# Cantilever beam formula derivation

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Jun 07, 2017 · In our previous topics, we have seen some important concepts such as deflection and slope of a simply supported beam with point load, deflection and slope of a simply supported beam carrying uniformly distributed load and deflection and slope of a cantilever beam with point load at free end in our previous post. the modulus of elasticity of the beam material; In considering deflection, the same assumptions are taken as in the derivation of the bending formula. The diagrams above show an enlarged portion of the loaded beam. The arc AB of length δs is on the neutral axis of the beam and subtends angle δi at the centre O of curvature.Develop the general equation for the elastic curve of a deflected beam by using double integration method and area-moment method. State the boundary conditions of a deflected beam Determine the deflections and slopes of elastic curves of simply supported beams and cantilever beams.Beam Stiffness The differential equation governing simple linear-elastic beam behavior can be derived as follows. Consider the beam shown below. CIVL 7/8117 Chapter 4 - Development of Beam Equations - Part 1 6/39Jun 07, 2017 · In our previous topics, we have seen some important concepts such as deflection and slope of a simply supported beam with point load, deflection and slope of a simply supported beam carrying uniformly distributed load and deflection and slope of a cantilever beam with point load at free end in our previous post. Plugging equation (9) into either (8a) or (8b) will lead to the frequency equation for a cantilever beam, (11) The frequency equation can be solved for the constants, k n L ; the first six are shown below in Figure 3 (note, k n =0 is ignored since it implies that the bar is at rest because =0).