Alternatively, it may be necessary to check the ability of a given beam to span between two supports and to carry a given load system before deflections become excessive. Procedure to find out the reaction of simply supported beam. It is thus a special case of timoshenko beam theory. Design aid 6 beam design formulas with shear and moment diagrams. Can assume plane stress in zdir basically uniaxial status axial force resultant and bending moment 2 0 xx 2 udvdu y xdx dx 00 du dx dv dx22 2 xx xx 0 2 dv eeey dx 2 0 2 2 2 0 2. For this reason, the analysis of stresses and deflections in a beam is an important and useful topic. The modal solution used to solve the linear theory will be used to solve the nonlinear theory. Note the distance of weight jaws from the support and value of weights. On the manner in which they are supported, the beams may readily be classified as cantilevers, simply supported, overhanging, continuous and fixended beam. The theory of timoshenko beam was developed early in the twentieth century by the ukrainianborn scientist stephan timoshenko. It is simple and provides reasonable engineering approximations for many problems.
This report will evaluate a simply supported beam that has a downward load p applied at the midpoint. First kinematic assumption in eulerbernoulli beam theory. Pdf the large deflection of a simplysupported beam loaded in the middle is a classic problem in mechanics which has been studied by many. Simply supported beam apparatus consisting of graduated beam supported on two. It is convenient to show a twodimensional crosssection of the threedimensional beam together with the beam cross section, as in fig. The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets of mechanics of materials. Deflection and stress analysis of a simply supported beam and its validation using ansys.
This project will deal with the analysis of a simply supported beam that consist of two materials with applied complex loading. Since we consider a simplysupported beam and plate, the solution is either a sine or double sine in. This section covers shear force and bending moment in beams, shear and moment diagrams, stresses in beams, and a table of common beam deflection formulas. While in this study we only consider a simplysupported members it may be possible to extend. Although several theories for the failure of cfrp strengthened structures have been proposed a satisfactory. Furthermore, assume the beam is made from a continuous fiber composite. The bent beam goes into tension stretched on one side and compression on the other. Design aid 6 beam design formulas with shear and moment.
Calculate the factored design loads without selfweight. Then hang the beam on the hooks and weights on bam with hangers. Stress distribution in terms of displacement field. A supported beam loaded by a force and a distribution of pressure it is convenient to show a twodimensional crosssection of the threedimensional beam together with the beam cross section, as in fig. Assume a general ply configuration for the laminate b. Generalize simple beam theory to three dimensions and general cross sections. Beam theory ebt is based on the assumptions of 1straightness, 2inextensibility, and 3normality jn reddy z, x x z dw dx. Therefore, we will analyze only the left half of the beam segment ab. Jan 14, 2017 cantilever beam is one which has its one end fixed and other end is free to vibrate trussed beam trussed beam is a special type of beam which has increased strength due to additional rods and cables in beam in this experiment only two types of beam will be discussed one is simple supported beam and other is cantilever beam. To study the vertical equilibrium of a a simply supported beam 2. A schematic of a statically determinate beam with distributed load is shown below. Their common basis is the differential equation that relates the deflection to the bending moment. Virtual work is a fundamental theory in the mechanics of bodies. Implementation of a beam element in fea using matlab.
The following image illustrates a simply supported beam. Deflection of simply supported beam and cantilever 1. Eulerbernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the loadcarrying and deflection characteristics of beams. Displacement, strain, and stress distributions beam theory assumptions on spatial variation of displacement components. For this one should know values o weight of beams, length of beams and weight of hanger. Timoshenko beam theory for the flexural analysis of. Design of simply supported deep beams using strutandtie models article pdf available in aci structural journal 1006. A simply supported beam is 6 m long and has a flexural stiffness of 3 mnm2. Design of simplysupported composite beams for strength. Cantilever beam is one which has its one end fixed and other end is free to vibrate trussed beam trussed beam is a special type of beam which has increased strength due to additional rods and cables in beam in this experiment only two types of beam will be discussed one is simple supported beam and other is cantilever beam. Mechanics of materials chapter 6 deflection of beams. By comparing the ansys solution with simple beam theory, you will be able to understand the accuracy of your model. Simple beam theory an overview sciencedirect topics. The simply supported composite beam shown is loaded with an eccentric axial force n at distance e above the midplane of the beam.
