The Twist Due To Bending Moment in Cantilevers Curved in flan

1956 ◽  
Vol 60 (544) ◽  
pp. 277-281
Author(s):  
W. Johnson
Keyword(s):  
Constant Curvature ◽  
Vertical Plane ◽  
Bending Moment ◽  
Shear Stresses ◽  
Bending Moments ◽  
Concentrated Load ◽  
Bending Stresses ◽  
Thin Walled ◽  
Shear Centre ◽  
The Web

The twist that arises from bending stresses in straight cantilevers of thin-walled section asymmetrical about any vertical plane, is well known and eventually leads to the concept of a shear centre. If an analysis is made along the same lines as that used for investigating straight beams, of cantilevers curved in plan, it is found that the bending moments transmitted are again responsible for shear stresses in the flanges of the beam and cause twisting.The following analyses refer, principally, to cases in which the cantilever carries a concentrated load at its end and are confined to the relatively simple forms of the channel and I-section. Each cantilever is perfectly built-in at one end and, for simplicity, it is considered that the web of a section offers no resistance to bending and that the beams are of constant curvature in plan.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

scholarly journals Silo with a Corrugated Sheet Wall

2013 ◽  
Vol 21 (3) ◽  
pp. 19-30 ◽  
Author(s):  
Csaba Németh ◽  
Ján Brodniansky
Keyword(s):  
Computational Models ◽  
Bending Moment ◽  
Physical Models ◽  
Experimental Measurements ◽  
Bending Moments ◽  
Bulk Materials ◽  
Production And Consumption ◽  
Thin Walled ◽  
The Mathematical Model

Abstract Silos and tanks are currently being used to create reserves of stored materials. Their importance is based on balancing the production and consumption of bulk materials to establish an adequate reserve throughout the year. The case study introduced within the framework of this paper focuses on thin-walled silos made of corrugated sheets and on an approach for designing these types of structures. The storage of bulk materials causes compression or tensile stresses in the walls of a silo structure. The effect of a frictional force in the silo walls creates an additional bending moment in a wave, which ultimately affects the resulting bending moments. Several mathematical and physical models were used in order to examine various types of loading and their effects on a structure. Subsequently, the accuracy of the computational models was verified by experimental measurements on a grain silo in Bojničky, Slovakia. A comparison of the experimental and mathematical models shows a reasonable match and confirms the load specifications, while indicating that the mathematical model was correct.

Stresses and deformations in overlapped diesel engine crankshafts, Part 2: Evaluation of results

1998 ◽  
Vol 212 (4) ◽  
pp. 255-270 ◽  
Author(s):  
I Bickley ◽  
V D'Olier ◽  
H Fessler ◽  
T. H. Hyde ◽  
N. A. Warrior
Keyword(s):  
Diesel Engine ◽  
Stress Concentration ◽  
Cross Sections ◽  
Shear Stresses ◽  
Previous Issue ◽  
Rectangular Section ◽  
Bending Stresses ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
The Web

The extensive results presented in Part 1 (in the previous issue*) have been supplemented and analysed further. A large number of cross-sections which could be reasonably used to calculate nominal stresses has been listed and evaluated. An inclined (flat, rectangular) section through the web is shown to be the best to calculate nominal stresses due to torsion, pure radial bending and bending due to crankpin forces; its width is h (see Fig. 1), the length of the shortest line joining crankpin and journal fillets in the plane of symmetry. Stress concentration factors based on these nominal stresses show only modest scatter from single curves for crankpin and journal fillets for torsion and radial bending. Predictions using the most commonly used method underestimate shear stresses due to torsion and overestimate bending stresses.

scholarly journals Assessment of internal pressure effect, causing additional bending of the pipeline

2020 ◽  
Vol 242 ◽  
pp. 160
Author(s):  
Ramil BAKTIZIN ◽  
Rail ZARIPOV ◽  
Gennadii KOROBKOV ◽  
Radik MASALIMOV
Keyword(s):  
Internal Pressure ◽  
Pressure Effect ◽  
Extreme Values ◽  
Bending Moment ◽  
Extreme Value ◽  
Bending Moments ◽  
Temperature Stresses ◽  
Working Pressure ◽  
Trunk Pipeline ◽  
Bending Stresses

