Bending Moment Diagram Research Articles

Structural Design of Agricultural Aircraft Fuselage

This paper aims to calculate the fuselage loads, and analyzing the structure to determine the margin of safety.Configuration of the aircraft was completed and frozen as addressed in a previous publications [1]. However, the aircraft should meet the agricultural requirements in Sudan. It could be manufactured locally and equipped with an engine that works with cheaper type of fuel (Jet-A1). Preliminary arrangement and sizing of structural component of fuselage hasbeen done. FEM software of ABAQUS® used for structure modeling and analysis, hence the shear forces and bending moment diagrams have been obtained. Accordingly, the working shear and bending stresses within the flight envelope have been calculated. The margin of safety is found to be positive along the fuselage structural parts, which showsgood enough strength.

Simplified Procedure for Evaluating the Effects of Creep and Shrinkage on Prestressed Concrete Girder Bridges and the Application of European and North American Prediction Models

The effects of time-dependent phenomena on concrete prestressed girder bridges are investigated. The study concerns the case of bridges built directly in their final configuration and that of bridges built by a sequence of stages in which geometry, restraints, and loads vary until the final configuration is achieved. An analytical approach based on the principles of aging linear viscoelasticity and the age-adjusted effective modulus method is followed. The paper has two aims: the first is to provide an efficient and simplified tool for the evaluation of the structural response in the early stages of design; the second is to compare the results of the analyses on actual cases of bridges when different shrinkage and creep prediction models are used. Numerical applications show that the influence of stress redistribution on bending moments, attributable to the change in static schemes, is reduced by the load-balancing effect of the dead load and prestressing and that bending moment diagrams for bridges in service do not change significantly with the different prediction models. Opposite results are found on deflections, which differ significantly in reference to the model used. Differences between predictions models are underlined, suggesting that designers should manage them with prudence to predict the long-term performance of concrete. Finally, Eurocode predictions always underestimate final deflections and stress redistribution because of the static scheme variation.

Design of a Cassava Uprooting Device

This study analyses the design of a simple, efficient, cheap and affordable cassava uprooting device for local cassava growing farmers. Processes involved in uprooting cassava were found out from local farmers, studied and mechanized using bevel gears, cams and followers, chain and sprockets. The principle of moments was used as a basis for the design. The effort applied by the foot of the operator is significantly magnified to overcome the load (cassava in the ground) at the extreme end of the device .The free body diagram of the frame helped to determine the average force needed to press the pedal by the foot. From the analysis, a little effort of 334.49 N can overcome about 2000 N of force and this gives a mechanical advantage of about 6. The bending moment diagram and the shear force diagrams helped to determine the part of the device which is subjected to greater force and where shear and bending can easily take place. Mild steel is used as the material for the device because it is cheap and easily available. Advantages of this design include faster uprooting with high productivity, less energy expended, reduction in the risk of health hazards of developing blisters in the palms, callus palms, arched spinal cord and waste pains over time.

Quick Drawing of Internal Forces Diagram of Beam

It is very important to draw internal forces diagram(shear diagram, bending moment diagram)of beam quickly and accurately for students. Only hold its regular and can use proficiently, we can laid a solid foundation for the study of specialized course .This article mainly based on the characteristics of the beam, analyzed shape and laws of the internal forces diagram and summary of the methods ----"pithy formula law"

Capacity of Composite Steel-concrete Columns

This paper studies the resistance of composite steel-concrete cross-section of columns at the ultimate limit state. The recommended design procedure is focused on solving the problem with the aid of the normal force vs. bending moment diagram, whose construction is time-consuming. This makes economical design difficult. Therefore a user-friendly application (a simple program on VBA platform) was developed for everyday use. The practical solution and some derivations are explained in this paper.

Some thoughts on a surprising result concerning the lateral-torsional buckling of monosymmetric I-section beams

This technical note addresses a surprising result concerning the lateral-torsional buckling of monosymmetric I-section beams: amongst all bending moment diagrams caused by any combination of applied end moments and transverse loads acting at the shear centre, the lowest critical moment does not necessarily correspond to uniform bending, which is at odds with the “intuitive expectation” of most engineers that such bending moment distribution is the most unfavourable with respect to lateral-torsional buckling. It is shown, by means of several illustrative examples, that this may not be the case for I-section beams with unequal flanges (monosymmeric cross-section – symmetry with respect to the minor axis). Moreover, the critical inspection of the terms (i) associated with the cross-section monosymmetry and (ii) appearing in the beam potential energy expression and differential equilibrium equation provides the mechanical/mathematical explanation for this surprising behavioural feature.

