Engineer's Story Problem

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

Engineer's Story Problem


DO NOT OPEN PHOTOS UNTIL YOU READ THE STORY PROBLEM BELOW!



A Backhoe weighing 8 tons is on top of a flatbed trailer and heading east on Interstate 70 near Hays, Kansas. The extended shovel arm is made of hardened refined steel and the approaching overpass is made of commercial-grade concrete, reinforced with 1-1/2 inch steel rebar spaced at 6 inch intervals in a criss-cross pattern layered at 1 foot vertical spacing.


Solve: When the shovel arm hits the overpass, how fast do you have to be going to slice the bridge in half? (Assume no effect for headwind and no braking by the driver...)

Extra Credit: Solve for the time and distance required for the entire rig to come to a complete stop after hitting the overpass at the speed calculated above.

[T. R. Oglodyte Moderator Find all posts View Profile Close T. R. Oglodyte]

My son (the structural engineer) and I spent a few moments figuring out how the damage was caused. when we first looked at the photos we were confused - we couldn't figure out how the arm could have punched through the bridge deck as shown in the photo on the right without also slicing through the entire bridge deck on the right side of that photo.

The flatbed carrying the excavator is traveling right to left as shown in the middle picture. The excavator is lowered down over the top of the cab, so the arm is parallel to the flat bed and the hoe is actually ahead of the cab. The arm of the cab is about two feet higher than the bottom of the bridge deck.

The arm of the excavator then begin tearing into the bottom two feet of the bridge deck, as shown in the photo on the right. As the truck's moentum continues, the excavator rotates pivots clockwise around the right end of the traick. That's because the bridge deck is restraining the excavator arm while the body of the excavator continues traveling with the flat bed.

As the excavator pivots, the arm moves upward, like the hand of a clock advancing from 9:00 to 12:00. This causes the arm to punch all the way through the bridge deck about two feet in.

In the middle photo, the spalling on the left bottom of the bridge deck, directly above the excavator cab, was caused by the cab slamming into the bottom of the bridge deck as the excavator rotated upwards around the tread on the right.

[bigfrank Administrator Find all posts View Profile Close bigfrank]

I say it is traveling at about 10mph. Looking at the picture it is hard to say how long it is
I say It is done by 45 sec at 45 ft.