A Comprehensive Study of the Fixed Edge Bending Moments of Thin Rectangular Cantilever Plates Under Point Loading

1976 ◽  
Vol 98 (3) ◽  
pp. 766-772
Author(s):  
O. L. Hageniers ◽  
W. P. T. North
Keyword(s):  
Aspect Ratio ◽  
Cantilever Beam ◽  
Bending Moment ◽  
Experimental Program ◽  
Plate Bending ◽  
Bending Moments ◽  
Cantilever Plate ◽  
Work Done ◽  
Theory And Experiment ◽  
Comprehensive Study

An experimental program was performed to determine the effect of aspect ratio on point loaded cantilever plate bending moments. The experimental results are compared to theoretical values based on an extension of the work done on cantilever plate deflections by Szmelter, Sulikowski, and Lipinski [1]. The theory and experiment give excellent agreement over the range of aspect ratio studied. A series of curves is presented which gives the maximum plate bending moment as a function of aspect ratio and load position. These curves indicate the transition of plate bending moments from the cantilever beam case to the infinitely wide cantilever plate case.

A Comprehensive Study of the Small Deflections of Thin Rectangular Cantilever Plates Under Point Loading

1974 ◽  
Vol 96 (3) ◽  
pp. 833-838
Author(s):  
O. L. Hageniers ◽  
W. P. T. North
Keyword(s):  
Aspect Ratio ◽  
Cantilever Beam ◽  
Experimental Program ◽  
Maximum Deflection ◽  
Cantilever Plate ◽  
Theory And Experiment ◽  
Good Agreement ◽  
Comprehensive Study

An experimental program was carried out to determine the effect of aspect ratio on cantilever plate deflections under point loadings. These results were compared to deflection information obtained using the theoretical technique outlined by Szmelter, Sulikowski and Lipinski [1]. The theory and experiment gave good agreement over the range of aspect ratio studied. A series of curves giving the maximum deflection of a cantilever plate as a function of aspect ratio and load position are presented. These curves show the transition of plate deflections from the cantilever beam case to the infinitely wide cantilever plate case.

An experimental investigation of a right-angled single unreinforced mitred-bend subjected to various bending moments

1966 ◽  
Vol 1 (3) ◽  
pp. 248-263 ◽  
Author(s):  
N Jones ◽  
R Kitching
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Straight Tube ◽  
Bending Moments ◽  
Curved Pipe ◽  
Design Procedures ◽  
Out Of Plane ◽  
Plane Bending ◽  
Comprehensive Study

It is well known that, upon the application of an in-plane bending moment, the initially circular cross-section of a curved pipe tends to flatten and become approximately elliptical in shape making it much more flexible than an equivalent straight tube. Mitred-bends exhibit similar properties though the behaviour is far more complex. A comprehensive study of a 90° single unreinforced mitred-bend having a radius/thickness ratio of 19 has been performed by means of a stress-probing method. In order to make the work more complete, results have been obtained for a similar bend when subjected to out-of-plane bending and twisting moments. Experimental measurements of stress and flexibility for each type of loading are discussed and certain modifications suggested to existing design procedures.

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.

BENDING OF ORTHOTROPIC RECTANGULAR CANTILEVER PLATE

2021 ◽  
pp. 2-9
Author(s):  
M.V. Sukhoterin ◽  
◽  
A.M. Maslennikov ◽  
T.P. Knysh ◽  
I.V. Voytko ◽  
...  
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Trigonometric Series ◽  
Bending Moment ◽  
Partial Solution ◽  
Numerical Results ◽  
Cantilever Plate ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Beam Function

Abstract. An iterative method of superposition of correcting functions is proposed. The partial solution of the main differential bending equation is represented by a fourth-degree polynomial (the beam function), which gives a residual only with respect to the bending moment on parallel free faces. This discrepancy and the subsequent ones are mutually compensated by two types of correcting functions-hyperbolic-trigonometric series with indeterminate coefficients. Each function satisfies only a part of the boundary conditions. The solution of the problem is achieved by an infinite superposition of correcting functions. For the process to converge, all residuals must tend to zero. When the specified accuracy is reached, the process stops. Numerical results of the calculation of a square ribbed plate are presented.

Investigation of Smooth Pipe Bends Under the Effect of In-Plane Bending

2017 ◽  
Author(s):  
Diana Abdulhameed ◽  
Michael Martens ◽  
J. J. Roger Cheng ◽  
Samer Adeeb
Keyword(s):  
High Stress ◽  
Circular Cross Section ◽  
Bending Moment ◽  
Bend Angle ◽  
Bending Moments ◽  
Bend Radius ◽  
Pipe Bend ◽  
Cross Sectional ◽  
Smooth Pipe ◽  
Plane Bending

