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Large Bay 'X' Bracing

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Dear Rich:
I have put your question as a Problem below and offered my solution to t. next semester I might give it as a HW or even a midterm!

Problem: Design an X-bracing in an industrial building to resist wind load. The height and width of the braced bay are 31' and 42' respectively. The braces are to be designed as tension only members. The service load in the diagonal is 21 kips. Use LRFD or ASD according to AISC 2005 Specification (ANSI/AISC 360-05) and ASCE-7-2005.

Solution: Two options will be considered; Round HSS and threaded rods with turnbuckle. LRFD methods will be used. (ASD will result in identical solution for tension members)

Option A- Round HSS Shape:
Tu=Factored Load= 1.6x21 =34 kips
According to AISC Manual 13th Ed, Page 2-39, the preferred round HSS material is A500-GrB(42/58 ksi). So, Fy=42 ksi and Fu=58 ksi.
Check yielding of gross area:
Ag=Tu/[(Fee-y)(Fy)= 34/(0.9x42)= 0.9 in2
Check fracture of net area:
An= Tu/(Fee-u)(Fu)(U)=34/(0.75x58x0.90)= 0.89 in2
Notice that a U factor of 0.90 is used for the net section at the ends of the member. More precise U can be established by using
U=1-x/L and knowing L, the length of welds on the round HSS at its ends.

If only strength is considered in design, a Round HSS2.375x0.218 with Ag= 1.2 in2 will be sufficient to carry the service load of 21 kips. With this section, probably a 3/8" gusset plate would be sufficient. In that case the net are left at the ends of the member will be:
An=1.39 in2-2x(3/8)(0.218)=1.22 > 0.89 in2 O.K.
Notice that a lighter section such as Round HSS 2.375x0.154 will also work resulting in An=0.893 > 0.89. But, I prefer to have some thickness in the pipe near 1/4' so that welding at the ends can be done properly. So, I choose Round HSS 2.375x0.218 for the braces for strength considerations. Now I like to check the "preferred" slenderness ratio for tension members. Notice that this is preferred and not "required' by the AISC Spec. It is preferred that KL/r < or = 300.

The value of K for members in X-brace can be taken as 0.75 (see S.C. Goel et al paper in the Engineering Journal of the AISC at AISC.org on this subject. Search under Goel). Gusset plates provide some fixity for in plane direction and the compression brace connected to the middle point provides fixity in out of plane direction. That is why K is 0.75. L for the member is 52 feet.
KL/r < 300 results in:
r>  0.75x52x12/300 = 1.56

If I want to satisfy this "preferred " criteria, the section to be used will be Round HSS 4.5x0.237 (again preferring a section with a wall thickness not too much smaller than the 1/4" for practicality of fabrication and welding. Since this criteria is a "preferred' one the choice between this heavier section and what we need to satisfy strength is ours. I choose the heavier section to satisfy the KL/r < 300 and possibly avoid complaints from the fabricators and erectors on flimsiness of the braces!

Option B- Threaded rods and turnbuckles:
Tu=Factored Load= 1.6x21 =34 kips
Let us use A36 threaded rods, with Fy=36 ksi and Fu=58 ksi.
Check tensile strength (see AISC Spec 2005 Table J3.2)
A=Tu/[(0.75)(Fu)]= 34/(0.75x58)= 0.89 in2
A 1-1/8" diameter A36 rod will be sufficient to carry the load. The rods would need turnbuckles and post-tensioning to about say 10% of the capacity to remove the sag which in that case there is no need to check the KL/r< 300 preferred criteria since it is not meant for post tensioned rods.Apparently when one goes back to bridge books, where this criteria was first mentioned, one finds out that this was meant only for rolled shapes and cold formed sections and for fabrication and erection purposes. Also, bridge engineers were concerned with the vibrations of very slender members in bridges under the impact of trucks passing over. I observed this phenomenon a few years back in Binicia-Martinez bridge near San Francisco when walking under the deck on the catwalk, you could clearly see the vibration of single angle cross braces. The vibration itself was not a major concern since no one can see those vibrating braces, but, I got concerned about fatigue issues since over the years such vibrations can cause fatigue fracture. i did some back of envelop dynamic analysis and it turned out that the vibration is because of dynamic resonance and the fact that these braces are long and have relatively small stiffness that their period of first mode is close to 1.0 Hz, the driving force frequency. Then you look at KL/r < 300 and you really get fascinated with the wisdom and knowledge of those bridge engineers of 19 and early 20th century who has put all of this dynamics and fabrication and erection concerns into very simple equation of KL/r < 300 and avoided all the pitfalls of using very slender members. Notice that KL/r has all the dynamic properties of geometry (L and A) and stiffness (I) in it! By the way, this was not the first time I was amazed how good those old time engineers were. the first time was during my dissertation work, I stumbled over the Whitmore's method for gusset plates which was used in late 1800's by bridge engineers , almost hundred years ahead of Whitmore's tests which showed this method works!

Well, sorry for taking your time too long.With your permission I plan to double check it and include in my upcoming textbook: "Behavior and Design of Steel and Composite Structures" by Abolhassan Astaneh-Asl, Volume One on Steel Structures to be released January 1, 2008). I know you will not trust my calculations and if you use above numbers in your actual design, you will double check them!

Best wishes and thank you for bringing up an interesting question.
"Hassan"
Abolhassan Astaneh-Asl, Ph.D., P.E.,
(http://www.ce.berkeley.edu/~astaneh)
=============================

From: "Rich Lewis" <seaint04(--nospam--at)lewisengineering.com>
To: <seaint(--nospam--at)seaint.org>
Subject: Large Bay 'X' Bracing

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I have a warehouse condition of a 'X' braced bay that is 31 feet high and 42
feet wide.  The diagonal length is over 51 feet.   I'm wondering if I should
try to use the bracing as one large bay, or add a wind column in the middle
and have two smaller bays.  The bracing is tension only for wind loads.  The
load in the diagonal is about 21 kips.  What makes me most uneasy is the
slenderness ratio of the brace.  If I try to limit the L/r ratio of the out
of plane axis to 300 then I get extremely large angles.  If I ad a column I
add almost 50% more bracing length, plus column and footing.



Thanks for your insight.



Rich

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