• Structural Engineering and Mechanics
• /
• v.6 no.4
• /
• pp.411-425
• /
• 1998

The effective length factor of a framed column may be determined by means of the alignment chart procedure. This method is based on many unrealistic assumptions, among which is that all columns have the same stiffness parameter, which is dependent on the length, axial load, and moment of inertia of the column. A new approximate method is developed for the determination of effective length factors for columns in unbraced frames. This method takes into account the effects of inelastic column behaviour, far end conditions of the restraining beams and columns, semi-rigid beam-to-column connections, and differentiated stiffness parameters of columns. This method may be implemented on a microcomputer. A numerical study was carried out to demonstrate the extent to which the involved parameters affect the K factor. The beam-to-column connection stiffness, the stiffness parameter of columns, and the far end conditions of restraining members have a significant effect on the K factor of the column under investigation. The developed method is recommended for design purposes.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.11a
• /
• pp.337-340
• /
• 2006

The purpose of this study is to propose the stiffness reduction factor for flat plate slabs under lateral loads. Current design code (e.g., ACI 318-05) requires considering the effects of cracks for calculating slab stiffness under lateral loads. This study collected the test results of 20 interior slab-column connections, from which stiffness reduction in each test was estimated with respect to the ratio of applied moment to cracking moment ($M_a/M_{cr}$). Based on collected data, this study proposed equations for calculating stiffness reduction with respect to $M_a/M_{cr}$. To verify the proposed equations, this study conducted the experimental test of interior slab-column connections under quasi-static cyclic loading. From the test, load-deformation curve is compared to that obtained from effective beam width method with the proposed equation for the stiffness reduction. It is shown that the effective beam width method with the proposed equation for stiffness reduction predicts accurately the test results.

• Structural Engineering and Mechanics
• /
• v.87 no.4
• /
• pp.363-373
• /
• 2023

Since the first family of structure-dependent methods can simultaneously integrate unconditional stability and explicit formulation in addition to second order accuracy, it is very computationally efficient for solving inertial problems except for adopting auto time-stepping techniques due to no nonlinear iterations. However, an unusual stability property is first found herein since its unconditional stability interval is drastically different for zero and nonzero damping. In fact, instability might occur for solving a damped stiffness hardening system while an accurate result can be obtained for the corresponding undamped stiffness hardening system. A technique of using a stability factor is applied to overcome this difficulty. It can be applied to magnify an unconditional stability interval. After introducing this stability factor, the formulation of this family of structure-dependent methods is changed accordingly and thus its numerical properties must be re-evaluated. In summary, a large stability factor can result in a large unconditional stability interval but also lead to a large relative period error. As a consequence, a stability factor must be appropriately chosen to have a desired unconditional stability interval in addition to an acceptable period distortion.

• Earthquakes and Structures
• /
• v.26 no.3
• /
• pp.229-237
• /
• 2024

This paper studied the subgrade spring stiffness and its influencing factors in the seismic deformation method of circular tunnel. Numerical calculations are performed for 3 influencing factors: stratum stiffness, tunnel diameter and burial depth. The results show that the stratum stiffness and tunnel diameter have great influence on the subgrade spring stiffness. The subgrade spring stiffness increases linearly with stratum stiffness increasement, and decreases with the tunnel diameter increasement. When the burial depth ratio (burial depth/tunnel diameter) exceeds to 5, the subgrade spring stiffness has little sensitivity to the burial depth. Then, a proposed formula of subgrade spring stiffness for the seismic deformation method of circular tunnel is proposed. Meanwhile, the internal force results of the seismic deformation method are larger than that of the dynamic time history method, but the internal force distributions of the two methods are consistent, that is, the structure exhibits elliptical deformation with the largest internal force at the conjugate 45° position of the circular tunnel. Therefore, the seismic deformation method based on the proposed formula can effectively reflect the deformation and internal force characteristics of the tunnel and has good applicability in engineering practice.