DYNAMIC SOIL-PILE-RAFT INTERACTION IN NORMALLY CONSOLIDATED SOFT CLAY DURING EARTHQUAKES

This paper examines the seismic response of clay pile-raft system with flexible and stiff piles using centrifuge and numerical studies. Centrifuge studies showed that interaction between pile-raft and clay will cause a significant softening in the clay adjacent to the pile-raft which produced a lengthening of resonance period in near-field soil compared to the far-field soil. The difference of response among the raft and the soil at both near- and far-field indicates that ground motion at both near- and far-field cannot be representative of raft motion. There is also significant difference between flexible and stiff pile response. It has been shown in a previous study that, for stiff pile, the soft clay acts as an inertial loading medium rather than a supporting medium. For this reasons, the bending moment diagram extends deep into the soft soil stratum. However, for flexible pile, the supporting effect of the surrounding clay is much more significant than in stiff pile. As a result, the bending moment envelope for flexible pile under earthquake shaking is very similar to the head-loaded test results, with an active length of pile below which no significant bending moment occurs.

Effects of Vehicle Impact Velocity, Vehicle Front-End Shapes on Pedestrian Injury Risk

Objective: This study aimed at investigating the effects of vehicle impact velocity, vehicle front-end shape, and pedestrian size on injury risk to pedestrians in collisions with passenger vehicles with various frontal shapes. Method: A series of parametric studies was carried out using 2 total human model for safety (THUMS) pedestrian models (177 and 165 cm) and 4 vehicle finite element (FE) models with different front-end shapes (medium-size sedan, minicar, one-box vehicle, and sport utility vehicle [SUV]). The effects of the impact velocity on pedestrian injury risk were analyzed at velocities of 20, 30, 40, and 50 km/h. The dynamic response of the pedestrian was investigated, and the injury risk to the head, chest, pelvis, and lower extremities was compared in terms of the injury parameters head injury criteria (HIC), chest deflection, and von Mises stress distribution of the rib cage, pelvis force, and bending moment diagram of the lower extremities. Result: Vehicle impact velocity has the most significant influence on injury severity for adult pedestrians. All injury parameters can be reduced in severity by decreasing vehicle impact velocities. The head and lower extremities are at greater risk of injury in medium-size sedan and SUV collisions. The chest injury risk was particularly high in one-box vehicle impacts. The fracture risk of the pelvis was also high in one-box vehicle and SUV collisions. In minicar collisions, the injury risk was the smallest if the head did not make contact with the A-pillar. Conclusion: The vehicle impact velocity and vehicle front-end shape are 2 dominant factors that influence the pedestrian kinematics and injury severity. A significant reduction of all injuries can be achieved for all vehicle types when the vehicle impact velocity is less than 30 km/h. Vehicle designs consisting of a short front-end and a wide windshield area can protect pedestrians from fatalities. The results also could be valuable in the design of a pedestrian-friendly vehicle front-end shape. [Supplementary materials are available for this article. Go to the publisher's online edition of Traffic Injury Prevention for the following free supplemental resource: Head impact conditions and injury parameters in four-type vehicle collisions and validation result of the finite element model of one-box vehicle and minicar. ]

Strength and ductility of R.C. columns strengthened with steel angles and battens

In this paper the behaviour of R.C. members externally strengthened with steel angles and battens subjected to axial force and bending moment is analysed. A fibre model was utilised to predict the moment–curvature diagrams of the strengthened members on the basis of stress–strain curves of the constituent materials (confined concrete, steel bars and angles) recently derived by the author. The stress–strain curves utilised for compressed concrete were able to take into account the confinement effects induced by longitudinal (bars and steel angles) and transverse (stirrups and battens) steel reinforcements. Constitutive laws in compression for confined concrete and steel bars and angles were utilised for a preliminary calibration of the compressive response of axially loaded columns strengthened with steel cages. Therefore axial force and bending moment diagrams and moment curvature diagrams were derived and verified against experimental data available in the literature. Finally, a parametric analysis showing the influence of the main parameters governing the problems (angle and strip geometry and mechanical properties of constituent material) was carried out, mainly referring to moment axial force domains, moment curvature diagrams. The analysis showed the effectiveness of this reinforcing technique in improving both the strength and the ductility of R.C. columns.

