Two distributed line loads act on a cantilever beam as shown in the diagram on the left. Both loads act through the center of the rectangular cross section in the directions shown. What is the maximum absolute bending stress in the wall?

Moments at Wall due to
Distributed Loads

To determine the bending stresses, the maximum moment needs to known. Since this is a cantilevered beam, the maximum bending moment will occur at the fixed end, or the wall.

     M_z = F_y d  = -[(1.5)(0.5)] (1.5 + 0.75)
          = -1.6875 kN-m
     M_y = F_z d = [(1.5)(0.5)] (0.75)
          = 0.5625 kN-m

The moment of inertia around each axis is

      I_z = (0.1)³(0.06)/12 = 5×10^-6 m⁴
      I_y = (0.06)³(0.1)/12 = 1.8×10^-6 m⁴

The maximum moment at one of the four corners. From inspection, both the M_y and M_z moments will cause tension stress in the upper left corner, point A (don't forget that M_z is negative value). Similarly, both moments will cause compression stress at point D. These two points, A and D, will be the maximum tension and conpression stress, respectively. In this case, the magnitudes for both the maximum compression and maximum tension will be equal.

Maximum stress at point A, y = 0.05 m, z = 0.03 m, is

     
        = 26.25 + 16.875 MPa

     σ_A = 26.25 MPa