REACTION OF SIMPLY SUPPORTED BEAM

Elastic beam apparatus

AIM

To investigate the reactions and deflections of proposed cantilever

APPARATUS

Elastic beam apparatus, load link, standard loads writing materials, e.t.c.

PROCEDURE

Lock the actuator arm of the left end support and clam the thicker still strip (2.64mm) in the position shown to form a cantilever of 400mm length. In first place, the adjustable prop assembly should be in the position shown dotted so that It does not support the cantilever. Clamp the load hanger 300mm from the fixed end and set up a gauge to measure the displacement at 400mm for that end.

Measure the displacement when loads of 5N and 10n are placed on the hanger. Now move the load hanger to the 400mm position and re-fix the dial gauge over it. Add weight to the hanger until the previous measured displacement are obtain again.

Move the load hanger back to its original positon. Set the dial gauge over the prop and note the reading as datum value; read “the load” condition of cantilever. Put the 5N load on the hanger and adjust the height of the prop assembly until the displacement and the end of the cantilever is zero (that is, the dial gauge reads its datum value).

Record the reaction reading of the prop.

Repeat this with the 10N load

Finally, move he displacement dial gauge to the load hanger position and then ensure that on the adjustable prop the height adjustment vernier reads the same as the reaction dial gauge.

Note the “no load” readings and place the 5N load on the load hanger. Cancel out the prop displacement by altering the height Vernier to agree with the new reaction reading. It will observed that as this is done the reaction reading will increase slightly. Record the reaction reading and the displacement at the load hanger. Repeat this with the 10N load.

Result

By superposition the results of the first two sections of the experiment should equate to the last two sections.

Hence, compare the reactions measured in the latter with two end loads found in the former. Use the results to construct a bending moment diagram for the propped cantilever.

CONCLUSION

Apply the area-moment method to calculate the deflection at the load point and compare this with the measured value 

Observed: how well does theory and experiment agree in this case?

Precaution: what are the precautions you took

Does the method of equating the end displacements lead to a solution for the propped cantilever

SIMPLY SUPPORTED BEAM

Elastic beam apparatus

AIM:  to study the behavior of simply supported beam with applied moments.

APPARATUS: bending moment equipment, end support with clamping fixtures, hanger clamp, hanger link, thicker steel beam, dial indicator, standard loads.

DIAGRAM:

PROCEDURE

Part 1

Set up simply supported beam with a span 500mm overhanging ends so that load can be applied at 200mm lever and as shown in the above diagram.

Now start with a dial gauge measuring the central deflection as shown. Adding equal weights of 1N to both load hangers simultaneously; make series of deflection readings as the load is increased up to, say 6N or 8N.

Repeat with a dial guage in two other positions plot a graph of deflections against load.

Part 2

Increase the simply supported span to 1m and at the centre attach the moment application fixture; arrange a dial guage  to measure the deflection at quarter span as shown below: then applied moment by adding a pair of 2N weight to the load hangers simultaneously, and read the dial gauges on the moment application fixures. Repeat this up to total of 10N on each hanger. If time permits take further gauge readings as the load is decreased  in 2N step back to zero.

On a graph plot against load the beam deflection at the end locations and the difference between  the two gauge reading on a moment application fixture.

Results/calculation

In each case, draw the best fit straight line through the plotted points. The central deflection in part one can be checked against the theoretical value. 

Where M is the end moment = load * 200 mm

Observation :

Precaution:

Conclution:

AREA MOMENT THEOREMS

Elastic beam apparatus

AIM: to check the accuracy and use of area-moment theorems for calculation deflections and slope of a cantilever.

APPARATUS: Elastic beam apparatus, hanger links, standard loads, e.t.c.

DIAGRAM:

PROCEDURE:

Lock the actuator arm of the left end support and clamp the thicker steel strip(2.64mm) in the position as shown above so that it forms a cantilever. Then fix the lever clamp about ¾ along the length of preferably  use two dial guage for measuring deflections 

Adjust the locking screw to rotate the clamped end anticlockwise, if the self-weight of the hanger and the cantilever cause induce initial deflection.

Takethe cantilever as it set up to be a “no load” condition resd the dial gauges, tthen applied load in increament of 0.5N up to above 6N. read the dial gauges at each load.

Load(N)

Deflection Y2R,d

Deflection Y1R,d

Deflection Y1 (mm)

Deflection Y2(mm)

Deflection

Y=

Graph

Plot a graph of deflection against load. Mark off the cantilever into eight or ten equal intervals along the length of load hanger. Set up the dial guages in turn over paris of mark and measure the dseflection when a load 6N is applied. Use the graph to obtain the best fit straight lines for the two sets of deflections reading and from the lines read off the different between the two deflections for each load. In addition to the above derive the end shape of the cantilever by dividing the deferent by the distance between the dial gauges at B and C

Compare the deflection and slopes measured on the bearer with the theoretical values given by:

            

 

  

From the deflection reading taken along the length of the cantilever, plot the curve shape of the loaded cantilever  with an enlarged vertical scale. And also draw bending moment digram and for two point along the cantlever and calculate the deflection using the area moment method.

Compare all the theoretical values with the experimental ones.\

Observation: why is a cantilever particularly suitable for using area-moment method?

Precaution: what are the precautions you have observed during the experiment?

Conclusion: did the experimental result verify the bending moment theory?