How to find reactions at supports

[shaheryarbhatti]

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.

 

[PhanthomJay]

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.

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?

 

[shaheryarbhatti]

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.

 

[PhanthomJay]

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.

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.

 

[shaheryarbhatti]

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.

Hahaha thanks 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.

 

[PhanthomJay]

Hahaha thanks 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.

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?

 

[shaheryarbhatti]

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?

Yeah man it is sensible but i have to confirm this with my lecturer let's see what he says about it.I am going to check with him today hope he co-operates.Thanx for help man