Deflection of beam theory at a glance for ies, gate, psu 5. As this deformation occur, the structure changes shape and points on the structure displace. The axis of the beam deflects from its initial position under action of applied forces. Beladi, pe mechanics of materials lab p a g e 1 experiment two beam deflection experiment three 3 tensile stress testing introduction. The amount of flexural deflection in a beam is related to the beams area moment of inertia i, the single applied concentrated load p. Lab manual for deflection of beam experiment three handout. You created this pdf from an application that is not licensed to print to. Beam deflection apparatus, steel beam, two dial testindicators and stands, micrometer, rule, two hangers. Studying bending of beams, this is a standard case found in any textbook in solid mechanics or strength of materials. Experiment two beam deflection the influence of the length x for the deflection at the free end should be demonstrated in this experiment. Although these deflections are normally small, as a part of the total. The beam apparatus allows an extensive range of experiments to cover virtually all course requirements relating to bending of beams. The objective of this laboratory experiment is to find the relationship between the deflection y at the centre of a simply supported beam and the span, width.
Shortcut method deflection of beam mechanicalcivil. Elastic deflection castiglianos method 1 obtain expression for all components of energy table 5. Cantilever beam concentrated load p at any point 2 pa 2 e i lei 2 3for0 px yax xa 6 ei 2. Shear force, bending moment, deflection beams, strut apparatus test. Deflection of simply supported beam and cantilever 1. The elastic deflection experienced by a beam under transverse loads was.
According to john case 1999 when a body is under stress, then that stress tries to change its shape and dimensions. Derive the differential equation for the elastic curve and describe a method for its solution. Under the action of the load, the axis of the beam deforms into a curve. In this experiment only two types of beam will be discussed one is simple supported beam and other is cantilever beam. Doc shear force, bending moment, deflection beams, strut. Experiment to measure the deflection of a cantilever beam introduction. There are situations when parts of a beam bend upwards, and in these cases the signs of the normal stresses will be opposite to those shown in fig. Deflections resulting from different loading situation on a given beam are analyzed for using different techniques. Beam deflection formulae beam type slope at free end deflection at any section in terms of x maximum deflection 1.
The axis of the beam deflects from its initial position under action. The student guide describes how to use the equipment and gives experiment procedures. To determine experimentally the deflection at two points on a simplysupported beam carrying point loads and to check the results by macaulays method. For this reason, building codes limit the maximum deflection of a beam to about 60 th of its spans. Test experiments were carried out on the apparatus, in the areas of youngs modulus of material determination under a given loading system. The change in the light intensity of the optical fiber is monitored using a lightdependent resistor ldr and a basic voltage divider circuit. Beam diagrams and formulas table 323 continued shears, moments and deflections. Change is shape of the body is called deflection and change in the dimensions is called strain. Talking about the material of the beam, in this lab experiment three materials brass, aluminum and steel will be. 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. There are four parts in this big experiment, including deflection of a cantilever, deflection of a simply supported beam, the shape of a deflected beam, and circular bending. 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.
In these four parts, a same set of laboratory instrument and apparatus is used, concluding a. Beam deflections double integration method example part. Deflection of a cantilever beam mechanics of material. Deflection of beams study notes for mechanical engineering. Beam apparatus sm1004 materials testing tecquipment. Bending of beam lab report essay 1003 words bartleby. Deflection of a beam considering the creep article pdf available in procedia engineering 190. Muhammad arif in azizan muhammad zulhelmi in sulaiman mohd firdaus bin saad muhammad hafifi in muhammad objective the experiment involves the bending and vibration of an test bar. Mechanics of materials chapter 6 deflection of beams.
Deflection of simply supported beam with concentrated point load on the mid of beam apparatus. General theory when a beam bends it takes up various shapes such as that illustrated in figure 1. Linear shafts and actuators are often secured at their ends, leaving their length unsupported, much like a simply supported beam. Sign conventions the x and y axes are positive to the right and upwards, respectively. The lecturer guide provides details of the equipment including sample experiment results. At any distance x metres from the left end, the beam will have a.
