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# Strength and material Essay Example

- Category:Engineering and Construction
- Document type:Assignment
- Level:Undergraduate
- Page:1
- Words:517

Strength and material

A frame is a structure with at least one multi-force. In the experiment deflection of a frame was determined by mathematical calculation and the results were validated using experimental results. The frame used in the experiment is rigid because if one side is removed, for example part CB is removed the other part will collapse that is part AB. It is a free body structure with two arms with loads placed on point A and B, the two frames are considered as distinct but related. The two loads exert forces on the two farms causing deflection, the forces exerted on it cannot be determined from equilibrium conditions that exist, they can be determined by treating the forces acting on the frames independently.

The deflection calculation is found by calculating the deflection in the first question. When the loads were placed, section AB bends and the bending momentum at point B turns the corner and it will push arm BC downwards bending it along its length; this is caused by the two forces. Both sections are considered differently. Deflection Y_{1} was calculated by carrying out partial differentiation with respect to F_{1}, as shown in the following equation, it was found that Y_{1} is

. Deflection Y_{2} was also calculated by carrying out partial differentiation with respect to F_{2}. And it was found to be

.The deflection at Y_{2} is more than the deflection at Y_{1}because the force produced by F_{1} is added to the force produced by F_{2} because they are both in the same direction.

The experimental part was carried out as per the procedures provided in the manual. It was found that the deflection at Y_{1} is 0.00357mm while deflection for Y_{2} was found to be 0.00392mm. There is a difference between the calculated and experimental results, but a common thing is that both shows that deflection at Y_{2} is more than at Y_{1}. The difference between calculated and experimented results for Y1 is 0.0033mm while for Y_{2} is 0.0039mm. It is well known that calculated results normally differ with experimental results when compared because of improper experimental setup. The experimental results were not expected because there is a significant difference between the experimental and calculated values. Though in mm it looks small but in percentage it is high, it could be as high as 50 percent. The differences are caused by errors encountered while carrying out the experiment; the errors are caused by improper measurement of deflection and poor theoretical calculations for example rounding off the numbers to one decimal place. To improve on the results modern methods of doing the experiment should be applied.

References

Gargi Majumder & Kaushik Kumar. (2013). “Deflection and Stress Analysis of a Cantilever and

its Validation Using ANSYS”. *International Journal of Mechanical Engineering and Research*. 3(6), p. 655-662

Dr. R. K. Bansal. (2013). *A textbook of Strength of Material (Mechanics of Solids), 5th edition*.

Laxmi Publication. p. 515-582

Biltu Mahato1, Anil2, Harish H.V. (2015). Experimental verification of deflection of beam using

theoretical and numerical approach. *International Journal of Advance Research in Engineering, Science & Technology (IJAREST)*. 2(3).