scholarly journals Towards Further Understanding the Secondary Fracture during Spaghetti Bent Break

Materials ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 189
Author(s):  
Long Long ◽  
Yuxuan Zheng ◽  
Fenghua Zhou ◽  
Huilan Ren
Keyword(s):  
Beam Theory ◽  
Bending Moment ◽  
Time Parameter ◽  
Initial Moment ◽  
Flexural Waves ◽  
Secondary Fracture ◽  
Sudden Release ◽  
The Moment ◽  
Extremum Value ◽  
Gradual Release

When a brittle thin rod, such as a dry spaghetti stick, is bent beyond its flexural limit, it often breaks into more than two pieces, typically three or more. This phenomenon and puzzle has aroused widespread interest and discussion since its first proposal by Feynman. Previous work has partly explained the inevitability of the secondary fracture, but without any adjustable time parameter. In order to further understand this problem, especially the secondary fracture, in this paper we propose and study the dynamics of a half-infinite model to mimic the physics that a spaghetti stick is half-infinite under uniform bending. When the breaking process starts, a gradual release of initial moment of a linearly declining time at the free end, instead of a sudden release, is adopted, resulting in the introduction of a characteristic time parameter to the model and agrees better with the real situation. A specific analytical solution in terms of the excited bending moment using Euler–Bernoulli beam theory is derived, and that the gradual release of initial moment induces a burst of flexural waves, and these flexural waves locally increase the moment in the stick and progressively get to the maximum value, and then lead to the secondary fracture are concluded. The excited moment increases with time and distance, and has an asymptotic extremum value of 1.43 times initial moment. The gradual release in our model requires and gives certain distance and time when the excited bending moment reaches its extremum value, which provides a possibility to predict the detailed fracture parameters such as fragmentation length and time and thus to further understand the secondary fracture during spaghetti bent break.

scholarly journals Brazier Effect of Thin Angle-Section Beams under Bending

2018 ◽  
Vol 10 (9) ◽  
pp. 3047
Author(s):  
Zhiguang Zhou ◽  
Liuyun Xu ◽  
Chaoxin Sun ◽  
Songtao Xue
Keyword(s):  
Nonlinear Response ◽  
Beam Theory ◽  
Bending Moment ◽  
Numerical Results ◽  
Experimental Results ◽  
Angle Section ◽  
Thin Walled ◽  
The Moment ◽  
Good Agreement ◽  
Brazier Effect

Thin-walled section beams have Brazier effect to exhibit a nonlinear response to bending moments, which is a geometric nonlinearity problem and different from eigenvalue problem. This paper is aimed at investigating the Brazier effect in thin-walled angle-section beams subjected to pure bending about its weak axis. The derivation using energy method is presented to predict the maximum bending moment and section deformation. Both numerical analyses and experimental results were used to show the validity of the proposed formula. Numerical results show that the boundary condition can influence the results due to the end effect, and that the influence tends to be negligible when the length of angle beam goes up to 30 times as the length of beam side. When the collapse in experiments is governed by Brazier flattening, the moment vs. curvature curve deviates significantly from the linear beam theory, but coincides well with the proposed formula in consideration of the restraint due to limited span of experimental setup. It can be concluded that the proposed formula shows good agreement with numerical results and experimental results.

Experimental study of moment carrying behavior of typical Tibetan timber beam-column joints

2021 ◽  
pp. 136943322110015
Author(s):  
Ting Guo ◽  
Na Yang ◽  
Huichun Yan ◽  
Fan Bai
Keyword(s):  
Bending Moment ◽  
Structural Performance ◽  
Test Results ◽  
Timber Beam ◽  
Rotational Stiffness ◽  
Trilinear Model ◽  
Column Joint ◽  
Loading Tests ◽  
The Moment ◽  
Relationship Of

