The deflection of the cantilever beam of Fig. P7.84 is governed by the differential equation.

\[ E I \frac{d^{2} y}{d x^{2}}=P(x-\ell) \]

where \(E\) is the modulus of elasticity and \(I\) is the moment of inertia of the beam cross section. The boundary conditions are \(y=0\) at \(x=0\) and \(d y / d x=0\) at \(x=0\).

(a) Rewrite the equation and boundary conditions in dimensionless form using the beam length, \(\ell\), as the reference length.

(b) Based on the results of part (a), what are the similarity requirements and the prediction equation for a model to predict deflections?

Figure P7.84

Transcribed Image Text:

d x-