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.

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.

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.

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.

Dynamic Fracture Process in Beams

1975 ◽  
Vol 42 (2) ◽  
pp. 435-439 ◽  
Author(s):  
J. D. Colton ◽  
G. Herrmann
Keyword(s):  
Dynamic Fracture ◽  
High Speed ◽  
Beam Theory ◽  
Bending Moment ◽  
Strain Gages ◽  
Second Stage ◽  
Deformation And Fracture ◽  
Initial Fracture ◽  
Beam Thickness ◽  
Stage Process

The relief waves created by the dynamic fracture of a brittle beam were determined. An experiment was conducted on an effectively infinite beam loaded over a finite area with sheet explosive. The time sequence of deformation and fracture was determined by terminal observation, high-speed framing camera photographs, and strain gages. Beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. Comparison of calculated and measured strains showed that the effect of an initial fracture in a beam at a location of pure bending can be approximated by a two-stage process that specifies how the bending moment at the fracture point is reduced to zero after fracture. In the first stage, the crack propagates to the neutral axis, and the stress distribution remains unchanged. In the second stage, the crack propagates through the remainder of the beam thickness while the stress continuously redistributes itself.

HYSTERESIS CHARATERISTICS OF SQUARE CFT COLUMNS SUBJECTED TO AXIAL FORCE AND BENDING MOMENT

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Kouta Jyouzaki ◽  
Masae Kido
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cyclic Loading ◽  
Axial Force ◽  
Rotation Angle ◽  
Bending Moment ◽  
Thickness Ratio ◽  
Skeleton Curve ◽  
Force Ratio ◽  
Unloading Stiffness

Hysteresis characteristics of concrete filled steel tubular columns have been proposed. However, it has not been clarified if the skeleton curve could be applied for slender columns, and there are few studies about the unloading stiffness of the hysteresis loop. The purpose of this study is to compare the skeleton curves of square CFT columns, which have been proposed by the moment-rotation angle relationships and the experimental data by the previous research. The relationship between the initial stiffness obtained by the theoretical calculation and the unloading stiffness obtained by the experimental study are shown. Also the effects of the axial force ratio and the width-thickness ratio on the above mentioned relationships are discussed. The loading condition of the experimental study is monotonic and cyclic loading. It is found that the skeleton curve evaluates conservatively the bending moment-rotation angle relationships obtained by the test in both loading conditions, except for the widththickness ratio 43 specimen with cyclic loading. The ratio of unloading stiffness exKr obtained from the experimental data and calculated theoretical stiffness K was shown. The effect of the axial force ratio on the exKr/K was observed when the rotation chord angle was more than 1% and the width-thickness ratio increased as exKr/K decreased.

A Dynamic Test of Fully Prestressed Concrete Beams

2011 ◽  
Vol 368-373 ◽  
pp. 2483-2490
Author(s):  
Yao Ting Zhang ◽  
Yi Zheng ◽  
Hong Jian Li
Keyword(s):  
Experimental Data ◽  
Elastic Modulus ◽  
Theoretical Analysis ◽  
Natural Frequency ◽  
Axial Force ◽  
Prestressed Concrete ◽  
Concrete Beams ◽  
Dynamic Test ◽  
Modified Formula

A dynamic test of two unbonded fully prestressed concrete beams has been conducted. The results indicate that the natural frequency of beams increases with the prestress force, which is opposite to the analytical arguments for homogeneous and isotropic beams subject to axial force. This paper explains the change in frequencies by discussing the change in the elastic modulus. A modified formula is also proposed, and the experimental data agree well with the theoretical analysis.

Closed-form moment-curvature relations for reinforced concrete cross sections under bending moment and axial force

2016 ◽  
Vol 129 ◽  
pp. 67-80 ◽  
Author(s):  
Pedro Dias Simão ◽  
Helena Barros ◽  
Carla Costa Ferreira ◽  
Tatiana Marques
Keyword(s):  
Reinforced Concrete ◽  
Closed Form ◽  
Axial Force ◽  
Cross Sections ◽  
Bending Moment

Preliminary Parametric Assessment of a Bolted Endplate Joint under Combined Axial Force and Cyclic Bending Moment

2011 ◽  
Vol 255-260 ◽  
pp. 718-721
Author(s):  
Z.Y. Wang ◽  
Q.Y. Wang
Keyword(s):  
Finite Element Analysis ◽  
Axial Force ◽  
Seismic Design ◽  
Axial Load ◽  
Failure Modes ◽  
Bending Moment ◽  
Element Analysis ◽  
Cyclic Behaviour ◽  
Joint Behaviour ◽  
Steel Joints

Problems regarding the combined axial force and bending moment for the behaviour of semi-rigid steel joints under service loading have been recognized in recent studies. As an extended research on the cyclic behaviour of a bolted endplate joint, this study is performed relating to the contribution of column axial force on the cyclic behaviour of the joint. Using finite element analysis, the deteriorations of the joint performance have been evaluated. The preliminary parametric study of the joint is conducted with the consideration of flexibility of the column flange. The column axial force was observed to significantly influence the joint behaviour when the bending of the column flange dominates the failure modes. The reductions of moment resistance predicted by numerical analysis have been compared with codified suggestions. Comments have been made for further consideration of the influence of column axial load in seismic design of bolted endplate joints.

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