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Q: Wide Flange Beam strength ( Answered 5 out of 5 stars,   0 Comments )
Subject: Wide Flange Beam strength
Category: Science > Physics
Asked by: mrstu2570-ga
List Price: $2.00
Posted: 21 Feb 2005 17:17 PST
Expires: 23 Mar 2005 17:17 PST
Question ID: 478387
I am constructing a slow pull machine to test various climbing gear
and i need to know if a wide flange I beam size:12, weight perfoot:14,
depth of section:11.91, flange width:3.97, flange thickness:.225, web
thickness:.200 will be able to width stand an electrical winch mounted
on one end and pulling a fixed point on the other end of a 15ft
section and max loads reaching 700lbs (30kN)

Request for Question Clarification by redhoss-ga on 21 Feb 2005 19:16 PST
How is the beam oriented and what is the distance from the outermost
part of the beam to the centerline of the pulling force. The
orientation of the beam determines whether you are bending it in the
weak or strong axis.

Clarification of Question by mrstu2570-ga on 21 Feb 2005 19:25 PST
The beam will be oriented on its side so the winch and fixed point
will be bolted through the top of the flange on either end of the 15ft
section. So the winch will be at point 0 and the winch cable will run
down to an attachment point at 15ft. Again the max load will be 30kN.
Will the beam bend?
Subject: Re: Wide Flange Beam strength
Answered By: redhoss-ga on 22 Feb 2005 07:06 PST
Rated:5 out of 5 stars
Hello mrstu2570, you ask if the beam will bend and the answer is
absolutely yes. When you apply any load to any steel shape it bends
some amount. This is called deflection. If a beam is loaded above the
yield strength of the steel, it not only deflects (bends), but will
permanently remain bent. However, if the load is small enough that the
stress is less than the yield strength of the steel, the beam will
return to the original shape. I think I understand your description of
how the winch will be mounted and the anchor point attached. You are
loading the beam on its strong axis. The properties that determine the
"strength" of a beam are its section modulus and moment of inertia.
For your beam (12WF x14#) those properties are:

Sx = 14.8 in.^3 
Ix = 88 in.^4

Sy = 1.18 in.^3
Iy = 2.34 in.^4

Comparing Sx and Sy you can see why I wanted to know how you were
mounting the winch and anchor. The beam is more than 12 times as
strong when loaded about the x axis (as you are doing).

We don't know the exact distance from the flange of the beam to the
centerline of the winch cable, but surely it won't be more than 12
inches. The bending moment in the beam would be:

M = 700# x 18 in. = 12,600 in.# 

The 18 in. number comes from adding the 12 inches to the distance from
the flange of the beam to the neutral axis (centerline) of the beam.

The stress in the steel is then found:

S = 12,600 in.# / 14.8 in.^3 = 851 psi

The yield strength of structural steel is normally 36,000 psi.
Comparing 851 to 36,000 you can see that there is no danger in doing
any damage to your beam.

The beam will deflect some when you are testing, but you will probably
not be able to notice the movement. Here is my best guess at how much
it will actually deflect.

d = (12,600 x 15 x 12)/(48 x 29,000,000 x 88) = .0000185 inch

I think the beam you are using will work just fine and hope that this
explanation hasn't confused you too much. Let me know if you have any

Good luck with your testing, Redhoss
mrstu2570-ga rated this answer:5 out of 5 stars
Fast response with a great answer and explanation!!

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