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    <title>Transport Research International Documentation (TRID)</title>
    <link>https://trid.trb.org/</link>
    <atom:link href="https://trid.trb.org/Record/RSS?s=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" rel="self" type="application/rss+xml" />
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    <language>en-us</language>
    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
    <docs>http://blogs.law.harvard.edu/tech/rss</docs>
    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
    <image>
      <title>Transport Research International Documentation (TRID)</title>
      <url>https://trid.trb.org/Images/PageHeader-wTitle.jpg</url>
      <link>https://trid.trb.org/</link>
    </image>
    <item>
      <title>Analytical Solution for In-Plane Displacement of Multi-Span Curved Bridge</title>
      <link>https://trid.trb.org/View/2283244</link>
      <description><![CDATA[Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. A real multi-span curved bridge subjected to concentrated loads caused by the friction force on the top of piers and thermo load due to temperature difference is analyzed by using the newly derived equations as well as FEM. The agreement further suggests the practicability of the proposed theory. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.]]></description>
      <pubDate>Thu, 17 Oct 2024 09:15:21 GMT</pubDate>
      <guid>https://trid.trb.org/View/2283244</guid>
    </item>
    <item>
      <title>Vibration of Straight and Curved Beam Coupled Systems</title>
      <link>https://trid.trb.org/View/1973293</link>
      <description><![CDATA[This paper presents an analytical method for in-plane and out-of-plane coupled vibration in thin curved panels which are commonly seen in the side structure of railway vehicle carbodies. To treat such coupled vibrations simply, a structure consist of combination of straight and curved beams is introduced. The analytical procedure to derive the equation of motion is described in this paper. Numerical result shows that the straight and curved beam coupled system (SCBS) can successfully express the coupling effect between roof-floor relative vertical displacement and side panel’s lateral deformation. The effect of lateral deformation of cantrail and side beam and curvature of the curved beams on the forced response are discussed.]]></description>
      <pubDate>Wed, 03 Jan 2024 09:13:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/1973293</guid>
    </item>
    <item>
      <title>Torsional behavior of curved concrete box beam with small radius</title>
      <link>https://trid.trb.org/View/2265788</link>
      <description><![CDATA[Curved concrete box beams are commonly used for their superior integrality performance and greater torsional stiffness. This paper investigates the torsional behavior of these beams using both experimental and finite element analyses. The experiment is based on a 1:6 scale model of a three-span curved girder bridge with a small radius. The study examines six different load cases, including central vertical and eccentric vertical loads. The study reports the detailed reaction forces of the supports, as well as the displacements and strains of the mid-span section. Finite element models are established to analyze the warping behavior of the curved concrete box beams. Based on the experimental and FEM analysis, the following conclusions are noted. Firstly, in the central load case, the strain of the curved concrete box girder is close to a straight line, so the curved concrete box girders follows the plane-section assumption. Besides, the warping normal stress is produced in curved concrete box girder in eccentric load cases. Moreover, the ratio of warping normal stress to bending normal stress is smaller and smoother in the section with diaphragms than that without diaphragms. And this ratio decreases with an increase in the curvature radius and diaphragm number. This study contributes to the theoretical and numerical modeling of a large span curved girder bridge with a small radius.]]></description>
      <pubDate>Mon, 23 Oct 2023 08:51:44 GMT</pubDate>
      <guid>https://trid.trb.org/View/2265788</guid>
    </item>
    <item>
      <title>Scanning the vertical and radial frequencies of curved bridges by a single-axle vehicle with two orthogonal degrees of freedom</title>
      <link>https://trid.trb.org/View/2138226</link>
      <description><![CDATA[This paper scans for the first time the vertical and radial (lateral) frequencies of a horizontal curved beam from the respective motions of a single-axle test vehicle by a theoretical approach. The vehicle is innovatively treated as a system with two orthogonal degrees of freedom (DOFs), each of a spring-dashpot unit, to capture both the vertical and lateral motions. To start, closed-form solutions are derived for the out-of-plane vibration (under the vertical and torsional contact forces) and in-plane vibration (under the centrifugal force) of the curved beam. Then the vertical and lateral motions of the vehicle are derived. Based on this, a generalized formula is derived for the corresponding contact responses. From the analyses using the generalized contact formula, it was demonstrated that: (1) the contact responses outperform the vehicle responses in that more higher bridge frequencies (out-of-plane and in-plane) can be identified; (2) the radius of curvature affects significantly the radial frequencies of the curved beam; (3) the eccentricity of the scanning vehicle has little effect on frequency identification; and (4) pavement roughness’ effect can be remedied by random traffic, and it does not appear in the radial contact response.]]></description>
