Section Stiffness Research Articles

Nonlinear deformation analysis for precast pre-stressed concrete beam systems

The structural systems such as road bridge beam systems (span superstructure) or beam systems used in high-rise buildings with precast pre-stressed reinforced concrete might be subjected to the load higher than the calculated load of the design process. In the process of operation the internal forces of the beams reach to a certain value, the section stiffness in elements will be changed. The change in section stiffness will lead to redistribution of internal forces in the whole system. However, that has not been included in the design process. The paper presents nonlinear deformation analysis of precast pre-stressed beam system used in road bridge span superstructure or high-rise buildings using nonlinear model of materials according to Russian construction codes to build the relationship between internal forces and section stiffness. From the calculation results, some comments will be recommended about increased load capacity in comparison with the results obtained from analysis using linear model of material.

Analysis of Torsional Stiffness of the Frame of a Formula Student Vehicle

This paper presents an analysis of the torsional stiffness of the frame of the Formula TU Ostrava team vehicle Vector 04. The first part introduces the Formula SAE project and the importance of torsional stiffness in frame structures. The paper continues with a description of the testing method used to determine torsional stiffness and an explanation of the experimental testing procedure. The testing method consists of attaching the frame with suspension to two beams. A force is applied to one of the beams, causing a torsional load on the frame. From displacements of certain nodes of the frame, overall and sectional torsion stiffness is then determined. Based on the experiment, an FEM simulation model was created and refined. Simplifications to the simulation model are discussed, and boundary conditions are applied to allow the results to be compared with the experiment for verification and the simulation to be tuned. The results of the simulation and experiment are compared and com-pared with the roll stiffness of suspension. The final part of the paper presents a conclusion section where the results are discussed.

Adjoint method for the sensitivity analysis of composite beam cross-sections

The structural components found in mechanical and aerospace engineering applications are often idealized as beams. The sectional stiffness and mass properties of beams made of homogeneous materials and presenting simple geometric shapes are evaluated easily. Axial and bending stiffness constants can be evaluated through simple formulas, whereas the computation of torsional stiffness is more cumbersome. In many aerospace and mechanical applications, wings and rotor blades present complex geometric shapes and are made of advanced, highly anisotropic composite materials. In such cases, the computation of the sectional stiffness properties is a complex task that requires the use of finite element models of the cross-section. The gradient-based optimization of these complex systems requires the evaluation of design sensitivities, which, in turn, calls for the evaluation of the sensitivity of sectional properties with respect to the parameters that define the configuration of the section. This paper presents an approach to this problem based on the adjoint method. Adjoint equations that enable the efficient computation of sensitivity derivatives of sectional stiffness properties with respect to composite design parameters are derived. Examples of cross-sections presenting various configurations and made of advanced composite materials are investigated. Real- and complex-step numerical differentiation methods are used to verify the proposed adjoint formulation.

Light-gauge frame construction: numerical analysis and research

The paper considers the frame construction behaviour numerical analysis of 18 meters bay from steel thin-walled profiles on the calculation results basis of a finite-element frame model made in ANSYS. Rated, equivalent, and tangential stresses values of frame construction on various parts were received during the work. The high efficiency of the wall stiffness intermediate element and section stiffness boundary elements can significantly increase the local resistance elements of thin-walled profile. The possibility of elements strain under the action of the design load is revealed as a calculation result of the finite-element model and taking into account bolted connections in a frame construction joints. The paper contains frame construction overall stability analysis at the decisions of bracing system. The frame construction field tests of 18 m bay from steel thin-walled profiles as a part of three frames block are carried out. As a result, the frame overall stability at the accepted bracing system and local stability of steel thin-walled profiles is provided; the rigidity of a design meets the regulatory requirements.

Constraint forces from imposed deformations

In statically indeterminate systems, imposed deformation generally cannot set freely. In order to achieve the deformation compatibility, constraint forces are required. From this, it can be deduced that the constraint forces for a given deformation are dependent on the stiffness of the system. The greater the stiffness, the greater the internal constraint forces. For this reason, constraint forces in reinforced concrete structures are generally worth mentioning and must be taken into account in the design. The accurate development of a constraint force depends on numerous factors. These are mainly the stiffness distribution over the length, stiffness of the cross section, ductility of the reinforcement and creep ability of concrete. To gain more information about the real behavior, experiments were carried out on reinforced concrete beams and prestressed beams.

