Problem: During the balanced cantilever construction of a concrete box girder bridge, the segments are cast symmetrically outward from a central pier. A construction equipment load (form traveler) of $500\text{ kN}$ acts at the tip of the cantilever, which is $20\text{ m}$ from the pier centerline on one side. The opposite side currently has a traveler load of $500\text{ kN}$ acting at $18\text{ m}$ from the pier centerline. The box girder segments themselves weigh $250\text{ kN/m}$.

Calculate the out-of-balance bending moment at the pier base caused by the construction loads and the dead load of the cantilevered segments. Determine if the structure requires temporary tie-downs if the maximum allowable out-of-balance moment at the pier base is $15,000\text{ kN}\cdot\text{m}$.

Problem: A continuous steel box girder bridge deck is being constructed using the incremental launching method. The completed segment to be pushed weighs $12,000\text{ kN}$. It slides over temporary bearings with a coefficient of static friction $\mu_s = 0.05$ and a coefficient of kinetic friction $\mu_k = 0.03$. The bridge is being launched up a longitudinal gradient of $2\%$.

Determine the maximum initial jacking force required to overcome static friction and start the launch, and the continuous pushing force required to maintain motion.