This study aimed to investigate the moment carrying behavior of typical Tibetan timber beam-column joints under monotonic vertical static load and also evaluate the influence of length ratio of Gongmu to beam (LRGB) and dowels layout on the structural performance of the joint. Six full-scale specimens were fabricated with same construction but different Gongmu length and dowels position. The moment carrying performance of beam-column joints in terms of failure mode, moment resistance, and rotational stiffness of joints were obtained via monotonic loading tests. Test results indicated that all joints are characterized by compressive failure perpendicular to grain of Ludou. Additionally, it was found that greater LRGB leads to greater initial rotational stiffness and maximum moment of the joint by an increase of restraint length for beam end; however, offsetting dowels toward column resulted smaller stiffness and ultimate bending moment of joints, particularly, offsetting Beam-Gongmu dowels toward column changed the moment-rotation curve pattern of the beam-column joint, accompanied by a hardening stiffness at last phase. Furthermore, a simplified trilinear model was proposed to represent the moment-rotation relationship of the typical Tibetan timber beam-column joint.

scholarly journals Generation of infrasonic signals during earthquakes under Lake Hovsgool (Northern Mongolia) on December 5, 2014

2018 ◽  
Vol 4 (4) ◽  
pp. 95-105
Author(s):  
Александр Сорокин ◽  
Aleksandr Sorokin ◽  
Анатолий Ключевский ◽  
Anatoliy Klyuchevskii ◽  
Владимир Демьянович ◽  
...  
Keyword(s):  
Seismic Wave ◽  
Initial Phase ◽  
Joint Analysis ◽  
Weak Signal ◽  
Flexural Waves ◽  
Small Magnitude ◽  
Infrasonic Waves ◽  
Northern Mongolia ◽  
The Moment ◽  
Infrasonic Signal

The paper discusses the results of the detection of seismic and infrasonic waves generated by a major earthquake and its aftershock (the moment magnitude MW=4.9 and MW=4.2 respectively), which occurred in northern Mongolia under Lake Hovsgool on December 5, 2014. The joint analysis of waveforms of seismic and infrasonic oscillations has shown that the signal recorded by the infrasound station of the Geophysical Observatory of the Institute of Solar-Terrestrial Physics SB RAS (ISTP SB RAS) is formed from sources of three generation types: local, secondary, and epicentral. This analysis enables us to propose a hypothesis of generation of epicentral infrasonic signal by flexural waves in an elastic ice membrane on the surface of Lake Hovsgool, which appear during the passage of seismic wave packets. This hypothesis explains the similarity between seismic and epicentral infrasonic signals, negative initial phase of epicentral infrasonic waves, and detection of a weak signal after a small-magnitude aftershock.

Experimental Evaluation of the Ultimate Bending Moment of a Slender Thin-Walled Box Girder

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
José Manuel Gordo ◽  
C. Guedes Soares
Keyword(s):  
Residual Stresses ◽  
Progressive Collapse ◽  
Bending Moment ◽  
Bending Test ◽  
Postbuckling Behavior ◽  
Box Girder ◽  
Collapse Mode ◽  
Collapse Analysis ◽  
The Moment ◽  
Progressive Collapse Analysis

The results of a four points bending test on a box girder are presented. The experiment is part of series of tests with similar configuration but with different thickness and span between frames. The present work refers to the slenderest plate box girder with a plate's thickness of 2 mm but with a short span between frames. The experiment includes initial loading cycles allowing for partial relief of residual stresses. The moment curvature relationship is established for a large range of curvature. The ultimate bending moment (UM) of the box is evaluated and compared with the first yield moment and the plastic moment allowing the evaluation of the efficiency of the structure. The postbuckling behavior and collapse mode are characterized. Comparison of the experiment with a progressive collapse analysis method is made taking into consideration the effect of residual stresses on envelop of the moment curvature curve of the structure.

