8 A cantilever beam carries a point load P as shown in the following figure. The deflection, δ, along the beam is governed by the following equation: where x is the distance from the support A; L is the total length of the beam; P is the point load acting at the free end; E is the Young’s modulus of the beam, and I is the moment of inertia of the section of beam. (Hint: L, P, E and I are constant parameters and ) Prove that: (a) the maximum slope is at the free end of the beam, that is at x = L; and (b) the maximum slope is . A L
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A cantilever beam carries a point load P as shown in the following figure. The deflection, δ, along the beam is governed by the following equation:
where x is the distance from the support A; L is the total length of the beam; P is the point load acting at the free end; E is the Young’s modulus of the beam, and I is the moment of inertia of the section of beam.
(Hint: L, P, E and I are constant parameters and )
Prove that:
(a) the maximum slope is at the free end of the beam, that is at x = L; and (b) the maximum slope is .
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