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

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I would like to add my 2 cents. 
I would characterize the "fan" scenario as a steady state forced vibration problem where adding mass changes the frequency of the support structure thereby changing the frequency ratio (= excitation frequency/natural frequency) and hence the magnification factor for the response changes.  Theoretically, the response could increase or decrease when mass is added but for a fan that operates at a relatively high frequency compared to 'natural frequencies' of supporting structures, the tendency will be to reduce the amplitude.  
The pressure wave in the tunnel is probably more like an impulsive loading condition where, as Chris says, the so-called dynamic load factor (DLF) = 2.0.  This is the theoretical upper bound value.  The actual DLF could be less than this. 
When the fan starts up, there will be a transient phase where it is possible for the vibration amplitudes to be larger than the steady state amplitudes - more like an "impulse" loading condition. 
One more item - I would expect that the engineers designing the tunnel roof would have considered the dynamic effects and sized the concrete panels such that the panel dead weight would not be exceeded by the pressure wave in order to keep the hangers in tension and to prevent impact loads when the panels drop down.  Regardless, there still would have been a time variation of the tension load on the anchors (always in tension but varying with time with each pressure wave) and I'm wondering if this type of anchor is suited for such loading conditions. 
Walter Sawruk
ABS Consulting
Shillington, PA

-----"Mark D. Anderson PE" <mark(--nospam--at)> wrote: -----

To: seaint(--nospam--at)
From: "Mark D. Anderson PE" <mark(--nospam--at)>
Date: 07/15/2006 10:10PM
Subject: Re: big dig structural failure - epoxy anchors overhead supporting gravity

If it helps to clarify a possible source of the difference in viewpoint
between Steve and Chris, it appeared that in Steve's analogy (the fan) he
was referring to a forced vibration problem, and Chris' focus is on free
vibration response.

Whether the original Big Dig issue concerned forced or free vibration
response is beyond me...

Mark D. Anderson

----- Original Message -----
From: "Christopher Wright" <chrisw(--nospam--at)>
To: <seaint(--nospam--at)>
Sent: Saturday, July 15, 2006 1:34 PM
Subject: Re: big dig structural failure - epoxy anchors overhead supporting

On Jul 15, 2006, at 4:15 PM, S. Gordin wrote:

> Now, if I place a sandbag on it - the vibrations will be much less without
> adding any rigidity to the system, just because of the increased mass.
Again, I don't see how that works, except if the decreased frequency
due to the added mass is enough less than the frequency of the
excitation of the fan. And you could get the same effect if you were to
stiffen the deck, say by adding a support.

The frequency of a flat slab carrying only its own weight is
proportional to the thickness and inversely proportional to the square
of the span. You get more bang for the buck by adding supports than you
do from adding thickness. Adding thickness means using stronger
supports, but adding supports decreases the load per support.

> If those panels would be made of, say, steel decking, they will vibrate;
> fill the deck with concrete - for all practical reasons, they won't.
I wonder if the purpose is to use the mass to hold them in place
against uplifting from the pressure wave. Strictly speaking that isn't
vibration, it's rigid body motion. Otherwise I think I'll stick to my

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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