# Deflections of Beams and Cantilevers

**Topics:**Beam, Dial indicator, Deflection

**Pages:**7 (1440 words)

**Published:**November 16, 2013

Summary:

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 these four parts, a same set of laboratory instrument and apparatus is used, concluding a bracket, a moveable digital dial test indicator, U-section channel, moveable knife-edge, and three material beams: brass, aluminum, and steel. The experiment methods, and fixed point to the beam are the differences between these four small experiments. The aim of this experiment is to improve the ability to use the precision engineering components like moveable digital dial test indicator, also understand the formula: Deflection= WL＾3/3EI. To explain this formula: W is load, its unit is N, L is distance from support to position of loading (m), E is Young’s modulus for cantilever material, and its unit is Nm＾-2, I is the second moment of area of the cantilever, its unit is m＾4. In addition, the experiment safety is very important. Objective:

(1) Operation techniques. In this experiment, measuring data is very important, because of comparing the actual deflection to theoretical deflection. Every step of this experiment should be precise. To obtain the correct data, you must be sure that the all components are secure and fastenings are sufficiently tight. Also position the equipment safely. Be sure it is on a solid, level surface. (2) Analyses experiment. As known, there are four parts in this experiment. The different structure of the experiment equipment affects the different results. So it is necessary to think about how the structure affects the experiment. (3) Application of controlling vitiates method. In this experiment, three material beams are used: brass, aluminum, and steel. Different material has its own Young’s modulus. Introduction & Theory:

As known, every material has its own disutility, because of the gravity, the beam should have a defection. Different material has different disutility, and the Young’s modulus for cantilever material is the measure of disutility. Its unit is Nm＾-2. In this experiment, there are three kinds of beam: brass, aluminum, and steel. Their Young’s moduluses for cantilever material are 105, 69, and 207. The defection of the cantilever is not only affected by the material, also the shape of the beam. A notation is used to describe the shape of the beam, it is I. It means the second moment of area of the cantilever, and its unit is m＾4, and it is calculated by the formula: I= (1/12)b d＾3, to explain this formula, b is the width of the beam, d is the depth of the beam. But in the experiment, the shape is not a variable, so the three beams’ shape is almost same.

Apparatus:

1. A frame

2. Two tracks

3. A set of loads (100g-500g)

4. A moveable digital dial test indicator

5. Two clamps

6. Two moveable knife-edges

7. Ruler

Procedure:

Experiment 1: Deflection of a Cantilever:

1. Select a material beam, and calculate the E and I.

2. Use only one clamp to hold the beam, and make it tight. 3. Use the load (100-500g), keep the distance from the load to the point be 200mm. 4. Select a material of beam, and determine its Young’s moBe sure the indication should be zero, when the digital dial test indicator on sliding bracket on the position far from the point 200mm and no load there. 5. Put the load on the knife-edge load hanger, and see the indication on the moveable digital dial test indicator, then write down the data. 6. Repeat the above the procedure with different load.

7. Use the formula: WL＾3/3EI to calculate the theoretical deflection. 8. Contrast the actual deflection and theoretical deflection. 9. Change the material, then repeat the above the procedure. Experiment 2: Deflection of a simply supported beam

10. Select an AL beam, and calculate the E and I.

11. Remove any clamps...

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