Problem $2$: Railroad ties can be made from wood, steel, concrete and fiber reinforced polymer. A train will apply load on the top of the rails which is then distributed to the tie. Pressure from

the ballast $($gravel fill$)$ will resist this load. There are a number of load cases, based on different

types of ballast condition. Assume only the following load case: a train axle of $76$ kips $(P=38$

kips$)$ and $L=12ft.$

Determine the intensity of the reacting bearing pressure $($w$)$ due to the train load. Assume ballast

is intact and creates a uniformly distributed load as shown below.

They are often highly structurally optimized. It is of particular importance for concrete ties

because concrete can easily crack in tension, making it important to design proper reinforcement

in these locations.