Article justifies accounting for internal pressure effect in the pipeline, causing additional bending of the pipeline. According to some scientists, there is an erroneously used concept of the equivalent longitudinal axial force (ELAF) Sx, which depends on working pressure, temperature stresses, and joint deformations of pipelines with various types of soils. However, authors of the article use ELAF Sx concept at construction of mathematical model of stress-strain state (SSS) for complex section of the trunk pipeline, and also reveal it when analyzing the results of calculating the durability and stability of the pipeline. Analysis of SSS for calculated section of the pipeline was carried out for two statements of the problem for different values of operation parameters. In the first statement, effect of internal pressure causing bending of the pipeline is taken into account, and in the second it is neglected. It is shown that due to effect of ELAF Sx at p0 = 9.0 MPa, Dt = 29 °C extreme value of bend increases by 54 %, extreme values of bending stresses from span bending moment increase by 74 %, and extreme value of bending stresses from support bending moment double with regard to corresponding SSS characteristics of the pipeline. In case of neglecting the internal pressure effect causing additional bending of the pipeline (second statement of the problem), error in calculating the extreme value of bend is 35 %, extreme value of bending stresses from span bending moments is 44 %, and extreme value of bending stresses from support bending moments is 95 %.

Assessment of the Total Ship’s Hull Girder Bending Stresses When Unified Model of Sagging and Hogging Bending Moments is Used

2009 ◽  
Author(s):  
Lyuben D. Ivanov
Keyword(s):  
Life Span ◽  
Bending Moment ◽  
Extreme Value Statistics ◽  
Bending Moments ◽  
Hull Girder ◽  
Section Modulus ◽  
Probabilistic Distribution ◽  
Bending Stresses ◽  
Distribution Laws ◽  
Wave Induced

A method is proposed for calculating the hull girder bending stresses following the procedure in the class rules but in probabilistic terms, i.e. the still water and the wave-induced bending moments; the total hull girder bending moment; the hull girder section modulus and the hull girder bending stresses are treated as random variables with corresponding probabilistic distributions. The still water and wave-induced hull girder hogging and sagging loads are presented in probabilistic format as one phenomenon, i.e. using bi-modal probability density functions. The probabilistic distribution of the total hull girder load is calculated using the rules of the composition of the distribution laws of the constituent variables. After that, the hull girder geometric properties are presented in probabilistic format as annual distributions and distributions for any given life-span. Thus, it becomes possible to calculate both the annual probabilistic distributions and the probabilistic distribution for any given ship’s life span of the hull girder stresses. Individual amplitudes statistical analysis and extreme value statistics are used. Then, the probability of exceeding the permissible hull girder bending stresses in the class rules is calculated. An example is given for 25K DWT bulk carrier.

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.

Improved Generalized Procedure for Determining Critical State of a Thin-Walled Beam Under Combined Symmetric Loads

2019 ◽  
Vol 19 (08) ◽  
pp. 1950098 ◽  
Author(s):  
Phung Van Binh ◽  
Nguyen Viet Duc ◽  
Prokopov Vladimir Sergeevich ◽  
Dang Hoang Minh
Keyword(s):  
Bending Moment ◽  
Complex Loading ◽  
Computational Procedure ◽  
Beam Length ◽  
Concentrated Load ◽  
Internal Forces ◽  
Thin Walled ◽  
The Stability ◽  
External Loads

This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force [Formula: see text], bending moment [Formula: see text] at both ends, and concentrated load [Formula: see text] at midspan was studied. The case of a concentrated load [Formula: see text] replaced by a distributed load [Formula: see text] over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.

A Note on the Bending Moment Induced in the Booms of a Spar at the Point of Application of a Concentrated Load

1950 ◽  
Vol 1 (4) ◽  
pp. 281-290
Author(s):  
H. F. Winny
Keyword(s):  
Shear Strain ◽  
Experimental Verification ◽  
Mathematical Theory ◽  
Bending Moment ◽  
Wave Form ◽  
Concentrated Load ◽  
Original Investigation ◽  
Wing Spar ◽  
The Web

SummaryThe effect of a concentrated load, such as occurs in a wing spar at the fuselage, is to cause a discontinuity in shear strain of the spar web, which induces a bending moment in the booms through the medium of the rivets (or bolts) which attach the booms to the web. A mathematical theory is developed which shows that this bending induced in the boom is of a damped wave form starting at the point of application of the shear, and in practice the magnitude of the stresses produced by the bending moment may be appreciable at the wing root when the boom is deep compared with the spar depth (say 20 per cent.).Further experimental verification is desirable, but a single wing test suggested the original investigation, and showed a measure of agreement with the theory.

