Truss structure square problem

[Bolter]

Homework Statement

See image below

Relevant Equations

Moments
Sum of horizontal and vertical forces = 0

Here is the full question. I have already tried to answer the questions and have put a red dot next to the answers I think are right?





Here is my working out to get the answers I had above







Have I done this question right? Sadly I don't have the answers to check for myself here so I'm asking here

Thanks for any help!

 

[Lnewqban]

Answer to question 18d may be incorrect, according to forces shown in answer to 18d.
What would happen if you eliminate or cut the BD member?

 

[Bolter]

Answer to question 18d may be incorrect, according to forces shown in answer to 18d.
What would happen if you eliminate or cut the BD member?

Must it be option C then for 18d? I tried to solve this from process of elimination. Option a or b cannot be the as answer as member AB has to be compression if it experiences a downward force of 170 KN and a upward force of 490 KN, so we can cross off a & b which then leads me to option c.

 

[haruspex]

Must it be option C then for 18d? I tried to solve this from process of elimination. Option a or b cannot be the as answer as member AB has to be compression if it experiences a downward force of 170 KN and a upward force of 490 KN, so we can cross off a & b which then leads me to option c.

To choose between options c and d, consider e.g. the horizontal forces acting on D. What does that tell you about the force direction in BD?
But all the options have one thing wrong. What is the force in CD? What would happen if it were removed?

Also, I find it strange that signs are not considered. Surely $R_{Dy}$ should be -320kN?

 

[Bolter]

To choose between options c and d, consider e.g. the horizontal forces acting on D. What does that tell you about the force direction in BD?
But all the options have one thing wrong. What is the force in CD? What would happen if it were removed?

Also, I find it strange that signs are not considered. Surely $R_{Dy}$ should be -320kN?

I think there would be no horizontal reactions at point d as there is a horizontal roller support there which only limits to vertical reactions. IF member CD was removed then the reaction at $R_{Dy}$ would be entirely supporting and pushing up on BD. Wouldn't that indicate a compression on BD and not a tension?

 

[haruspex]

there would be no horizontal reactions at point d as there is a horizontal roller support there

You need to consider all the forces acting on the joint D that have a horizontal component.
(One thing I'm unclear on in regard to the notation. Is the roller shown allowed to provide a downward force? Seems to me it must be doing that or the truss would tip anticlockwise.)

IF member CD was removed then the reaction at $R_{Dy}$ would be entirely supporting and pushing up on BD.

Again, you are not considering all the forces. But look at C instead: what forces acting on that joint have a vertical component?

 

[Bolter]

You need to consider all the forces acting on the joint D that have a horizontal component.
(One thing I'm unclear on in regard to the notation. Is the roller shown allowed to provide a downward force? Seems to me it must be doing that or the truss would tip anticlockwise.)

Again, you are not considering all the forces. But look at C instead: what forces acting on that joint have a vertical component?

I have tried labelling the diagram to see what is going on and I get this

Clearly from the figure I can deduce that member AB, AD and BC are in compression

BD is also in tension and so is CD as it experiences a downward force of CD of 320 KN

So this gives me answer C as a result

 

[haruspex]

a downward force of CD of 320 KN

No, there is a downward force of 320kN at D, but it is not coming from C. It comes from the roller support.
I ask again, what forces acting on joint C have a vertical component?

 

[Bolter]

No, there is a downward force of 320kN at D, but it is not coming from C. It comes from the roller support.
I ask again, what forces acting on joint C have a vertical component?

I think there are no vertical components at joint C, just a horizontal force of 320KN to the left of it

 

[haruspex]

I think there are no vertical components at joint C, just a horizontal force of 320KN to the left of it

Well, there are two equal and opposite horizontal forces acting on joint C; otherwise it would accelerate.
But yes, there are no vertical forces acting on C. So what does that say about the force along member CD?

 

[Bolter]

Well, there are two equal and opposite horizontal forces acting on joint C; otherwise it would accelerate.
But yes, there are no vertical forces acting on C. So what does that say about the force along member CD?

That CD is in tension as joint D is the only joint along CD that has a vertical force exerting downwards

 

[haruspex]

That CD is in tension as joint D is the only joint along CD that has a vertical force exerting downwards

That's a bit garbled. I hope you mean "the only vertical force acting at joint D is along the member CD." (You do not know whether it is in tension yet - that is what we are trying to determine.)

And therefore the magnitude of that force is..?

 

[Bolter]

That's a bit garbled. I hope you mean "the only vertical force acting at joint D is along the member CD." (You do not know whether it is in tension yet - that is what we are trying to determine.)

And therefore the magnitude of that force is..?

Zero. CD is a zero force member

From what I can see forces acting on the pin at D are:

Force AD to the right (by the way, Force AD = Rax), Rdy downward, and BD upward to the left.

So if Force BD is upward and to the left on the pin, then it must act downward and to the right on the member BD (flip the direction of the forces when moving from one body to another, in this case, moving from the pin at D to the member BD).

So BD should be in tension. Is this sufficient enough to prove member BD is in tension.

This leaves me with answer c for 18d)

 

[haruspex]

Zero. CD is a zero force member

From what I can see forces acting on the pin at D are:

Force AD to the right (by the way, Force AD = Rax), Rdy downward, and BD upward to the left.

So if Force BD is upward and to the left on the pin, then it must act downward and to the right on the member BD (flip the direction of the forces when moving from one body to another, in this case, moving from the pin at D to the member BD).

So BD should be in tension. Is this sufficient enough to prove member BD is in tension.

This leaves me with answer c for 18d)

Yes, that's all correct. Option c is the best fit, but it should say CD is neither under tension nor compression (if you ignore its weight).