Adapting the Simple Through Girder to Sit in Nature, The Wupperthal Footbridge

2021 ◽  
Author(s):  
John Anderson ◽  
Warrick de Kock
Keyword(s):  
South Africa ◽  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Cad Model ◽  
Tourist Destination ◽  
Box Section ◽  
The Town ◽  
Elegant Form

<p>Some places are hard to get to and Wupperthal, a small town nestled deep within in the Cederberg Mountains, in South Africa is one of those places. Founded by German missionaries in 1830 the town is home to 1400 inhabitants and a growing tourist destination. An adjacent river, however, is a barrier during the wet seasons for farm children trying to reach the town’s school. A permanent footbridge was therefore recently commissioned to replace temporary structures that have proved dangerous. This paper tells the story of the single span through girder footbridge. Designed to sit as a comfortable object in its natural surroundings the new footbridge is both functional and attractive. The tapering steel plated cross section presents a profiled elevation that splits to create an arched opening at the midspan of the bridge. To create this elegant form the design had to prevent the buckling of the unbraced top chord of the girder. This was achieved through an iterative study of various cross sections and the transitioning of the plate girder into a box section over the opening. Developing a three-dimensional CAD model of the bridge helped engineers conceive the slender form. The model was then exported to create the finite element plated model and then developed into full workshop drawings. The bridge is considered simple but striking in its appearance and this paper aims to highlight that standard solutions can be transformed where appropriate within limited means.</p>

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

scholarly journals Dynamic modeling of tunnel survey spatiotemporal data

2014 ◽  
Vol 20 (2) ◽  
pp. 354-375
Author(s):  
Xiaolong Li ◽  
Jiansi Yang ◽  
Bingxuan Guo ◽  
Hua Liu ◽  
Jun Hua
Keyword(s):  
Survey Data ◽  
Cross Section ◽  
Cross Sections ◽  
3D Modeling ◽  
3D Model ◽  
Three Dimensional ◽  
Spatiotemporal Data ◽  
Excavation Process ◽  
Special Cases ◽  
Time Stamps

Currently, for tunnels, the design centerline and design cross-section with time stamps are used for dynamic three-dimensional (3D) modeling. However, this approach cannot correctly reflect some qualities of tunneling or some special cases, such as landslips. Therefore, a dynamic 3D model of a tunnel based on spatiotemporal data from survey cross-sections is proposed in this paper. This model can not only playback the excavation process but also reflect qualities of a project typically missed. In this paper, a new conceptual model for dynamic 3D modeling of tunneling survey data is introduced. Some specific solutions are proposed using key corresponding technologies for coordinate transformation of cross-sections from linear engineering coordinates to global projection coordinates, data structure of files and database, and dynamic 3D modeling. A 3D tunnel TIN model was proposed using the optimized minimum direction angle algorithm. The last section implements the construction of a survey data collection, acquisition, and dynamic simulation system, which verifies the feasibility and practicality of this modeling method.

Stress and Strength of Butt Circular Shaft With Metal Columns Subjected to Torques

2004 ◽  
Author(s):  
Jiemin Liu ◽  
Jintang Liu ◽  
Toshiyuki Sawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Yield Stress ◽  
Cross Section ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Circular Shaft ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Stress analysis of the butt circular shaft with three uniformly distributed metal columns subjected to external torques are carried out by using three-dimensional finite element method. The loading capability of the butt circular shaft is measured. It was found that torque acting on the cross-section of adhesive layer is simultaneously withstood by the adhesive layer and the metal columns; The ratio of the torque withstood by metal columns to that withstood by adhesive layer increases with increase of the ratio of Young’s modulus of metal columns to that of the circular shaft; The metal columns enhance and improve the reliability of the joints; The strength of the butt adhesive circular shafts increases with increase of the ratio of the yield stress of the metal columns to that of circular shafts.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

Residual stress distribution in built-in beams

2020 ◽  
pp. 146442072095861
Author(s):  
FA de Castro ◽  
Paulo P Kenedi ◽  
LL Vignoli ◽  
I I T Riagusoff
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Cross Section ◽  
Cross Sections ◽  
Element Model ◽  
Residual Stress Distribution ◽  
Concentrated Load ◽  
Load Growth ◽  
Final Failure

Metallic hyperstatic structures, like beams, submitted to excessive loads, do not fail completely before fully yielding in more than one cross section. Indeed, for built-in beams, three cross sections must be fully yielded before the final failure can occur. So, modeling the evolution of the cross-section residual stress distribution is an important subject that should be addressed to guarantee the stress analysis modeling correctness. This paper analyses the residual stress distribution evolution, in critical cross sections, of built-in beams during a transversal concentrated load growth, until the final failure through hinges formation. A finite element model is also presented. The results show good matches with the numerical model, used as a reference.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

scholarly journals Hierarchical Beam Finite Elements Based Upon a Variables Separation Method

2016 ◽  
Vol 08 (02) ◽  
pp. 1650026 ◽  
Author(s):  
Gaetano Giunta ◽  
Salim Belouettar ◽  
Olivier Polit ◽  
Laurent Gallimard ◽  
Philippe Vidal ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Three Dimensional ◽  
Finite Element Solution ◽  
Stress Fields ◽  
Element Solution ◽  
One Dimensional ◽  
Kinematic Approximation ◽  
The Cross

A family of hierarchical one-dimensional beam finite elements developed within a variables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equivalent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.

Numerical Modelling of Metal Foams with Weaire-Phelan Cell

2013 ◽  
Vol 334-335 ◽  
pp. 122-126 ◽  
Author(s):  
Sid Ali Kaoua ◽  
Haddad Meriem ◽  
Dahmoun Djaffar ◽  
Azzaz Mohammed
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Metal Foam ◽  
Metallic Foam ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Geometrical Characteristics ◽  
Structural Network ◽  
Regular Network

The mechanical properties of open-cell metal foam structures are investigated using the finite element method. The foam structure is modelled by a regular network of anisotropic Weaire-Phelan cells in which the strands are modelled as 3D finite element beams. We consider four types of strand cross sections: (i) circular, (ii) square, (iii) triangular and (iv) Plateau border shape. The numerical results obtained with our proposed mathematical model are checked against the experimental results obtained on real Nickel metallic foam and an excellent agreement is found. In addition, we conducted a parametric analysis to study the effect of some geometrical characteristics on the elasticity of the metal foam. Among these geometrical parameters, the shape, the dimensions of strand cross section, the inertia, the alignment of strands and the structural network irregularities are investigated, discussed and documented.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

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