Effect of Shear and Rotary Inertia on Dynamic Fracture of a Beam or Plate in Pure Bending

1982 ◽  
Vol 49 (4) ◽  
pp. 773-778 ◽  
Author(s):  
C. Levy ◽  
G. Herrmann
Keyword(s):  
Dynamic Fracture ◽  
Axial Force ◽  
Opposite Effect ◽  
Bending Moment ◽  
Rotary Inertia ◽  
Pure Bending ◽  
Strain Fracture ◽  
The Moment ◽  
Tip Velocity ◽  
Total Fracture

The dynamic fracture response of a long beam of brittle material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased quasi-statically to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the moment and induced axial load at the fracturing section is included in the present analysis. Thus an improved formulation is presented by means of which the crack length, crack-tip velocity, bending moment, and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the axial force effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded and better agreement with experimental data is achieved. The results also apply for plane-strain fracture of a plate in pure bending provided the value of the elastic modulus is appropriately modified.

Effect of Axial Force on Dynamic Fracture of a Beam or Plate in Pure Bending

1977 ◽  
Vol 44 (4) ◽  
pp. 647-651 ◽  
Author(s):  
H. Adeli ◽  
G. Herrmann ◽  
L. B. Freund
Keyword(s):  
Experimental Data ◽  
Dynamic Fracture ◽  
Axial Force ◽  
Fracture Process ◽  
Bending Moment ◽  
Critical Value ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness ◽  
Tip Velocity

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, a dynamically induced axial force which is generated during the fracture process is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment, and axial force at the fracturing section are determined as functions of time after crack initiation. It is found that the effect of the axial force becomes significant after the crack travels about one third of the beam thickness, and better agreement with experimental data is achieved. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Numerical Simulations for Bending Moment Distribution on Linings of Tunnel Excavated by Shield

2015 ◽  
Vol 744-746 ◽  
pp. 1033-1036
Author(s):  
Zi Chang Shangguan ◽  
Shou Ju Li ◽  
Li Juan Cao ◽  
Hao Li
Keyword(s):  
Numerical Simulations ◽  
Axial Force ◽  
Shear Force ◽  
Bending Moment ◽  
Geological Data ◽  
Fem Model ◽  
Maximum Moment ◽  
Moment Distribution ◽  
Negative Moment ◽  
The Moment

In order to simulate moment distribution on linings of tunnel excavated by shield, FEM-based procedure is proposed. According to geological data of tunnel excavated by shield, FEM model is performed, and the moment, axial force and shear force distributions on linings are computed. The maximum moment on segments decreases while Poisson’s ratio of soil materials touching to segments increases. The moment value and distribution vary with Young’s modulus of soil materials. The maximum positive moment on linings is approximately equal to the maximum negative moment.

The Vibration Based on Non-Zero Point Force Moment Elasticity Theory

2014 ◽  
Vol 590 ◽  
pp. 27-31 ◽  
Author(s):  
Wen Ba Han ◽  
Shuang Hua Huang ◽  
Jie Liu ◽  
Jin Kun Sun
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Elasticity Theory ◽  
Damage Mechanics ◽  
Natural Frequencies ◽  
Bending Moment ◽  
Zero Point ◽  
Pure Bending ◽  
Force Moment ◽  
The Moment

The traditional elastic theory believes that there exists normal stress in pure bending body (PBB) and shear stress in pure torsion body (PTB). However, the author proved that there is no normal stress but ‘Bent Point Moment’ (BPM) in PBB. And it also concluded that there is no shear stress but ‘Shear Point Moment’ (SPM) in PTB. This article overturns the preliminary theorems of the Elasticity Theory, which believes that the value of the moment (Bending moment & Torsion moment) on a unit area converges to zero. Just as the completely different natural frequencies of the forced vibration can lead to completely different resonant conditions. Besides, this theory has also been validated in the Damage Mechanics National Key Laboratory of Tsinghua University. Therefore, it is significant to avoid destruction produced by resonance.

scholarly journals Non-linear Analysis of Slender High Strength Concrete Column

2019 ◽  
Vol 5 (7) ◽  
pp. 1440-1451
Author(s):  
Ernesto Fenollosa ◽  
Iván Cabrera ◽  
Verónica Llopis ◽  
Adolfo Alonso
Keyword(s):  
Bearing Capacity ◽  
Cross Section ◽  
Axial Force ◽  
High Strength Concrete ◽  
Bending Moment ◽  
High Strength ◽  
Concrete Columns ◽  
Strength Concrete ◽  
The Moment ◽  
High Strength Concrete Columns

This article shows the influence of axial force eccentricity on high strength concrete columns design. The behavior of columns made of normal, middle and high strength concrete with slenderness values between 20 and 60 under an eccentric axial force has been studied. Structural analysis has been developed by means of software which considers both geometrical and mechanical non-linearity. The sequence of points defined by increasing values of axial force and bending moment produced by eccentricity has been represented on the cross-section interaction diagram until failure for each tested column. Then, diagrams depicting the relationship between failure axial force and column's slenderness have been drawn. The loss of bearing capacity of the member for normal and middle strength columns when compared with the bearing capacity of their cross-section is more noticeable as axial force eccentricity assumes higher values. However, this situation reverses for high strength columns with high slenderness values. On the basis of results obtained, the accuracy level for the moment magnifier method was checked. Despite the good concordance in most of the cases, it was verified that the moment magnifier method leads to excessively tight results for high strength concrete columns with high slenderness values. In these specific cases, a coefficient which amends the column rigidity is proposed so as to obtain safer values.

