For the loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, and (c) the slope at the free end. Assume that EI is constant for the beam. Let w = 8 kN/m, L = 3.0 m, E = 205 GPa, and I = 100 x 106 mm4. Cut a cross-section through the beam at any point and draw a free body diagram. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for M at x = 1.5 m.

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Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.