Optimization of Single-Strap Composite Joints

2006 ◽  
Author(s):  
Khaled Shahin ◽  
Farid Taheri
Keyword(s):  
Finite Element ◽  
Complete Solution ◽  
Bending Moment ◽  
Adhesive Layer ◽  
Upper And Lower Bounds ◽  
Complete Analysis ◽  
Shear Stresses ◽  
Bending Moments ◽  
Shear Forces ◽  
Analytical Expressions

Adhesive joints are increasingly being utilized in joining primary structural components made of fiber reinforced polymer composites (FRP). While adhesively bonded joints transfer loads by means of shear stresses the eccentricity of the load path found in such joints results in the lateral deformation of the joint assembly and the creation of bending moments at the end portions of the adhesive layer. In the case of the single-strap joint, the magnitude of such bending moments can render the joint structurally inefficient. That said, in many practical situations, the single-strap joint leads to be the only feasible joint configuration; therefore, the understanding of its characteristics is of paramount importance. A detailed analytical investigation of the deformations of single-strap joints was carried out to better understand the dependence of edge moments on various parameters influencing the joint capacity and performance. Accurate expressions were also developed for evaluating the magnitude of the bending moment and shear forces at the ends on the adhesive layer. A complete solution is provided that can accurately predict the magnitude of the edge forces in both balanced and unbalanced single-strap joints. The edge forces obtained from the solution can be used as boundary conditions for the complete analysis of shear and peel stresses in the adhesive layer. The analytical expressions of the bending moment and shear forces can also be used to determine the upper and lower bounds of the magnitudes of the edge forces. These limits show that the efficiency of a single-strap joint can be easily made comparable to that of the commonly used single-lap joint. It will also be shown that on the other hand, a carelessly designed single-strap joint can be nothing more than a so-called "built-in stress concentration". The integrity of the analytical expressions was also verified by geometrically nonlinear finite element analysis. The results obtained from the proposed solution showed better agreement to the finite element results than those obtained from the currently available solutions cited in the literature.

The Effect of the Secondary Bending Moment on the Fracture Strength Evaluation of the Laser Welded Joints from a Web Core Sandwich Structure

2014 ◽  
Vol 601 ◽  
pp. 124-128 ◽  
Author(s):  
Anghel Cernescu ◽  
Jani Romanoff ◽  
Heikki Remes
Keyword(s):  
Fracture Strength ◽  
Welded Joints ◽  
Sandwich Structure ◽  
Sandwich Structures ◽  
Weight Ratio ◽  
Bending Moment ◽  
Design Criterion ◽  
Bending Moments ◽  
Small Thickness ◽  
The Web

During the last period the interest on the sandwich structures has became more favorable due to the strength to weight ratio. In the same manner, in ship building field the lightweight structures became more and more attractive. With increasing the usage fields has increased the need to study the behavior of these structures. In general all the sandwich structures loaded in bending shows an effect of the secondary bending moment. In the case of web core sandwich panels used in ship structures has been observed a pronounced effect of the secondary bending moment on laser welded joints. Considering this, the paper presents an analysis of the fracture strength of laser welded joints of a web core sandwich structure, due to the effect of secondary bending moment. In the first part, the paper analytical formulation of the secondary bending moments and their effect on welded joints. This effect is explained on the basis of angle α defined in the paper and which depends on the thickness of the face plate, the thickness of the web plate and respectively the height. The paper continues with a numerical analysis of the stress and strain state from a web core sandwich beam and where also it is analyzed the effect of the secondary bending moment on the fracture strength of laser welded joints. Based on the carried out study it was observed that for high thickness of the web plate the effect of secondary bending moments is the overloading of the welded joints, instead for small thickness of the web plate the effect of the secondary bending moments can be of the unloading the welded joints. However, a small thickness of the web plate can affect the rigidity of the structure. Therefore, based on this study was proposed a solution to reduce the secondary bending moment without reducing the stiffness of the sandwich panel. The analysis conducted in this paper can be a design criterion for the web core sandwich structures.

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