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.

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.

scholarly journals NUMERICAL INVESTIGATION OF THE ELASTIC-PLASTIC LINEAR HARDENING STRESS-STRAIN STATE OF THE FRAME ELEMENT CROSS-SECTION

2016 ◽  
Vol 8 (3) ◽  
pp. 94-100
Author(s):  
Andrius Grigusevičius ◽  
Gediminas Blaževičius
Keyword(s):  
Cross Section ◽  
Axial Force ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Software Environment ◽  
Stress Strain ◽  
Hardening Material ◽  
Frame Element ◽  
Nonlinear Stress

The aim of this paper is to present a solution algorithm for determining the frame element crosssection carrying capacity, defined by combined effect of bending moment and axial force. The distributions of stresses and strains inside a cross-section made of linearly hardening material are analysed. General nonlinear stress-strain dependencies are composed. All relations are formed for rectangular cross-section for all possible cases of combinations of axial force and bending moment. To this end, five different stress-strain states are investigated and four limit axial force values are defined in the present research. The nonlinear problem is solved in MATLAB mathematical software environment. Stress-strain states in the cross-sections are investigated in detail and graphically analysed for two numerical experiments.

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.

scholarly journals Investigation of Load Capacity of Steel Concrete Composite Columns Src Reinforced by IPE

2019 ◽  
Vol 29 (2) ◽  
pp. 101-116
Author(s):  
Peyman Beiranvand ◽  
Matin Abdollahifar ◽  
Ahmad Moradpour ◽  
Saeideh Sadeghi Golmakani
Keyword(s):  
Finite Element ◽  
Axial Force ◽  
Axial Load ◽  
Load Capacity ◽  
Axial Loading ◽  
Bending Moment ◽  
Axial Deformation ◽  
Composite Columns ◽  
Finite Element Software ◽  
Deformation Interaction

Abstract In this study, a column with section IPE and different lengths, completely embedded in concrete, is modelled by finite element software ABAQUS. Columns under different bi-axial loading were used and graphs of axial force-axial deformation, interaction axial force, and bending moment and column curve were mapped. The results show that the load capacity of the column, with increasing length and also increasing eccentricity of the axial load, will be reduced. With increasing length, the effect of an increased eccentricity of the reduced load capacity was increased. Equations for the design of the column are also presented. The results of the presented equations were compared with the values obtained from finite element and building national institute 10th topic.

Unsymmetrical Bending and Bending Combined with Axial Loading of a Beam of Rectangular Cross Section into the Plastic Range

1953 ◽  
Vol 57 (512) ◽  
pp. 503-509 ◽  
Author(s):  
Anthony J. Barrett
Keyword(s):  
Cross Section ◽  
Axial Load ◽  
Rectangular Cross Section ◽  
Form Factors ◽  
Strain Curve ◽  
Bending Moment ◽  
Theoretical Work ◽  
Mathematical Form ◽  
Stress Strain Curve ◽  
Stress Strain

SummaryThis note considers two cases of bending beyond the limit of proportionality which have not received a great measure of attention in the past. These are Case(i). A beam subjected to a pure bending moment acting in a plane other than one of symmetry. Case(ii). A beam subjected to a bending moment and an axial load.A mathematical form is used for the stress–strain curve in order that the results shall be applicable to a large number of materials and to avoid the tedious arithmetical summations which would be necessary if actual stress-strain curves were used. All the results are presented in terms of form factors since this notation is convenient for design purposes and is consistent with current British practice. Although the method adopted in the analysis is applicable to a number of different types of beam cross section, only rectangular cross sections are considered in detail at the present time.Curves are presented showing the variation of the form factor with respect to the angle of the plane of loading, for Case(i), and with respect to the ratio of bending moment to axial load for Case(ii). These curves are based upon a standardised form of the stress–strain curve which may be taken as representative of a range of aircraft materials. Consideration is given to the automatic satisfaction of present military proof loading requirements when these form factors are used for the estimation of maximum permissible bending moments and axial loads under ultimate loading conditions.The recommendations of F. P. Cozzone, for dealing with these two problems are examined and comparison is made between the theoretical work of this note and a limited number of test results available for Case(i).

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.

Development and testing of rolling cutter bit with a new arrangement of teeth on the balls

2020 ◽  
pp. 60-68
Author(s):  
V. A. Pyalchenkov ◽  
D. V. Pyalchenkov
Keyword(s):  
Axial Force ◽  
Axial Load ◽  
Vertical Line ◽  
Ball Joint ◽  
Line Passing

Research has found that the axial load applied to the bit is distributed unevenly along the crowns of the balls. The middle crowns are the busiest. The value of the axial force perceived by a separate ring is associated with the deformation of the details of the ball joint. You can reduce the uneven loading of crowns by shifting them along the ball along the radius of the bit, placing them so that the vertical line passing through the center of the lower ball of the lock bearing passes through the middle of the gap between the crowns of neighboring balls. The bits with the new option of placing the teeth on the balls were tested on the stand and in industrial conditions. For the bits of this design, the axial load was distributed more evenly over the crowns, which allowed increasing the efficiency of their work.

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.

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