Write 9 pages with APA style on Effect of Material and section shape in bending. It is therefore a complicated endeavour.
In selecting materials for beams, various properties other than the cost and the availability, are taken into consideration. These properties include the Type, Yield Strength, Ductility, Youngs Modulus, Hardness, Poissons ratio, and behaviour in low or high temperatures (Charles, Crane & Furness, 1997, p. 43). Yield strength is the amount of stress at which deformation of a material starts to occur. The Youngs modulus is the measure of a beams resistance to deformation. Materials show different behaviour at low and high temperatures. The strength of material reduces with increasing temperature. For example the Youngs modulus of copper is at room temperature and at almost 100°C. The selected material should be able to withstand all the applied forces without failure. A beam under bending stress experiences a negative strain on the side whereby force is applied, and a positive strain on the opposite side (Dupen, 2012, p.68). This results in the change of size on either side. The stiffness of beam under stress depends on the product of modulus of elasticity () and the second moment of area (), that is (Krenik, 2001, p.27). For a simply supported beam, the deflection () of beam is determined by the following equation, that is
When the load () is increased, the defection () also increases and if the length is increased, greater deflections are obtained as a result of the cubed term. An increase in the modulus of elasticity and the second moment of area results in a decrease in the deflection.
The stiffness of a material is determined by the Youngs modulus, which is expressed by rearranging the deflection equation as . A graph of load plotted against the has a gradient equal to the Youngs modulus . The stiffness is derived by plotting the load against deflection. It is the slope of the graph.
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