This article was posted 08/03/2006 and is most likely outdated.

An Engineer's Story Problem
 

 
Topic - Unusual and Special Issues
Subject - An Engineer's Story Problem

August 3, 2006  

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An Engineer's Story Problem



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 ½ 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.  Yes, you can neglect friction...

Demonstrative Solution: (Doesn't look as though he could get up enough speed to make it all the way...)

 

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Comments
  • Inquiring minds also want to know:

    1) What the heck is the difference between a "track hoe" and a back hoe? 2) Why the heck was the boom facing forward rather than the usual rearward.

    Answer to speed question: Not necessarily all that fast. at all. With the boom facing forward it could have easily scissored (jackknifed) upward after initial contact with the first or second girder. Then inertia and leverage would pull the boom up poking it thru the bridge deck. Once the original cut is made, the answer to the extra credit problem is given. Namely it took only about half of the width of the bridge for a complete standing stop. You can't ignore friction on this one since both shearing and friction energy are expended by the boom while substantial friction energy is exerted by the flat bed trailer undercarriage in sliding and eroding the road bed beneath the bridge. Ditto for the drivers side tractor tread.

    I also agree that the hydraulic cylinder or links were busted early on.

    BTW, I think that the back hoe (track hoe) very nearly wound up wearing the bridge.

    Inquiring minds further want to know what does a new overpass cost these days.

    P.S.: The above analysis is the result of a rather long E-mail thread among a group of engineers that analyzed this thing to death a few weeks ago.

    Best regards . . .

    Jim

    Jim S. Nasby

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