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Structural Exam Problem

Structural Exam Problem

Structural Exam Problem

(OP)
Not really, but interesting none the less.

We all have extended metal tape measures to see how far we could make the cantilever before it failed.

Considering the degree of concave arcing of the tape, the materials, and the angle of inclination to the horizontal to the tape, what is the equation to determine how far the tape can be pulled from the holder before snap-thru occurs, causing a hinge to form and the tape to drop?

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: Structural Exam Problem

Mike, either you have too much free time or it is Friday afternoon.

I do not think it is an easy question. The tape fails by buckling, does it not?

RE: Structural Exam Problem

some tapes are thicker than others and have varying curvatures....but I can extend my FatMax 15' before it buckles.

RE: Structural Exam Problem

I am sure this is a problem my old professor Dr. Ray Plaut would be interested in :)

Regardless, my little experiment with different angles on a 12' stanley leverlock tape , 44" is the longest that it would go before it snap-buckled.

Starting off at a angle of 0 or 90 gave better results than any other angle. It seems like sway and the clip at the ends had some effect as well. Steady hands would be needed:)

RE: Structural Exam Problem

Sounds like local buckling of a portion of the cupped part of the tape.  I think a mechanical, rather than structural, engineer would be more accurate in assessing this.  The failure doesn't result from yield, but from a spring action.

As for loads, you'd have to eliminate air movement, vibration, etc.

You might be able to approximate it empirically, but the theory and math would get dirty, really fast.

RE: Structural Exam Problem

I may actually know of a practical application for this theory.

Last year I spent some time looking at pedestrian bridges that were bottom chord suspended from arch / vierendeel trusses on either side of the deck.  The trusses were splayed outwards 15 degrees or so.  The question of interest was LTB of the trusses and whether or not they would prefer to buckle inwards or outwards.

For shits & giggles, we made some models using bent up cardboard (U shaped).  We'd cantilever them off the end of a desk, load the ends, and observe the buckling patterns.  They always buckled such that the side walls would tend towards the horizontal.  Ditto for the walls sloping inwards.

All this, it seems to me, bears some similarity to your tape measure problem.  As for the equation... beats me.  Time to call on Teddy G.

 

RE: Structural Exam Problem

(OP)
Yep...

Build on this example, but with a uniform dead load and a cantilever instead of the point load and two-hinged arch.

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VJS-4GHRC76-1&;
_user=10&_coverDate=07%2F31%2F2006&_rdoc=1&_fmt=high&_orig=search&_sort=d&
_docanchor=&view=c&_searchStrId=1235364331&_rerunOrigin=google&
_acct=C000050221&_version=1&_urlVersion=0&_userid=10&
md5=fbad658f9eb8c50204475f4baf75cc04

WOW!  I didn't think the link was that long...  Oh well...

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

RE: Structural Exam Problem

You can find the bending stresses in the tape assuming the shape remains the same.  Then take a short section of the curved beam as a freebody, and the bending stresses acting at an angle at each end are also the forces tending to flatten it out.  As it flattens, section modulus drops, stresses increase.  I think the problem is solveable.

Suppose you have a thin dome.  Cut one pie-shaped section out of that dome.  Can you support it at the center and the outside without it collapsing?

RE: Structural Exam Problem

Mike, you make us all want to spring into action. It's Saturday night, go hug your wife.

RE: Structural Exam Problem

Horizontally or vertically? And does the tape have nay previous kinks in it?

RE: Structural Exam Problem

vandede-
There must be a bigger FatMax now than the one I have becasue it is a bona fide fact that one cannot be extended more than 11' when horizontal.

I am the all-time King of tape extending.I will challenge any one on earth to a tape-off.
I was the unrivaled king of tape extension for nearly ten years in my state during my construction years.
I once extended a regular 1" Stanley Powerlock tape the full 25 feet (albeit nearly vertically) in order to measure a wall in the 2 story open foyer. People still ask me about it when I go out for coffee at the local Dunkin Donuts and that was nearly 10 years ago now.

 

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