Create a 5 pages page paper that discusses the design of mechanical structures. The principal aim of this lab activity was to carry out the experimental deflection measurements on statically determinate and later statically indeterminate beams. After the exercise, a comparison of the data obtained, and the beam theory predictions are to be made. Besides, the lab experiment aims at verifying the principle of superposition for beam deflection. When a beam is bent, it ends up taking various shapes. These different forms may be represented on an x –y graph where the origin is located at the left end of the beam. At any distanced meters from the left end, the beam will have a deflection y and a gradient given by the differential formulae dy/dx. The equation relating to the bending moment and the radius of curvature of a beam is given by the equations M/I=E/R, where the parameters M represents the bending moment, I represents the second moment of area about the centroid, E represents the modulus of elasticity, and R gives the radius of curvature. After rearranging the equation, the following is obtained: I/R=M/E. The figure below illustrates the radius of curvature that is usually defined as the radius of a circle having a tangent similar to the point on the x-y when plotted on a graph (Callister & Rethwisch, 2007).
When a simply supported beam holding a central concentrated load is deflected, its deflection varies when several changes occur. Among them include, change in the Load, change in Span, variation in the Breadth of cross-section, and alteration in the Depth of cross-section. In simple terms, the relationship in all these parameters can be given by the formulae:
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