Design and behavior of super-long span cable-stayed bridge with CFRP cables and UHPC members

This paper proposes a cable-stayed bridge with carbon fiber-reinforced polymer (CFRP) cables and ultra-high performance concrete (UHPC) members and presents its design and structural behavior to analyze its feasibility with a super-long span. Based on the geometrical dimensions of a real cable-stayed bridge with a steel girder and cables in addition to a normal concrete (NC) pylon and main-span of 1088 m, a new counterpart cable-stayed bridge using CFRP cables and a UHPC girder and pylon was designed. The dimensions of the UHPC girder were quantified by the section stiffness, punching resistance, local stability, and shearing resistance. The cross-section sizes of the CFRP cables were determined by the principle of equivalent strength. The geometric and physical conditions of the UHPC pylon satisfied the principle of similarity theory. Using the finite element method, a comparative analysis of the mechanical behavior of two cable-stayed bridge schemes was conducted, specifically regarding the static behavior, global stability, aerostatic stability, dynamic mode, and seismic performance. The results indicated that the detailed design and superior performance of the CFRP and UHPC made it practical to form a highly efficient and durable concrete cable-stayed bridge system with CFRP cables and UHPC members. Moreover, these properties could enlarge the main-span of a concrete cable-stayed bridge to approximately 1000 m.

Analytical solution for longitudinal bending stiffness of shield tunnels

The longitudinal bending stiffness of tunnels is one of the most important parameters for the structural design of the tunnel longitudinal deformations during seismic loading. The aim of the paper is to derive an analytical solution for the longitudinal bending stiffness of a segmental liner, typically used on tunnels built with a shield. For the derivation, it is assumed that the tunnel liner includes bolts, segments and rubber gaskets. All the elements are considered as linear elastic. The bolts are assumed to work only in tension and the rubber gaskets are assumed to work only in compression. The deformation of any tunnel cross section complies with the assumption that normals to the neutral axis remain normal and thus the neutral axis does not change along the tunnel during deflection. Based on these assumptions, a longitudinal equivalent model for shield tunnels is developed and the governing equations are obtained. A closed-form analytical solution for the longitudinal bending stiffness is developed and verified by providing comparisons between its results and those from the Finite Element program ABAQUS. A parametric analysis, using the new analytical solution, is included to investigate the influence of key parameters such as the thickness of the rubber gaskets, the ratio of the liner thickness to the internal tunnel diameter, and the transverse bending stiffness of the tunnel cross section on the longitudinal bending stiffness of the tunnel.

Oval cylindrical shells under asymmetric bending: a singular-perturbation solution

A singular asymptotic limit of the bifurcation instability experienced by short oval cylindrical shells under asymmetric pure bending is explored both analytically and numerically. Of primary interest here is the interplay between the variable geometrical stiffness of the cross section and the arbitrary orientation of the applied bending moments. By using boundary layer arguments, it is shown that the localised cross-sectional eigen-deformations are concentrated around a point determined by the solution of a simple trigonometric equation. The non-symmetric shape of the eigenmodes is also captured by a reduced fourth-order ordinary differential equation, which represents a generalisation of an earlier form found previously for the case of circular cylindrical shells under the same type of loading.

Compressive buckling analysis of orthotropic composite plates restrained by stringers

Closed section stiffeners have much larger rotational stiffness than open section stiffeners and contribute significantly to the panels’ buckling strength. The buckling analysis formulae developed for open-section stringer-reinforced panels underestimate the buckling strength of closed-section stringer-stiffened panels, such as composite fuselage panels stiffened by hat-shaped stringers. This study proposes a unified approach for compressive buckling analysis of stiffened composite plates, which takes into account the contribution of stringers’ rotational stiffness, and achieves a closed-form solution.

Hybrid model for determining the stiffness of a spatial rod with consideration geometric nonlinearity

The mathematical model for elastoplastic calculation of spatial rod is considered with taking into account shear deformation. It is supposed to use this model in hybrid method of finite elements for determination of elastoplastic deformation in rod systems with geometric nonlinearity. In this case the rod stiffness matrix will be determined by force method or by functions of element’s form using the matrix of tangent stiffness of cross section. This matrix counts the stress state in each elementary area of cross section given the shear. The hybrid approach allows to eliminate the finite elements along the rod length and replace them with integration sites. The calculation algorithm of elastoplastic deformation for a spatial rod is provided considering the geometric nonlinearity. The proposed nonlinear model can be used in finite element method in form of displacement and force methods to elaborate a special mechanism for building a system of resolving equations. The results are compared based on the example of spatial console rod calculation.

Effect of pitting degradation on ductile fracture initiation of steel butt-welded joints

Monotonic tensile experiments and corresponding finite element (FE) analyses including a ductile fracture damage criterion have been conducted to investigate the ductility degradation behaviours of steel butt-welded joints with corrosion pits. The results showed that the ultimate elongation of welded joint samples rapidly decreased because the existence of pits led to the earlier initiation of ductile cracks after necking. Pit location was the main factor affecting ductility degradation, pits located in the weakest region of sectional stiffness were the biggest threat to the overall deformability of welded joints. In addition, both pit depth and aspect ratio had a significant effect on local ductile crack initiation and propagation, the local stress triaxiality and plastic strain accumulation increased steadily with the increase of pit size, resulting in the decrease of equivalent plastic fracture strain. Furthermore, based on the parametric numerical analyses, equivalent ductile fracture criterion considering pitting parameters was proposed to replicate the effects of actual pits on ductility degradation.