Bending With Axial Force of Curved Bars in Plasticity

1952 ◽  
Vol 19 (3) ◽  
pp. 327-330
Author(s):  
Aris Phillips
Keyword(s):  
Axial Force ◽  
Strain Distribution ◽  
Axial Load ◽  
Bending Moment ◽  
High Accuracy ◽  
Pure Bending ◽  
Stress Strain

Abstract The problem of symmetrical pure bending with axial force of a curved bar in plasticity is considered. A method is given for finding the axial load and bending moment which produce a given strain distribution. This method is based upon approximating the stress-strain curves by means of broken lines. By increasing the number of sides of these broken lines it is possible to solve our problem with as high accuracy as is desired.

Research on Internal Force Analysis of Shaking Table Test for Prestressed Pipe Piles Used in Tang Shan-Cao Feidian Expressway

2013 ◽  
Vol 740 ◽  
pp. 750-754
Author(s):  
Huan Sheng Mu ◽  
Ling Gao ◽  
Yu Guo Liang ◽  
Wen Dong Ma
Keyword(s):  
Axial Force ◽  
Shaking Table Test ◽  
Bending Moment ◽  
Internal Force ◽  
Sine Wave ◽  
Shaking Table ◽  
Pile Diameter ◽  
Pipe Model ◽  
Table Model ◽  
The Moment

In order to study the applicability of pipe piles in Tang-Cao expressway, shaking table model test was carried out. The results shows that, the internal force distribution of the pile under the action of seismic wave is basically the same with the behavior that is under the action of sine wave ; in the position of the 4 times pile diameter (distance the top of the pipe model about 200mm) appears the maximum axial force and bending moment; the change of the additional axial force in the upper portion of the pile is more complex, and tends to increase downward; the change of the moment tends to stable blow the distance of 20times the pile diameter from the pile top (distance the top of pipe model about 1000mm)

Experimental Investigation on Cold-formed Steel Beams under Pure Bending

2012 ◽  
pp. 13-20 ◽  
Author(s):  
Yeong Huei Lee ◽  
Yee Ling Lee ◽  
Cher Siang Tan
Keyword(s):  
Local Buckling ◽  
Bending Moment ◽  
Steel Beams ◽  
Pure Bending ◽  
Lateral Instability ◽  
Moment Capacity ◽  
British Standard ◽  
Cold Formed Steel ◽  
The Moment ◽  
Design Yield

This paper presents the flexural behaviour of cold-formed double lipped channels beams under pure bending action. Two channel sections are bolted back-to-back to form an I-shape structural beam member. A series of six experiment tests were carried out on beam specimens DC200 and DC250, each with 200 mm depth and 250 mm depth respectively. The thickness of beam section is 2 mm and the design yield strength is 350 N/mm2. All beams failed at local buckling at top-flange due to lateral instability of the cold-formed steel structural members. The moment resistance for DC200 is 17.87 kNm and DC250 is 31.53 kNm. The experimental results are compared to theoretical resistance prediction based on British Standard and Eurocode. The comparison showed that the experimental moment capacity is lower than the theoretical bending moment resistance but higher than theoretical buckling moment resistance from Eurocode. This showed that a better agreement is achieved between experimental data and Eurocode buckling moment resistance for cold-formed steel beam under pure bending. Kertas kerja ini membentangkan sifat lenturan rasuk keluli tergelek sejuk di bawah tindakan lenturan tulen. Dua channel dihimpunkan berkembar dan diperketatkan dengan bolt untuk membentuk rasuk struktur bentuk-I. Satu siri ujian lenturan telah dijalankan ke atas spesimen rasuk DC200 dan DC250, dengan kedalaman 200 mm dan 250 mm masing-masing. Ketebalan keratan rasuk adalah 2 mm dan kekuatan reka bentuk adalah 350 N/mm2. Semua rasuk gagal pada momen kilasan sisi di bahagian atas bebibir akibat ketakstabilan sisi anggota keluli tergelek sejuk. Rintangan momen bagi DC200 adalah 17.87 kNm dan DC250 adalah 31.53 kNm. Keputusan eksperimen dibanding dengan ramalan teori yang berdasarkan British Standard dan Eurocodes. Perbandingan tersebut menunjukkan bahawa rintangan momen lenturan eksperimen adalah lebih rendah daripada ramalan teori momen lenturan tetapi lebih tinggi daripada ramalan teori momen rintangan kilasan sisi mengikut Eurocode. Ini menunjukkan bahawa persetujuan baik dicapai di antara keputusan eksperimen dengan ramalan teori Eurocode momen rintangan kilasan sisi bagi rasuk keluli tergelek sejuk.

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.

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