(a) Give three assumptions underpinning the Euler-Bernoulli beam model.
Consider the beam shown in Fig 2, which has a modulus of elasticity E [N/m^2] and second moment of area I [m^4], and where L is the length [m] and x is the arc length [m], w(x) is the deflection [m]. The beam has a guided support at x = 0 and a roller/pin at x = L. It carries a triangularly distributed load of maximum intensity wo, such that w(x) = wo - woL.
Figure 2: This Figure refers to Q 4
The boundary conditions are as follows:
w(L) = 0
d^2w/dx^2 = 0
d^3w/dx^3 = 0
dw/dx|_(x=0) = 0
(b) State what each of Eqs 16-19 mean.
(c) By successive integration of the following differential equation:
dw/dx = EI(x)
determine the constants of integration C1, C2, C3, C4 and find the maximum deflection w(x).
(d) Comment on the appropriateness of the Euler-Bernoulli model for the analysis of large deflections and explain what the key difference would be for a large deflection mathematical model.