The basic unit provides facilities for supporting beams on simple, builtin and sinking supports, applying point loads, and measuring support reactions and beam deflections. Determine the allowable load given to the following allowable stresses for the following beams. Lecture 12 deflection in beams linkedin slideshare. It can be integrated in each particular case to find the deflection.
Verification of reciprocal theorem of deflection using a simply supported beam. Teaching engineering reasoning using a beam deflection lab. Load versus deflection response is then plotted using test data. 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. The tested bfrc model beams have been made of concrete class c3037 and reinforced with flexural basalt bars of 8 mm in diameter with the characteristic identified in strength tests in tension. An interchangeable plate allows students to find the shear centre of the specimen. From this plot, the elastic stiffness of the beam is determined and compared to published values for. In this video how to remember all the importants formulas of slope and deflection is explained by using a simple algorithm, which will help you to remember i. Excessive deflection of a beam not only is visually disturbing but also may cause damage to other parts of the building. Accordingly an experimental setup is designed and developed to obtain deflections from experiment. In a truss, bars in tension elongate and bars in compression shorten. The results obtained from experimentation are compared, which are in closely match with analytical and ansys. Figure 5 is a sketch of the mechanical experiment built to measure.
This video shows how to calculate beam deflections using the double integration method. Experimental and theoretical analysis of deflections of. Deflection of beams with special reference to shear. However, the moments and shear forces shown in fig. A number of analytical methods are available for determining the deflections of beams.
Measurements are made of the deflection, strain rates, fundamental frequency, and damping constant. The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. The reference axes have their origin at the fixed end of the beam. In these four parts, a same set of laboratory instrument and apparatus is used, concluding a bracket, a moveable digital dial test. Two digital deflection indicators measure deflection in the x and y directions. Accurate values for these beams deflections are sought in many practical case.
The report of deflections of beams and cantilevers summary. Deflection of beams effect of beam length and width 1. Deflectionof simply supported beam and cantilever 2. Following is the equation which can be used for calculating deflection in beams. The uniform load on the beam, the shaft or actuators own weight, will induce maximum deflection at the center of the beam, which can be calculated as. To design and fabricate an experimental rig that can be used to test deflection of all types. In engineering, deflection is the degree to which a structural element is displaced under a load due to its deformation. This paper presents a theoretical and experimental study on large deflection behavior of initially curved cantilever beams subjected to various types of loadings. Another method of determining the slopes and deflections in beams is the areamoment method, which. Introduction beams are common elements of many architectural, civil and mechanical engineering structures 15 and the study of the bending of straight beams forms an important and essential part of the study of the broad field of. In the four parts of the experiment, midspan deflection is measured but a different variable is changed, thus each part has a distinct tech nical objective. The physical system as a straight cantilever beam subjected to a tip concentrated load is considered in this study. Cantilever beam concentrated load p at the free end 2 pl 2 e i nm 2 3 px ylx 6 ei 24 3 max pl 3 e i max 2.
Strength and testing of materials engr211204 uploaded by. Additionally, the experiment enables students to apply these wellunderstood concepts to a practical problem. Numerical and experimental analysis of a cantilever beam. Deflection of simply supported beam and cantilever slideshare. When a structure is loaded, its stressed elements deform. Experiment to measure the deflection of a cantilever beam. The amount of flexural deflection in a beam is related to the beams area moment of inertia l, the single applied concentrated load p, length of the beam l, the modulus of elasticity e, and the position of the applied load on the beam. Lab manual for deflection of beam experiment three. The shape may be superimposed on an x y graph with the origin at the left end of the beam before it is loaded. Consider a cantilever beam with a concentrated load acting upward at the free end. Brief description a plastic optical fiber is attached to a cantilever beam to monitor its deflection. 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. The deflection of the free end of the beam is linear elastic material is assumed 1.
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