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?