Whoops, forgot that to get to 1.09 for the required section modulus, you
first have to divide PL by 4, then by 15,000. See how easy it is for
even a smart aleck like me to make a mistake? The answer was correct,
but the explanation was flawed, that's why my teachers always asked to
show the work.
65,696.4divided by 4= 16,421 and that divided by 15,000 = 1.094
Forgetting a step like that got me much lower grades.
*
PARSLEY CONSULTING
*
Ken Wagoner
760.745.6181 voice
760.745.0537 fax
website: www.ParsleyConsulting.com <http://www.ParsleyConsulting.com>
On 6/3/2013 7:51 AM, ParsleyConsulting wrote:
Brad,
Part 1 - Gibberish. Pure and simple. The tables in NFPA 13
didn't reduce the "force" and "distance" by half in their
calculations. It simply used the formula to calculate the maximum
moment at the point of the load for a simple beam, based on the
maximum length of various pipe sizes between hangers. That's why the
figures for 1" and 1-1/4" are based on 12' between hangers.
The maximum moment is the "worst case", and was what the committee saw
as providing system designers with enough information to allow them to
not use trapeze members which would have excessive loads placed on them.
The formula to determine maximum moment is PL/4, with P=weight of
pipe being supported in pounds (including 250#), and L=the length of
the span of the trapeze in inches. The moment is then divided by the
maximum allowable bending stress, which for steel is 15,000.
The resulting equation looks like this: (PL/4)/15,000 = required
section modulus. So, for 15' of 1-1/2" sch 40 pipe, the value of P
would equal 15' x 3.61 = 54.15 + 250 = 304.15#. For an 18' span, the
value of L = 216". Multiply PxL = 65,696.4, and then divide that
value by 15,000, and the result is a required section modulus for the
worst case location of the load (mid span) of 1.09 in³. That is just
slightly less than doubling the value for a 9'-0" span, however using
that method would result in a larger required section modulus, so it
would work out in the end.
The 4ab/a+b you reference is a method to calculate the equivalent
length of the trapeze, in order to reduce the value of "L" in the
original equation. Going back to your 18' span, if the load were 3'
from one end, and 15' from the opposite end, that results in the
equation 4x180x36/180+36, which equals 120", or 10'. The value of L
in the above equation is changed from 216"to 120", reducing the
required section modulus. PL/4 now becomes 304.15 x 120 = 36,498which
is divided by 4, resulting in 9,124.5, which is further divided by the
allowable bending stress of 15,000 for steel, with a final required
section modulus of 0.6083 in³. Round that up to 0.61, and it matches
the value in NFPA 13, Table 9.1.1.7.1(a) (2013).
No reduction by half anywhere in those equations.
Part 2 - Relatively correct regarding doubling the require section
modulus for a 9' span, however as the structural engineers in the room
when this table was expanded to include spans up to 16'-0" notedyou
can keep increasing the span to the point where the weight of the
trapeze itself now becomes an issue in the overall capacity to resist
bending, and that sort of calculation was one they were reluctant to
provide without a significant amount of additional information.
Please note that this is my opinion only, and does not reflect that of
the NFPA 13 Hanging and Bracing Committee.
*
PARSLEY CONSULTING
*
Ken Wagoner
760.745.6181 voice
760.745.0537 fax
website: www.ParsleyConsulting.com <http://www.ParsleyConsulting.com>
On 5/31/2013 7:36 PM, Brad Casterline wrote:
saw an e-mail the other day about 18 foot trapeze spans.
wished someone had asked me.
i would have said---either:
section modulus is moment divided by stress. moment is half the
force(lb)
times half the distance(in).
the force is the weight of the water-filled pipe plus 250. the
distance is
4ab/a+b.
the stress is 15,000.
or: double the required section modulus for a nine foot span.
Brad Casterline, NICET IV
Fire Protection Division
FSC, Inc.
P: 913-722-3473
[email protected]
www.fsc-inc.com
Engineering Solutions for the Built Environment
_______________________________________________
Sprinklerforum mailing list
[email protected]
http://lists.firesprinkler.org/listinfo.cgi/sprinklerforum-firesprinkler.org
_______________________________________________
Sprinklerforum mailing list
[email protected]
http://lists.firesprinkler.org/listinfo.cgi/sprinklerforum-firesprinkler.org
_______________________________________________
Sprinklerforum mailing list
[email protected]
http://lists.firesprinkler.org/listinfo.cgi/sprinklerforum-firesprinkler.org
