How to find reactions at supports

  1. In my question i have a square cloth piece of dimension 8m*8m and the mass per area of the cloth is 0.5kg/m^2 .I need to find the reactions at 4 supports.IN first case Cloth is attached in such a way that first i attach one corner to one support then the other corner which is on a diagonal to the first corner is attached.For this situation i have to find the Reactions at the 2 supports.Then for the second case when the remaingin two corners are also attached in the same way as the first two were attached i need to calculate the reactions at all four corners.

    IN both cases when there is a sag of 250mm in the middle of the cloth.

    the situation is described in pictures attached.
     

    Attached Files:

  2. jcsd
  3. PhanthomJay

    PhanthomJay 6,284
    Science Advisor
    Homework Helper
    Gold Member

    The catenary equations are too tough for me to handle, so i've always used a parabolic approximation of the catenary with good results when the sag is just a few percent of the span. For the 2 support case, the vertical reactions will be just 1/2 apiece of the total cloth weight. What attempt have you made to calculate the tensions at the support?
     
  4. well i have applied the follwoing principle and equations described in link http://www.du.edu/~jcalvert/math/catenary.htm over the first case but i am totally unsure abt the second case.
     
  5. PhanthomJay

    PhanthomJay 6,284
    Science Advisor
    Homework Helper
    Gold Member

    OK, you should compare the results of the catenary equation for the horizontal tension (if you did it that way) with the parabolic approximation, T=wL^2/8D, where w is the unit weight of the cloth per foot across the diagonal, L is the diagonal measure, 8 is itself, and D is the mid-point sag. Now for the 4 support case, each vertical reaction would be 1/4th the total cloth weight. As for the tension at each of the 4 supports, with the midpoint deflection staying the same, I'd just take an educated guess from symmetry and call each tension equal to 1/2 the former result, directed radially outward at the supports, but don't hold me to it. :wink:
     
  6. Hahaha thanx for a symmetrical idea man.Well i think its not possible if we divide the solution for case 1 by 2 to find the solutoin for tension in case 2.Still more solutions are welcomed.
     
  7. PhanthomJay

    PhanthomJay 6,284
    Science Advisor
    Homework Helper
    Gold Member

    And why not? Do you agree that for the 4 point case, the vertical load will be supported equally at each support, and equal to 1/4 the cloth weight vertically at each support? And therefore 1/2 the value of the 2 point support case vertical reaction? And that the tension at each of the 4 supports, whatever it might be, must be equal in magnitude at each support?
     
  8. Yeah man it is sensible but i have to confirm this with my lecturer lets see what he says about it.I am going to check with him today hope he co-operates.Thanx for help man
     
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?