ANALYSIS OF A SIMPLY SUPPORTED BEAM.

EXPERIMENT REPORT.

AIM:

The determination of the reaction forces, and the deformation of a simply supported beam, and to compare the experimental results with the analytical ones.

DESCRIPTION OF THE SETUP:

Test Structure Dead weight Beam Load cells Dial gauges Multimeters Power supply

PROCEDURE:

Measure some dead weights and label them and then measure the loading fixture.

Wire up the electrical resistance strain gages which is bonded to the load cells and the two ends of the test structure and on which the beam will be balanced. Since the strain gage is just a single conductor, there are only two connections to make, one at each end. There are three wires coming from each gage. The strain gages are connected into a power supply which is adjusted to 10volts using the array of electrical terminal, and connect a multimeter to the S+ and S- terminals to read the strain.

We mount the beam on the frame, then clamp two dial gauges at location of our choice then we measure

their position. Set the ring of the gauges to indicate zero deflection in this no-load case.

Add a dead weight to the beam and measure their positions.

We then compile a list all outputs of load cells and dial gauges.

CALIBRATION OF LOAD CELLS:

I calibrated the load cells before measuring my values, and i noticed that the loads cells are set so close to each other to get approximate results with lesser errors.

Placing of the dial gage is an important factor in analysing the deflection of beams correctly, they are mounted on a gage stand on the surface plate the dial is set to zero and the beam is inserted onto the setup, then we take the dial gage reading. It is important to check the smoothness of the beam surface to get approximation with lesser error.

Calibration values and calculations:

Mass(kg) Measurement A (mV) Measurement B (mV)

0 0 -0.5

0.38 0.8 0.3

1.41 3.7 3.1

1.99 5.3 4.7

3.39 9.2 8.5

5.01 13.7 13

TEST AND RESULTS:

M1(kg) M2(kg) L1(cm) L2(cm) V1(v) V2(v) G1 G21.98 1.14 14.8 17.4 5.1 3.2 30.5 8.1

Diameter of beam (m): 0.006 [error: 0.1]

Length of beam (m): 0.46 [error: 0.1]

ANALYTICAL CALCULATIONS:

M1 M2

R1 R2

L1 L2 L3

M1 M2 F1 F2 V1 V2 B1 B3 X1 X21.14 1.98 11.1834 19.4238 3.8 4.2 17 18.5 2.6 3.461.42 1.98 13.9302 19.4238 3.3 4.2 17.5 9.4 2.46 3.261.42 1.98 13.9302 19.4238 4.5 3.3 13.5 16 2.23 3.031.98 1.14 19.4238 11.1834 5.1 3.2 14.8 17.4 3.05 8.011.42 1.14 13.9302 11.1834 4.6 3.5 16 16.5 2.06 1.911.42 1.98 13.9302 19.4238 4.5 4.5 16 9 2.63 51.42 1.98 13.9302 19.4238 4.3 3.2 20 16.2 3.17 4.4451.14 1.42 11.1834 13.9302 2.5 4.3 20.6 7.4 2.83 1.341.42 1.14 13.9302 11.1834 4.3 3.2 5 8.5 2.55 3.51

3.8 3.3 4.5 5.1 4.6 4.50

5

10

15

20

25

load cell 1

load cell 1

4.2 4.2 3.2 3.2 3.3 3.2 3.5 4.50

5

10

15

20

25

load cell2

load cell2

DISCUSSION AND CONCLUSION:

I understood about the load cells and the measurement techniques. In the experiment i analysed the deflection of beams and understood how to adjust the instruments. At the end of the experiment i derived some data about the experiment and compared them with the analytical results, and i noticed some differences.

The reason for this differences that directly affected our experiment are;

Error in the instruments Approximation errors Variation in position distances and loads