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# RE: Lateral Brace Deflection

• To: <seaint(--nospam--at)seaint.org>
• Subject: RE: Lateral Brace Deflection
• From: "Ed Fasula" <tibbits2(--nospam--at)metro.lakes.com>
• Date: Sun, 15 Aug 1999 22:54:36 -0500

```Mark,

>My reading of S&J says that  Kreqd = 2*Kideal does not require an

The confusion between the editions is that 2ed uses a different definition
for Kideal.  In it, Kideal = Pcr/L = 2*P/L, hence the (second) factor of
safety of 2 is included.  My 2ed uses Kideal = P/L and Keqd=4Kideal.

I compounded the confusion by saying Pcr when I meant P.

Sorry about that, and thanks for the help.

Ed

The multiplier of 2 is a
>function of the
> An exception
>would be if other loads increased the initial crookedness
>of the member.
>
>Kreqd is the translational stiffness at the point of
>bracing and may be
>provided by members acting in tension or bending.  In other
>words if you
>imposed a unit translational displacement at the point of
>concern the
>resistance should exceed Kreqd.  You should consider not
>only the bending
>stiffness of the beam and the diagonal brace but also any other
>flexibilities in the bridge structure that would have a
>significant impact
>on this term.
>
>Assuming that the transverse beams contribute to the
>bracing of  chords for
>each of the trusses I would be inclined to calculate the
>stiffness by
>imposing a unit displacement inword for both truss chords
>at the same time.
>
>If there were other transverse loads such as wind on the
>truss chord or
>vehical loads on the transverse beam that produced
>deflections in the chord
>consistent with the buckling shape you are trying to
>suppress, then a
>stiffer structure would be required.  Note that these loads could be
>thought of as increasing the initial crookedness of the
>member and would
>not need to be considered when considering the availible stifness.
>
>Hopefully you will be able to show that the transverse
>deflection of the
>truss chord is not significantly influenced by other loads
>and that the
>overall flexibilities of the bridge do not significantly
>influence the
>stiffness of your brace.  If this is not the case or if it
>becomes too
>involved you might want to consider performing an
>eigenvalue buckling
>analysis.
>
>
>Mark Gilligan
>
>
>------------------------------------------------------------
>---------------
>-----
>Message text written by INTERNET:seaint(--nospam--at)seaint.org
>>
>Mark,
>   >Salmon & Johnson has a good treatment of point bracing for
>   >beams.  You want
>   >to make the brace stiff enough to inhibit undesirable
>   >buckling shapes.  The
>   >strength of the brace is then calculated as a function of
>   >the crookedness
>   >of the brace.
>They mention members braced by transverse members, but they
>
>By their method,
>The required lateral brace capacity, Q, is:
>Q = 0.004*Kideal*L
>Kideal = 4*Pcr/L  (with beta=4), Pcr = 156k (service) and L
>= 120" so,
>Kideal = 5.2 k/in and
>Q = 2.5k (conservative compared to 0.002*P, in this case)
>
>2.5k is not hard to accommodate, but Kreqd:
>Kreqd = 2*Kideal*FS  (FS = 2.12 for AASHTO) so,
>Kreqd = 22 k/in
>
>As I understand the derivation, Kreqd would simply be
>directly related to
>the bending stiffness of the beam in this case, rather than
>the axial
>stiffness of a brace for the case addressed in the book.  Given the
>geometry, 1" vertical deflection of the beam = 1.7" lateral
>deflection of
>the top chord.  Therefore, the beam's stiffness must be at
>least 22*1.7 =
>37.5 k/in!
>
>With a 6' cantilever, this is quite the beam.  If this is
>correct, I have
>some serious re-thinking to do!
>
>Ed
><
>
>
>

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