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Effect of Material and section shape in bending

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An increase in the modulus of elasticity and the second moment of area results in a decrease in the deflection. Te stiffness of a material is determined by the Youngs modulus, wich is expressed by rearranging the deflection equation as . Agraph of load plotted against the has a gradient equal to the Youngs modulus. Te stiffness is derived by plotting the load against deflection. I is the slope of the graph. Te three point bending rig, sown in the picture below, ws used to measure the central for various beams.

Bams of different materials were first tested to determine the effect of material properties. I order to determine the effect of section shape, te aluminium beams of different cross sections were used. Te cross sectional dimensions of the square solid aluminium specimen and the hollow aluminium specimens were measured. Te second moment of area for each of the specimens and that of the flat aluminium specimen lying on its edge were determined. Te aluminium square, auminium hollow and aluminium flat sections were placed on the knife and each loaded with the 5N masses up to 25 N.

Te deflections for each of the set up were then recorded. Te results show that Youngs modulus is proportional to the stiffness of a material. Fr example, te square solid aluminium recorded a Youngs modulus of and a stiffness of. Te Hollow aluminium beam had a Youngs modulus of and a stiffness of. Tis shows that stiffness increased with an increase in the Youngs modulus. Te calculations also showed that both the Youngs modulus and stiffness varied the section shape of the beams.

Te second moment of area of beams is used to predict the behaviour of beams to deflection and bending. Teoretically, te higher the second moment of area of a beam, te more the beam will be resistant to bending and it is thus stiffer (Lawrence, Bll and Bailey, 2013, p Also, acording to the results, siffness increased with increasing second moment of area. Te copper beam had the least stiffness count and also the least second moment of area. Hllow aluminium recorded the amount of stiffness due to its larger second moment of area.

I also changed with the section shape of the beam. Fr example, te Hollow aluminium was much stiffer than the solid aluminium beam, ad it also had a higher second moment of area. Te...

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