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Q: deflection of steel rectangular tubing ( Answered 5 out of 5 stars,   0 Comments )
Question  
Subject: deflection of steel rectangular tubing
Category: Science > Physics
Asked by: mikeinmesquite-ga
List Price: $10.00
Posted: 21 Dec 2005 16:04 PST
Expires: 20 Jan 2006 16:04 PST
Question ID: 608669
I am building an open staircase with a single stringer using 6in. x 4
in. rectangular steel tubing, with the long dimension vertical.  The
overall tube length will be approx. 166 inches.  It will be supported
at the floor and welded to a steel I beam at about 96in. off the
floor, so that the angle off horiz. will be about 35 degrees.  The
dead load will be about 900 pounds (evenly supported) and the live
load will be 300 pounds center-loaded.  Question: what tube wall
thickness is required to keep the beam (tubing) deflection safe and in
an acceptable range so the stair does not feel ?bouncy?(my guess is
less than  in.).  I had planned to use 6x4x inch wall tubing with a
moment of inertia of 11.1 (in)4.
Is this acceptable?  What is the calculated deflection?  Doesn?t it
help that the ?beam? is angled, not horizontal?

Clarification of Question by mikeinmesquite-ga on 21 Dec 2005 16:23 PST
Since my question looks like gibberish on my screen, I will restate:

I am building an open staircase with a single stringer using 6 in. x 4
in. rectangular steel tubing, with the long dimension vertical.  The
overall tube length will be approx. 166 in.  It will be supported at
the floor and welded to a steel I beam at about 96 in. off the floor,
so that the angle of elevation off horizontal will be about 35
degrees.  The dead load will be about 900 pounds, evenly supported and
the live load will be about 300  pounds, center-loaded.
Question: What tube wall thickness is required to keep the beam
(tubing)deflection safe and in an acceptable range so that the stair
does not feel "bouncy"(my guess is that it should be less than 1/4
in).  I had planned to use 6x4x 1/4 in. wall tubing with a moment of
inertia of 11.1 (in)4.   Is this acceptable? What is the calculated
deflection?  Doesn't it help that the "beam" is angled, instead of
horizontal?
Answer  
Subject: Re: deflection of steel rectangular tubing
Answered By: redhoss-ga on 22 Dec 2005 09:19 PST
Rated:5 out of 5 stars
 
Hello mike, it is a crappy day here and because I have nothing better
to do we will work on your project. First we need to get the component
of the loads in the direction perpendicular to the neutral axis of
your rectangular tubing. As you guessed it "helps" that the beam in on
an angle. Both loads need to be multiplied by the cosine of 35 degrees
or 0.82:

Point load = 300 x 0.82 = 246 lb.
Distributed load = 900 x 0.82 = 738 lb.

Each side of the staircase supports 1/2 of the point load and the
distributed load. Even though the distributed load is applied evenly
along the length of the beam there is very little difference between
that case and assuming that the entire load is applied at the center
of the span. Also, the formula for a point load in combination with an
evenly distributed load gets much more complicated. For our simple
(worst case) solution we will assume:

P(1) = 246 x 1/2 = 123 lb.
P(2) = 738 x 1/2 = 369 lb. 
P(total) =         482 lb.

Deflection = (P x L^3) / (192 x E x I)

Where:
L = 166 in. and L^3 = 4,574,298 in.^3
E = 30,000,000 psi (a constant for any steel)
I = 21.6 in.^4 (your value of 11.1 is for the wrong axis)

D = (482 x 4,574,298) / (192 x 30,000,000 x 21.6) = 0.01 inch

Your design looks very good to me and you should feel no bounce.

Please ask for a clarification if you have any questions about what is shown here.

Good luck with your project, Redhoss
mikeinmesquite-ga rated this answer:5 out of 5 stars
excellent answerer!  very fast response as well

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