Pipe bends are frequently used to change the direction in pipeline systems and they are considered one of the critical components as well. Bending moments acting on the pipe bends result from the surrounding environment, such as thermal expansions, soil deformations, and external loads. As a result of these bending moments, the initially circular cross-section of the pipe bend deforms into an oval shape. This consequently changes the pipe bend’s flexibility leading to higher stresses compared to straight pipes. Past studies considered the case of a closing in-plane bending moment on 90-degree pipe bends and proposed factors that account for the increased flexibility and high-stress levels. These factors are currently presented in the design codes and known as the flexibility and stress intensification factors (SIF). This paper covers the behaviour of an initially circular cross-sectional smooth pipe bend of uniform thickness subjected to in-plane opening/closing bending moment. ABAQUS FEA software is used in this study to model pipe bends with different nominal pipe sizes, bend angles, and various bend radius to cross-sectional pipe radius ratios. A comparison between the CSA-Z662 code and the FEA results is conducted to investigate the applicability of the currently used SIF factor presented in the design code for different loading cases. The study showed that the in-plane bending moment direction acting on the pipe has a significant effect on the stress distribution and the flexibility of the pipe bend. The variation of bend angle and bend radius showed that it affects the maximum stress drastically and should be considered as a parameter in the flexibility and SIF factors. Moreover, the CSA results are found to be un-conservative in some cases depending on the bend angle and direction of the applied bending moment.

scholarly journals AIRFOIL SHAPED STRUTS FOR VERTICAL AXIS WIND TURBINE

2021 ◽  
Vol 5 (9) ◽  
Author(s):  
Samyak Jain ◽  
Gautam Singh ◽  
Varun Yadav ◽  
Rahul Bisht
Keyword(s):  
Aspect Ratio ◽  
Wind Energy ◽  
Wind Turbine ◽  
Energy Resource ◽  
Bending Moment ◽  
Clean Energy ◽  
Vertical Axis ◽  
Vertical Axis Wind Turbine ◽  
Aspect Ratios ◽  
Cost Of Energy

Currently, many countries are racing towards switching to clean energy resource (1). Among the options available Solar and Wind are two viable options that are economically feasible. Each day a new development is helping in bringing down the cost of energy extracted from these sources. With currently available technologies, solar energy is almost as expensive as the energy generated from burning coal, whereas wind energy is still slightly expensive (2). However, wind energy could be made cheaper by the use of a vertical axis wind turbine (3). However, structure is a major factor that is holding back the development of VAWTs with better efficiency (4). The efficiency of a VAWT depends upon its aspect ratio. Aspect Ratio is the ratio of the height of the blade to the diameter of the turbine. The lower the aspect ratio, the higher the efficiency (5). However, decreasing the AR would mean either increasing the diameter of the turbine or the height of the blade. In either case, the bending moment would increase on the struts, that connect the blades to the shaft. In this paper we propose, struts with airfoil cross-section. This is because, the lift generated by airfoil struts acts as additional support for the blade, thus increasing our ability to work at lower aspect ratios.

scholarly journals On homogenous solutions of the problem of a rectangular cantilever plate bending

2016 ◽  
Vol 2 (3) ◽  
pp. 247-255
Author(s):  
Mikhail V. Sukhoterin ◽  
Sergey O. Baryshnikov ◽  
Kseniya O. Lomteva
Keyword(s):  
Plate Bending ◽  
Cantilever Plate

Structural Reliability of Oil Tanker in the Adriatic Sea Damaged in Collision and Exposed to Combined Bending Moments

2018 ◽  
Author(s):  
Maro Ćorak ◽  
Joško Parunov
Keyword(s):  
Structural Reliability ◽  
Adriatic Sea ◽  
Bending Moment ◽  
State Function ◽  
Regression Equations ◽  
Bending Moments ◽  
Damage Stability ◽  
Safety Indices ◽  
Oil Tanker ◽  
Damaged Ship

The aim of the paper is the assessment of structural reliability of oil tanker which may be damaged in collision accident in the Adriatic Sea and exposed to combined, horizontal and vertical bending moments. Damage size is assumed based on the direct numerical simulation of the ship-ship collision. This is justified for some specific sea environments, as the Adriatic Sea, where ship sailing routes and representative ship types involved in accidents are known, so possible collision scenarios may be reasonably predicted. Residual bending moment capacity under combined bending moment is calculated using regression equations developed based on non-linear finite element analysis. Still water vertical bending moments are obtained by damage stability analysis. Vertical and horizontal wave bending moments are determined by short-term response analysis of damaged ship in the Adriatic Sea, using transfer functions obtained by 3D panel hydrodynamic method. Limit state function is defined using interaction equation for damaged ship exposed to combined bending moments. Safety indices are calculated by FORM for different collision scenarios that are generated by MC simulations. Such approach enables to determine the safety indices for the most frequent damages and also to reveal the most critical situations resulting in the lowest safety indices.

Design Charts for Symmetrical Ring Girders

1957 ◽  
Vol 24 (1) ◽  
pp. 144-147
Author(s):  
G. P. Fisher
Keyword(s):  
Energy Analysis ◽  
Bending Moment ◽  
Bending Moments ◽  
Bending Energy ◽  
Normal Loading ◽  
Critical Design ◽  
Design Charts ◽  
Ring Location

Abstract Charts, based on classical bending-energy analysis, are presented for the determination of critical design moments in symmetrical ring girders varying in shape from circular through round to sharp-cornered rings. The girders are subjected to uniform normal loading in the plane of the ring. Location and magnitude of all critical bending moments are given, from which the maximum bending moment is easily selected.

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