Space Frame Element Research Articles

Design of scaled down model of a tower crane mast by using similitude theory

In this study, a tower crane mast which is very sensitive to the dynamic effects that will occur due to its delicate structure was scaled by similitude theory for the purpose of using in experimental studies. The variables that describe the structure in terms of dynamic were determined and pi groups were created by using the Buckingham Pi Theorem. A finite element model that is able to calculate the natural frequencies, mass participation factors, and draw the mode shapes of a structure composed of space frame elements was developed. The mast was scaled down to use in the laboratory environment with two different scale factors as 30 and 40. The most suitable model which represents the dynamic behavior of the real-size tower crane mast for the experimental studies was determined by comparing the modal analysis results of the real-size and scale models.

Boundary-integral-based process for calculating stiffness matrices of space frame elements with axially varying cross section

This paper presents a strategy to directly compute the stiffness matrix of 3D (space) frame elements having arbitrary cross sections and generic rigidity variation along their axes. All the necessary section properties are determined by means of formulations based purely on boundary integrals. To determine the torsional constant and the torsion center, this strategy applies the Boundary Element Method (BEM). To model thin-walled cross-sections, the strategy calls for activating integration algorithms devised specifically to deal with the nearly singular integrals involved. To express all other section properties (i.e. area, first and second moments of area, and the shear form factors) in terms of boundary integrals, the strategy employs Green's theorem. The existing boundary-element meshes, used to determine the torsion constants, are employed to evaluate the corresponding boundary integrals. In applying the proposed strategy – the pure boundary-integral-based process (PBIP) – we consider space frame elements with geometrically complex cross-sections varying along their axes.

WITHDRAWN: Boundary-integral-based process for calculating stiffness matrices of space frame elements with axially varying cross section

Abstract This paper presents a strategy to directly compute the stiffness matrix of 3D (space) frame elements having arbitrary cross sections and generic rigidity variation along their axes. All the necessary section properties are determined by means of formulations based purely on boundary integrals. To determine the torsional constant and the torsion center, this strategy applies the Boundary Element Method (BEM). To model thin-walled cross-sections, the strategy calls for activating integration algorithms devised specifically to deal with the nearly singular integrals involved. To express all other section properties (i.e. area, first and second moments of area, and the shear form factors) in terms of boundary integrals, the strategy employs Green's theorem. The existing boundary-element meshes, used to determine the torsion constants, are employed to evaluate the corresponding boundary integrals. In applying the proposed strategy – the pure boundary-integral-based process (PBIP) – we consider space frame elements with geometrically complex cross-sections varying along their axes.

Multiscale Modeling of Dynamic Characteristics of Carbon Nanotube Reinforced Nanocomposites

A unique atomic structure of carbon nanotube unveils outstanding properties. This makes it potentially highly valued reinforcing material to strengthen composite materials. The methodology is established in this research paper to investigate the static and dynamic characteristics of the nanocomposites. Repol polypropylene H110MA is used as a matrix material along with the different percentages of single-walled carbon nanotubes (SWCNTs). A concept of representative volume element (RVE) is considered to study the various properties of the nanocomposite material. The carbon–carbon bond of nanotube is modeled using Tersoff–Brenner potential and represented by space frame element. The matrix material properties are tested in the laboratory which are further used to model it and represented by three-dimensional continuum elements. The interaction between nanotube and polymer matrix is modeled using “Lennard–Jones 6-12” potential represented by nonlinear spring elements. The effect of reinforcement, chirality, % volume of SWCNT, atomic vacancy defect and Stone–Wales defect on the properties of nanocomposite are investigated. To see the effect of reinforcement, the eigenvalues of the RVE are extracted for different boundary conditions. The viscoplastic behavior of the matrix material is considered and the rate-dependent characteristics of the nanocomposite are studied. The damping property of the nanocomposite material is also investigated based on the phase lag between stress and strain field by applying harmonic strain at different frequencies.

