A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

Method of reverberation ray matrix for static analysis of planar framed structures composed of anisotropic Timoshenko beam members

Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.

Investigation of dynamics of discrete framed structures by a numerical wave-based method and an analytical homogenization approach

In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.

Selection and modification of ground motion records using Newmark-Hall spectrum as target spectrum for long-period structures

Input ground motions have significant impacts on the uncertainty of structural responses in time-history analysis.In this study,records were selected and scaled for the evaluation of mean structural responses according to the target spectrum.The Newmark-Hall spectrum is closely related to seismic response of short,medium and long-period structures,so it was taken as the target spectrum here.The nonlinear time-history analyses of 9-story and 20-story steel moment-resisting frame structures were carried out as examples.They represent medium and long-period buildings,respectively.Three target spectra with risk of 50%,10%and 2%probabilities for exceedance in 50 years were calculated by the average Newmark-Hall spectrum method for three ground motion sets developed in the SAC Steel Project.The predicted structural mean responses of these Newmark-Hall spectra were compared with those calculated by the average spectral acceleration method for the same record set.It is found that both methods have similar accuracy for estimating the structural mean response.However,the method proposed herein is more effective in reducing the variability of the structural responses.Also,the proposed method is more advantageous for the time-history analysis of long-period structures or structures with more severe nonlinear responses under strong seismic excitations.

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.

Evaluation of collapse resistance of RC frame structures for Chinese schools in seismic design categories B and C

According to the Code for Seismic Design of Buildings （GB50011-2001）, ten typical reinforced concrete （RC） frame structures, used as school classroom buildings, are designed with different seismic fortification intensities （SFIs） （SFI=6 to 8.5） and different seismic design categories （SDCs） （SDC=B and C）. The collapse resistance of the frames with SDC=B and C in terms of collapse fragility curves are quantitatively evaluated and compared via incremental dynamic analysis （IDA）. The results show that the collapse resistance of structures should be evaluated based on both the absolute seismic resistance and the corresponding design seismic intensity. For the frames with SFI from 6 to 7.5, because they have relatively low absolute seismic resistance, their collapse resistance is insufficient even when their corresponding SDCs are upgraded from B to C. Thus, further measures are needed to enhance these structures, and some suggestions are proposed.

Self-centering seismic retrofit scheme for reinforced concrete frame structures:SDOF system study

This paper presents the results of a parametric study of self-centering seismic retrofit schemes for reinforced concrete (RC) frame buildings. The self-centering retrofit system features flag-shaped hysteresis and minimal residual deformation. For comparison purpose,an alternate seismic retrofit scheme that uses a bilinear-hysteresis retrofit system such as buckling-restrained braces (BRB) is also considered in this paper. The parametric study was carried out in a single-degree-of-freedom (SDOF) system framework since a multi-story building structure may be idealized as an equivalent SDOF system and investigation of the performance of this equivalent SDOF system can provide insight into the seismic response of the multi-story building. A peak-oriented hysteresis model which can consider the strength and stiffness degradation is used to describe the hysteretic behavior of RC structures. The parametric study involves two key parameters -the strength ratio and elastic stiffness ratio between the seismic retrofit system and the original RC frame. An ensemble of 172 earthquake ground motion records scaled to the design basis earthquake in California with a probability of exceedance of 10% in 50 years was constructed for the simulation-based parametric study. The effectiveness of the two seismic retrofit schemes considered in this study is evaluated in terms of peak displacement ratio,peak acceleration ratio,energy dissipation demand ratio and residual displacement ratio between the SDOF systems with and without retrofit. It is found from this parametric study that RC structures retrofitted with the self-centering retrofit scheme (SCRS) can achieve a seismic performance level comparable to the bilinear-hysteresis retrofit scheme (BHRS) in terms of peak displacement and energy dissipation demand ratio while having negligible residual displacement after earthquake.

Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the independent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization interpolation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimization model based on the minimum structural compliance and the specified fiber material volume constraint has been established. The sensitivity information about the two geometrical scales design variables are also deduced considering the characteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can further explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultralight design of the composite frame structure. The novel two geometrical scales optimization model provides a new opportunity for the design of composite structure in aerospace and other industries.

