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