scholarly journals Stress Analysis of Suspended Pipe Partially Buried in Linear Elastic Soil

2016 ◽  
Vol 10 (1) ◽  
pp. 161-169
Author(s):  
Kun Huang ◽  
Xia Li ◽  
Yiheng Zhang
Keyword(s):  
Beam Theory ◽  
Bending Moment ◽  
Critical Length ◽  
Beam Model ◽  
Linear Elastic ◽  
Limit Value ◽  
Axial Tension ◽  
Calculation Results ◽  
Stress And Deformation ◽  
Elastic Soil

Based on the small deflection beam theory, bending equation with axial tension of suspended pipe partially buried in the linear elastic soil is established. And the corresponding boundary conditions are given according to the stress and deformation characteristics of suspended section and buried section. Then deflection equation for the suspended section is deduced. Afterwards, the stress and critical length of a suspended pipeline are calculated and analyzed. The results show that the tensile stress and bending stress on the endpoint of the suspended section meet the requirement of first strength theory and the critical suspended length is greater than the real suspended length, which is consistent with the actual situation. When the stiffness of soil tends to approach infinity, both the limit value of axial tension and endpoint bending moment agree well with the calculation results of fixed-fixed supported beam model.

Micro Cantilever Beam Theory for Transverse Dynamics Using a Continuum Mechanics Model

2011 ◽  
Vol 415-417 ◽  
pp. 760-763
Author(s):  
Cheng Li ◽  
Wei Guo Huang ◽  
Lin Quan Yao
Keyword(s):  
Scale Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Beam Model ◽  
Cantilever Beams ◽  
Mechanics Model ◽  
Axial Tension ◽  
Vibrational Characteristics ◽  
Micro Cantilever

The vibrational characteristics of cantilever beams with initial axial tension were studied using a nonlocal continuum Euler-Bernoulli beam model. Small size effects are essential to nanotechnology and it can not be ignored in micro or nano scale. Nonlocal elasticity theory has been proved to work well in nanomechanics and it is considered into the governing equation which can be transformed into a fourth-order ordinary differential equation together with a dispersion relation. Boundary conditions are applied so as to determine the analytical solutions of vibrational mode shape and transverse deformation through a numerical method. Relations between natural frequency and the small scale parameter are obtained, including the fundamental and the second order frequencies. It is found that both the small scale parameter and dimensionless initial axial tension play remarkable roles in dynamic behaviors of micro cantilever beams and their effects are analyzed and discussed in detail.

Numerical Simulation on Combined Deformation of Tip-Loaded Cantilever Beam with Particle Flow Code

2011 ◽  
Vol 378-379 ◽  
pp. 31-34
Author(s):  
Yi Bo Xiong ◽  
Chun Ming Wang ◽  
Lu Peng
Keyword(s):  
Cantilever Beam ◽  
Axial Load ◽  
Beam Theory ◽  
Bending Moment ◽  
Transverse Load ◽  
Particle Flow ◽  
Particle Flow Code ◽  
Shear Stresses ◽  
Axial Tension ◽  
Theory Solution

In order to calculate the combined deformations of an Euler-Bernoulli cantilever beam subjected to bending moment, twisting moment, transverse load and axial load, particle flow code in 3 dimensions (PFC3D) is used with parallel bonds model. The computed deformations, including transverse deflections, rotations about axis, maximum normal and shear stresses, were compared with the analytical beam-theory solution in terms of axial tension, axial compression and none axial load, respectively. Between computed results and analytical beam-theory solution, the error bands are greater than 99.7% at the beam tip, while the error of the transverse deflection of the whole beam is less than 0.6%. So, the PFC3D is able to precisely simulate the combined deformation of cantilever beam, and this work has special reference to engineering calculations and designs when PFC is applied to model the mechanical behaviors of continuum materials.

