Showing papers on "Bending moment published in 1978"

Structural Analysis: A Unified Classical and Matrix Approach

Abstract: Introduction to the analysis of statistically indeterminate structures force method of analysis displacement method of analysis use of force and displacement methods strain energy and virtual work method of virtual work and its application to trusses further applications of method of virtual work important energy theorems - Betti's and Maxwell's theorems, application of Betti's theorem to transformation of forces and displacements, Engesser's theorem of compatability, Castigliano's theorem of compatability, Catigliano's theorems displacement of elastic structures by special methods application of the force method - column analogy application of the displacement method - slope deflection and moment distribution moment distribution with sway - multistorey and multibay frames influence lines for beams, frames and grids - Muller-Breslau's principle influence lines for arches, trusses and prestressed concrete members effects of axial forces analysis of shear-wall structures method of finite differences analysis of plates by finite differences finite-element method further development of finite-element method plastic analysis of continuous beams and frames yield-line and strip methods for slabs structural dynamics computer analysis of framed structures implementation of computer analysis. Appendices: matrix algebra, displacements of prismatic members, fixed-end forces of prismatic members, end-forces caused by end-displacements of prismatic members, reactions and bending moments of supports of continuous beams due to unit displacement of supports, properties of geometrical figures, torsional constants, values of the integral, deflections of a simple beam of constant EI subjected to unit end-moments, geometrical properties of some plane areas commonly used in the method of column analogy, forces due to prestressing.

