Employing the membrane analogy, develop an approximate solution to the torsion problem of a thin rectangular section as shown. Neglecting end effects at y =± b, the membrane deflection will then depend only on x, and the governing equation can be integrated to give z = ∅ = μα(a² – x²), thus verifying that the membrane shape is parabolic. Formally compute the maximum membrane slope and volume enclosed to justify relations (9.5.15).

Equation 9.5.15

Transcribed Image Text:

Ay b a X Parabolic Membrane Z a a X