Truss problem. How to calculate the force in the member?

[John111]

Briefly, I need to design a framework which would support a plug which is used to fill in the hole in water tank, 4.8m above the ground. In other words, 10.69kN load at angle of 30 degrees is therefore applied to the framework.

So I came up with my design. The problem is that I get zero value for C member. I really think that it should not be zero, as a part of applied force really affects the member. Also, modelling software shows that there must be a force on member C.
There is a hinge support on the left and the roller support on the right.

Here is my solution together with Matchcad matrix calculations.

Thank you for any help!

http://postimg.org/image/6tmh81zx5/ Solution
http://postimg.org/image/9am5ychph/ Mathcad

 

[PhanthomJay]

Briefly, I need to design a framework which would support a plug which is used to fill in the hole in water tank, 4.8m above the ground. In other words, 10.69kN load at angle of 30 degrees is therefore applied to the framework.

So I came up with my design. The problem is that I get zero value for C member. I really think that it should not be zero, as a part of applied force really affects the member. Also, modelling software shows that there must be a force on member C.
There is a hinge support on the left and the roller support on the right.

Here is my solution together with Matchcad matrix calculations.

Thank you for any help!

http://postimg.org/image/6tmh81zx5/ Solution
http://postimg.org/image/9am5ychph/ Mathcad

you correctly summed forces in the y direction at joint 3 to determine that the force in C must be zero. Then you questioned your good work.

 

[John111]

you correctly summed forces in the y direction at joint 3 to determine that the force in C must be zero. Then you questioned your good work.

I agree now. I was badly confused with the truss analysis software where I could only enter approximate values and therefore got wrong result.

However, how could I set the bars so that the framework would support that load without buckling in the B member?
I have tried all the following and checked each design calculating the forces twice...
http://postimg.org/image/z8snthd2l/

 

[PhanthomJay]

I agree now. I was badly confused with the truss analysis software where I could only enter approximate values and therefore got wrong result.

However, how could I set the bars so that the framework would support that load without buckling in the B member?
I have tried all the following and checked each design calculating the forces twice...
http://postimg.org/image/z8snthd2l/

Removing member C and adding a redundant zero force member from mid point of B to the left support as in your image 2 will mitigate in plane buckling of member B, but not out of plane buckling.

 

[John111]

Removing member C and adding a redundant zero force member from mid point of B to the left support as in your image 2 will mitigate in plane buckling of member B, but not out of plane buckling.

I understand that. I cannot think of any more solutions, so I am asking at least for a hint..

 

[PhanthomJay]

what sort of solution are you looking for? You need to design the members to take the loads based on allowable stresses in tension and compression.

 

[John111]

what sort of solution are you looking for? You need to design the members to take the loads based on allowable stresses in tension and compression.

I don't know how to position the members so that they could support the load - that no member would be buckled.
The triangle does not work as the hypotenuse is being buckled, and I need to attach new members but I cannot think of anything else than I showed. That's the reason I'm writing here.

 

[PhanthomJay]

So far you have done some analysis but I don't see any design that shows that the diagonal will buckle under the loading. Compression in a member does not mean it will buckle if it is sized properly, or adequately braced..

 

[John111]

So far you have done some analysis but I don't see any design that shows that the diagonal will buckle under the loading. Compression in a member does not mean it will buckle if it is sized properly, or adequately braced..

The force loaded on diagonal is -18kN (compression).

Fbuckling = (k * pi^2 * E * I)/ L^2
k=0.6
E=70kN/mm^2
I=10x10^4 mm^4
L=5.54 m.

The maximum possible load of the member is therefore less than the current one. For this reason the structure will fail..

 

[PhanthomJay]

The force loaded on diagonal is -18kN (compression).

Fbuckling = (k * pi^2 * E * I)/ L^2
k=0.6
E=70kN/mm^2
I=10x10^4 mm^4
L=5.54 m.

The maximum possible load of the member is therefore less than the current one. For this reason the structure will fail..

I haven't checked your numbers, but your buckling equation is wrong. And if the member buckles and you can't adequately brace it, try using a larger sized member and/or a stiffer material like steel. This is homework, right, and not an actual real-world design problem?

 

[John111]

I haven't checked your numbers, but your buckling equation is wrong. And if the member buckles and you can't adequately brace it, try using a larger sized member and/or a stiffer material like steel. This is homework, right, and not an actual real-world design problem?

Yes, it is homework. However, I am given this equation and I see it for the first time, so I don't know if its wrong, but should be correct...

And I cannot change the material. Trying with longer member did not give any changes in regards of buckling.

 

[PhanthomJay]

Can you change the member size? What size member are you using to give the value of I you are using? Exactly how is your problem worded? The buckling formula by the way is pi^2(EI)/(kL)^2, where k ideally is 1 for a pinned-pinned end connection. Don't forget to use safety or overload factors.