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lab 9 - Year 2010 Month 11 Day 19 Beam Deflection of...

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Year 2010 Month 11 Day 19 Beam Deflection of Cantilever Beam Aerospace Engineering Laboratory II Name : Martin Suhartono Student ID : 20106182
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1. Objective A cantilever is basically a beam that is supported on one end. Cantilever facilitates one to build an overhanging structure without external bracing and thus it is widely used in construction of bridge, aircraft wing, balcony and automobiles. A cantilever beam usually has variable cross sectional area along its axes and is usually subjected to various loads. However, for our experiment, the cross sectional area is constant and the load is put only on the free-end. The load on the cantilever beam will produce a shear stress on its cross sectional area. This shear stress may be expressed as Where M is bending moment due to the load, V is the shear force in Newton, and x is the discretionary distance from the loading point in meter. The axial stress along the axes, in contrast, can be expressed as Where c is the distance between the surface of the beam and the neutral axis, I is the moment inertia of the cross sectional area of the beam in m 4 , P is load in Newton, b is the beam width, t is the beam thickness, and Z is the section modulus of the beam in m 3 . The strain of the beam’s surface can then be expressed according to Hooke’s law as Where ε is the deformation rate (called strain) and E is the modulus of elasticity in N/m 2 . Based on the above equations, we can get the longitudinal strain at a particular discretional distance x expressed as In this experiment, the strain gauges are placed at different discretionary distances from the point of loading. Based on the assumption that the strain varies linearly the strain formula can be expressed as This, in turn, gives us the following equation Which, when applied to a pair of strain gauges give us The shear strength as expressed by the above formulas can be regarded as the load imposed on the beam. Nonetheless, there are experimental errors that render this calculation to be rather inaccurate. Using average values to calculate the load is then
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