scholarly journals Dynamic Gust Load Analysis for Rotors

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Yuting Dai ◽  
Linpeng Wang ◽  
Chao Yang ◽  
Xintan Zhang
Keyword(s):  
Structural Model ◽  
Beam Theory ◽  
Bending Moment ◽  
Iteration Algorithm ◽  
Beam Model ◽  
Euler Beam ◽  
Helicopter Rotors ◽  
Aeroelastic Model ◽  
Flap Deflection ◽  
The Time Domain

Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

Analysis of Full-Scale Hull Girder Loads of a Container Carrier and Its Simulation Using a Nonlinear Seakeeping Program

2010 ◽  
Author(s):  
Seung Jae Lee ◽  
Han C. Yu ◽  
Sungeun Peter Kim ◽  
Mun-Keun Ha ◽  
Gun-Il Park ◽  
...  
Keyword(s):  
Interaction Analysis ◽  
Elastic Beam ◽  
Bending Moment ◽  
Frequency Component ◽  
Full Scale ◽  
Beam Model ◽  
Stress Monitoring ◽  
Hull Girder ◽  
Navigation Data ◽  
Calculation Results

ABS, SHI, and OOCL have been conducting a project on full-scale measurement of hull stress of a container carrier since 2006. A Hull Stress Monitoring System (HSMS) was installed on an 8063 TEU container carrier recording hull girder loads and other navigation data. Vibratory responses of the hull girder were recorded at certain conditions, such as in the limited fetch storm waves in the Mediterranean Sea. The recorded data has been analyzed to determine the level of vibratory responses and the conditions in which they occurred. Since the vibratory response is superposed to the wave frequency component of the hull girder loads, it also affects the statistics of the maximum hull girder loads in waves. The effects of the vibratory responses in the long-term have been investigated for the dynamic Vertical Bending Moment (VBM) and bow acceleration. While the full-scale measurement provides valuable data for what actually happened in real vessel operations, the actual conditions can not be controlled, such as the wave environments or loading conditions. Hence, numerical calculation results are also desirable to investigate the vibratory responses under controlled conditions taking into account the elastic hull girder properties under exact conditions for validation purposes. ABS has been applying a time domain nonlinear wave/body interaction analysis program, NLOAD3D, for the assessment of the structural responses of vessels in large waves. The NLOAD3D program has been further developed to incorporate an elastic beam model to reproduce vibratory hull girder responses, with the simulations being carried out on motions and moments for selected notable events recorded during the voyages. Comparisons of the simulation and the measurement are presented.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

scholarly journals Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 610
Author(s):  
Chunbao Li ◽  
Hui Cao ◽  
Mengxin Han ◽  
Pengju Qin ◽  
Xiaohui Liu
Keyword(s):  
Analytical Method ◽  
Bending Moment ◽  
Nonlinear Problems ◽  
Weather Conditions ◽  
Order Effect ◽  
Practical Calculation ◽  
Geometrically Nonlinear ◽  
Uniform Load ◽  
Safety Research ◽  
Calculation Results

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.

Effect of Torsion on Collapse Bending Moment for 24-Inch Diameter Schedule 80 Pipes With Wall Thinning

2012 ◽  
Author(s):  
Kunio Hasegawa ◽  
Yinsheng Li ◽  
Bostjan Bezensek ◽  
Phuong Hoang
Keyword(s):  
Power Plants ◽  
Bending Moment ◽  
Combined Loading ◽  
Bending Moments ◽  
Compressive Stresses ◽  
Wall Thinning ◽  
Nominal Thickness ◽  
Calculation Results ◽  
Loading Modes ◽  
Local Wall Thinning

Piping items in power plants may experience combined bending and torsion moments during operation. Currently, there is a lack of guidance in the ASME B&PV Code Section XI for combined loading modes including pressure, torsion and bending. Finite element analyses were conducted for 24-inch diameter Schedule 80 pipes with local wall thinning subjected to tensile and compressive stresses. Plastic collapse bending moments were calculated under constant torsion moments. From the calculation results, it can be seen that collapse bending moment for pipes with local thinning subjected to tensile stress is smaller than that subjected to compressive stress. In addition, equivalent moment is defined as the root the sum of the squares of the torsion and bending moments. It is found that the equivalent moments can be approximated with the pure bending moments, when the wall thinning length is equal or less than 7.73R·t for the wall thinning depth of 75% of the nominal thickness, where R is the mean radius and t is the wall thickness of the pipe.