It is the one of the simplest structural elements in existence. So fundamental in fact, that newtons 3 equations of equilibrium can be derived from it. To determine the reactions of the beams by a the experimental setup and b by using the principles of statics and method of consistent deformation apparatus tecquipment sm 104 beam apparatus mk iii figure 1 experimental procedures 1. Other mechanisms, for example twisting of the beam, are not allowed for in this theory. A beam is a member subjected to loads applied transverse to the long dimension, causing the member to bend. Review simple beam theory generalize simple beam theory to three dimensions and general cross sections consider combined e ects of bending, shear and torsion study the case of shell beams 7. Beam stiffness comparison of fe solution to exact solution under uniformly distributed loading, the beam theory solution. Furthermore, assume the beam is made from a continuous fiber composite material with the properties e 1 22. Since this load is in the middle location departure from the notch vertical line, it must generate a complex crack at the notch tip, which propagates alone a zigzag route and toward the loading position. It carries a point load of 800 n at the middle and a u. To determine the support reactions for a simply supported beam using parallel force apparatus.
A simply supported beam is the simplest structural element, as the name itself suggests, it is supported at its both ends, at one end it is pinned and the other is either pinned or rollers are used. For instance, in the case of a simply supported beam with rigid supports, at x 0 and x l, the deflection y 0, and in locating the point of maximum deflection, we simply set the slope of the elastic curve y to zero. The large deflection of a simply supported beam loaded in the middle is a classic problem in mechanics which has been studied by many people who have implemented different methods to determine the. The dead load does not include the selfweight of the beam. There is a load of lb acting in the downward direction at the center of the beam. Neglecting shear deformation, use advance beam theory to determine expressions for w 0 x and u 0 x. Calculate the slope at the ends and the deflection at the middle. Pdf large deflection of a simply supported beam researchgate. A finite element solution of the beam equation via matlab. The maximum deflection at the center of the beam is. Eulerbernoulli beam theory can be used to predict the theoretical values of beam deflection among other quantities. Beam diagrams and formulas table 323 continued shears, moments and deflections.
Note that the maximum stress quoted is a positive number, and corresponds to the largest stress magnitude in the beam. Integrated into each beam case is a calculator that can be used to determine the maximum displacements, slopes, moments, stresses, and shear forces for this beam problem. The large deflection of a simplysupported beam loaded in the middle is a classic problem in mechanics which has been studied by many people who have implemented different methods to determine the. Solution the bending moment and the elastic the dashed line in fig. A simply supported beam is 4 m long and has a load of 200 kn at the middle. Eulerbernoulli beam theory kinematics equilibrium equations governing equations in terms of the displacements timoshenko beam theory. Deflectionof simply supported beam and cantilever 2. Eulerbernoulli beam theory also known as engineers beam theory or classical beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the loadcarrying and deflection characteristics of beams. Pdf design of simply supported deep beams using strut. The crosssection of the steel beam must be symmetrical about the vertical axis. The end supports of the beam are capable of exerting forces on the beam but will rotate as the member deflects under any loads.
Alternatively, it may be necessary to check the ability of a given beam to span between two supports and to carry a. Assume simple beam theory is applicable for the simply supported beam shown. Calculation of the airy stress function, stress tensor, principal stresses, maximum shear stress, and octahedral shear. Many structures can be approximated as a straight beam or as a collection of straight beams. The eulerbernoulli beam theory, sometimes called the classical beam theory, is the most commonly used. A simply supported beam is a type of beam that has pinned support at one end and roller support at the other end. Deflection of simply supported beam with concentrated point load on the mid of beam apparatus. A simply supported beam is made from a hollow tube 80 mm outer diameter and 40 mm inner diameter. It covers the case for small deflections of a beam that are subjected to lateral loads only.
Depending on the load applied, it undergoes shearing and bending. The fe solution for displacement matches the beam theory solution for all locations along the beam length, as both vx and yx are cubic functions. Figure 3 the complete formula that relates bending stress to the various properties of the beam is r e y 1 i m. Simply supported beam an overview sciencedirect topics. Figure 2 transverse loading causes bending and bending is a very severe form of stressing a structure. Unlike the eulerbernoulli beam, the timoshenko beam model for shear deformation and rotational inertia effects. Pdf deflection and stress analysis of a simply supported. A supported beam loaded by a force and a distribution of pressure. Free vibrations of simply supported beams 53 theory and application the partial differential equation p. These values of beam deflection will be used in the analysis, as they will be compared to the experimental data obtained.
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