Question Statement:
A cantilevered beam is subjected to a parabolic distribution of shear traction at the right edge while
the top and bottom surfaces are traction free. To solve this problem, following Airy's stress
function is proposed: 𝜙𝜙 = CC1xxyy + CC2xxyy3 + CC3xx2yy2 + CC4xx3yy. This is an admissible Airy's
function that would satisfy the bi-harmonic equation as well as the boundary conditions if and only
if
(A)CC1 = 0,CC2 = 𝜆𝜆, CC3 = 0, CC4 = 𝜆𝜆
3dd2 (B)CC1 = 𝜆𝜆,CC2 = 𝜆𝜆
3dd2, CC3 = 0, CC4 = 0
(C)CC1 = 0,CC2 = 0, CC3 = 𝜆𝜆,CC4 = - 𝜆𝜆
3dd2 (D)CC1 = 𝜆𝜆,CC2 = - 𝜆𝜆
3dd2, CC3 = 0,CC4 = 0