Field assessment of a Cold-In place-recycled pavement: Influence on rolling noise

Abstract This work aims to study some surface characteristics (tire/pavement noise, texture, roughness and dynamic stiffness) of an experimental test track section fabricated with Cold-In place-Recycled (CIR) pavement. The field assessment of the experimental section was carried out after two months curing, and prior to being overlaid with a hot bituminous mixture. CIR pavement may be a good paving solution in some cases. These mixtures present some characteristics that make them environmentally friendly mixes regarding conventional hot bituminous mixtures, such as their lower temperature of fabrication (low greenhouse gas emissions and fuel consumption) and the use of recycled materials from the same pavement to be rehabilitated. According to the research results, CIR pavement could be presented as a reduced noise surface regarding other conventional hot bituminous mixtures. Dynamic stiffness and macrotexture of this studied section mitigate noise at medium frequencies of the tire/pavement noise spectrum, which are the main frequencies of the overall tire/pavement noise levels. Tire/pavement noise generation mechanisms in CIR pavements are discussed according to the achieved results.

On the nonlinear extension-twist coupling of beams

Abstract In many applications, beams carry large axial forces, such as centrifugal forces, for instance, and the resulting axial stresses affect their torsional behavior. To capture this important coupling effect within the framework of beam models, a nonlinear theory must be developed that takes into account higher-order strain deformations. The proposed development starts with a three-dimensional elasticity model of beam-like structures. While strain components are assumed to remain small, the strain energy expression is expanded to retain strain components up to cubic order. This expansion of the three-dimensional model leads to material and geometric stiffness matrices. For linear problems, the three-dimensional warping fields induced by each of the six unit sectional strain components can be obtained. These warping fields are used to reduce the three-dimensional elasticity model to one-dimensional beam equations. Byproducts of this reduction process include the sectional stiffness matrix and six nonlinear stiffness matrices representing the geometric stiffness induced by unit sectional strains. It is shown that the nonlinear extension-twist coupling is captured by these geometric stiffness matrices. Comparison of the predictions of the proposed approach with analytical and experimental results demonstrate their effectiveness and accuracy.

The effective stiffness of modern unreinforced masonry walls

SummaryCode design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness of URM walls. Eurocode estimates the effective stiffness as 50% of the gross sectional elastic stiffness, but comparisons with experimental results have shown that this may not yield accurate predictions. In this paper, 79 shear‐compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective‐to‐initial stiffness ratios are approximately 75% rather than the stipulated 50%. An empirical relationship that estimates the E‐modulus as a function of the axial load and the masonry compressive strength is proposed, yielding better estimates of the elastic modulus than the provision in Eurocode 6, which calculates the E‐modulus as a multiple of the compressive strength. For computing the ratio of the effective to initial stiffness, a mechanics‐based formulation is built on a recently developed analytical model for the force‐displacement response of URM walls. The model attributes the loss in stiffness to diagonal cracking and brick crushing, both of which are taken into account using mechanical considerations. The obtained results of the effective‐to‐initial stiffness ratio agree well with the test data. A sensitivity analysis using the validated model shows that the ratio of effective‐to‐initial stiffness is for most axial load ratios and wall geometries around 75%. Therefore, a modification of the fixed ratio of effective‐to‐initial stiffness from 50% to 75% is suggested.

Calculation on the flexural stiffness of the section of PC hollow slab beam in the life cycle

PurposeDuring service period, due to the overload or other non-load factors, cracks of the pre-stressed concrete beam are seriously affecting the safety of the bridge structure. The purpose of this paper is to quickly realize the bearing capacity and the loss of the section stiffness through fracture characteristics and make correct judgments.Design/methodology/approachThrough the flexural failure test of two test beams: collecting data of fracture characteristics and section stiffness loss value. According to the fracture characteristic data, the flexural stiffness of the section is obtained by the nonlinear calculation method, and the results are verified by test data. Data regression method is used to establish the section flexural stiffness loss ratio calculation formula, nominal tensile strain at the bottom edge of the cross-section used as a variable factor, and the accuracy of this formula is verified by comparing the flexural failure test results of pre-stressed hollow plates.FindingsThe loss of the flexural stiffness of section shows the decrease trend of first-fast-then-slow and the structural stiffness is sensitive to the initial cracking of beam. The calculation formula on the loss ratio of the flexural stiffness of section established with the nominal tensile stress at the bottom edge of beam as a variable is accurate and feasible, it realizes the possibility of assessing the stiffness loss of pre-stressed concrete structure by adopting the statistic parameters on crack characteristics.Originality/valueA method for quickly determine the stiffness loss of structures by using fracture characteristics is established, and using this method, engineers can quickly determine whether a bridge is a dangerous bridge, without loading test. So, this method not only ensures the safety of human life, but also saves money.