Force Performance Research for the Interior Joint of New Light-Weight Portal Rigid Frame

The portal frame is one kind of the common structural styles in the light steel structure. And the portal frame is designed by tapered members, which can be suitable for the variety of the bending moment diagram. This paper introduces the new structure dividing the middle column into two parts on the top of the middle column and analysis the frame with SAP2000. The parameters are investigated such as the hinge joint and firm joint at the bottom of the column and also the parameter of the science of geometry, which influence the load-carrying behavior of the portal frame. The analysis gives that it’s avail for the frame if the angle of the dividing is thirty. Besides, some corresponding design proposal is obtained according to the analysis of the internal force.

Numerical analysis of stainless steel beam-columns in case of fire

This paper presents an evaluation of the accuracy and safety of the design rules from Eurocode 3, for the fire resistance of stainless steel beam-columns, with and without lateral-torsional buckling. These evaluations are carried out performing an extensive numerical parametric study on beam-columns with equivalent welded H-cross-sections. In this study the influences of the residual stresses, the cross-sectional slenderness, the shape of the bending moment diagrams and the stainless steel grade are considered.New proposals for the design equations of stainless steel beam-columns in case of fire are presented. These proposals revealed to be safer than the design equations of Eurocode 3 when compared with numerical results.Additionally, the lateral-torsional buckling of stainless steel beams subjected to combined end moments and transverse loads in case of fire is also studied.

The Influence of Constructional Detail to Lateral-Torsional Buckling of Beams

The resistance of steel members in bending can be influenced by the lateral-torsional stability phenomenon. This paper investigates the influence of end plates in beam to column joint on the value of elastic buckling moment Mcr. The investigated beam is considered as simply supported in bending about horizontal and vertical axis. The rotation about its longitudinal axis is prevented. The warping is partially restrained by the use of a constructional detail which is represented by warping restraints on both ends of the beam. The investigated beam is loaded with equal and opposite end moments, which deduce the constant bending moment diagram, the worst one in the theory of LTB. The National Annex to STN EN 1993-1-1 [1] recommends for the design of steel members to LTB to use for the buckling length factor for torsion 1.0 for a simple support and for warping fixity of both ends 0.5. Both assumptions are very frequently used in design practice, but the real behaviour of steel joints is different. The parametric study considering only the influence of end plates on LTB was presented in [2,3]. The presented parametric study takes into account the end plates together with the torsional stiffness of columns. The results are in the form of ratios Mcr,approx/Mcr,exact. Both values of Mcr were calculated with the influence of constructional detail, but each value with a different manner. The Mcr,approx is approximative value calculated via the proposed two steps procedure and Mcr,exact is calculated with the computer program [1P]. The buckling length factors in torsion kw which are inputs for the two steps analysis of Mcr,approx proposed in this paper are also presented.

Typical Sectional Form of Circular Pipe Culvert beneath High Embankment

AbstractBy using the finite element method, the sizes of circular pipe culvert with different depths of fill were calculated based on the modeling to obtain each kind of stress characteristics of structure pattern culvert under different operating modes. With combination of finite element stress nephogram and the finite element computed result, the circumferential stresses of control cross—section and the control bending moments of circular pipe culvert under different operating modes were analysed, and the bending moment diagram was drawn. The calculation results of finite element method was verified and compared by simplified structural calculation and the typical sectional form of circular pipe culvert was obtained. The calculation result indicates that using the limited unit law computation, are possible reasonably to the collaboration of soil body and the structure could be reflected by finite element method to analyze the culvert structural stress characteristics. Therefore the computed result is mo...

Bending moments in D-regions of reinforced concrete beams

This paper presents a study of the behaviour of D-regions in reinforced concrete frames. Within the study, 12 two-span beams were tested to failure. The type of discontinuity imposed on the test beams reflects some common layouts that take place in nodes of actual reinforced concrete frames. The beams, 6 m long, were divided into two series (a first set had six beams with no crossing column and a second set had six beams with a crossing column at the inner support). The strength and the deformation capacity in beams with geometric discontinuities were studied as well as the influence of the column presence in the development of the plastic hinges. The main results are presented and discussed: evolution of the bending moment diagrams, moment–curvature relationships, plastic rotation behaviour, stiffness of the connection between the two spans and moment redistribution. As explained in the paper, the presence of a geometric discontinuity at the inner support region leads to a sharp decreasing of the ultimate moment at this region and consequently to a great decreasing of the ultimate load of the beam. Other consequences of having discontinuity in beams are explained. A strut-and-tie model was developed and presented. This model could be useful for the design D-regions.

