Replacing column by equivalent force and couple

  • Thread starter wee VooDoo
  • Start date
  • #1
The Problem
I've been given the beam shown below to carry out the Hardy Cross method (Moment Distribution) too. I have no problems with the method but I'm struggling with part b, which states "Replace column by an equivalent force and couple at point C"
http://img696.imageshack.us/img696/1705/problemat.jpg [Broken]

Uploaded with ImageShack.us
Excuse the crude photoshopping! The column is 1unit in length and infinitely stiff.

Part a of the question was work out stiffness and distribution factors which were easy.
But part b states "Replace column by an equivalent force and couple at point C" and I can't do the rest of the question without this. I've tried and failed many times.

I've tried replacing with what I think is right, and replacing by guessing but I don't think I understand what to do. I tried inserting a column straight underneath with the same length and the 10kN load acting to the left. But that would double the moment around C so I'm stumped.

Any help pointing me in the right direction is very appreciated. Feel stupid that I can do the hard bits but can't figure out the couple! lol
 
Last edited by a moderator:

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,670
What the problem is asking you to do is replace the horizontal force at D with an equivalent force and moment at C such that equilibrium is maintained. In other words, the force at C will have the same direction and magnitude as the force at D. The moment acting at C due to the force at D should be easy to determine (not guess).
 
  • #3
Thanks SteamKing. I know it sounded stupid but I just could not figure it out for the life of me. Too much studying frying my head! Thanks again!
 
  • #4
741
27
another to look at it is: Add a 10 kN to the right at C, and another 10 kN force at C to the left. In other words nothing has changed. Now you can regard the rightwards force at D and the leftwards force at C as a moment (at C if you like, it doesn't matter where). The remainder is the rightwards force at C.
 

Related Threads on Replacing column by equivalent force and couple

  • Last Post
Replies
2
Views
779
Replies
7
Views
13K
Replies
1
Views
3K
Replies
2
Views
721
Replies
31
Views
2K
Replies
5
Views
10K
Replies
0
Views
7K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
2K
Top