Applied Strength of Materials

Abstract: Preface 1 Basic Concepts in Strength of Materials The Big Picture 1-1 Objective of This Book - To Ensure Safety 1-2 Objectives of This Chapter 1-3 Problem-solving Procedure 1-4 Basic Unit Systems 1-5 Relationship Among Mass, Force, and Weight 1-6 The Concept of Stress 1-7 Direct Normal Stress 1-8 Stress Elements for Direct Normal Stresses 1-9 The Concept of Strain 1-10 Direct Shear Stress 1-11 Stress Element for Shear Stresses 1-12 Preferred Sizes and Standard Shapes 1-13 Experimental and Computational Stress 2 Design Properties of Materials The Big Picture 2-1 Objectives of This Chapter 2-2 Design Properties of Materials 2-3 Steel 2-4 Cast Iron 2-5 Aluminum 2-6 Copper, Brass, and Bronze 2-7 Zinc, Magnesium, Titanium, and Nickel-Based Alloys 2-8 Nonmetals in Engineering Design 2-9 Wood 2-10 Concrete 2-11 Plastics 2-12 Composites 2-13 Materials Selection 3 Direct Stress, Deformation, and Design The Big Picture and Activity 3-1 Objectives of this Chapter 3-2 Design of Members under Direct Tension or Compression 3-3 Design Normal Stresses 3-4 Design Factor 3-5 Design Approaches and Guidelines for Design Factors 3-6 Methods of Computing Design Stress 3-7 Elastic Deformation in Tension and Compression Members 3-8 Deformation Due to Temperature Changes 3-9 Thermal Stress 3-10 Members Made of More Than One Material 3-11 Stress Concentration Factors for Direct Axial Stresses 3-12 Bearing Stress 3-13 Design Bearing Stress 3-14 Design Shear Stress 4 Torsional Shear Stress and Torsional Deformation The Big Picture 4-1 Objectives of This Chapter 4-2 Torque, Power, and Rotational Speed 4-3 Torsional Shear Stress in Members with Circular Cross Sections 4-4 Development of the Torsional Shear Stress Formula 4-5 Polar Moment of Inertia for Solid Circular Bars 4-6 Torsional Shear Stress and Polar Moment of Inertia for Hollow Circular Bars 4-7 Design of Circular Members under Torsion 4-8 Comparison of Solid and Hollow Circular Members 4-9 Stress Concentrations in Torsionally Loaded Members 4-10 Twisting - Elastic Torsional Deformation 4-11 Torsion in Noncircular Sections 5 Shearing Forces and Bending Moments in Beams The Big Picture 5-1 Objectives of this Chapter 5-2 Beam Loading, Supports, and Types of Beams 5-3 Reactions at Supports 5-4 Shearing Forces and Bending Moments for Concentrated Loads 5-5 Guidelines for Drawing Beam Diagrams for Concentrated Loads 5-6 Shearing Forces and Bending Moments for Distributed Loads 5-7 General Shapes Found in Bending Moment Diagrams 5-8 Shearing Forces and Bending Moments for Cantilever Beams 5-9 Beams with Linearly Varying Distributed Loads 5-10 Free-Body Diagrams of Parts of Structures 5-11 Mathematical Analysis of Beam Diagrams 5-12 Continuous Beams - Theorem of Three Moments 6 Centroids and Moments of Inertia of Areas The Big Picture 6-1 Objectives of This Chapter 6-2 The Concept of Centroid - Simple Shapes 6-3 Centroid of Complex Shapes 6-4 The Concept of Moment of Inertia 6-5 Moment of Inertia for Composite Shapes Whose Parts have the Same Centroidal Axis 6-6 Moment of Inertia for Composite Shapes - General Case - Use of the Parallel Axis Theorem 6-7 Mathematical Definition of Moment of Inertia 6-8 Composite Sections Made from Commercially Available Shapes 6-9 Moment of Inertia for Shapes with all Rectangular Parts 6-10 Radius of Gyration 6-11 Section Modulus 7 Stress Due to Bending The Big Picture 7-1 Objectives of This Chapter 7-2 The Flexure Formula 7-3 Conditions on the Use of the Flexure Formula 7-4 Stress Distribution on a Cross Section of a Beam 7-5 Derivation of the Flexure Formula 7-6 Applications - Beam Analysis 7-7 Applications - Beam Design and Design Stresses 7-8 Section Modulus and Design Procedures 7-9 Stress Concentrations 7-10 Flexural Center or Shear Center 7-11 Preferred Shapes for Beam Cross Sections 7-12 Design of Beams to be Made from Composite Materials 8 Shearing Stresses in Beams The Big Picture 8-1 Objectives of this Chapter 8-2 Importance of Shearing Stresses in Beams 8-3 The General Shear Formula 8-4 Distribution of Shearing Stress in Beams 8-5 Development of the General Shear Formula 8-6 Special Shear Formulas 8-7 Design for Shear 8-8 Shear Flow 9 Deflection of Beams The Big Picture 9-1 Objectives of this Chapter 9-2 The Need for Considering Beam Deflections 9-3 General Principles and Definitions of Terms 9-4 Beam Deflections Using the Formula Method 9-5 Comparison of the Manner of Support for Beams 9-6 Superposition Using Deflection Formulas 9-7 Successive Integration Method 9-8 Moment-Area Method 10 Combined Stresses The Big Picture 10-1 Objectives of this Chapter 10-2 The Stress Element 10-3 Stress Distribution Created by Basic Stresses 10-4 Creating the Initial Stress Element 10-5 Combined Normal Stresses 10-6 Combined Normal and Shear Stresses 10-7 Equations for Stresses in Any Direction 10-8 Maximum Stresses 10-9 Mohr's Circle for Stress 10-10 Stress Condition on Selected Planes 10-11 Special Case in which Both Principal Stresses have the Same Sign 10-12 Use of Strain-Gage Rosettes to Determine Principal Stresses 11 Columns The Big Picture 11-1 Objectives of this Chapter 11-2 Slenderness Ratio 11-3 Transition Slenderness Ratio 11-4 The Euler Formula for Long Columns 11-5 The J. B. Johnson Formula for Short Columns 11-6 Summary - Buckling Formulas 11-7 Design Factors and Allowable Load 11-8 Summary - Method of Analyzing Columns 11-9 Column Analysis Spreadsheet 11-10 Efficient Shapes for Columns 11-11 Specifications of the AISC 11-12 Specifications of the Aluminum Association 11-13 Non-Centrally Loaded Columns 12 Pressure Vessels The Big Picture 12-1 Objectives of this Chapter 12-2 Distinction Between Thin-Walled and Thick-Walled Pressure Vessels 12-3 Thin-Walled Spheres 12-4 Thin-Walled Cylinders 12-5 Thick-Walled Cylinders and Spheres 12-6 Analysis and Design Procedures for Pressure Vessels 12-7 Spreadsheet Aid for Analyzing Thick-Walled Spheres and Cylinders 12-8 Shearing Stress in Cylinders and Spheres 12-9 Other Design Considerations for Pressure Vessels 12-10 Composite Pressure Vessels 13 Connections The Big Picture 13-1 Objectives of this Chapter 13-2 Modes of Failure 13-3 Riveted Connections 13-4 Bolted Connections 13-5 Allowable Stresses for Riveted and Bolted Connections 13-6 Example Problems - Riveted and Bolted Joints 13-7 Eccentrically Loaded Riveted and Bolted Joints 13-8 Welded Joints with Concentric Loads Appendix Answers to Selected Problems Index

