×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Balance Beam formula

Balance Beam formula

Balance Beam formula

(OP)
Hi folks,
Sorry to have to ask a seemingly simple question.  Ive been out of practice for some time, and the "googling" route is not providing me any clarity.

I need to calculate how much weight to put on one side of an asymmetric beam.  This is somewhat easy to figure if the loading was balanced, and i had the weight of all materials including the beam.

However Im working with evenly distributed loads on either side of the fulcrum.
my example is thus:
Beam is 20ft long
Fulcrum is at 8ft from left end
I need to figure how much weight (distributed) say over 2ft from extreme left to apply to the beam to create equilibrium across the fulcrum.

I know there is an easy solution to this, but I just cannot put my finger on it.

Can someone advise me on a formula or location of one?

Thanks,
Sam
 

RE: Balance Beam formula

summation of moment @ fulcrum = 0
W= weight of beam
W1= weight of distributed load 2ft from left

W(12)(12/2) = W(8)(8/2) + W1(2)(7)

RE: Balance Beam formula

i'm guessing it's slightly more complicated than that ...

LL = span on the left of the fulcrum = 12'
LR = span on the right, 8'
W = weight (per ft) of the beam
WL = weight added on the left side
XL = distance from the fulcrum (of WL)
WR = weight added to the right
XR = where this is
if you're applying a distributed load, apply a concentrated load in the middle of the distributed span (clear as mud)

LHS moments = W*LL*LL/2+WL*XL
RHS moments = W*LR*LR/2+WR*XR

RE: Balance Beam formula

(OP)
delagina & rb1957,
Thanks for your responses.....It didnt even occur to me I could turn the dist. load into a point load.  This will help me figure this out.  I know that the moment needs to "null" out at the fulcrum to be in equilibrium, I was just having a bear of a time dealing with the loading on the beam (being distributed).
Thanks again for your responses, this made my afternoon.
-Sam
 

RE: Balance Beam formula

What exactly is this for?

 

RE: Balance Beam formula

So, now that you know how to do it, what is the answer? What is the uniform load required to balance the beam?  No hinting from the audience.

BA

RE: Balance Beam formula

be careful of changing distributed loads to point loads when the distributed load goes past the hinge point or support, treat the load on each side of this as a separate point load.

RE: Balance Beam formula

delagina and rb1957 showed a nice way of solving the problem.  Another way would be to say that the first 8' of the 12' portion is already balanced, so the unbalanced moment is 4*w*(8+4/2) or 40w where w is the uniform load of the beam.

If the additional load on the end of the 8' span is w1, then 2*w1*(8-2/2) or 14w1 is its moment about the fulcrum.

The beam is balanced when those two expressions are equal.

BA

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources