“To study deflection in a simply supported beam”
This lab is aimed to study the behavior of simply supported beam under the action of a point load.
The goal of comprehending the simply supported beam in an effective way can be achieved through step by step approach. It is very important that we follow the below given steps in the same order as they are listed.
Grasp the basic design of the beam and its working
Strain produced in the beam under the action of load
Perform experiment to study the strain produced in the beam and using strain gauge to measure strain
Beam is one of the simplest but very important component of every structure or building. A simply supported beam has supports at both ends. It features roller support at one end and pinned support at the other. These beams can undergo both bending and shear stress. Therefore, these beams should be designed such that they are able to bear shear and bending stress applied on them.
Bending stresses in beam
When a beam is under the action of any load, reactions are produced at its supports which subsequently generate stresses within the beam. These stresses act to curve the beam about its supports. Therefore, these stresses are called bending stresses. Moreover, in bending the layers above neutral axis of the beam will be subjected to compression whereas bottom layers will be subjected to tension.
Deflection of beam
Once the bending stress produced in the beam surpasses a certain value, beam starts to alter its shape and it moves in the direction of applied load. This deformation phenomenon is known as deflection of the beam. Mathematically, it can be expressed as,
Maximum deflection= (W × L^3)/(48 × E × I)
L is the length of the beam
W is the applied load
I is the moment of inertia of the beam
E is the modulus of elasticity of the beam
Modulus of elasticity
Young’s Modulus of elasticity of a material defines its ability to withstand the applied load remaining within its elastic limit. In a way, this property can also indicate the strain produced in a material. Mathematically, this can be obtained by simply dividing stress by strain.
modulus of elasticity=E=Stress/Strain
Moment of inertia
It is the geometric property of the beam. This property tells us about the resistance that a beam offers against angular motion when it is subjected to a stress.
Mathematically, it is expressed as,
I = 1/12 × b × h^3
Experiment to find the deflection in a simply supported beam has following steps:
First of all, place the apparatus on a flat horizontal surface. Carefully, mount the dial gauge and attach load hanger to the apparatus.
Take all necessary measurements of the beam and also measure the distance of the point where the force or load is being applied. Use the above formulas to calculate the deflection theoretically.
Now, use load hanger to exert a load of 100 grams at the center of the beam.
Use strain gauge to note the value strain produced.
Repeat step iii and iv for different weights available in the laboratory and compare the experimental reading with the theoretical readings.
Strain in beam was measured using strain gauge for different load ranging from 100 gram to 1000 grans or 1 kg. Reading from strain gauge circuit were taken for each different load and when graph was plotted for loading condition it show that the relationship between strain and load applied is directly proportional. Means the strain and load applied are directly proportional to each other because as load on the beam was increased from 100 g to the value of 1000 grams the value of strain was increased from 15 to 181 linearly. When this case of loading of beam was compared with the reference value of strain in beam for the same loading condition, result show vary small difference in the value of strain obtain form the class experiment and that obtained from the reference value.
Graphs shows that the value of strain obtained from class results were greater than that of the reference value. This difference can be due to number of reasons; first is that the beam used for the class experiment was already deformed and has a small value of strain in it even before the strain circuit was installed and experiment was conducted. Second can be defect in strain gauge circuit due to which it shows greater value of strain as compared to the actual value. Third can be due to human error means operator performing the experiment does not have proper experience and knowledge and is not performing the experiment correctly.
When the strain value loading case of beam where strain of beam was recorded for every increase in load, was compared to the unloading condition where strain of beam was recorded for every decrease in load from the maximum value shows that the this loading and unloading condition of beam was in the elastic region of the beam material as when load was removed the strain produce in beam also disappear fully and beam regain its original shape. This also show that beam loading as well as unloading case have directly proportional relation between strain and load applied and removed.