For the given narrow triangular section, show that the approximate torsional load carrying capacity is given by T = 2/3 c 3 o h. Use

For the given narrow triangular section, show that the approximate torsional load carrying capacity is given by T = 2/3 μαc³_oh. Use the parabolic membrane scheme outlined in Exercise 9.8 for any level y in the section.

Data from exercise 9.8

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

Ay b a X Parabolic Membrane Z a a X