Estimation of Aleatory Randomness by S_(a)(T_(1))-Based Intensity Measures in Fragility Analysis of Reinforced Concrete Frame Structures

Based on the multiple stripes analysis method,an investigation of the estimation of aleatory randomness by S_(a)(T_(1))-based intensity measures(IMs)in the fragility analysis is carried out for two typical low-and mediumrise reinforced concrete(RC)frame structures with 4 and 8 stories,respectively.The sensitivity of the aleatory randomness estimated in fragility curves to various S_(a)(T_(1))-based IMs is analyzed at three damage limit states,i.e.,immediate occupancy,life safety,and collapse prevention.In addition,the effect of characterization methods of bidirectional ground motion intensity on the record-to-record variability is investigated.It is found that the damage limit state of the structure has an important influence on the applicability of the ground motion IM.The S_(a)(T_(1))-based IMs,considering the effect of softened period,can maintain lower record-to-record variability in the three limit states,and the S_(a)(T_(1))-based IMs,considering the effect of higher modes,do not show their advantage over S_(a)(T_(1)).Furthermore,the optimal multiplier C and exponentαin the dual-parameter ground motion IM are proposed to obtain a lower record-to-record variability in the fragility analysis of different damage limit state.Finally,the improved dual-parameter ground motion IM is applied in the risk assessment of the 8-story frame structure.

STUDIFS ON OPTIMAL TOPOLOGY DES IGN OF STRUCTURES WITH DISCRETE VARIABLES

Some problems in the optimal topology design of structures with discrete variables are studied in this paper.The problem of a model of discrete optimization is discussed and a neglected fact that discrete optimum design may be controlled by the discreteness of sizing variables and global con- straints is pointed out.A heuristic algorithm for solving discrete topology optimization problems of trusses and frames is proposed.

Research on Seismic Design of High-Rise Buildings Based on Framed-Shear Structural System

Under the rapidly advancing economic trends,people’s requirements for the functionality and architectural artistry of high-rise structures are constantly increasing,and in order to meet such modern requirements,it is necessary to diversify the functions of high-rise buildings and complicate the building form.At present,the main structural systems of high-rise buildings are:frame structure,shear wall structure,frame shear structure,and tube structure.Different structural systems determine the size of the load-bearing capacity,lateral stiffness,and seismic performance,as well as the amount of material used and the cost.This project is mainly concerned with the seismic design of frame shear structural systems,which are widely used today.

Experimental and Numerical Study on Progressive Collapse Analysis of a Glulam Frame Structure:I.Side Column Exposed to Fire

This paper presents experimental and numerical investigations on progressive collapse behavior of a two-story glulam frame when the side column is exposed to ISO834 standard fire.The collapse mechanism initiated by fire is identified.The experimental results show that the progressive collapse of a glulam frame could be described for three stages,namely bending effect stage,catenary effect stage and failure stage,respectively.These stages are discussed in detail to understand the structural behavior before and during collapse.It is demonstrated that the entire frame slopes towards the side of the heated column,and the“overturning”collapse occurs eventually.The catenary effect of beams is the main reason for the progressive collapse of the frame.In addition,a finite element model of a glulam frame is established to simulate the progressive collapse behavior.The effects of axial loads on the columns are summarized.The numerical simulation results agree well with the experimental results,which could verify the effectiveness and practicability of finite element simulation.Furthermore,the progressive collapse resistance of the frame in practical design were proposed.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

Discussion on Construction Technology and Welding Deformation of High-Rise Steel Frame Structure

Because of urbanization,land resources in China’s cities has become increasingly scarce.Therefore,modern buildings are becoming taller,making high-rise steel frame structures the new favorite of the construction industry.However,the construction of high-rise steel frame structures requires advanced technology.If the construction technology is effectively implemented and the welding techniques of the construction personnel align with the requirements for high-rise steel frame structures,it can help mitigate deformations in the steel structure,thus preserving the overall construction quality of high-rise steel frame structures.To enhance the applicability of steel frame structures in high-rise buildings,this paper focuses on analyzing the optimization path for the construction process of high-rise steel frame structures.It introduces a tailored approach to control welding-induced deformations in steel frame structures,aiming to make a valuable contribution to the advancement of China’s construction industry.

