Simple Portal Frame Research Articles

Optimum target stiffness allocation for design of a reinforcing member on an existing structure

The reinforcing members are often added on an existing structure to improve stiffness of the structure up to required level. In general, the design targets for the reinforcing members need to be allocated for their designs. However, since the members are additively designed, it is difficult to predict behavior of the reinforcing members and their influence on the existing structure. Therefore, allocating the design targets is challenging task, and the targets based on engineering experience and intuition can lead to the repetitive design cycles. This paper proposes a method for determining target stiffness of a reinforcing member which makes an existing structure achieve the required performances. To utilize individual models of an existing structure and the reinforcing members in a design, the system of equations of the assembled structure is decomposed by using a substructuring technique. Additional boundary conditions are imposed on the interfaces between the structure and members to ensure consistency between models, and the target stiffness of the member is defined by using the boundary conditions. The optimal target stiffness and design of the members are determined through the use of a multidisciplinary design optimization technique, analytical target cascading. This method is applied to a simple portal frame and a body-in-white with reinforcing member of a vehicle manufactured by Hyundai Motor Company. By using the optimal target stiffness, reinforcing member of any shape can be designed independently and at little cost, without access of the existing structure model.

On vibration mitigation and energy harvesting of a non-ideal system with autoparametric vibration absorber system

This paper demonstrates that vibration mitigation and energy harvesting can be achieved simultaneously by using of an electricity-generating from autoparametric vibration absorber system (AVAS) and non-ideal system (NIS). The NIS consists of a simple portal frame excited by a small dc motor with eccentric mass, with limited power supply and located on the top. The AVAS consists of a cantilever beam with tip mass parallel coupled to NIS. A piezoelectric material is considered for energy harvesting installed in the base of the AVAS and an electric circuit is connected to the piezoelectric material in order to produce voltage output. Several numerical simulations were carried out focusing on the passage through the resonance of NIS, when the motor rotational frequency is near the portal frame natural frequency and when the non-ideal subsystem frequency is approximately twice the absorber beam frequency (two-to-one internal resonance). The results showed the existence of Sommerfeld effect in NIS and saturation phenomenon in the NIS–AVAS.

Experimental Tests on a Dowel-Type Timber Connection and Validation of Numerical Models

This paper examines the dynamic behaviour of timber framed buildings under wind and dynamic loads, focusing on the role of connections being experimentally tested. The main aim of this manuscript is to analyze the in-service dynamic behaviour of a semi-rigid moment-resisting dowel-type connection between timber beam and column. For this purpose, two laboratory tests have been performed, the first on a connection and another one on a portal frame. The results are used to validate a numerical model of the simple portal frame, analyzed in OpenSees. The obtained relationships are also discussed and compared with Eurocode rules. The main result is that the joint stiffness is calculated through the Eurocode (EC) formulation underestimates the experimental one. A mutual agreement is obtained between the numerical model, validated from the experimental stiffness value for the connections, and the experimental results on the portal frame.

Using passive control by a pendulum in a portal frame platform with piezoelectric energy harvesting

This work presents a passive control strategy using a pendulum on a simple portal frame structure, with two-to-one internal resonance, with a piezoelectric material coupling as a means of energy harvesting. In addition, the system is externally base-excited by an electro-dynamical shaker with harmonic output. Due to internal resonance the system may present the phenomenon of saturation, which provides some nonlinear dynamical behavior to the system. A pendulum is coupled to control nonlinear behaviors, leading to a periodic orbit, which is necessary to maintain energy harvesting. The results show that the system presents, most of the time, as being quasiperiodic. However, it does not present as being chaotic. With the pendulum, it was possible to control most of these quasiperiodic behaviors, leading to a periodic orbit. Moreover, it is possible to eliminate the need for an active or semi-active control, which are usually more complex. In addition, the control provides a way to detune the energy captured to the desired operating frequency.

Nonlinear piezoelectric vibration energy harvesting from a portal frame with two-to-one internal resonance

In the few decades, the study of electro-mechanical systems which are capable to extract energy from an operating system in the environment has been of most importance. In this work, we present the extraction of energy from a simple portal frame structure excited by a harmonic force, where the energy harvesting is computed by using of a nonlinear piezoelectric material. The dynamical response of the system is examined, when there is 2:1 internal resonance between the symmetric and the sway mode, resulting the saturation phenomenon and vibration energy transfer between the symmetric (vertical) mode and the horizontal (sway) mode. An evaluation of the energy available for harvesting, in each of the considered modes, is computed.