Strength of a Pipe Mitred Bend

1970 ◽  
Vol 92 (4) ◽  
pp. 767-773 ◽  
Author(s):  
Jaroslaw Sobieszczanski
Keyword(s):  
Internal Pressure ◽  
Maximum Stress ◽  
Cylindrical Shells ◽  
Beam Theory ◽  
The Self ◽  
Design Work ◽  
Stress And Deformation

Single and multiple mitred bends are analyzed for stress and deformation due to inplane bending and internal pressure. Theory of cylindrical shells is used as a tool of analysis. Results show maximum stress at the elbow increased up to more than 400 percent of the stress predicted by elementary beam theory. Influence of the elbow on the self-compensation of the heated pipeline is discussed and the local reinforcements proposed. Solutions are presented as graphs which may be directly applied in design work.

Load Regime Diagram of a Pipe With Cyclically Plastic Bending

2002 ◽  
Author(s):  
Yanping Yao ◽  
Ming-Wan Lu
Keyword(s):  
Axial Force ◽  
Bending Moment ◽  
Boundary Curve ◽  
Plastic Behavior ◽  
Cyclic Bending ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Load Regime ◽  
Reversed Cyclic ◽  
Cyclic Bending Moment

The criteria of piping seismic design based on linear elastic analysis has been proved to be conservative, which is mainly because the influence of plastic deformation on piping dynamic response is neglected. In the present paper, a pipe under seismic excitation is simplified as an beam with tubular cross section subjected to steady axial force and fully reversed cyclic bending moment, and the elastic-plastic behavior of the pipe is studied. Various behavior of the pipe under different combinations of axial force and cyclic bending moment is discussed and the boundary curve equations between them are obtained. Also the load regime diagram for a pipe which is formed by the boundary curve equations in the loading plane is given, from which the elastic-plastic behavior of the pipe can be determined directly.

scholarly journals Effect of Slam Force Duration on the Vibratory Response of a Lightweight High-Speed Wave-Piercing Catamaran

2015 ◽  
Vol 59 (02) ◽  
pp. 69-84
Author(s):  
Jason John McVicar ◽  
Jason Lavroff ◽  
Michael Richard Davis ◽  
Giles Thomas
Keyword(s):  
High Speed ◽  
Bending Strength ◽  
Experimental Studies ◽  
Bending Moment ◽  
Higher Order ◽  
Acute Angle ◽  
Beam Model ◽  
Higher Order Modes ◽  
Hull Structure ◽  
Vertical Bending Moment

When the surface of a ship meets the water surface at an acute angle with a high relative velocity, significant short-duration forces can act on the hull plating. Such an event is referred to as a slam. Slam loads imparted on ships are generally considered to be of an impulsive nature. As such, slam loads induce vibration in the global hull structure that has implications for both hull girder bending strength and fatigue life of a vessel. A modal method is often used for structural analysis whereby higher order modes are neglected to reduce computational effort. The effect of the slam load temporal distribution on the whipping response and vertical bending moment are investigated here by using a continuous beam model with application to a 112 m INCAT wave-piercing catamaran and correlation to full-scale and model-scale experimental data. Experimental studies have indicated that the vertical bending moment is dominated by the fundamental longitudinal bending mode of the structure. However, it is shown here that although the fundamental mode is dominant in the global structural response, the higher order modes play a significant role in the early stages of the response and may not be readily identifiable if measurements are not taken sufficiently close to the slam location. A relationship between the slam duration and the relative modal response magnitudes is found, which is useful in determining the appropriate truncation of a modal solution.

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