Simplified and Accurate Stiffness of a Prismatic Anisotropic Thin-Walled Box

Background:Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.Objective:A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.Methods:Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.Results:Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.Conclusion:For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

Flange local buckling of pultruded GFRP box beams

An experimental program investigating the flange local buckling (FLB) behavior of pGFRP box-sections is reported. The commonly accepted design equation based on plate theory was validated although importance of accurate assessment of the rotational stiffness of the web-flange junctions was identified. It is concluded that the lower bound solution, assuming the flange is a simply-supported plate subject to uniform compressive stress, results in uniformly conservative predictions of the critical FLB moments. The theoretical solution accounting for flange plate edge support stiffness based only on web stiffness, material and geometric properties of the cross section over predicts the support stiffness resulting in unconservative predictions of FLB behavior. The rotational stiffness of flange-web junction of the pGFRP box-section is also investigated experimentally. It is found that the actual rotational stiffness of flange-web junction is relatively low, closer to the simply-supported boundary condition. The role of fiber architecture at the web-flange junction is identified as affecting this behavior. The conclusions of this study support the use of the lower bound solution for design of pGFRP box-sections.

Interaction of a Circular Cylindrical Shell with an Elastic Foundation

The problem of static analysis of a circular cylindrical shell, which is located on elastic Winkler foundation and reinforced by the longitudinal edges are considered. There is rib stiffness of rectangular cross section. Exposure is represented evenly distributed along the longitudinal axis forces. The forces acting on the edges of the rigidity of the upper structure. Agreed that the ends of the envelope is flat, vertical walls, giving the contour of the absolute rigidity in the transverse direction and does not prevent the longitudinal displacement of points of the envelope. To solve the problem, the total moment theory of circular cylindrical shell was used. To implement the proposed algorithm is the calculation of computer program. With the help of the program is executed a number of examples of calculation. In these examples, analyze the impact of stress on the shell of such factors as the relative length and thickness, angle mortar shell, the value of the relative rigidity of airborne elements and other.

Hysteretic Behaviour of Stockbridge Dampers: Modelling and Parameter Identification

Stockbridge dampers are widely used to mitigate the vortex-induced vibrations of overhead electrical line conductors and of many other cable or cable-like structures exposed to the action of wind. Aim of this work is to develop a simple, but accurate, mechanical model of a Stockbridge damper to use in the assessment of such structures vibrations. The model is based on a beam-like description of the messenger cable and on a nonlinear formulation of the cross sections cyclic bending behaviour. At the cross-sectional level, the mechanical behaviour of the messenger cable is reproduced with the classic Bouc-Wen hysteretic model, which has been recognized as adequate to represent the local behaviour mainly controlled by interwire sliding processes. The Bouc-Wen model parameters are identified from experimental results available in literature and used at the local (cross-sectional) level to characterize the mechanical behaviour of the messenger cable. The descending global behaviour of the Stockbridge damper compares very favourably with the experimental results in terms of the impedance function at the clamp and allows for the confident use of the proposed model inside the assessing process of full power lines. The important role of the end zones of the messenger cable is highlighted. In these zones, a boundary layer like transition is found to occur for the bending stiffness of the messenger cable cross section. This largely affects the global behaviour of the Stockbridge damper. The length of these zones complements the model parameters.

Shear model with shear-flexure interaction for non-linear analysis of reinforced concrete frame element

This paper presents the shear constitutive model for the reinforced concrete (R/C) frame structures analysis under monotonic and cyclic loading. The proposed model is adopted and modified from Mergos and Koppos model [1] that accounts the shear stiffness degradation effect by the shear-flexure interaction in the plastic hinge region. Firstly, the proposed shear model starts from the primary curve without the damages due to the shear-flexure interaction effect. Then, the shear-flexure interaction effect is taken into consideration at the locations of plastic hinges and this effect leads to the degradation of the shear strength and shear stiffness on the undamaged primary curve that is replaced with the damaged primary curve. To determine the sectional shear stiffness with the shear-flexure interaction, an alternative way of the iterative procedure is proposed here. Finally, a numerical example is used to verify the characteristics and behavior of the R/C frame system and confirm accuracy and computational efficiency of the proposed model among the experimental data.