Acoustical response of hair receptors in insects

Abstract: A detailed mechanical model is developed to account for the behaviour of hair-like acoustical sensory receptors in insects. For the small hair diameters commonly found, it is concluded that the force acting on the moving hair is caused almost entirely by the viscosity of the air, as analyzed long ago by Stokes. The result of this viscous force is to provide a bending moment about the base of the hair that is proportional to the acoustic particle velocity but that lags behind it by about 135°. In addition the viscous force increases the moment of inertia of the hair by a large and frequency dependent addition, and provides a viscous damping term of sufficient magnitude to reduce the Q value to near unity.

The mechanical testing of a sliding meniscus knee prosthesis.

Abstract: A 3-component sliding meniscus knee prosthesis was tested mechanically to evaluate the direct loads and the anteroposterior and mediolateral bending moments on the prosthetic components during the loading phase on a pendulum prosthesis testing machine. The bending moments changed with variation of the component positions. Tilting the tibial plateau produced the greatest change in lateral bending moment on the femoral component but alteration in plateau rotation or femoral tilting produced little change in the low values of the 2 bending moments. It is necessary to ensure that the tibial component is positioned horizontally on the tibial plateau, but it is not necessary to be concerned about the angle of the femoral component to the vertical or the misalignment rotationally of the tibial component. The load ideally passes through the condylar component to the tibia much more centrally than if it were a constrained prosthesis system during the loading range, reducing the likelihood of displacement of the 2 fixed components.

Method and apparatus for bending elongated materials

Abstract: The disclosure relates to a method of bending elongated materials such as pipe by applying a compressive primary bending force to the material at locations on either end of the portion of the material to be bent and locally stimulating bending of that portion of the material by the application of heat or a secondary bending force. The end portions of the materials are engaged by clamps, each clamp having an arm extending normal to the principle axis of the material. The compressive primary bend force is applied by exerting a force on locations on the arms displaced from the principal axis of the material, which force tends to draw the ends of the arms together.

Wind-tunnel test results of a full-scale multicyclic controllable twist rotor

Abstract: Results of wind tunnel testing of a multicyclic controllable twist rotor at several flight conditions and advance ratios of 0.22 and 0.33 are evaluated. It is found that blade flatwise bending moments and root control actuator loads (fixed system) can be reduced with multicyclic control. Flatwise bending moment reductions of 22-30% with concurrent 83% reductions in control loads were predicted. Analysis of profile power changes indicates a decrease in profile power coefficient of 0.00016, corresponding to a loss of 0.12 sq m of equivalent drag area.

Force and bending moment sensing arrangement and structure

Abstract: To prevent friction forces from falsifying output readings obtained upon lication of load between a base plate (1) and a load support plate (2), the base plate and the load support plate are rigidly connected by posts extending from one of the plates to an intermediate coupling element (3) and spokes extending from the coupling element (3) to the other one of the plates, bending deformation strain gauges being applied to the spokes and to the posts, respectively, so that forces applied in any direction will cause bending deformation of the spokes and posts, respectively, which can be evaluated with respect to the applied force.

Pipeline bending method

Abstract: A method for the controlled bending of a submerged pipeline is disclosed. The section of the pipeline which is to be bent is slightly elevated off the sea floor, preferably by buoys attached to the pipeline along its length. The end of the elevated section of pipeline is pulled in to the desired point of termination while a drag force is simultaneously applied to the elevated portion of the pipeline. The applied drag force should be sufficient to create a bending moment which causes the pipeline to bend along a well defined arc. Preferably, dragging means such as chains, cables, or clump weights extending from the pipeline to the sea floor are used to impose the necessary drag force on the pipeline and to control elevation of the pipeline above the sea floor.