      <pubDate>Wed, 29 Mar 2023 16:48:37 GMT</pubDate>
      <guid>https://trid.trb.org/View/2138226</guid>
    </item>
    <item>
      <title>A Finite Element Program for Elastic Straight and Curved Beams</title>
      <link>https://trid.trb.org/View/1810480</link>
      <description><![CDATA[The amount of structural problems that can be solved by the use of classical analytic concepts of Mechanical Engineering is limited, in most cases, to simple uniaxial structures. Any additional aspect, as excessive number of constrains or arc shaped structures, can increase the difficult to obtain the solution or even prevent at all. A numerical approach, as utilization of FEM (Finite Element Method), can make possible the solution of these structures. A finite element program for elastic straight and curved beams is developed to provide an alternative way to solve planar uniaxial structures problems. Statical Variational Formulation approach is used to build a FEM model. Routines are implemented using VB (Visual Basic), needed to make extensive calculations and to present the results in a professional way. A couple of examples are solved to make a quantitative comparison with analytic solutions.]]></description>
      <pubDate>Mon, 17 Oct 2022 13:38:58 GMT</pubDate>
      <guid>https://trid.trb.org/View/1810480</guid>
    </item>
    <item>
      <title>Topology optimization of horizontally curved box girder diaphragms</title>
      <link>https://trid.trb.org/View/1919486</link>
      <description><![CDATA[Curved girders are widely used in bridge construction to overcome geographical obstacles. In such cases, girders with a box cross-section are preferred due to their large flexural and torsional rigidity. Internal diaphragms are used to limit cross-section distortion and the distortional warping stress induced in the box girders. However, the use of such diaphragms hinders girder maintenance. To facilitate the maintenance process, typical cross frames such as X- or V-shape truss members are used. Alternatively, access holes are provided in the solid plate diaphragms. In this paper, finite element models for horizontally curved box girders were constructed and topology optimization method was used to obtain the optimal shapes for the internal and external diaphragms. In this analysis the optimization objective was set to reduce the diaphragm mass while maximizing its rigidity. The mass retained percentage was assigned to various values from 20% to 40%. The deformations and distortional stresses induced in the girders were compared between girders having solid plate diaphragms and girders with optimized cross-frame diaphragms. The parametric study included the cross-section aspect ratio and curved girder central angle as they have large effect on distortional warping stresses. The results showed that the increase in distortional warping normal stress was less than 4% and the increase in the cross-section distortion angle was less than 37% between optimized diaphragms and solid plate diaphragms. The optimized diaphragms were then simplified into more practical configurations that differed depending on the girder aspect ratio. The simplified diaphragms were then tested against the optimized diaphragms for girders with different numbers of internal diaphragms to check its practicality.]]></description>
      <pubDate>Wed, 23 Mar 2022 10:51:58 GMT</pubDate>
      <guid>https://trid.trb.org/View/1919486</guid>
    </item>
    <item>
      <title>Novel Finite Element Analysis of Curved Concrete Box Girders Using Hybrid Box Elements</title>
      <link>https://trid.trb.org/View/1745779</link>
      <description><![CDATA[Horizontally curved concrete bridges are widely used in urban viaducts and overpasses all over the world. A box cross-section is often used in curved concrete girders because of its high resistance to both bending and torsion. This study focuses on the development of a new finite element analysis (FEA) methodology incorporating a novel formulation for curved box sections using orthotropic constitutive models for reinforced concrete, along with a layered shell theory approach. In the new approach, the box section is treated as a frame consisting of curved shell elements modeling webs and flanges and curved beam elements in the web-flange junctions. The use of shell and beam elements in the formulation significantly reduces the number of elements needed to model the box-section girder while maintaining the accuracy of the model. A degenerate superparametric shell element with reduced integration is used to avoid shear-locking, membrane-locking, and zero-energy problems. Prestrain effects are considered in the formulation to account for prestressing forces. The simulation results are compared to the available experimental results on four straight and curved, reinforced and prestressed, concrete box-section girders, with good agreement in terms of the deflections, twist angles, and strains in the prestressed reinforcement. Some critical issues in the analysis of concrete box girders, such as postpeak-strength behaviors, distortion of box section, are also discussed.]]></description>
      <pubDate>Mon, 23 Nov 2020 17:26:50 GMT</pubDate>
      <guid>https://trid.trb.org/View/1745779</guid>
    </item>
    <item>