Vibration characteristics of open- and capped-end single-walled carbon nanotubes using multi-scale analysis technique incorporating Tersoff–Brenner potential

This research work addresses questions on the vibration characteristics of single-walled carbon nanotubes (SWCNTs) using multi-scale analysis. Atomistic finite element method (AFEM) is one such multi-scale technique where sequential mode is used to transfer information between two length scales to model and simulate the nanostructures at continuum level. This method is used to investigate the vibration characteristics of SWCNTs. Open- and capped-end armchair and zigzag nanotubes are considered with clamped-free and clamped–clamped boundary conditions. The dependence of vibration characteristic of SWCNTs on their length, diameter and atomic structure is also demonstrated. The body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two carbon atoms. Based on the TB potential, a new set of force constant parameters is established for carbon nanotubes and presented in this paper. Molecular and structural mechanics analogy is used to find the equivalent geometric and elastic properties of the space frame element to represent the carbon–carbon bond. To validate the vibration results of AFEM incorporating the proposed new set of force constants, molecular dynamics simulation is also carried out on the same structure of carbon nanotube, and it is found that they are in good agreement with each other.

Vibration analysis of single-walled carbon nanocones using multiscale atomistic finite element method incorporating Tersoff–Brenner potential

This research work addresses the free and forced vibration characteristics of single-walled carbon nanocones (SWCNCs) using multiscale atomistic finite element method (AFEM) incorporating Tersoff–Brenner (TB) potential. The multibody interatomic TB potential is used to represent the energy between two carbon atoms. Based on the TB potential, new set of force constant parameters is established for carbon nanocones, and the equivalent geometric and elastic properties of the space frame element to represent carbon–carbon bond are derived which are consistent with the material constitutive relations. The eigenvalues of clamped and cantilevered SWCNCs with different disclination angles are extracted using AFEM, and the effect of these angles on the resonant frequencies is investigated. A computational sine sweep test is carried out on the atomic structure of SWCNCs within the frequency range of 0–10 THz to investigate the steady-state forced vibration response under harmonic excitation. The frequency response of the SWCNCs to the cyclic and impulse load over an applied frequency range is calculated. Based on the forced vibration response spectra, the resonant frequency components of SWCNCs are identified. The results have been validated using molecular dynamics simulation.

Multiscale Analysis Approach to Find the Dynamic Characteristics of Graphene Sheet

The research work addresses question on dynamic characteristic of structure which exhibit periodicity at nanoscale viz. single layer graphene sheet using multiscale analysis approach. The carbon-carbon bond of graphene sheet is modeled as space frame element whereas the carbon atom is modeled as 3D-mass element without rotary inertia. Molecular structural mechanics (MSM) model has been used to find the equivalent geometric and elastic properties of space frame element to represent carbon-carbon bond. In molecular structural mechanics model, force field is expressed in the form of steric potential energy by omitting the electrostatic interaction. Sectional stiffness parameters are linked with the force field constants to derive the equivalent elastic and geometric properties of space frame element. This approach is used here to investigate the dynamic behavior of single layer graphene sheet. Simulations have been carried out with different values of aspect ratio to know the effect of variation in length and width on the natural frequencies of graphene structure. Molecular dynamic simulation has also been carried out on the same structure of graphene sheet to validate the results of proposed molecular structural mechanics model.

Improved methods for determining the 3 dimensional initial shapes of cable-supported bridges

The TCUD method (Kim and Lee, 2001) can minimize undesirable lateral displacements in cable bridge structures by including the unstrained lengths of the cable members as unknowns and introducing additional constraint conditions. The axial deformations in the girder and the main tower deviating from the target configuration are, however, unavoidable when self-anchored cable bridges are considered. On the other hand, the IFM (initial force method) can be used to adjust the axial deformations to conform to the initial shape but it is critical that the unstrained lengths of the cables are accurately evaluated. In this study, improved schemes for the TCUD method and the IFM for finding the initial shape of 3 dimensional cable-supported bridges under dead load, are presented. For this purpose, the TCUD method and the initial force method are firstly reviewed. Two improved algorithms, which can overcome shortcomings of the previous initial-shaping analysis methods, are developed based on an elastic catenary cable element and a nonlinear space frame element. Finally, the accuracy and effectiveness of the proposed analysis algorithms are demonstrated through the numerical application to 3 dimensional initial shape problems for self-anchored suspension and cable-stayed bridges.