Potential Application in Energy Harvesting of Intermodal Energy Exchange in a Frame: FEM Analysis

This paper presents a Finite Element Analysis (FEA) of modal energy exchange and harvesting in a simple portal frame structure. We consider both horizontal and vertical support excitations resonant first with the first mode (sway mode) and latter with the second mode (the first symmetrical mode). As 2:1 internal resonance is present between these two modes, the phenomena of mode saturation and energy exchange (modal coupling) may occur. Thus, energy pumped into the system through one of the modes, is partially transferred to the other mode, not directly excited. An evaluation of the energy available for harvesting in each of the considered mode is computed.

A non-ideal portal frame energy harvester controlled using a pendulum

A model of energy harvester based on a simple portal frame structure is presented. The system is considered to be non-ideal system (NIS) due to interaction with the energy source, a DC motor with limited power supply and the system structure. The nonlinearities present in the piezoelectric material are considered in the piezoelectric coupling mathematical model. The system is a bi-stable Duffing oscillator presenting a chaotic behavior. Analyzing the average power variation, and bifurcation diagrams, the value of the control variable that optimizes power or average value that stabilizes the chaotic system in the periodic orbit is determined. The control sensitivity is determined to parametric errors in the damping and stiffness parameters of the portal frame. The proposed passive control technique uses a simple pendulum to tuned to the vibration of the structure to improve the energy harvesting. The results show that with the implementation of the control strategy it is possible to eliminate the need for active or semi active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.

Application of passive control to energy harvester efficiency using a nonideal portal frame structural support system

An analysis of a new energy harvester model is presented, based on a simple portal frame structure, considered a nonideal system due to the kind of excitation influenced by the response of the system, such as a direct current motor with limited power supply. The horizontal motion of the portal frame is considered under a nonideal excitation, and the approximated mathematical model of the system is obtained, considering the coupled oscillators. To model the piezoelectric coupling, the nonlinearities of the piezoelectric material were considered. A constantly sustained energy harvesting is essential for using these devices in real applications; for this, a control strategy is required. Passive control was obtained by means of a nonlinear substructure with properties of nonlinear energy sink. Numerical simulations were performed in order to find best values of control parameters. To check the robustness of the control strategy, an analysis considering uncertainties in the parameters of the model was performed, showing the efficiency of the passive control (energy pumping) in the suppression of the chaotic behavior, as well as the sensitivity of the control system to parametric errors. Passive control leads the system to a stable periodic orbit, allowing a more efficient energy harvest, due to the higher peak-to-peak amplitude of oscillation mean value. The passive control strategy eliminates the need for an active microcontroller to stabilize the system in a periodic orbit, improving the energy budget (harvested versus expended). The results show the displacement of the structure and the maximum power harvested by the device with and without passive nonlinear energy sink. It can be concluded that the application of passive control was successful. The control was robust and improved the energy harvested through the suppression of the chaotic motion, leading the system to a periodic orbit with stable amplitude of vibration, without damaging the structure.

A novel beam finite element with singularities for the dynamic analysis of discontinuous frames

In this work, a model of the stepped Timoshenko beam in presence of deflection and rotation discontinuities along the span is presented. The proposed model relies on the adoption of Heaviside’s and Dirac’s delta distributions to model abrupt and concentrated, both flexural and shear, stiffness discontinuities of the beam that lead to exact closed-form solutions of the elastic response in presence of static loads. Based on the latter solutions, a novel beam element for the analysis of frame structures with an arbitrary distribution of singularities is here proposed. In particular, the presented closed-form solutions are exploited to formulate the displacement shape functions of the beam element and the relevant explicit form of the stiffness matrix. The proposed beam element is adopted for a finite element discretization of discontinuous framed structures. In particular, by means of the introduction of a mass matrix consistent with the adopted shape functions, the presented model allows also the dynamic analysis of framed structures in presence of deflection and rotation discontinuities and abrupt variations of the cross-section. The presented formulation can also be easily employed to conduct a dynamic analysis of damaged frame structures in which the distributed and concentrated damage distributions are modelled by means of equivalent discontinuities. As an example, a simple portal frame, under different damage scenarios, has been analysed and the results in terms of frequency and vibration modes have been compared with exact results to show the accuracy of the presented discontinuous beam element.