      <title>Curved Beam Based Model for Piston-Ring Designs in Internal Combustion Engines: Closed Shape Within a Flexible Band, Free-Shape and Force in Circular Bore Study</title>
      <link>https://trid.trb.org/View/1561573</link>
      <description><![CDATA[A new multi-scale curved beam based model was developed for piston-ring designs. This paper describes the free-shape, force in circular bore and closed shape within a flexible band (ovality) related parts. Knowing any one of these distributions, this model determines the other two. This tool is useful in the sense that the characterization of the ring is carried out by measuring its closed shape within a flexible band which is more accurate than measuring its free shape or force distribution in circular bore. Thus, having a model that takes the closed shape within a flexible band as an input is more convenient and useful based on the experiments carried out to characterize the ring.       ]]></description>
      <pubDate>Tue, 11 Feb 2020 09:53:30 GMT</pubDate>
      <guid>https://trid.trb.org/View/1561573</guid>
    </item>
    <item>
      <title>Experimental and analytical investigation of system of horizontally curved bridge girders with tubular top flanges</title>
      <link>https://trid.trb.org/View/1573832</link>
      <description><![CDATA[The behaviour of horizontally curved bridge girders with a tubular top flange and a flat plate bottom flange (i.e., a TFG1) was investigated experimentally and analytically. The investigation focused on the behaviour of a curved TFG1 bridge under loading conditions simulating construction of the concrete deck. The objectives include (1) to generate experimental data for the response of a curved TFG1 bridge system under vertical loading up to and beyond the load capacity; (2) to assess the adequacy of finite element (FE) models to predict this response by comparing experimental data and FE analysis results and (3) to use the experimental data and FE results to validate criteria used to design a curved TFG1 bridge. The experimental data demonstrate that the curved TFG1 bridge system satisfies the design criteria, and has a significant safety margin for the anticipated loads. The comparisons between the experimental data and the FE results show that the FE models have sufficient accuracy to predict the detailed response of curved TFG1 bridge systems.]]></description>
      <pubDate>Fri, 14 Dec 2018 09:32:56 GMT</pubDate>
      <guid>https://trid.trb.org/View/1573832</guid>
    </item>
    <item>
      <title>Crashworthiness Design for Bi-Graded Composite Circular Structures</title>
      <link>https://trid.trb.org/View/1506142</link>
      <description><![CDATA[An innovative double functionally graded composite circular beam comprised of axial and radial graded foam filler is proposed to improve the safety of vehicle under lateral load. The numerical model is established and validated by three-point bending experimental testing. To explore the benefits of the novel functionally graded foam (FGF) material, graded foam filled circular beams with axial and radial graded directions are compared with homogenous foam filled counterparts. FGF filled beams are credited with primarily outward fold which leads to expanded crushing zone. Then, parametric studies are carried out to investigate the effect on thickness and yield stress of column wall of functionally graded circular beams. Furthermore, the bending behaviors of effective FGF filled circular beams are also investigated to improve the weight efficiency. Lastly, multiobjective optimizations of FGF filled beams, effective FGF filled beams and uniform foam filled beams are conducted to enhance crashworthiness. The optimization results show that FGF filled beams exhibit superior Pareto solutions to the uniform foam-filled beams. Especially, effective FGF filled configuration can significantly improve weight efficiency without compromising bearing capacity. The findings of this research offer a new route of designing novel lightweight bumper absorbers with improved crash characteristics.]]></description>
      <pubDate>Tue, 29 May 2018 16:04:58 GMT</pubDate>
      <guid>https://trid.trb.org/View/1506142</guid>
    </item>
    <item>
      <title>Widening Methods of Existing Cast-in-Situ Continuous Curved Beams</title>
      <link>https://trid.trb.org/View/1369704</link>
      <description><![CDATA[An existing cast-in-situ continuous curved bridge was located at the acceleration lane of a new Interchange, widening was needed to meet the width requirements. The original lateral bump walls of the bridge were removed, cantilever sections of beam were cut off about 50cm, and medial bump walls were replaced with corrugated guardrails for balance. With the help of the finite element modeling, conditions of limit and normal state with different load combinations were analyzed. The results, numerical simulations of ultimate flexural capacity and stress of both the top and bottom sides under normal state, showed that the widening project was practicable. On the basis of numerical simulations, vertical deformations between existing and new beams under using stage were calculated, and by comparison on advantages and disadvantages of different splicing scheme, Polyurethane elastic expansion joint was finally recommended to treat Joints between new and old beams.]]></description>
      <pubDate>Fri, 23 Oct 2015 09:35:11 GMT</pubDate>
      <guid>https://trid.trb.org/View/1369704</guid>
    </item>
    <item>