ANALYSIS OF MATERIAL MECHANICAL PROPERTIES FOR SINGLE-WALLED CARBON NANOTUBES

Abstract The carbon-carbon bond between two nearest-neighboring atoms is mod- eled as a beam and the single-walled carbon nanotubes are treated as the space frame structures in order to analyze the mechanical properties of carbon nanotubes. Based on the theory of Tersof- Brenner force feld, the energy relationships between the carbon-carbon bond and the beam model are obtained, and the stifness parameters of the beam are determined. By applying the present model, the Young’s moduli of the single-walled carbon nanotubes with diferent tube diameters are determined. And the present results are compared with available data.

Study of the seismic response of a recycled aggregate concrete frame structure

Based on six-degree-of-freedom three-dimensional shaking table tests, the seismic response of a recycled aggregate concrete （RAC） frame was obtained. The analysis results indicate that the maximum story shear force and overturning moment reduce proportionally along the height of the model under the same earthquake wave. The story shear force, base shear coefficient and overturning moment of the structure increase progressively as the acceleration amplitude increases. The base shear coefficient is primarily controlled by the peak ground acceleration （PGA）. The relationships between the PGA and the shear coefficient as well as between the PGA and the dynamic amplification factor are obtained by mathematical fitting. The dynamic amplification factor decreases rapidly at the elastic-plastic stage, but decreases slowly with the development of the elastic-plasticity stage. The results show that the RAC frame structure has reasonable deformability when compared with natural aggregate concrete frame structures. The maximum inter-story drift ratios of the RAC frame model under frequent and rare intensity 8 test phases are 1/266 and 1/29, respectively, which are larger than the allowable value of 1/500 and 1/50 according to Chinese seismic design requirements. Nevertheless, the RAC frame structure does not collapse under base excitations with PGAs from 0.066 g up to 1.170 g.

Seismic performance analysis and design suggestion for frame buildings with cast-in-place staircases

Many staircases in reinforced concrete （RC） frame structures suffered severe damage during the Wenchuan earthquake. Elastic analyses for 18 RC structure models with and without staircases are conducted and compared to study the influence of the staircase on the stiffness, displacements and internal forces of the structures. To capture the yielding development and damage mechanism of frame structures, elasto-plastic analysis is carried out for one of the 18 models. Based on the features observed in the analyses, a new type of staircase design i.e., isolating them from the master structure to eliminate the effect of K-type struts, is proposed and discussed. It is concluded that the proposed method of staircase isolation is effective and feasible for engineering design, and does not significantly increase the construction cost.

An Assembly Coastal Building Technique in Port Engineering

The assembly coastal building technique initiated at home and abroad,is for a novel vertical standing harbor structure.Its main concept is the assembling components which can be combined and locked together to form a large caisson.Its application and future are discussed for a building.After many years of application and tests,the technique has a high stability,a wide range of application,low workload and fast construction speed.It can be widely applied in future for harbor engineering projects.

Research on stretching flame correction technology of aluminum alloy ship frame skin welding structure

At present,conventional flame correction has shortcomings such as random heating route and low efficiency.The welding seam of the aluminum alloy ship frame skin structure is concentrated and the frame restraint is large.It is difficult to control and eliminate the local convex deformation after welding.In order to improve the conventional orthopedic technology and improve the orthopedic efficiency,the pre-elastic deformation technology is proposed.Using the method of combining numerical simulation and experiment,the orthopedic effect of conventional and pre-elastic orthopedic technology is studied,and the influence of pre-deformation variables and heating path on deformation control of the frame skin structure after welding is simulated.The simulation results show that the technical key to the control of convex deformation lies in the control of the pre-elastic deformation and the setting of the heating route.The experimental verification results show that the pre-elastic deformation technology has a better control effect than conventional orthopedics,can significantly improve the orthopedic efficiency,and provides a new method for deformation control in the shipbuilding industry.

METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE

The optimality criteria （OC） method and mathematical programming （MP） were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.