Buckling Behavior of Well Tubing: The Packer Effect

1982 ◽  
Vol 22 (05) ◽  
pp. 616-624 ◽  
Author(s):  
R.F. Mitchell
Keyword(s):  
Virtual Work ◽  
Beam Theory ◽  
Bending Moment ◽  
Radial Clearance ◽  
Bending Moments ◽  
Principle Of Virtual Work ◽  
Equilibrium Equations ◽  
Conventional Model ◽  
Shear Loads ◽  
Buckling Behavior

Abstract The equilibrium equations for a helically buckled tubing are developed and solved directly. The results show that the packer has a strong influence on the pitch of the helix, and that the pitch developed by the helix is different from the pitch calculated by conventional methods. In addition, the solution providesshear loads and bending moments at the packer andconstraining force exerted on the tubing by the exterior casing. This last result can be used to estimate friction effects on tubing buckling. Introduction The buckling behavior of well tuning and its effect on packer selection and installation have received much attention in the industry. The most well-known analysis of this problem is by Lubinski et al. Later analyses. such as by Hammerlindl, have extended and refined these results. There were two major contributions of this analysis:to clarity the roles of pressures, temperatures, fluid flow, pretension, and packer design in the buckling problem andto present a mechanical model of well buckling behavior that predicted the buckled well configuration as a function of applied loads. The principal results from this model were the motion of the tubing at the packer and the stresses developed in the tubing as a result of buckling. The major features of the conventional model of buckling behavior are summarized as follows.Slender beam theory is used to relate bending moment to curvature.The tubing is assumed to buckle into a helical shape.The principle of virtual work is used to relate applied buckling load to pitch of the helix.Friction between the buckled tubing and restraining casing is neglected. The geometry of the helix is described by three equations: (1) (2) and (3) where u1, u2, and u3 are tubing centerline locations in the x, y, and z coordinate directions, respectively; Theta is the angular coordinate (Fig. 1); r is the tubing-casing radial clearance: and P is pitch of the helix. The principle of virtual work relates P to the buckling force, F, through the following formula. (4) Several questions are not addressed by this analysis:What is the shape of the tubing from packer to fully developed helix?What are the resulting shear loads and moments at the packer caused by buckling?What are the forces exerted on the helically buckled tubing by the restraining casing? Solutions to Questions 2 and 3 would be particularly useful for evaluating friction effects on the tubing and the effect of induced loads on the packer elements. This information would allow better estimates of tubing movement and provide detailed load reactions at the packer for improved packer design. The solution to Question 1 could be particularly interesting because of its effect on results obtained by virtual work methods. SPEJ P. 616^

On Torsion and Transverse Flexure of Orthotropic Elastic Plates

1980 ◽  
Vol 47 (4) ◽  
pp. 855-860 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Cross Section ◽  
Beam Theory ◽  
Bending Moment ◽  
Rate Of Change ◽  
Elastic Plates ◽  
Shear Center ◽  
Explicit Consideration ◽  
The Difference ◽  
Shear Deformable ◽  
Shear Deformable Plates

The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.

The effect of three factors on the incidence of tender wool in deferred grazing management

1971 ◽  
Vol 11 (53) ◽  
pp. 607 ◽  
Author(s):  
TH Brown
Keyword(s):  
Management System ◽  
Grazing Management ◽  
Sudden Release ◽  
Gradual Release

The effects of three factors on the incidence of tender wool were studied in a deferred autumn grazing management system with Merino wethers. The factors were age of wethers, level of hand feeding during the deferment period, and rate of release to saved pasture at the end of the deferment period. Sudden release to saved pasture resulted in a higher incidence of tenderness than did gradual release. The incidence of tenderness also increased as the level of hand feeding was reduced. Age had no significant effect.

