Right at the beginning of the chapter don't go in the direction of the crane, but backtrack a little to the hole through which you came a moment ago.
Go inside and take the COG Tag CSID:444526-MI2K9-3B. After that go to the crane and use it to get over the gap.
You control the crane with the analog stick. Steer it so that Damian can get on the arm. Afterwards steer the arm right and let him get on the ground.
Exit the crane and wait from Dom to knock down the arm of the second machine. Cross the gap and use the Hammer of Dawn to eliminate the foes.
In the corner of one of the rooms you will find the Stranded's Journal: Russell.
Cut the steel cables holding the tower.
And enter the knocked down structure.
You will receive and order of finding the entrance to the cave and through the windows you will see a horde of attacking Locusts. The whole construction will crumble.
Escape the burning building as fast as you can. Run to the other side, switch on the elevator and jump in.
A Brumak also got stuck in the ruins. His guns are shooting all the time, so the safest way to pass him is to hide behind one cover and immediately go to another. After that kill the Brumak's driver.