Motion and Longitudinal Strength of a Ship in Head Sea and the Effects of Non-Linearities. (2nd Report)

Abstract: Assuming ship's hull as a rigid body, in the previous paper, the authors calculated the motion and longitudinal strength of a ship in waves taking account of the effects of nonlinearities due to bottom emergence, bottom impact and so on, and it showed good agreements with experiments. However, the vibratory structural responses is more important in case of slamming.In this paper, we regard the ship hull as an elastic beam and calculate the longitudinal bending moment based on the deformations of the ship hull, which is treated as a rigid body in the previous paper. The present procedure, in addition, includes the effects of the Smith Correction that was ignored previously.Conclusions obtained are as follows : (1) In the rigid body responses, the peak value of bending moment of slamming is influenced by the Smith Correction only slightly. (2) As for the whipping vibration, the amplitudes of bending moment is of the order of the peak value of that obtained by the rigid body assumption, and it oscillates about that of rigid body responses. (3) A ship in the ballast condition of the Segregated Ballast Tank standard proposed by IMCO may suffer from slamming damages in rough sea, for instance Hw/L>1/25, and therefore heavier ballast should be required in such cases.

Lateral buckling of roof purlins with diaphragm restraints

Abstract: The roof sheeting connected to metal roof purlins may provide effective restraints against lateral buckling. One important restraining action is that where the sheeting acts as a diaphragm so that its in plane shear stiffness opposes minor axis rotation of the purlin. The effectiveness of diaphragm restraints depends not only on their stiffness but also on their height above the shear centre axis of the purlin. Another important influence on the resistance to lateral buckling is the height of the load above the shear centre. In this paper the effects of bending moment distribution, cross section geometry, load height, and restraint stiffness and height on the elastic lateral buckling of uniform purlins are investigated by using a finite element computer program for the analysis of the lateral buckling of continuously restrained beam columns. (A)

Dynamic response of skew bridge decks

Abstract: In this paper the dynamic response of a skew bridge deck has been investigated, treating it as an orthotropic plate and using the finite strip method. Employing the normal mode method, the response of the deck due to a moving force has been calculated. Williams' method has been used to accelerate the convergence of the solution. Numerical work has been done for different skew angles and speed ranges. In this study, the history curves and the maximum amplification spectra for deflection and bending moment are presented.

Controller for sheet metal bending press beam - has difference between actual and required angular beam position electronically evaluated

Abstract: The moving beam of a sheet metal bending press is controlled by a pressure control valve. The bending beam can be stopped at any angular position whilst the bull bending force remains present. The control valve is operated by a servo control direct current motor. The electronic motor controller evaluates the actual angular position of the bending beam and the difference with the programmed required position. Thus the bending operation is monitored until the correct bending angle is reached.

Formulae for Landslide-Restraint Piles as Elastically Supported Elastic

Abstract: Discussed herein are formulae for designing landslide-restraint piles with the horizontal subgrade reactions in consideration. With the intensity of the subgrade reaction p assumed to be lineally proportional to the horizontal displacement of pile axis y, that is, p=kh⋅δ⋅ywhere δ is the pile diameter and kh is the coefficient of horizontal subgrade reaction, there are still three different approaches: the first one assumes the force of landsliding H as acting only along the slip surface and the pile length as being infinite both upwards and downwards from the slip surface; the second one assumes, with the loading condition as the same, the pile length as being infinite downwards only; and the third one assumes H as distributing all along the pile above the slip surface while the root part of the pile being infinite.Observations in large-scale shearing tests in situ and excavations of yielded piles in situ present us three markedly different curves of pile deflection as illustrated in Fig. 5. Any of piling formulae are to explain the differences between these three.Fig. 1 shows a case in which the pile was so constructed as to yield only to the shearing force but actually ran to rupture by bending moment. Landsliderestraint piles are recommended to be due tested against the rupture by bending moment.§1 presents the general solution to the elastically supported elastic pile under distributed load; §2.1 the solution particular for the case with additional lateral force H0 and bending moment M0 at the head; §2.2 that for the free-head pile and §2.3 that for the pile only under H0 and M0. §2.4 deals with pile of finite lengths both above and below the slip surface. As is seen in Fig. 6 or in Fig. 11 the point of y2=0 is likely to deepen far below the slip surface with the value βh decreased: the finite-length-pile formula presented in §2.4 will be warranted. Fig. 10 is the chart for easy calculation of Mmax and based on exps. (11), (6), (7) and (8), the parameter being n, the fourth root of the ratio of kh values. Fig. 11 gives values for calculating resultant subgrade reaction and necessary length of pile below the slip surface. The meanings of symbols are:EI: rigidity of pile, δ: diameter of pilekh: coefficient of horizontal subgrade reactiony: displacement of pile axis, Es=kh·δ·y and β=4√Es/4EI: for the landsliding mass, Es, and β for the part below the slip surfacen=β/η, h: depth to the slip surfaceK=η/Es H: resultant force of landslidingη: load conversion factor=2H/h2 for hydrostatically distributed loadi: deflection angle, M: bending moment, S: sheare, ν and ν: dimensionless factors of deflection, bending moment and shear, respectively.ρ and λ0: dimensionless factors of rusultant subgrade reaction and root length of pile, respectively.Note: Suffix 0, 1 and 2 or head bar denote pile head, sliding mass and the root part of the pile, respectively. Numbers with asterisk refer to those in the literature.

