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Re: big dig structural failure - epoxy anchors overhead supporting gravity

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In long enough pedestrian bridges with wood decks, it is practically impossible to satisfy the vibration criterion, practically no matter what you do with the steel trusses or girders.  This is why, in lieu of special damping measures, concrete decks become a must in longer bridges. 
However, here we are dealing with concrete "ceiling", so the mass is of value for curbing vibrations.  The anchorage of these massive structures is a different story, though, and this appears to be the issue at hand.
Steve Gordin SE
Irvine CA
----- Original Message -----
Sent: Saturday, July 15, 2006 12:06 PM
Subject: Re: big dig structural failure - epoxy anchors overhead supporting gravity

On Jul 15, 2006, at 1:26 PM, S. Gordin wrote:

> This is not how I understand it. With bridges, for example, there are
> two criteria to limit vibrations - one based on rigidity (natural
> frequency) and the other one based on the mass of the structure.
It's first principles--frequency = (1/2pi)sqrt(k/m). Increase m and the
frequency decreases. The system gets relatively (stiffness relative to
mass) softer. With frequency dependent excitation, adding mass might
move the system frequency away from the excitation frequency, but that
won't happen with suddenly applied loads, like the pressure wave.
Unless the system is extremely stiff, a suddenly applied load always
produces twice the stress and deflection as the same load statically
applied, and the system goes through a couple of cycles of vibration at
a lower or higher frequency depending on how stiff it is. The system
frequency affects the displacement and how long it takes the response
to die out.

Those two bridge criteria are related because mass and frequency are
related, but there are counter tendencies. What usually happens with
steel frameworks is that it's difficult to increase the stiffness
without also adding mass--moreover the square root dependency means
that a 20% stiffness increase only increases the frequency  by
10%--such a small change gets lost in the white noise. Sometimes you
can play tricks like changing from girders to trusswork, but only in
special circumstances. I've played around with trying to increase first
mode frequencies for years, and with steel frames like crane
structures, once you've set the span, you're pretty much stuck with the
frequency you get.

I expect with concrete supported by steel, most of the mass is concrete
and most of the stiffness is steel, so you have a little more latitude
to make meaningful changes. I don't do concrete so there's probably
more to it than just that, especially with bridges.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)   | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania

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