Preliminary Design of the Tail Unit of a Newly Designed Agricultural Aircraft

This project work undertakes the task of analyzing stresses and preliminary designing of the tail structure members of a newly designed light agricultural aircraft. Schrenk’s method has been used for estimating the span-wise lift distribution, while the tail weight was assumed to be uniformly distribution along the span. Hence, the shear force and bending moment diagrams have been obtained. Accordingly, the working shear and bending stresses within the flight envelope have been calculated. The design has been based on the limit load while the maximum bending and shear values are encountered at the tail root, with the gust load being neglected. The bending and shear margins are found to be positive along the semi-span/height, which shows good enough strength.

Analysis of loading of lower extremities based on bending moment in car-to-pedestrian collisions

In this study, simulations of car-to-pedestrian collisions were conducted using multibody pedestrian models and a finite-element (FE) car model in order to examine the loadings on the lower extremity of the pedestrian. Bending moment diagrams were plotted versus time for the tibia, knee and femur; and the loadings on the lower extremities were evaluated using time-series comparisons. An analysis using a human FE pedestrian model also was conducted. The bending moment of the lower extremity was found to be comparable between the multibody and FE models. Car-to-pedestrian collisions were also simulated for various sizes of pedestrians. The bending moments were larger as the pedestrian size was larger, whereas the curve shape of the bending moment diagrams was similar for all sizes of pedestrians. It was shown that the bending moment diagrams using the multibody pedestrian models were useful for investigating the loading on the lower extremities for various sizes of pedestrians.

Simple SQP approach for out-of-plane loaded homogenized brickwork panels, accounting for softening

A simple homogenized model for the non linear analysis of masonry walls out-of-plane loaded is presented. In the model, the panels are assumed to behave as Kirchhoff-Love plates. A rectangular running bond elementary cell (RVE) is subdivided into several layers along the thickness and, for each layer, a discretization where bricks are meshed with plane-stress three-noded triangular elements and joints are reduced to interfaces is assumed. Non linearity is concentrated on brick-brick and joint interfaces, which exhibit a frictional behavior with limited tensile and compressive strength with softening. Finally, macroscopic curvature bending moment diagrams are obtained integrating along the thickness in-plane micro-stresses of each layer. Homogenized masonry flexural response is then implemented at a structural level in a FE non linear code based on a discretization with three-noded elements and elasto-damaging interfaces. Three different models of increasing accuracy are presented. The first (EPP) relies in assuming an elastic-perfectly plastic behavior for the interfaces. The incremental problem is solved at a structural level through a well known quadratic-programming approach. The second (ED) accounts in an approximate way for the softening behavior and consists in a preliminary homogenized limit analysis of the structure, which allows to identify the failure mechanism and in the subsequent FE non linear analysis of the whole structure assuming that all the non linearity is concentrated on the yield line defining the failure mechanism. The last (EPD) is a sequential quadratic programming approach. Here, deteriorating bending moment curvature curves obtained through homogenization are approximated through a linear piecewise constant discontinuous function. At each load step, all interfaces are assumed to behave as an elastic-perfectly plastic material and the discretized non linear problem is solved by means of the quadratic programming algorithm used for the EPP model. The two step model proposed is validated both a cell level and at a structural level comparing results provided with both experimental data and existing macroscopic numerical approaches available in the literature.

EQUIVALENT MOMENT APPROACH FOR ELASTIC LATERAL-TORSIONAL BUCKLING OF TAPERED BEAMS

The assessment of the design buckling resistance of single members is usually based either directly on the elastic buckling resistance of the member or indirectly on its non-dimensional slenderness computed from the elastic buckling resistance. Specifically, Eurocode 3 buckling curves define the buckling reduction factors as a function of non-dimensional slenderness and, according to EC3 "General Method", these curves may also be used for non-uniform members. In this context, a new procedure will be presented for the computation of the elastic critical moment of tapered members. As is well known, the elastic critical moment strongly depends on both the bending moment diagram and end support restrictions. For uniform members, elastic critical moments may be computed using a relatively simple formula in which the bending moment distribution is taken into account by an equivalent uniform moment factor, and the end support restrictions are introduced through the buckling length. Unfortunately, this formula has not been extended to tapered members and, as a consequence, the elastic critical moment for tapered beams must be obtained using numerical methods such as the finite element methods. Based on a comprehensive parametric study for the elastic critical moment of tapered beams with different moment diagrams, this paper offers a new procedure, called the Equivalent Moment Approach, for the substitution of a tapered beam with any moment diagram by an equivalent uniform beam. One advantage of the present procedure is that closed form expressions valid for uniform beam can be generalized and used for tapered beams.

