Each wood railroad tie supports part of the weight of a train (plus the relatively small weight of a section of rail). This is modeled with two point loads representing the force of the rail on the tie. The reaction from the ground is modeled as uniformly distributed since the railroad tie is supported along its whole length. Determine the smallest allowable dimension s of the square cross section if both of these conditions must be met:
a. The largest normal stress in the railroad tie cannot exceed 9 MPa.
b. The largest shear stress in the railroad tie cannot exceed 1 MPa.
