Question 13.16: Determine the deflection of the free end of the cantilever b...
Determine the deflection of the free end of the cantilever beam shown in Fig. 13.19. The second moments of area of its cross section about a horizontal and vertical system of centroidal axes are I_z,I_y and I_{zy} .
The method of solution is identical to that in Ex. 13.15 except that the bending moments M_z and M_y are given by
M_z = −w(L − x)^2/2 M_y = 0
The values of the components of the deflection at the free end of the cantilever are
u_{fe}= \frac{wI_{zy}L^4}{8E(I_zI_y – I_{zy}^2)} v_{fe}= – \frac{wI_{y}L^4}{8E(I_zI_y – I_{zy}^2)}
Again, if either Gz or Gy is an axis of symmetry, I_{zy} = 0 and these expressions reduce to
u_{fe} = 0, \ \ \ \ \ v_{fe} = – \frac{wL^4}{8EI_z} (compare with Eq. (v) of Ex. 13.2)