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Unsymmetrical Bending of a Cantilever - Lab Report Example

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After compiling the data for cantilever, the direction of deflection is resolved both for the right and left indicator as shown in the…
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Unsymmetrical Bending of a Cantilever
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Lab Report on Unsymmetrical Bending of a Cantilever Theory The free end deflection will have two components as follows; one in the direction of pull (U) and at right angles (V) (Bansal, 2010, 43). After compiling the data for cantilever, the direction of deflection is resolved both for the right and left indicator as shown in the following formula:
(1)
(2)
.
From this resolve, a graph U and V (mm) against the pulling mass, P(g) is plotted for each angle. The gradient for each graphs is determined for both U and V plots as follows
Gradient for U = dU/dp
Gradient for V = dV/dp
The results from the above calculations are put in Table 1 as shown (units being mmg-1) followed by converting the values to mN-1, which is considered as the fundamental unit. From this, the Mohr’s circle is constructed by plotting dU/dP against dV/dP. The major use of Mohr’s circle, in this case is to calculated principal second moments of area using the following formula (Rajput, 2007, 87):
(3)
(4)
Whereb y is effective length of the specimen (m),
is the Youngs modulus for aluminium,
OC is the distance from origin to centre of Mohr’s Circle (mN-1) and
R is the radius of Mohr s Circle (mN-1).
Procedure
The equipment was set up as shown in the laboratory manual. The two rearward were loosened and the inner two datum pegs made to contact by setting the angle between the two indicators at 900. One of the specimens was selected and fitted in the bottom chuck with the top chuck fitted with the top of the specimen and the extension piece to the bottom chuck. The cord was then placed on the groove and passed over the sliding pulley. The specimen was then rotated after undoing the top chuck. The indicators were allowed to travel 10 mm forward and 3 mm backward. The frame was tapped to reduce friction and loads applied in 100 g increments upto 500 g on the end of the cord. The resulting deflectins were recorded under Head angle: 0°’ title. The procedure was repeated while rotating the specimen clockwise 22.5° while tightening.
Discussion
By using dU/dP and dV/dP as a point’s coordinate, the points therein formed the Mohr’s circle as shown in the results. From the circle, the IX and IY were calculated for the experiment and compared to the theoretical calculation. Further, the graph of U and V (mm) against the pulling mass was used to determine the influence of the readings on load’s eccentricity. This graph was useful in finding the position at which the readings of the two indicators were equal. From this, the shear center was established by determining the intersection point. In which case, whenever the load is placed at the intersection point (shear center), the beam does not twist, since the two indicators’ readings are equal (Ross, 2009, 198).
In order to verify the completeness of the results, hand calculations were done and then compared with the theoretical values. In which case, the distance between shear center and line L was calculated to confirm the accuracy of the results. However, there was a difference that can be contributed to the inconsistency of the shear center beam “0” notch. This calls for the need for modifying the design of the apparatus used for this case.
Even though the experiment was successful in meeting the aforementioned objectives, comparing the experimental results and theoretical calculations indicates that there is a little deviation of 2.33%. This error can be attributed to error in measurement especially in the process of constructing Mohr’s circle. Relatively fewer points were used, something that did not guarantee accuracy. Consequently, if more data obtained from the other head angles were used then the error could have been avoided.
Bibliography
Bansal, R. K. (2010). A textbook of strength of materials: (in S.I. units). Bangalore: Laxmi Publications.
Rajput, R. K. (2007). Strength of materials: (mechanics of solids) in SI units. New Delhi: S. Chand & Co.
Ross, C. T. F. (2009). Mechanics of solids. Chichester : Horwood Pub. Read More
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