On an Energy Exchange Process and Appearance of Chaos in a Non-ideal Portal Frame Dynamical System

The dynamics of a structure excited by a non-ideal excitation device, such as a DC motor with limited power capacity, is considered in this paper. When non-ideal excitation sources are attached to structures that consume energy at levels similar to the source power capacity, some characteristic phenomena such as jumps can occur. These behaviors are related to the Sommerfeld effect, where a part of the excited system behaves as energy sink. One of the problems often faced by designers of such structures is how to drive a system through resonance and avoid this “energy sink”. The basic structural model proposed in this paper is a simple portal frame driven by a non-ideal power source (NIPF). The vibrations absorption (in resonance, nonlinear and chaotic) is also analyzed by means of a nonlinear sub-structure known as a nonlinear energy sink (NES). An energy exchange process between NIPF and NES in the passage through resonance as well the suppression of chaos are investigated.

On elimination of chaotic behavior in a non-ideal portal frame structural system, using both passive and active controls

In this paper, an application is considered of both active and passive controls, to suppression of chaotic behavior of a simple portal frame, under the excitation of an unbalanced DC motor, with limited power supply (non-ideal problem). The adopted active control strategy consists of two controls: the nonlinear (feedforward) in order to keep the controlled system in a desirable orbit, and the feedback control, which may be obtained by considering state-dependent Riccati equation control to bringing the system into the desired orbit using a magneto rheological (MR) damper. To control the electric current applied in control of the MR damper the Bouc-Wen mathematical model was used to the MR damper. The passive control was obtained by means of a nonlinear sub-structure with properties of nonlinear energy sink. Simulations showed the efficiency of both the passive control (energy pumping) and active control strategies in the suppression of the chaotic behavior.

Optimizing Structures Subject to Multiple Deflection Constraints and Load Cases Using the Principle of Virtual Work

This paper presents an iterative automated method for optimizing structures with multiple deflection criteria and load cases. The method is based on the principle of virtual work. Discrete sections are selected for structures with fixed geometries. An optimal structure is one which meets all strength and deflection criteria using minimal material. Four case studies are considered in this paper. A simple portal frame is presented to show how the method works. A 60-story frame is optimized to demonstrate the effectiveness of the method for large structures. A warehouse designed by professional engineers is presented to show how the method can be used for structures subjected to complex loading conditions and deflection criteria. The automated method’s solution is 4.5% lighter than the engineers’. Finally, a stepped cantilever is optimized and compared to results in literature. Material savings of up to 14.4% are realized.

Structural reliability and finite element methods

The Finite Element Methods has become a common tool for engineering analysis and design subsequent to phenomenal increase in computing power available even on laptop and personnel computers. Further, design optimization and reliability analysis techniques and methodologies needing a number of evaluations of design problem at hand are becoming accessible and affordable. This paper concerns to review various techniques and methods that may be used in Reliability Analysis (RA) based on Finite Element Methods (FEM). A review of reliability analysis tools available within the ANSYS commercial FEA software as well as that of STRUREL, the commercial RA software is carried out. A simple portal frame structure analysis has been done using various methods, and the results are compared for computational cost and accuracy.

Centrifuge modelling-based verification of response spectra design methods for some vulnerable structures

Residential RC framed structures suffered heavily during the 2001 Bhuj earthquake in Gujarat, India. These types of structures also saw severe damage in other earthquakes such as the 1999 Kocaeli earthquake in Turkey and 921 Ji-Ji earthquake in Taiwan. In this paper the seismic response of residential structures was investigated using physical modelling. Idealised soft storey and top heavy, two degrees of freedom (2DOF) portal frame structures were developed and tested on saturated and dry sand models at 25 g using the Schofield Centre 10-m Beam Centrifuge. It was possible to recreate observed field behaviour using these models. As observed in many of the recent earthquakes, soft storey structures were found to be particularly vulnerable to seismic loads. Elastic response spectra methods are often used in the design of simple portal frame structures. The seismic risk of these structures can be significantly increased due to modifications such as removal of a column or addition of heavy water tanks on the roof. The experimental data from the dynamic centrifuge tests on such soft storey or top-heavy models was used to evaluate the predictions obtained from the response spectra. Response spectra were able to predict seismic response during small to moderate intensity earthquakes, but became inaccurate during strong earthquakes and when soil structure interaction effects became important. Re-evaluation of seismic risk of such modified structures is required and time domain analyses suggested by building codes such as IBC, UBC or NEHRP may be more appropriate.

On the dynamics of free and excited oscillations of a simple portal frame foundation

In this paper we search for the dynamics of a simple portal structure in the free and in the periodic excitation cases. By using the Center Manifold approach and Averaging Method, we obtain results on both stability and bifurcation of equilibrium points and periodic orbits.