Nonlinear Hydroelastic Response of a Two-Dimensional Mat-Type VLFS by the Green-Naghdi Theory

2004 ◽  
Author(s):  
Dingwu Xia ◽  
R. Cengiz Ertekin ◽  
Jang Whan Kim
Keyword(s):  
Elastic Plate ◽  
Mechanical Energy ◽  
Beam Theory ◽  
Bending Moment ◽  
Open Water ◽  
Beam Equation ◽  
Two Dimensional ◽  
Jump Conditions ◽  
Numerical Predictions ◽  
Hydroelastic Response

The two-dimensional, nonlinear hydroelasticity of a mat-type VLFS is studied within the scope of linear beam theory for the structure and the nonlinear, Level I Green-Naghdi (GN) theory for the fluid. The beam equation and the GN equations are coupled through the kinematic and dynamic boundary conditions to obtain a new set of modified GN equations. These equations model long-wave motion beneath an elastic plate. A set of jump conditions that are necessary for the continuity (or the matching) of the solutions in the open water region and that under the structure is newly derived through the use of the postulated conservation laws of mass, momentum and mechanical energy. The resulting governing equations, subjected to the boundary and jump conditions, are solved by the finite-difference method in the time domain. The present model is applicable, for example, to the study of the hydroelastic response of a mat-type VLFS under the action of a solitary wave, or a frontal tsunami wave. Good agreement is observed between the present results and other published theoretical and numerical predictions, as well as experimental data. The nonlinear results show that consideration of nonlinearity is important for accurate predictions of the bending moment of the floating elastic plate. It is also found that the rigidity of the structure also greatly affects the bending moment and displacement of the structure in this nonlinear theory.

EFFECTS OF THE INITIAL DEFLECTION SHAPE ON THE MOMENT AMPLIFICATION FACTOR OF BEAM-COLUMNS

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Haruna Utsunomiya ◽  
Masayuki Haraguchi ◽  
Masae Kido ◽  
Keigo Tsuda
Keyword(s):  
Amplification Factor ◽  
Slenderness Ratio ◽  
Compressive Force ◽  
Bending Moment ◽  
Load Ratio ◽  
Longitudinal Direction ◽  
Initial Deflection ◽  
Axial Compressive Force ◽  
Beam Columns ◽  
The Moment

In the design of slender steel beam-columns, the moment amplification factor is used to estimate the maximum moment along with the longitudinal direction. While formulas for evaluating the factor have been presented on the basis of elastic or elastic-plastic analysis, the initial deflection of the column is not considered. The effect that the initial deflection on the strength and behavior of the column has been shown only when the initial deflection shape is half sine wave. This paper discusses the effect of the initial deflection shape on the value of the moment amplification factor by performing the analytical work. The analytical model is the hinged-end beam-column subjected to constant axial compressive force and end moments. First of all, the equilibrium differential equation which governs the problem is solved and the formula for calculating the bending moment is presented. In the parametric study, magnitude of initial deflection, initial deflection shape, axial load ratio, slenderness ratio and end moment ratio are selected as the parameters. In this paper, we discuss the effects of the amount of the initial deflection and the initial deflection shape.

Analytical Model for a Superelastic SMA Beam

2017 ◽  
Author(s):  
N. V. Viet ◽  
Wael Zaki ◽  
Rehan Umer
Keyword(s):  
Analytical Model ◽  
Bending Moment ◽  
Analytical Relation ◽  
Beam Model ◽  
Element Analysis ◽  
Austenitic Phase ◽  
Martensite Variant ◽  
The Moment ◽  
Reversible Phase ◽  
Good Agreement

We propose an analytical model for a superelastic shape memory alloy (SMA) beam. The model considers reversible phase transformation between austenite and a single martensite variant driven by mechanical loading/unloading. In particular, we consider a cantilever beam subjected to a concentrated transverse force acting at the tip. The force is gradually increased from zero to a maximum value sufficient to cause complete transformation of the initially austenitic phase into martensite away from the beam core. The force is then gradually removed, resulting in complete strain recovery. In each stage of the loading/unloading process, an analytical relation is established between bending moment and curvature in terms of position along the axis of the beam. The model is compared to a uniaxial numerical beam model and to finite element analysis (FEA) results for the same beam in 3D, with very good agreement in each case. The moment-curvature relation is then integrated to obtain a nonlinear expression for the deflection and stress distribution in terms of position along the length of the beam. The expression is validated against 3D simulation results.

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