Determining Efficient Strut-and-Tie Models for Simply Supported Beams Using Minimum Strain Energy

2014 ◽  
Vol 111 (5) ◽  
Author(s):  
Qinang Hu ◽  
M. Tyler Ley ◽  
Bruce W. Russell
Keyword(s):  
Strain Energy ◽  
Simply Supported ◽  
Strut And Tie ◽  
Minimum Strain Energy

scholarly journals ON THE OPTIMAL STRUT-AND-TIE MODELS AND DESIGN APPROACH FOR THE CABLE-PYLON ANCHORAGE ZONE

2019 ◽  
Vol 25 (6) ◽  
pp. 576-586 ◽  
Author(s):  
Nannan Cui ◽  
Shiping Huang
Keyword(s):  
Strain Energy ◽  
Design Method ◽  
Design Procedure ◽  
Optimization Techniques ◽  
Strut And Tie ◽  
Cable Stayed Bridge ◽  
D Region ◽  
Minimum Strain Energy ◽  
The One ◽  
Application Scope

The cable-pylon anchorage zone is a typical D-region in a cable-stayed bridge, for which there has been no uniform simplified design method until now. In this paper, based on the extensive statistics of actual projects, topology optimization techniques and principle of minimum strain energy, two precise strut-and-tie models for the cable-pylon anchorage zone are proposed, which can clearly reveal the load-transmitting mechanism of the anchorage zone. Th e explicit geometric parameters of the strut-and-tie models are derived; thus, the designers can directly use these models. A simple design procedure to deploy prestressing tendons in the anchorage zone is also introduced, whose effectiveness and convenience are demonstrated by two design examples. A new design named the “one-way prestressing tendons PC cable-pylon” is also discussed regarding its application scope.

scholarly journals Proposition and analysis of strut and tie models for short corbels from techniques of topology optimization

2021 ◽  
Vol 14 (2) ◽  
Author(s):  
Matheus Barbosa Moreira Cedrim ◽  
Eduardo Nobre Lages ◽  
Aline da Silva Ramos Barboza
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Strain Energy ◽  
Volumetric Fraction ◽  
Penalization Method ◽  
Strut And Tie ◽  
Method Formulation ◽  
Minimum Strain Energy ◽  
Automated Process ◽  
Stress Flow

Abstract Reinforced concrete short corbels are components characterized to represent typical conditions of geometrical and static discontinuity. In general, the classical bending theory is not valid for their design. With the strut and tie method, a model of a self-balanced truss, a strategy of representation of the principal stress flow appears as a representation of the trajectories of the main stresses in these components. Within the context of obtaining the strut and tie models, topology optimization is an indicated technique for an automated process. Combined with a numerical analysis based on finite elements, the SIMP (Solid Isotropic Material with Penalization) method formulation, which is defined with the criterion of minimum strain energy restricted by the volumetric fraction, is used for the development of the models with the ABAQUS® v. 6.14.1 software. Therefore, with the material distribution posterior to the optimization and the validation based on normative codes, it is demonstrated that the tool is effective in the development of strut and tie models.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

scholarly journals Experimental Testing of Reinforced Concrete Deep Beams Designed by Strut-And-Tie Method

2020 ◽  
Vol 10 (18) ◽  
pp. 6217
Author(s):  
Anka Starčev-Ćurčin ◽  
Andrija Rašeta ◽  
Mirjana Malešev ◽  
Danijel Kukaras ◽  
Vlastimir Radonjanin ◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Experimental Testing ◽  
Deep Beams ◽  
Simply Supported ◽  
Strut And Tie ◽  
The Third ◽  
Variation Parameter ◽  
The One

The aim of the research presented in this paper is the experimental confirmation of the numerically defined shapes of the Strut-and-Tie models, designed according to the EN 1992-1-1 recommendations, and obtained from the software “ST method”. Three reinforced concrete deep beams with openings were tested. Each of them had the same dimensions and quality of the material characteristics. The specimens, constructed as simply supported beams, were loaded with two concentrated forces and were tested for bending until failure. Each specimen was reinforced with different reinforcement layout determined by variation parameter β, incorporated in the software “ST method”. For the determination of the Strut-and-Tie models, all of the reinforcement layouts were equally favored in the first specimen (β = 1.0 for 0°, 45°, and 90°), only the horizontal direction was favored in the second (β = 1.0 for 0°), while in the third specimen the one at the angle of 45° (β = 1.0 for 45°). Based on the results of experimental research, it was concluded that the behavior of loaded members was in agreement with the proposed shapes of the Strut-and-Tie models that were used for their design, and it was confirmed that the program “ST method” can be used for obtaining Strut–and-Tie models.