Introduction to engineering mechanics: a continuum approach

Introduction A Motivating Example: Remodeling an Underwater Structure Newton's Laws: The First Principles of Mechanics Equilibrium Definition of a Continuum Some Mathematical Basics: Scalars and Vectors Problem-solving Examples Strain and Stress in One Dimension Kinematics: Strain The Method of Sections and Stress Stress-Strain Relationships Limiting Behavior Equilibrium Stress in Axially Loaded Bars Deformation of Axially Loaded Bars Equilibrium of an Axially Loaded Bar Statically Indeterminate Bars Thermal Effects Saint-Venant's Principle and Stress Concentrations Strain Energy in One Dimension Properties of Engineering Materials A Road Map for Strength of Materials Examples Case Study 1: Collapse of the Kansas City Hyatt Regency Walkways Strain and Stress in Higher Dimensions Poisson's Ratio The Strain Tensor The Stress Tensor Generalized Hooke's Law Equilibrium Formulating Two-Dimensional Elasticity Problems Examples Applying Strain and Stress in Multiple Dimensions Torsion Pressure Vessels Transformation of Stress and Strain Failure Prediction Criteria Examples Case Study 2: Pressure Vessels Why Pressure Vessels Are Spheres and Cylinders? Why Do Pressure Vessels Fail? Beams Calculation of Reactions Method of Sections: Axial Force, Shear, Bending Moment Shear and Bending Moment Diagrams Integration Methods for Shear and Bending Moment Normal Stresses in Beams and Geometric Properties of Sections Shear Stresses in Beams Examples Case Study 3: Physiological Levers and Repairs The Forearm Is Connected to the Elbow Joint Fixing an Intertrochanteric Fracture Beam Deflections Governing Equation Boundary Conditions Beam Deflections by Integration and by Superposition Discontinuity Functions Beams with Non-Constant Cross-Section Statically Indeterminate Beams Beams with Elastic Supports Strain Energy for Bent Beams Deflections by Castigliano's Second Theorem Examples Case Study 4: Truss-Braced Airplane Wings Modeling and Analysis What Does Our Model Tell Us? Conclusions Instability: Column Buckling Euler's Formula Effect of Eccentricity Examples Case Study 5: Hartford Civic Arena Connecting Solid and Fluid Mechanics Pressure Viscosity Surface Tension Governing Laws Motion and Deformation of Fluids Examples Case Study 6: Mechanics of Biomaterials Nonlinearity Composite Materials Viscoelasticity Case Study 7: Engineered Composite Materials Concrete Plastics Ceramics Fluid Statics Local Pressure Force due to Pressure Fluids at Rest Forces on Submerged Surfaces Buoyancy Examples Case Study 8: St. Francis Dam Fluid Dynamics: Governing Equations Description of Fluid Motion Equations of Fluid Motion Integral Equations of Motion Differential Equations of Motion Bernoulli Equation Examples Case Study 9: China's Three Gorges Dam Fluid Dynamics: Applications How Do We Classify Fluid Flows? What Is Going on Inside Pipes? Why Can an Airplane Fly? Why Does a Curveball Curve? Case Study 10: Living with Water, and the Role of Technological Culture Solid Dynamics: Governing Equations Continuity, or Mass Conservation Newton's Second Law, or Momentum Conservation Constitutive Laws: Elasticity References Appendix A: Second Moments of Area Appendix B: A Quick Look at the del Operator Appendix C: Property Tables Appendix D: All the Equations Index

Equivalent uniform moment diagram factor for structural concrete columns

The equivalent uniform bending moment diagram factor (Cm) was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, to compute the effect of moment gradient, along the column height, caused by unequal column end moments. The expression currently in use in the Canadian Standards Association (CSA) A23.3 standard is a simplified equation based on the elastic behaviour of columns, and does not include the inelastic material behaviour of structural concrete. This study was conducted to investigate the influence of different variables on Cmof slender, tied, reinforced concrete columns, and composite steel–concrete columns in which steel sections are encased in concrete, and also to examine existing expressions for Cm. Approximately, 38 000 simulated columns, each with a different combination of specified values of variables, were used to generate the Cmdata. The columns studied were subjected to short-term ultimate loads and unequal end moments causing moment gradient in single curvature and double curvature bending. Two Cmdesign equations are proposed in this paper. One of the proposed equations is a modified version of the current CSA design equation for Cm.