The Influence of Hyperbolic Notches on the Transverse Flexure of Elastic Plates

1940 ◽  
Vol 7 (2) ◽  
pp. A53-A56
Author(s):  
George H. Lee
Keyword(s):  
Infinite Plate ◽  
Bending Moment ◽  
Bending Moments ◽  
Elastic Plates ◽  
Transverse Bending ◽  
Narrow Section ◽  
Kirchhoff Theory

Abstract This paper considers the solution of the two problems of the infinite plate, with two symmetrically disposed hyperbolic notches, subjected to (a) transverse bending and (b) twisting. The transverse-bending moments and torsional couples are so applied that the narrow section between the notches transmits the bending moment or the torsional couple. Using the Poisson-Kirchhoff theory, finite expressions were obtained for the deflection and stress in each problem.

Mathematical Analogy between Non-Uniform Torsion and Transverse Bending of Thin-Walled Open Section Beams

2015 ◽  
Vol 725-726 ◽  
pp. 746-751 ◽  
Author(s):  
Vladimir Rybakov ◽  
Alexander Sergey
Keyword(s):  
Bending Moment ◽  
Maximum Deviation ◽  
Bending Moments ◽  
Distributed Load ◽  
Transverse Bending ◽  
Open Section ◽  
Uniformly Distributed Load ◽  
Thin Walled ◽  
And Function ◽  
Mathematical Analogy

The objective of this work is to identify and make an analysis of correlation between functions of bimoments and function of bending moments arising in the beams under the same loads. This article shows the possibility of using a diagram of bending moment multiplied by a factor as a diagram of bimoment. The maximum deviation between diagram of bending moment and diagram of bimoment made up 3.6 % of maximum bending moment in case of uniformly distributed load on one side of fixed supported beam.

Transverse Flexure of a Semi-Infinite Thin Plate Containing an Infinite Row of Circular Holes

1959 ◽  
Vol 26 (4) ◽  
pp. 661-665
Author(s):  
O. Tamate
Keyword(s):  
Thin Plate ◽  
Infinite Plate ◽  
Mutual Interference ◽  
Thin Plates ◽  
Bending Moments ◽  
Circular Holes ◽  
Kirchhoff Theory

Abstract The problem of finding stress resultants in a semi-infinite plate under plain bending and containing an infinite row of equal and equally spaced circular holes is discussed on the basis of the Poisson-Kirchhoff theory of thin plates. A method of perturbation is adopted for the determination of parametric coefficients included in the solution. The maximum bending moments occurring on the rim of the hole across the minimum section are calculated for several cases and shown in graphs, from which the mutual interference of adjacent boundaries will be informed.

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.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

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.

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.

Ship Operational and Safety Aspects of Ballast Water Exchange at Sea

1994 ◽  
Vol 31 (04) ◽  
pp. 315-326
Author(s):  
John B. Woodward ◽  
Michael G. Parsons ◽  
Armin W. Troesch
Keyword(s):  
Bending Moment ◽  
Bending Moments ◽  
University Of Michigan ◽  
Bulk Carrier ◽  
Rough Water ◽  
Design Values ◽  
Wave Heights ◽  
Ballast Tanks ◽  
The University ◽  
Wave Induced

A dry bulk carrier, a tanker, and a containership—taken as typical of ships trading to U.S. ports—are analyzed for possible hazards caused by emptying and refilling ballast tanks at sea. Using hydrostatic data furnished by the shipowners, hull bending moments and stabilities are investigated to find the tank-emptying operations that produce the greatest changes in those parameters. As should be expected, bending moment changes do not exceed allowable stillwater values. Changes in GM are insignificant. The worst hydrostatic cases serve as a guide to conditions that should be analyzed in rough water. The University of Michigan SHIPMO program shows that in waves of 10-ft significant height wave-induced bending moments and shears are far below the design values published by the American Bureau of Shipping. On the other hand, in waves of 20-ft significant height, the maximum wave heights that occur occasionally can cause moments or shears that exceed design values. For the 20-ft case, both linear and nonlinear versions of SHIPMO are used.

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