Question

A simply supported beam carries a uniformly distributed load as shown in the following figure. The deflection, ?, along the beam is governed by the following equation: ? = wx / (24 EI) * (L³ - 2 Lx² + x³) where x is the distance from the support A; L is the total length of the beam; w is the load per unit length; E is the Young's modulus of the beam, and I is the moment of inertia of the section of beam. (Hint: w, L, E and I are constant parameters) Prove that: (a) the maximum deflection is at the mid-span of the beam, that is at x = L/2; and (b) the maximum deflection is (5 wL?) / (384 EI).

          A simply supported beam carries a uniformly distributed load as shown in the following figure. The deflection, ?, along the beam is governed by the following equation:

? = wx / (24 EI) * (L³ - 2 Lx² + x³)

where
x is the distance from the support A;
L is the total length of the beam;
w is the load per unit length;
E is the Young's modulus of the beam, and
I is the moment of inertia of the section of beam.

(Hint: w, L, E and I are constant parameters)

Prove that:

(a) the maximum deflection is at the mid-span of the beam, 
that is at x = L/2; and

(b) the maximum deflection is (5 wL?) / (384 EI).

A simply supported beam carries a uniformly distributed load as shown in the following figure. The deflection, ?, along the beam is governed by the following equation:

? = wx / (24 EI) * (L³ - 2 Lx² + x³)

where
x is the distance from the support A;
L is the total length of the beam;
w is the load per unit length;
E is the Young's modulus of the beam, and
I is the moment of inertia of the section of beam.

(Hint: w, L, E and I are constant parameters)

Prove that:

(a) the maximum deflection is at the mid-span of the beam,
that is at x = L/2; and

(b) the maximum deflection is (5 wL?) / (384 EI).

Added by Christopher D.

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