic loading condition. Parameters of tests includes the stiffness of the column and the axial load ratio. Result showed that reduction in column stiffness promoted P- effect, which considerably influenced the frame's stability.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.109-118
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• 2000

In this paper, we introduce strict extensions on a ${\delta}$-frame, and show that if L is a regular strong ${\delta}$-frame, then $\mathcal{T}_XL$ is regular ${\delta}$-frame.

• Steel and Composite Structures
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• v.14 no.1
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• pp.1-20
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• 2013

This paper presents the formulation for a novel force-based 1-D compound-element that captures both material and second order P-${\Delta}$ nonlinearities in steel frames. At the nodal points, the element is attached to nonlinear rotational and a translational springs which represent the flexural and axial stiffness of the connections respectively. By decomposing the total strain in the material as well as the generalised displacements of the flexible connections to their elastic and inelastic components, a secant solution strategy based on a direct iterative scheme is introduced and the corresponding solution strategy is outlined. The strain and slope of the deformed element are assumed to be small; however the equilibrium equations are satisfied for the deformed element taking account of P-${\Delta}$ effects. The formulation accuracy and efficiency is verified by some numerical examples on the nonlinear static, cyclic and dynamic analysis of steel frames.