Prediction of Cylinder Flow Pressures in Mass-Flow Bins Using Minimum Strain Energy

1976 ◽  
Vol 98 (4) ◽  
pp. 1370-1374 ◽  
Author(s):  
A. G. McLean ◽  
P. C. Arnold
Keyword(s):  
Mass Flow ◽  
Strain Energy ◽  
Plane Flow ◽  
Geometry Design ◽  
Numerical Effort ◽  
Minimum Strain Energy ◽  
Flow Pressure ◽  
Energy Theory ◽  
Cylinder Flow ◽  
Complete Variation

Jenike, et al. [1] have presented a minimum strain energy theory to predict cylinder flow pressures in mass-flow bins. The complete variation of strain energy pressures is depicted by bounds requiring considerable numerical effort to develop for a specific cylinder geometry. Design charts are presented, but these are available for only two circular cylinder geometries. This paper summarizes and clarifies the minimum strain energy theory for predicting cylinder flow pressures. A single bound approximation which allows the magnitude of the peak flow pressure to be determined for both axisymmetric and plane flow cylinders is presented. This peak pressure may also be estimated by a single calculation of strain energy pressure. The usefulness and accuracy of these procedures are illustrated by reworking the example presented by Jenike, et al. [1].

Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

Exploration of Local Blade Motions During Blade Shaping for Thick Layered Foam Cutting

2004 ◽  
Author(s):  
J. J. Broek ◽  
A. Kooijman
Keyword(s):  
Strain Energy ◽  
Cutting Tool ◽  
Cutting Speed ◽  
General Rule ◽  
Free Form ◽  
Linear Change ◽  
Minimum Strain Energy ◽  
Blade Cutting ◽  
Tool Position ◽  
Cutting Direction

The FF-TLOM (Free Form Thick Layered Object Manufacturing) technology is a Rapid Prototyping process based on flexible blade cutting of polystyrene foam. The heated blade is shaped by three parameters, which allows an infinite amount of minimum strain energy blade shapes with none, one or two inflexions. In the shaping domain stable and unstable blade shapes can exist. Stable shapes are defined as curves with none and one-inflexion and are applied for operational cutting of foam layers with the FF-TLOM technology. The tool motions are generated from the static tool poses and are calculated for a linear change of the flexible blade, when the cutting tool moves from one tool position to the next. The cutting blade is positioned to the foam slab with help of a point relative positioned on the flexible blade. The tool frame is positioned with a point fixed relatively to the tool frame. During the tool motions the blade curvature is changed and will introduce a shift of the half way point fixed on the blade (especially in the case of asymmetrical support inclinations and high curvature). Next the local displacement of the blade points in the bending plane of the blade due to blade shaping and tool pitching are quantified during the tool motions. These displacements induce an angle of attack of the blade in cutting direction, and will influence cutting speed and cutting accuracy. The quantification software is developed and will be used in the future for an overall prediction of the total tool curve displacements due to blade shaping, such as roll, pitch, yaw and linear positioning motions of the tool. A general rule for FF-TLOM cutting is minimization of all tool motions, which are not related to the forward cutting motion.

Fracture of aluminum-epoxy layered composites containing cracks

1982 ◽  
Vol 17 (2) ◽  
pp. 75-78 ◽  
Author(s):  
E E Gdoutos
Keyword(s):  
Composite Plate ◽  
Strain Energy ◽  
Crack Extension ◽  
Critical Value ◽  
Layered Composites ◽  
Parallel Cracks ◽  
Two Parallel Cracks ◽  
Minimum Strain Energy ◽  
Uniaxial Compressive Stress ◽  
Strain Energy Density Theory

The plane problem of a composite plate consisting of two aluminum half-planes bonded together through an epoxy layer and containing two parallel cracks, one in the layer and the other in one of the half-planes was considered. The composite plate was loaded by a uniform uniaxial compressive stress distribution applied along the surfaces of the crack of either the layer or the half-plane. The critical value of the applied stress as well as the corresponding angle for crack extension were determined by using the minimum strain energy density theory. Valuable results governing the dependence of the critical failure stress of the composite plate as well as the angle of crack extension from the more vulnerable crack on the geometry of the plate were derived.

Optimization Research on Geometric Parameters of Scallop-Shaped Lattice Shells

2015 ◽  
Vol 724 ◽  
pp. 192-196
Author(s):  
Na Li ◽  
Ren An Chang ◽  
Wei Zong ◽  
Qi Hang Yu
Keyword(s):  
Mechanical Properties ◽  
Strain Energy ◽  
Geometric Parameters ◽  
Free Form ◽  
Spatial Structures ◽  
Shaped Surface ◽  
Minimum Strain Energy ◽  
Optimal Values ◽  
Lattice Shells

<p>Free-form and bionic spatial shells are popular in the area of spatial structures. Scallop-shaped surface is the product of evolution and a kind of spatial shells that can satisfy the mechanical requirements. Based on the scallop-shaped lattice shells, this paper focused on the optimization of geometric parameters. The principle of minimum strain energy was applied to conclude the influence law of the geometric parameters on mechanical properties. Finally the optimal values of geometric parameters were obtained. The results show that the optimization of geometric parameters presents the integrated significance to improve scallop-shaped lattice shells.</p>

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