Analysis on the Moment-Curvature Relationship for Prestressed UHPFRC Beams without Stirrup

2011 ◽  
Vol 255-260 ◽  
pp. 236-240
Author(s):  
Sang Mook Han ◽  
Qing Yong Guo
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Steel Fibre ◽  
Fibre Reinforcement ◽  
Cracking Behavior ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Good Agreement

To simplify the analysis, an elastic perfectly plastic stress-strain law was presented for UHPFRC. The post-cracking behavior was described by the average constant post-crack tensile strength. A strain parameter μ is proposed to evaluate the performance and efficiency of steel fibre reinforcement. 8 rectangular beams were tested in this investigation. Based on the proposed constitutive model, the full history of their flexural moment-curvature relationship for UHPFRC beams was calculated and compared with experimental data on prestressed UHPFRC beams. Good agreement between calculated strengths and experimental data was obtained.

The Indentation of an Elastic-Perfectly-Plastic Half-Space by a Hard Sphere

1972 ◽  
Vol 94 (1) ◽  
pp. 251-253 ◽  
Author(s):  
C. Hardy ◽  
C.-N. Baronet ◽  
G.-V. Tordion
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Hard Sphere ◽  
Present Note ◽  
Plane Surface ◽  
Metallic Materials ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Good Agreement

The indentation of hard steel spheres into the plane surface of quasi elastic-perfectly-plastic metallic materials has been investigated experimentally. It is shown in the present note that uniform results are obtained when the experimental data corresponding to some materials are reduced to a common base. These results are in fairly good agreement with the predictions of a previous finite element analysis by the same authors.

scholarly journals KUHN-TUCKER CONDITIONS IN SHAKEDOWN PROBLEMS

1996 ◽  
Vol 2 (5) ◽  
pp. 14-28
Author(s):  
Juozas Atkočiūnas
Keyword(s):  
Cyclic Loading ◽  
Mathematical Programming ◽  
Safety Factor ◽  
Strain Field ◽  
Analysis Problem ◽  
Cyclic Plastic ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment

An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

scholarly journals Fatigue Modeling and Numerical Analysis of Re-Filling Probe Hole of Friction Stir Spot Welded Joints in Aluminum Alloys

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2171
Author(s):  
Armin Yousefi ◽  
Ahmad Serjouei ◽  
Reza Hedayati ◽  
Mahdi Bodaghi
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Fatigue Life ◽  
Fatigue Strength ◽  
Fatigue Behavior ◽  
Element Model ◽  
Plastic Strain Amplitude ◽  
Friction Stir ◽  
Probe Hole ◽  
Good Agreement

In the present study, the fatigue behavior and tensile strength of A6061-T4 aluminum alloy, joined by friction stir spot welding (FSSW), are numerically investigated. The 3D finite element model (FEM) is used to analyze the FSSW joint by means of Abaqus software. The tensile strength is determined for FSSW joints with both a probe hole and a refilled probe hole. In order to calculate the fatigue life of FSSW joints, the hysteresis loop is first determined, and then the plastic strain amplitude is calculated. Finally, by using the Coffin-Manson equation, fatigue life is predicted. The results were verified against available experimental data from other literature, and a good agreement was observed between the FEM results and experimental data. The results showed that the joint’s tensile strength without a probe hole (refilled hole) is higher than the joint with a probe hole. Therefore, re-filling the probe hole is an effective method for structures jointed by FSSW subjected to a static load. The fatigue strength of the joint with a re-filled probe hole was nearly the same as the structure with a probe hole at low applied loads. Additionally, at a high applied load, the fatigue strength of joints with a refilled probe hole was slightly lower than the joint with a probe hole.

The Elastic-Softening Failure of Floating Beams

1988 ◽  
Vol 32 (01) ◽  
pp. 37-43
Author(s):  
Paul C. Xirouchakis
Keyword(s):  
Carrying Capacity ◽  
Maximum Load ◽  
Point Load ◽  
Negative Stiffness ◽  
Load Carrying Capacity ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Elastic Softening

The solution is presented for an infinite elastic-softening floating beam under a point load. The response depends on two nondimensional parameters: the negative stiffness coefficient that characterizes the descending part of the moment-curvature curve, and the nondimensional softening region half-length. The solution exhibits two important features that the elastic-perfectly plastic solution does not show. First, in certain ranges of parameters, the elastic-softening beam has a clearly defined maximum load carrying capacity. Second, in some other ranges of parameters, the elastic-softening beam has a minimum load or residual strength. The beam stiffens up upon further deformation due to the reactions of the water foundation. Critical softening parameters are calculated that separate stable from unstable behavior.

Scaling of Solutions for the Lateral Buckling of Elastic-Plastic Pipelines

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Ralf Peek ◽  
Heedo Yun
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Finite Element Solution ◽  
Reference Solution ◽  
Element Solution ◽  
Lateral Buckling ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
The Moment

Analytical solutions for the lateral buckling of pipelines exist for the case when the pipe material remains in the linearly elastic range. However for truly high temperatures and/or heavier flowlines, plastic deformation cannot be excluded. One then has to resort to finite element analyses, as no analytical solutions are available. This paper does not provide such an analytical solution, but it does show that if the finite element solution has been calculated once, then that solution can be scaled so that it applies for any other values of the design parameters. Thus the finite element solution need only be calculated once and for all. Thereafter, other solutions can be calculated by scaling the finite element solution using simple analytical formulas. However, the shape of the moment-curvature relation must not change. That is, the moment-curvature relation must be a scaled version of the moment-curvature relation for the reference problem, where different scale factors may be applied to the moment and curvature. This paper goes beyond standard dimensional analysis (as justified by the Bucklingham Π theorem), to establish a stronger scalability result, and uses it to develop simple formulas for the lateral buckling of any pipeline made of elastic-plastic material. The paper includes the derivation of the scaling result, the application procedure, the reference solution for an elastic-perfectly plastic pipe, and an example to illustrate how this reference solution can be used to calculate the lateral buckling response for any elastic-perfectly plastic pipe.