Response Characteristic of Cable Stayed Bridges under Static Loading and Due to the Earthquakes in Longitudinal Direction

This paper presents the dynamic (earthquake response) analysis of cable stayed bridges under different types of static loading and due to longitudinal directions of earthquake base excitations. The deck and the tower of the bridge were idealized by discrete element idealization scheme (space frame element) with warping considered as a seventh degree of freedom. For comparison purposes, the discrete element with six degrees of freedom (warping neglected) were also used to model the structure under investigation. The cables were modelled by the nonlinear truss elements. It was found that the warping becomes of significant influence on the behaviour of the bridge deck only if the deck is acted upon by loading that is coupled with initial torsional moment.

Considerations for the design of doubly unsymmetrical precast pretensioned beams used for box girder construction

AbstractMany box girder bridges are constructed with doubly unsymmetrical precast beam units. The aim of this paper is to present special considerations for the optimum arrangement of pretensioned strands in a simply supported precast pretensioned beam with a doubly unsymmetrical section. The goal of the optimum arrangement is to minimize the distortion (lateral sway phenomenon) caused by the doubly unsymmetrical characteristic of the beam section at transfer. The study shows that the distortion of the unsymmetrical section is minimized when the resultant stresses at transfer are constant over all of the top flange and over all of the bottom flange of the precast beam for most of the sections within the beam length. In this case, the neutral axes of these sections will be horizontal with respect to the beam section. This approach is verified with the help of two different finite element models. In the first model, the beam is modelled as one‐dimensional space frame elements; in the second model, the beam is modelled using three‐dimensional solid elements. A practical example of a box girder bridge made from doubly unsymmetrical precast pretensioned beams in the APM (Automated People Mover) elevated bridge project in Saudi Arabia is also presented.

Inelastic second order analysis of steel frame elements flexed about minor axis

Frame elements may be subjected to significant bending moments about cross-sectional minor axis such as space frame elements and struts that buckle about minor axes. In some cases such as columns with compound cross-sections, the major bending moment acts about minor axes of cross-sectional components. The present paper proposes a simplified model for predicting the second order inelastic behavior of steel frame elements under axial compression force and bending moment about minor axis. New formulae are proposed to describe the plastic strength surface for steel I- and H-shaped cross-sections under axial force and bending moment about minor axis. Moreover, empirical formulae are developed to predict the tangent modulus for those cross-sections. The tangent modulus formulae are extended to evaluate the secant stiffness that is used for internal force recovery. The formulae are derived for steel sections considering the residual stresses as recommended by the European Convention for Construction Steelwork (ECCS). A finite element program is prepared to predict the inelastic second order behavior of plane frames using the derived formulae. The derived model exhibits good correlations when compared with the fiber model results. The analysis results indicate that the new model is accurate, furthermore it saves a lot of calculation time that may be consumed by iterations on the cross-sectional level.

원추형 코일스프링의 강성해석

Springs are widely utilized in machine element. To find out stiffness of frustum-shaped coil spring, the space beam theory using the finite element method is adopted in this paper. In three dimensional space, a space frame element is a straight bar of uniform cross section which is capable of resisting axial forces, bending moments about two principal axes in the plane of its cross section and twisting moment about its centroidal axis. The corresponding displacement degrees of freedom are twelve. To find out load vector of coil spring subjected to distributed compression, principle of virtual work is adapted. And this theory was programming using MATLAB software.<BR> To compare FEM using MATLAB software was applied MSC.Nastran software. The geometry model for MSC.Patran was produced by 3-D design modeling software. Finite element model was produced by MSC.Patran. Finite element was applied tetra (CTETRA) having 10 node.<BR> The analysis results of the MATLAB and MSC.Nastran are fairly well agreed with those of various experiments. Using MATLAB program proposed in this paper and MSC.Nastran, spring constants and stresses can be predicted by input of few factors.