      <title>Steady-state response of a curved beam on a viscously damped foundation subjected to a sequence of moving loads</title>
      <link>https://trid.trb.org/View/1351936</link>
      <description><![CDATA[In this paper, an analytical solution to the steady-state response of a curved beam resting on a viscously damped foundation and subjected to a single or sequence of moving loads is presented. Trigonometric functions are employed as the trial functions in approximating the displacement of the curved beam. The accuracy of the solution is gauged through comparison against available analytical results in the literature. To further examine the accuracy of the proposed analytical method, a computational study of the problem was carried out using the moving element method based on piecewise straight beam elements. Excellent agreement is found between all these results.]]></description>
      <pubDate>Tue, 28 Apr 2015 15:08:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/1351936</guid>
    </item>
    <item>
      <title>The Advantages of the Analysis of Curved Box Beam Using the Grillage Method</title>
      <link>https://trid.trb.org/View/1309362</link>
      <description><![CDATA[This paper first introduces the basic principles and stimulation methods of the grillage method, using such method to conduct stimulation analysis of a certain curved beam bridge—a ramp bridge of Jingkai Road in Beijing—as its engineering background. By using MIDAS/CIVIL, a software finite element method to analyze structures, a single beam model and grillage method model were built, and the comparisons and the analysis about deflection and stress among these models was conducted. The conclusion indicates that the calculation results obtained from the grillage method are closer to the values required in actual construction. The analysis revealed that the models based on the grillage method can reflect the mechanical properties and stress state more efficiently and accurately. Therefore, the grillage method is a very convenient and practical method for analyzing urban curved beam bridges, and it is verified that it can be used in the analysis of urban curved bridges.]]></description>
      <pubDate>Thu, 26 Jun 2014 09:31:38 GMT</pubDate>
      <guid>https://trid.trb.org/View/1309362</guid>
    </item>
    <item>
      <title>Time-Dependent Response of Spatially Curved Steel-Concrete Composite Members. II: Curved-Beam Experimental Modeling</title>
      <link>https://trid.trb.org/View/1277790</link>
      <description><![CDATA[This paper presents a comprehensive experimental study of the time-dependent creep and shrinkage behavior of a simply supported steel-concrete composite beam that is curved in its plan; it is a companion to the first paper that presented a numerical model for spatially curved members for which a beam curved in plan is a limiting case. The full-scale beam was tested under sustained uniformly distributed loading for approximately 250 days; its time-dependent deformations and strains were monitored throughout the period of loading. Separate companion concrete specimens were tested under the same ambient conditions as the test beam to determine the creep and shrinkage characteristics of the concrete component of the beam. The test observations show that the creep and shrinkage behavior of the concrete component has a significant effect on the long-term response of curved composite beams. The experiment also provides benchmark data to test the validity of theoretical models and shows that the developed numerical technique is able to predict the deflections of the test beam accurately; hence, it is able to provide a reliable computational model from which to formulate design guidance.]]></description>
      <pubDate>Mon, 25 Nov 2013 09:58:55 GMT</pubDate>
      <guid>https://trid.trb.org/View/1277790</guid>
    </item>
    <item>
      <title>Time-Dependent Response of Spatially Curved Steel-Concrete Composite Members. I: Computational Modeling</title>
      <link>https://trid.trb.org/View/1277791</link>
      <description><![CDATA[This paper develops a numerical formulation for the nonlinear time-dependent analysis of steel-concrete composite members that are curved arbitrarily in space, which includes the effects of concrete shrinkage, creep, and geometric nonlinearity. This formulation is applicable to the analysis of composite arches and composite beams curved in plan, representing the limiting cases of members that are vertically and horizontally curved. The flexibility of the shear connection at the interface surface between the steel girder and the concrete deck is taken into consideration in the formulation. For an accurate serviceability limit state analysis of composite curved members, it is essential to include the shrinkage and creep response of the concrete component in the analysis. To also include the effects of geometric nonlinearity, a step-by-step incremental iterative solution procedure is adopted. Comparisons of the numerical solutions with those based on much less efficient and tractable viscoelastic ABAQUS shell element models, and with available experimental results, verify the accuracy of the computational formulation that is developed. Examples are chosen to illustrate the effects of partial interaction and initial curvature on the time-dependent behavior of spatially curved composite beams.]]></description>
      <pubDate>Mon, 25 Nov 2013 09:58:54 GMT</pubDate>
      <guid>https://trid.trb.org/View/1277791</guid>
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