Loading History Effects for Deepwater S-Lay of Pipelines

2003 ◽  
Author(s):  
Heedo D. Yun ◽  
Ralf R. Peek ◽  
Paul P. Paslay ◽  
Frans F. Kopp
Keyword(s):  
Numerical Solutions ◽  
Loading History ◽  
Material Models ◽  
Plastic Deformations ◽  
Perfectly Plastic ◽  
History Effects ◽  
Departure Angle ◽  
Numerical Finite Element ◽  
Elastic Perfectly Plastic ◽  
The Moment

For economic reasons S-Lay is often preferred to J-Lay. However in very deep water S-Lay requires a high curvature of the stinger to achieve the required close-to-vertical departure angle. This can lead to plastic deformations of the pipe. The high top tension increases the plastic deformations in two ways: firstly it adds an overall tensile component to the strains, thereby increasing the strains at the 12 o’clock position. Secondly it increases the strain concentrations which arise due to discontinuous support of the pipe on the stinger. Typically the pipe is guided over a series of roller beds. The high top tension tends to straighten the spans between the roller beds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures are required at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an elastic-perfectly-plastic pipe, but can also be applied for other material models provided that: (i) the moment-curvature relation for the pipe under tension is known, and (ii) no cyclic plastic ratchetting occurs due to repeated bending of the pipe over the roller beds and straightening in the spans between roller beds. Agreement between the analytical and numerical (finite element) results is excellent, if the proper loading history is used in the numerical simulation. Otherwise the level of strain concentration can be overpredicted.

Dynamic Motion of RC Beams and One-Way Slabs Impacted by a Missile at Medium Velocity: Models for Spreadsheet Application

2010 ◽  
Author(s):  
Jean-Mathieu Rambach
Keyword(s):  
Velocity Models ◽  
Perfectly Plastic ◽  
Finite Differences Method ◽  
Order Of Magnitude ◽  
Sensitivity Studies ◽  
Rectangular Slab ◽  
Elastic Perfectly Plastic ◽  
Method Show ◽  
Spreadsheet Application ◽  
Good Agreement

This paper deals with the simulation of the motion of a one-span slender rectilinear RC beam or a thin one-way RC rectangular slab when impacted by a missile, within and beyond the elastic domain, up to a maximal displacement equal to the height of the section. The loading is variable in time and in space and the supporting conditions at each extremity are either of simply resting type or of clamping type. The equation of motion for each beam segment is expressed, through finite differences method, by relations between velocity and flexural moment that are decomposed on the basis of the first N modes of beam deformation. The plastic deformations are taken into account by constraining the flexural moment to follow elastic/perfectly plastic flexural moment–curvature law. The algorithms are well adapted to a spreadsheet application that allows easily: i) presizing such a structure against this type of loading, ii) the sensitivity studies regarding the mechanical parameters, iii) checking the order of magnitude of the results of big FEM models by using highly sophisticated codes. Simulations by this method show good agreement with experimental results and give access to some mechanical properties of the structure when damaged.

Net-Section Limit Pressure and Engineering J Estimates for Axial Part-Through Surface Cracked Pipes

2007 ◽  
Author(s):  
Yun-Jae Kim ◽  
Chang-Sik Oh ◽  
Tae-Kwang Song
Keyword(s):  
Estimation Method ◽  
Small Strain ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Axial Part ◽  
Elastic Perfectly Plastic ◽  
Axial Surface ◽  
Good Agreement ◽  
J Estimation

This paper provides net-section limit pressures and a reference stress based J estimation method for pipes with internal axial surface cracks under internal pressure. Based on systematic small strain FE limit analyses using elastic-perfectly plastic materials, closed-form approximations of net-section limit pressures are presented. Then, based on proposed net-section limit moments, a method to estimate elastic-plastic J is proposed based on the reference stress approach. Comparison with extensive FE results shows overall good agreement.

Reference Stress Solutions for Idealized Branch Junctions

2007 ◽  
Author(s):  
Yun-Jae Kim ◽  
Kuk-Hee Lee
Keyword(s):  
Three Dimensional ◽  
Limit Load ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Pipe Radius ◽  
Plastic Limit Load ◽  
The Mean ◽  
Elastic Perfectly Plastic ◽  
Good Agreement

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) FE limit analyses using elastic-perfectly plastic materials. The proposed solutions are valid to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparison with FE results shows good agreement.

Deformation, Displacement, and Work Bounds for Structures in a State of Creep and Subject to Variable Loading

1972 ◽  
Vol 39 (4) ◽  
pp. 953-958 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Time Constant ◽  
Variable Loading ◽  
Constant Loading ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic

General bounds on the deformation of a structure in a state of creep are derived for an elastic/perfectly plastic/time-hardening creep material, and subject to an arbitrary history of loading. Previously derived bounds for time constant loading are recovered and extended. The bounds are specialized to cyclic histories of loading. A simple example indicates that very accurate bounds are possible in some circumstances.

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