How to find reactions at supports

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In summary, the conversation discusses the calculation of reactions at four supports for a square cloth piece with dimensions 8m*8m and mass per area of 0.5kg/m^2. Two cases are considered, one where the cloth is attached to two supports and the other where it is attached to all four supports. In both cases, there is a sag of 250mm in the middle of the cloth. The conversation also mentions using a parabolic approximation of the catenary and comparing it to the catenary equation for calculating horizontal tension. It is suggested that for the 4 support case, each vertical reaction would be 1/4th the total cloth weight and the tension at each support would be equal in magnitude. Confirmation from
  • #1
shaheryarbhatti
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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.
 

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  • #2
shaheryarbhatti said:
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?
 
  • #3
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.
 
  • #4
shaheryarbhatti said:
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. :wink:
 
  • #5
PhanthomJay said:
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:

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.
 
  • #6
shaheryarbhatti said:
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?
 
  • #7
PhanthomJay said:
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
 

1. What is the purpose of finding reactions at supports?

Finding reactions at supports is an essential step in analyzing and designing structures such as bridges, buildings, and machines. These reactions determine the forces that act on the supports and are crucial in ensuring the stability and safety of the structure.

2. How do I determine the type of support in a structure?

The type of support in a structure can be determined by considering the degree of restraint it provides to the structure. There are three types of supports: fixed support, roller support, and pin support. A fixed support prevents translation and rotation of the structure, a roller support allows translation but not rotation, and a pin support allows both translation and rotation.

3. What are the steps to find reactions at supports?

The steps to find reactions at supports include drawing a free body diagram, summing the forces and moments in the horizontal and vertical directions, and solving the equations to determine the unknown reactions. It is also essential to consider any external loads and moments acting on the structure.

4. Can software be used to find reactions at supports?

Yes, there are various software programs available that can accurately determine reactions at supports. These programs use mathematical equations and algorithms to analyze the structure and provide the necessary reactions. However, it is still essential to have a basic understanding of the process and manually verify the results.

5. How do I ensure the accuracy of my calculated reactions at supports?

To ensure accuracy, it is crucial to follow the correct steps and consider all external loads and moments acting on the structure. It is also recommended to double-check the calculations and use multiple methods to verify the results. If using software, make sure to input all the necessary information correctly and review the output carefully.

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