78 CHAPTER 3 Torsion of Solid Sections
Fig.3.7
Membrane analogy: in-plane and transverse loading.
Fig.3.8
Equilibrium of element of membrane.
Equation(3.24)mustbesatisfiedatallpointswithintheboundaryofthemembrane.Furthermore,
atallpointsontheboundary
w= 0 (3.25)andweseethatbycomparingEqs.(3.24)and(3.25)withEqs.(3.11)and(3.7),wisanalogoustoφ
whenqisconstant.Thus,ifthemembranehasthesameexternalshapeasthecrosssectionofthebar,
then
w(x,y)=φ(x,y)