Determine the magnitudes and nature of forces in space truss

[DevonZA]

Homework Statement

Homework Equations

equivalent tension coefficient t_DE= applied force/distance between points D and E
= 17/SQRT(1[^2+2^2+4^2) = 3.7097

The component of the 17kN in the x-direction = Δx X t_DE = -1 X 3.7097
= -3.7097
The component of the 17kN in the y-direction = Δy X t_DE = -2 X 3.7097
= -7.4194
The component of the 17kN in the z-direction = Δz X t_DE = 4 X 3.7097
= 14.8388

There are three unknown forces, therefore we need three equations.

The Attempt at a Solution

x -3.7097-3t_AD+2t_BD+3t_DC=0 a)
y -7.4194-t_AD+3t_BD-2t_DC=0 b)
z 14.8388+t_AD-t_DC=0 c)

I then need to multiply or divide one of these equations to get the unknown values the same so that I can add or divide to get rid of unknown term(s) to solve.
I've tried various options and cannot seem to get to the correct answers.
Working backwards from the given answers I get:
F_AD/t_AD = SQRT[3^2+1^2+1^2}
t_AD = 3.0242

F_BD/t_BD = SQRT[2^2+3^2=0^2]
t_BD = 2.3796

F_CD/t_CD = SQRT[3^2=2^2=1^2]
t_CD = 1.5528

The answers given are:
F_AD= 10.03kN (S)
F_BD= 8.58kN (S)
F_CD= 5.81kN (S)

 

[haruspex]

You seem to be treating the applied force as being along the line DE, but the diagram makes it look as though it is vertical and the text does not mention E. Is there a later part to the question which mentions E?

 

[haruspex]

The component of the 17kN in the z-direction = Δz X tDE = 4 X 3.7097
= 14.8388

Would that be up or down?

 

[haruspex]

z 14.8388+tAD-tDC=0 c)

Check thecoefficients on t_AD and t_CD, and why no t_BD?

 

[DevonZA]

Hi Haruspex

Thanks for your responses.
Firstly there is no mention made of E.
How will I get equivalent tension coefficient without using point E?

Component of 17kN would be down? Therefore -14.8388.
No tBD because the Z co ordinate at B is 0.

 

[haruspex]

Firstly there is no mention made of E.

Then none of your calculations related to E have any value. Why is it in the picture? Just to confuse, maybe?

Component of 17kN would be down? Therefore -14.8388.

If it is straight down, as pictured, then the z component is ...?

No tBD because the Z co ordinate at B is 0.

Your equation c) is inconsistent with the other two. E.g. in the x direction for t_AD you had a coefficient -3. I can see that this comes from subtracting the x coordinate of point D from that of point A. All the coefficients in a) and b) follow that pattern, but not those in c).
The z coordinate of D is ... and the z coordinate of A is ... so the coefficient of t_AD in the z equation should be ...?

 

[DevonZA]

I believe E is in the picture to confuse. Unfortunately there are no similar examples in my textbook which makes this question rather difficult to attempt.

If straight down then the z component is negative?

Z coordinate of D is 4.
Z coordinate of A is 1.
Z coordinate of B is 0.
Z coordinate of C is 1.

14.8388+3tAD+4tBD+3tCD=0

Does this look correct?

 

[haruspex]

I believe E is in the picture to confuse. Unfortunately there are no similar examples in my textbook which makes this question rather difficult to attempt.

If straight down then the z component is negative?

Z coordinate of D is 4.
Z coordinate of A is 1.
Z coordinate of B is 0.
Z coordinate of C is 1.

14.8388+3tAD+4tBD+3tCD=0

Does this look correct?

How are you getting 14.8388? Seems to me you are still using E to get that.
The coefficients look like the right magnitudes now, but not sure about the signs. It depends how you are defining t_AD etc.
What equations do you have now for the x and y directions?

Regarding point E, it looks to me that in the examples on which you based your equations E would have been a point along the line of action of the applied force. I.e. the force was applied along the line DE, not vertically. If you wish to follow those examples then you need to change E to be a point in the line of action of the force in this case. The origin would be an easy choice.

 

[DevonZA]

How are you getting 14.8388? Seems to me you are still using E to get that.
The coefficients look like the right magnitudes now, but not sure about the signs. It depends how you are defining t_AD etc.
What equations do you have now for the x and y directions?

Regarding point E, it looks to me that in the examples on which you based your equations E would have been a point along the line of action of the applied force. I.e. the force was applied along the line DE, not vertically. If you wish to follow those examples then you need to change E to be a point in the line of action of the force in this case. The origin would be an easy choice.

The same question appears in the textbook but only the solutions are given. E is not shown here so I am going to ignore it especially as they do not refer to it anywhere in the question.

I need to find the equivalent tension coefficient:
t_eq = the applied force / distance between points D and ?

To find the x,y and z component of the 17kN force: t_eq is then multiplied by Δ x, y and z (again I assume I need to calculate the difference in coordinates between point D and ?)

 

[haruspex]

points D and ?

not sure I can do much more than reiterate my last post. Please try to understand it.
Judging from your attempt to use E, I assume that such a point existed in some earlier example, and that E was in the line of the applied force. That is the only way your method would make sense. In the present case, the shown point E is not in the line of the applied force, so if you want to use exactly the same method then you must replace it with a point E which is in that line. The origin would look like an easy choice. So just repeat what you did before but using (0, 0, 0) for the coordinates of E.

 

[DevonZA]

not sure I can do much more than reiterate my last post. Please try to understand it.
Judging from your attempt to use E, I assume that such a point existed in some earlier example, and that E was in the line of the applied force. That is the only way your method would make sense. In the present case, the shown point E is not in the line of the applied force, so if you want to use exactly the same method then you must replace it with a point E which is in that line. The origin would look like an easy choice. So just repeat what you did before but using (0, 0, 0) for the coordinates of E.

Thanks Haruspex, I realized what you meant about the origin after I had posted my reply.
I will be back with an updated attempt :)

 

[DevonZA]

Got it please see attached.

Thank you for your help Haruspex

 

[haruspex]

Got it please see attached.

Thank you for your help Haruspex

View attachment 136275
View attachment 136306

Ok!