• Structural Monitoring and Maintenance
• /
• v.11 no.3
• /
• pp.219-234
• /
• 2024

The strength reduction factor spectrum is traditionally obtained from a single-degree-of-freedom (SDOF) system with a constant damping coefficient. However, according to the principle of Rayleigh damping, the damping coefficient matrix of a system changes with the stiffness matrix, and the damping coefficient of an equivalent SDOF system changes with the tangent stiffness coefficient. In view of that, this study proposes an equivalent SDOF system with an adaptive damping coefficient and derives a standardized reaction balance equation. By iteratively adjusting the strength reduction factor, the corresponding spectrum with an equivalent ductility factor is obtained. In addition, the ratio between the strength reduction factor that considers adaptive damping and the traditional strength reduction factor, denoted by η, is determined, and the η-μ-T relationship is obtained. Seismic records of Classes C, D, and E sites are selected as excitations. Moreover, a nonlinear response time-history analysis is performed to establish the relationship between the η and T values for the equivalent ductility factor μ. Further, by exploring the effects of the site class, ductility factor, second-order stiffness coefficient, and period T on the mean value of η, a simplified calculation equation of mean η is derived, and η is used as a modified value for the traditional strength reduction factor R spectrum.

• Journal of the Korean Society for Railway
• /
• v.17 no.4
• /
• pp.281-288
• /
• 2014

The objective of this study was to estimate the vibration reduction capacities of a floating track system using a resilient rubber mat, and to compare the results with the track support stiffness and track impact factor of a conventional slab track system by performing field tests using actual vehicles running along a service line. The theoretically designed track support stiffness and track impact factor were compared with the measured track support stiffness and track impact factor for each tested track. The calculated and measured track support stiffness of the floating track system were found to be similar, and the floating track system satisfied the design specifications of the track impact factor. The overall vibration level and track support stiffness of the floating track system were thereupon found to be significantly lower than those of the conventional slab track system. The experimental results thus showed that the vibration reduction effect of the floating track system is greater than that of the conventional slab track.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.9
• /
• pp.2284-2296
• /
• 1994

Force control of robotic mechanisms continues to be a challenging area. Previous implementation have seldom produced satisfactory results, and researchers in the past have experienced significant instability problems associated with their force controllers. In this study, a new stability factor in force control will be pointed out. When a manipulator is constrained to an environment(force-controlled), geometric instability due to the relationship between the manipulator configuration and the force-controlled direction is shown to be a significant factor in overall system stability. This exploratory study points out a rather intuitive, geometrically based stability factor in terms of an effective system stiffness and analyzes the phenomenon both analytically and graphically. Also, a stiffness control algorithm using the kinematic redundancy of a kinematically redundant manipulator is proposed to improve the overall stability in force control.

• Earthquakes and Structures
• /
• v.20 no.4
• /
• pp.389-403
• /
• 2021

Skewed bridges, being irregular structures with complicated dynamic behavior, are more susceptible to earthquake damage. Reliable seismic-resistant design of skewed bridges can be achieved by accurate determination of nonlinear seismic demands. However, the effect of geometric characteristics on the response modification factor (R-factor) is not accounted for in bridge design practices. This study attempts to investigate the effects of changes in the number of spans, skew angle and bearing stiffness on R-factor values and to assess the seismic fragility of skewed bridges. Results indicated that changes in the skew angle had no significant effect on R-factor values which were in consonance with code-prescribed R values. Also, unlike the increase in the number of spans that resulted in a decrease in the R-factor, the increase in bearing stiffness led to higher R-factor values. Findings of the fragility analysis implied that although the increase in the number of spans, as well as the increase in the skew angle, led to a higher failure probability, greater values of bearing stiffness reduced the collapse probability. For practicing design engineers, it is recommended that maximum demands on substructure elements to be calculated when the excitation angle is applied along the principal axes of skewed bridges.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2009.05a
• /
• pp.125-126
• /
• 2009

Effective beam width model (EBWM) has been used for analysis of post-tensioned (PT) flat plate slab frames under lateral loads. For analyzing PT flat plate slab structure under lateral loads with good precision, reduction in slab stiffness has to be accurately estimated for Effective beam width model(EBWM). For this purpose, this study collected test results of PT flat plate system conducted by former researches. And this study reduced the width of slab so that the stiffness of the EBWM converged into the lateral stiffness of each test specimens by trial and error. By conducting nonlinear regression analysis, an equation for calculating stiffness reduction factor for the PT flat plate is proposed.

• Structural Engineering and Mechanics
• /
• v.4 no.2
• /
• pp.139-148
• /
• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.