How Do You Calculate Forces in a Pin-Jointed Truss?

• iviv
In summary, the Homework statement is that by removing the right hand side, and having CD and IH in tension, and CH in compression, you can solve for the vertical force in each member.
iviv
Hi all, been here several times and found good help for several questions, but this time I'm out of luck, so here I go.

Homework Statement

By taking a section through the pin-jointed frame as shown, and considering the quilibrium of the structure to either the left or right of the section, what is the force in members CD, CH and IH?

Each member of the frame has a length of 2.0 m so the height of the frame is 2 × sin 60º = 1.732 m.
http://img705.imageshack.us/img705/2225/pjfasection.gif
I'm trying to solve this using method of sections, and none of the examples I've found seem to help, though I feel I'm missing something obvious with regards to using sine and cosine to find the vertical values.

So you remove the right hand side, and have CD and IH in tension, and CH in compression.

http://img38.imageshack.us/img38/9983/pjt2.jpg

And this is where I'm getting lost, trying to resolve the forces vertically in order to find force CH, since that is the only unknown vertical force. There's the 15KN being applied upwards, and 15KN being applied downwards, but the value for CH can't be 0, because its in compression so it has to have a value.

Now, from my lectures notes I have http://img220.imageshack.us/img220/9484/pjt3.jpg but that doesn't help much since it is dealing with the unknown vertical force being directed downwards. But the other problem I'm seeing is that if I were to just use the same formula, for my example it would end up as 15 = Csin60 + 15

And that's obviously wrong, since Csin60 isn't 0!

I fear I'm getting rather confused, I used to think I understood maths pretty well until I met these trusses! Thanks in advance for any help!

Last edited by a moderator:
Welcome to PF!

Hi iviv ! Welcome to PF!
iviv said:
… And this is where I'm getting lost, trying to resolve the forces vertically in order to find force CH, since that is the only unknown vertical force. There's the 15KN being applied upwards, and 15KN being applied downwards, but the value for CH can't be 0, because its in compression so it has to have a value.

But it is 0 … your equations tell you so!

Hint: Imagine the two top forces were 20 on the left and 10 on the right (instead of 15 and 15).

Then the left half would be top-heavy, wanting to turn clockwise, while the right half would want to turn anti-clockwise.

Would that put CH in tension or compression? And DH?

Thanks for the welcome, but oh dear, I think you've lost me there! You're saying that the equations are right, and it does equal zero, so the member isn't in compression or tension?Also, a related question I'm trying to get my head around. I think I'm doing it right, but I seem to have an answer which doesn't make much sense. I tried to illustrate the problem in paint, showing why I'm really a surveyor and not an architecht :D

http://img408.imageshack.us/img408/1285/stuckt.jpg

AH is simple, it has to be 10, GH is also 0.

AG was found because AGsin45 = 10 so FG = 14.1
And AB = AGcos45 so AG = 9.97?

Carrying on from there, FG = AGcos45 as well, so is 9.97 again.
BG = AGsin45 = 9.97

And that doesn't look like it makes sense, because to resolve vertically at B it would be:

9.97+BFsin45 = 10 so BF = 0.0424?

I'm still working through the question, but that seems like a rather silly answer, so while I'm here I thought I'd ask to see if there's something I'm obviously doing wrong.

Last edited by a moderator:
Hi iviv!

erm … isn't cos45º = sin45º ?

Yeah it is, but that doesn't change any of the maths in those equations, does it? I mean, you use sin to resolve horizontally, and cos to resolve vertically?

iviv said:
Yeah it is, but that doesn't change any of the maths in those equations, does it?

well … it does change your 9.97 to 10, and your 0.0424 to … ?

Oh god, its a rounding error, isn't it? XD

Well, that makes things add up a whole lot better now! Thanks!

Do you understand the term take moments eg take moments about C in your post#1 diagram?

1. What is a pin jointed truss?

A pin jointed truss is a structural system made up of interconnected bars or members that are connected by pins at their joints. This type of truss is often used in engineering and architecture to create stable and durable structures.

2. What is the purpose of analyzing a pin jointed truss?

The purpose of analyzing a pin jointed truss is to determine the internal forces and stresses acting on each member. This information is crucial in designing and constructing a safe and efficient truss structure.

3. How is a pin jointed truss analyzed?

A pin jointed truss is typically analyzed using the method of joints or the method of sections. The method of joints involves analyzing each individual joint to determine the forces acting on each member, while the method of sections involves cutting the truss into sections to analyze the internal forces and stresses.

4. What factors affect the analysis of a pin jointed truss?

The analysis of a pin jointed truss can be affected by factors such as the type of loading, the properties of the truss members, and the type of support at the joints. The geometry and orientation of the truss can also impact the analysis.

5. What are the limitations of pin jointed truss analysis?

Pin jointed truss analysis assumes that all joints are perfectly pinned and that the truss is loaded at the joints only. This may not always be the case in real-world structures, and other factors such as bending and shear may need to be considered for a more accurate analysis.

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