The Force Ratio of Bolted Joints : The case where clamped parts are flanges

Abstract: In designing a bolted joint it is important to find the ratio of an increment of an axial force produced in a bolt to a load applied to an assembly, that is the force ratio. In previous paper, the tensile spring constant Kpt for the clamped part is introduced when a load is applied on the outer circumference of clamped parts and the force ratio is calculated by using Kpt. In this paper, the similar method is applied to calculation of the force ratio of flanged connections. Moreover, the bending moment produced in the bolt corresponding to the applied load is analysed. In order to verify these theoretical analyses, an experiment if carried out. The obtained results are as follows. (1) The theoretical values show a fairly good agreement with experimental ones. (2) In evaluation of sealing effect of flanged connections the raised face joints are more effective than the flat face joints.

Norm Optimization Method in Structural Design

Abstract: A general method for the minimization of a class of nondifferenti able merit functions is presented. The merit functions are defined as the maximum absolute value of the components of a vector of functions. These merit functions have gradient discontinuities in the design space and cannot be minimized by efficient algorithms of mathematical programming. The technique consists of sequential minimizations of an appropriate family of substitute merit functions, namely, the pth order norm of the vector. The efficiency of the technique is illustrated by the design of continuous beams for optimum geometry and is shown to give good results. It is further indicated that the method could be applied to general nonlinear inequality constrained mathematical programming problems and a few encouraging numerical examples are presented.

Design of a D‐shaped toroidal field coil

Abstract: A method for making a multilayer toroidal field coil free from the bending moment is studied by applying File’s theory to each layer of the coil According to this method, the shape of a multilayer toroidal field coil is determined so that the layers in the winding are in pure tension and, therefore, are not subject to any bending moment The winding thickness of the resultant coil is not uniform along the winding Successive layers are no longer in contact, leaving some empty space between them Tension on a conductor varies in magnitude from layer to layer and is constant in the same layer, as in a solenoidal coil A toroidal field coil with a magnetomotive force of 188 MA T, a vertical bore of 151 m, and a horizontal bore of 107 m is designed with this method

Balanced snubber apparatus

Abstract: An apparatus for axial support and shock suppression of a pipe includes a walking beam having an inner portion secured to the pipe and an outer portion. The inner and outer portions of the walking beam are pivotally interconnected above an axis extending through the centerline of the pipe. A pair of support members are pivotally connected to the outer portion of the walking beam on opposite sides of the pipe so that longitudinal loads to the pipe are reacted without effecting a bending moment in the pipe. In the preferred embodiment, a rigid strut and a yieldable snubber device comprise the support members.

Statistical description of service loads for concrete crosstie track

Abstract: Measurements of loads and bending moments on concrete crossties for several days of revenue traffic were used to develop a statistical description of track loads for tangent and curved tracks that have variable tie spacing. The measured data show large tie-to-tie variations in loads and a load-dependent tie support condition. Many ties were center-bound for loads from light or empty cars, but the tie support became more uniform for heavy wheel loads. Maximum tie bending moments measured on curved track were considerably higher than those on tangent track because of the increase in vertical and lateral loads on the high rail when trains exceed the balance speed of the curve. Tie bending moments measured in this program were considerably lower than the current static flexural strength requirements for a probabilistic prediction of maximum load for a 50-year life. These and data from other concrete-tie test installations indicate a need to identify the failure mechanism for concrete ties so that statistical load descriptions can be used for future design and testing. Low-probability maximum loads will be very important if failures result from infrequent loads that exceed the static strength. However, the higher probability means cyclic loads will be the more important factor if fatigue is identified as the governing failure mechanism.