Short Comments on Self-Synchronization of Two Non-Ideal Sources Supported by a Flexible Portal Frame Structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

BEHAVIOUR OF ALUMINIUM ALLOY STRUCTURES UNDER FIRE

In the paper the attention is focused on the influence of high temperatures on the mechanical properties of the aluminium alloys selected by Eurocode 9 for structural uses. Therefore, based on the analysis of existing data taken from technical literature, the variation of the Young's modulus, the conventional yielding strength, the ultimate strength, the hardening factor and the material ultimate strain are represented as a function of the temperature. A mechanical model, based on the well‐known Ramberg‐Osgood formulation, which appropriately takes into account the peculiarities of such materials at high temperatures, is provided. In particular, the combined influence of the hardening factor and temperature on the material stress‐strain relationship is considered and analysed. Then, the proposed model has been introduced in a finite element program, devoted to the global analysis of structures under fire. Finally, the results obtained for a simple portal frame structure, designed with different aluminium alloys, are presented, showing the valuable effect of the material modelling on the structural behaviour of aluminium structures under fire.

Behaviour of aluminium alloy structures under fire

In the paper the attention is focused on the influence of high temperatures on the mechanical properties of the aluminium alloys selected by Eurocode 9 for structural uses. Therefore, based on the analysis of existing data taken from technical literature, the variation of the Young's modulus, the conventional yielding strength, the ultimate strength, the hardening factor and the material ultimate strain are represented as a function of the temperature. A mechanical model, based on the well‐known Ramberg‐Osgood formulation, which appropriately takes into account the peculiarities of such materials at high temperatures, is provided. In particular, the combined influence of the hardening factor and temperature on the material stress‐strain relationship is considered and analysed. Then, the proposed model has been introduced in a finite element program, devoted to the global analysis of structures under fire. Finally, the results obtained for a simple portal frame structure, designed with different aluminium alloys, are presented, showing the valuable effect of the material modelling on the structural behaviour of aluminium structures under fire. First Published Online: 14 Oct 2010

Improved control algorithm for real‐time substructure testing

AbstractReal‐time substructure testing is a novel method of testing structures under dynamic loading. The complete structure is separated into two substructures, one of which is tested physically at large scale and in real time, so that time‐dependent non‐linear behaviour of the substructure is realistically represented. The second substructure represents the surrounding structure, which is modelled numerically. In the current formulation this numerical substructure is assumed to remain linear. The two substructures interact in real‐time so that the response of the complete structure, incorporating the non‐linear behaviour of the physical substructure, is accurately represented. This paper presents several improvements to the linear numerical modelling of substructures for use in explicit time‐stepping routines for real‐time substructure testing. An extrapolation of a first‐order‐hold discretization is used which increases the accuracy of the numerical model over more direct explicit methods. Additionally, an integral form of the equation of motion is used in order to reduce the effects of noise and to take into account variations of the input over a time‐step. In order to take advantage of this integral form, interpolation of the model output is performed in order to smooth the output. The improvements are demonstrated using a series of substructure tests on a simple portal frame. While the testing approach is suitable for cases in which the physical substructure behaves non‐linearly, the results presented here are for fully linear systems. This enables comparisons to be made with analytical solutions, as well as with the results of tests based on the central difference method. Copyright © 2001 John Wiley & Sons, Ltd.

Effect of random material variability on seismic design parameters of steel frames

AbstractWhereas an increase in material yield stress beyond the code specified characteristic value enhances plastic capacity, it may cause a reduction in overall ductility and energy absorption capability of steel frames. Since quality control of various shapes of sections used on site is difficult to impose, the effect of this random variability on design response parameters should be accounted for in earthquake‐resistant regulations. Moreover, the required weak‐beam/strong‐column design principle in particular, and failure mode control in general, could be undermined if the yield stresses in beam and column assume two opposite extremes in a random sample. This paper addresses the problem of defining the expected range of response parameters in a steel frame with randomly varying yield stress. A simple portal frame is designed using code specified characteristic values and verified by non‐linear transient dynamic analysis. The influence of yield stress variability, including the degree of correlation between beam and column material properties, on several response parameters is assessed through a Monte Carlo simulation study. Results are presented from both univariate and bivariate statistical analyses that quantify the relationship between input (material) and output (response) parameters. Assessment of the interdependence of output parameters given a particular model for yield stress variability is also undertaken. It is shown that certain response parameters exhibit more favourable statistical properties than others. Thus, the implications for seismic code design are discussed in the light of these results.