AASHTO-LRFD Live Load Distribution for Beam-and-Slab Bridges: Limitations and Applicability

This paper presents a comparison between the live load distribution factors of simple span slab-on-girders concrete bridges based on the current AASHTO-LRFD and finite-element analysis. In this comparison, the range of applicability limits specified by the current AASHTO-LRFD is fully covered and investigated in terms of span length, slab thickness, girder spacing and longitudinal stiffness. All the AASHTO-PCI concrete girders (Types I–VI) are considered to cover the complete range of longitudinal stiffness specified in the AASHTO-LRFD. Several finite-elements linear elastic models were investigated to obtain the most accurate method to represent the bridge superstructure. The bridge deck was modeled as four-node quadrilateral shell elements, whereas the girders were modeled using two-node space frame elements. The live load used in the analysis is the vehicular load plus the standard lane load as specified by AASHTO-LRFD. The live load is positioned at the longitudinal location that produced the extreme ...

An improved formulation of space stiffeners

This paper presents a displacement based finite element model for predicting the constraint torsion effect of stiffeners. In structural modelling, the plate/shell and the stiffeners are treated as separate elements where the displacement compatibility transformation between these two types of elements takes into account the constraint torsional warping effect in the stiffeners. The development is based on a general beam theory which includes flexural-torsion coupling, constrained torsion warping, and shear-centre location. The virtual work principle includes the second order terms of finite beam rotations. For finite element analysis, cubic Hermitian polynomials are used as shape functions of the straight space frame element with two nodes. Elastic stiffness and geometric stiffness matrices for an arbitrary cross-section are evaluated in a closed form, and load correction stiffness for eccentric stiffener loads are considered. To demonstrate the importance of torsion warping constraints and to illustrate the accuracy of this formulation, finite element solutions are presented and compared with available solutions.

이산폰툰형 부유식교량의 지진응답해석

이산폰툰형 부유식교량의 시간영역 지진응답해석을 지진파의 공간분포를 고려하여 수행하였다. 지반운동의 공간변화는 파의 통과 영향, 엇결성 뎡향 및 국부지반 영향을 반영하는 결맞음 함수 모델로 고려하였다. 부유식 교량의 상부구조는 공간뼈대요소와 탄성현수케이블요소를 이용하여 모델링 하였고, FHWA 가이드라인의 스프링 모델을 사용하여 교대의 지반 구조물 상호작용에 대한 영향을 고려하엿으며, 경계요소법으로 산정한 폰툰 동수력계수의 주파수 의종성을 고려하기 위해서 시간지연함수를 사용하였다. 지반운동의 공간변화를 고려한 다중지점 지진입력을 교량의 양단에 도입하였고 응답의 시간이력을 동시 가진 시와 비교하였다. 장주기의 동적특성을 갖는 이산폰툰형 부유식 교량의 지진응답 해석에서 지반운동의 공간분포를 고려할 경우에 주몰할만한 응답의 증폭이 나타날 수 있음을 확인하였다. Dynamic response analysis in time dimain is conducted for floating bridges with discrete pontoons subject to spatial variation of ground motions. The Spatial variation of ground motions is considered with the coherency function model which represents wave passage, incoherence and local site effects. The superstructure of the bridge is represented by space frame and elastic catenary cable elements, the abutment us modelde with the spring element of FHWA guideline for considering soil structure interaction and the concept of retardation function is utilized to consider the frequency dependency of the hydrodynamic coefficients which are obtainde by boundary element method. multiple support excitations considering the spatial variation. The noticeable amplification of the response can be shown when the spatial variation of ground motions is incorporated in the anallysis of floating bridges.

Derivation of the higher-order stiffness matrix of a space frame element

A physical concept, the rigid body rule, is applied for the derivation of the higher-order stiffness matrix of a space frame element. The derivation has a physical meaning that is the higher-order stiffness matrix can be derived by regarding that there is a set of incremental nodal forces existing on the element, then the element undergoes a small rigid body rotation. The incremental forces should keep their magnitude and follow the rigid body motions. Then taking advantage of the established geometric stiffness matrix derived by former researchers, the higher-order stiffness matrix can be analogy derived in explicit forms without any difficulty. It can be used at the forces recovery stage in the geometric nonlinear analysis of frame structures. Meanwhile an effective numerical method, the generalized displacement control method, was adopted to trace the load–deflection curves of structures. Some famous numerical examples were tested by the element which included the proposed higher-order stiffness matrix in tangential stiffness matrix.

Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. I: Theoretical Considerations Based on Semitangential Property

To present the spatial postbuckling analysis procedures of shear deformable thin-walled space frames with nonsymmetric cross sections, theoretical considerations based on the semitangential rotation and the semitangential moment are presented. First, similarity and difference between Rodriguez' rotations and semitangential rotations are addressed. Next, the improved displacement field is introduced using the second-order terms of semitangential rotations and rotational properties of off-axis loads and conservative moments are discussed based on the proposed displacement field. Finally, it is deduced that the resulting potential energy due to stress resultants corresponds to semitangential bending and torsional moments. In a companion paper, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is newly derived and a clearly consistent finite-element procedure is presented based on the updated Lagrangian corotational formulation. Tangent stiffness matrices of the thin-walled space frame element are derived using Hermitian polynomials considering shear deformation effects, and a new scheme to evaluate incremental member forces and load correction stiffness matrices due to off-axis loads is presented and its physical meaning is addressed. Furthermore, finite-element solutions displaying spatial postbuckling behaviors are evaluated and compared with available solutions.

Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frames

A consistent finite element formulation is presented for the free vibration and spatial stability analysis of thin-walled tapered beams and space frames. The kinetic and potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential rotation and moment is obtained, in which the elastic strain energy terms are coupled due to axial–flexural–torsional coupling effects but the potential energy due to initial stress resultants has a relatively simple expression. For finite element analysis, cubic polynomials are utilized as the shape functions of the two-noded Hermitian space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled cross-section are precisely evaluated, and load-correction stiffness matrices for off-axis concentrated and distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and lateral–torsional buckling problems of thin-walled tapered beam-columns and space frames are presented and compared with available solutions.

Nonlinear analysis of 3D seismic interaction of soil–pile–structure systems and application

To investigate more precisely the seismic response of interactive soil–pile–structure systems, a three-dimensional finite element subsystem methodology with an advanced plasticity-based constitutive model for soils has been developed. The structure subsystem is represented by space frame elements while the pile–soil subsystem is idealized as an assemblage of solid elements. By means of the δ*-version of the hierarchical single surface (HiSS) modelling approach for cyclic behavior of soft clays, tangent matrices of the soil properties are formulated with distinct constitutive laws for individual stress–strain regimes such as virgin loading, unloading, and reloading. A successive-coupling, incremental solution scheme in the time domain is created to take account of both inertial and kinematic soil–pile–structure interactions simultaneously. The seismic inputs can be any combination of three-dimensional motions. The proposed methodology may be used to analyse the seismic responses of structures for different support excitations such as rigid ground motion, interactive pile-foundation motion, and, for long span structures, non-uniform free-field motion.

SPATIAL STABILITY ANALYSIS OF THIN-WALLED SPACE FRAMES

A clearly consistent finite element formulation for spatial stability analysis of thin-walled space frames is presented by applying linearized virtual work principle and introducing Vlasov's assumption. The improved displacement field for unsymmetric thin-walled cross-sections is introduced based on inclusion of second-order terms of finite rotations, and the potential energy corresponding to the semitangential moments is consistently derived. In the present formulation, displacement parameters of axial and bending deformations are defined at the centroid axis and parameters of lateral and torsional deformations at the shear centre axis, and all bending-torsional coupling effects due to unsymmetric cross-sections are taken into account. For finite element analysis, cubic Hermitian polynomials for the flexural beam with four types of end conditions are utilized as shape functions of Hermitian space frame element. Also, load correction stiffness matrices for off-axis point loadings are derived based on the second-order rotation terms. Finite element solutions for the spatial buckling analysis of thin-walled space frames are compared with available solutions and other researcher's results.