experiment 3(practical 2)

8/12/2019 Experiment 3(Practical 2)

1/4

DEFLECTION AND SLOPE IN THE BEAM

EXPERIMENT 3b: Cantilever Beam with a Point Load

OBJECTIVE: To compare the value of deflection and gradient (slope) from the test and

theory for the simply supported beam

THEORY:

Macaulays methods

The application of a double integration method to a beam subjected to a discontinuous

load leads to a number of bending equations and their constant. The derivation of the

deflection curve by this method is tedious to say the least. We therefore use a step functionwhich is more commonly known as Macaulys method. The method of solution requires only

one equation for the entire beam and thus only two constant of integration. The step function

is a function of x of the form f(x) = such that for x < a, f(x) = 0 and for x > a, f(x)

= . The important feature to mote is that if the quantity inside the square brackets

becomes negative we omit it from any subsequent analysis. Care must be taken to retain the

identity of the square bracket term under integration. For mathematical continuity where we

have a distributed load we continue it to x = 1 and superimpose additional loadings which

cancel out the extra load we added to the problem in order to obtain a solution. Three

common step functions for Bending Moment are shown below;

x=a

x=a

x=a

x = a, M =

x = a, M = W

x = a, M =


2/4

APPARATUS:

a) Built in supportsb) Stirrupc) Double end hooked) Dial gaugee) Steel beam (25mm x 6mm)f) One Load hangerg) Weights

PROCEDURE:

i. Placed the support at the left side.ii. Put the test beam with a distance of 500mm as in the figure 2. Clip the test beam by

tighten screw at the support.

iii. Placed the load hanger and dial gauge at the free end of the beam. Ensure that thereare no weights in the hangers.

iv. Set the dial gauge to the zero.v. Apply the loads in increase of 5 N up to a maximum of 10 N and in each case note the

readings of the dial indicator. Tabulate your results as the table 3a. Remember,

Experiment Deflection, = Dial gauge reading x 0.01 mm

Experiment Slope, =

x 0.01 radian

500mmSupport

Figure 2: Force diagram


3/4

RESULT:

Load (N) Dial gauge

reading

Experimental

Deflection(mm)

Theoretical

Deflection(mm)

Experimental

Slope(radian)

Theoretical

Slope(radian)

0 0 0 0 0 0

5 546 5.46 2.24 0.0546 0.0134

10 945 9.45 4.47 0.0945 0.0268

Table 2b: Results for Experiment

DISCUSSION:

Based on calculation.

CONCLUSION:

Based on the result, the value by using theory is different than the experimental. This

happen because when we do the experiment many errors can we get. So, to avoid the error we

must take some precaution to get the real value for experimental. The error that we can get

when do the experiment are parallax error, systematic error and person error. The Macaulays

theory was accepted.


4/4

ATTACHMENT:

REFERENCES:

1. http://www.electronicsinstrumentsmanufacturer.com/strength-of-materials.html2. http://mac6.ma.psu.edu/em213/sampleExamProblems/p042.html3. http://virtual.cvut.cz/beams/4. http://www.sciencedirect.com/science/article/pii/S0020768304005487
http://www.electronicsinstrumentsmanufacturer.com/strength-of-materials.htmlhttp://mac6.ma.psu.edu/em213/sampleExamProblems/p042.htmlhttp://virtual.cvut.cz/beams/http://www.sciencedirect.com/science/article/pii/S0020768304005487http://www.sciencedirect.com/science/article/pii/S0020768304005487http://virtual.cvut.cz/beams/http://mac6.ma.psu.edu/em213/sampleExamProblems/p042.htmlhttp://www.electronicsinstrumentsmanufacturer.com/strength-of-materials.html

experiment 3(practical 2)

Documents