Degree of indeterminacy 4

[SKJ25POL]

I like to get some opinions on the correct degree of indeterminacy of below frame?

Thank you

 

[r13]

One.

 

[SKJ25POL]

r13 (Civil/Environmental)
Thank you for your response but how do you come with one?
I came up with 2 and my reason is the structure frame is one degree indeterminate (due to having pin supports) and force in the cable will be another unknow so it makes it in total 2 degree indeterminate. Where is my solution wrong?
Appreciate it helping

 

[r13]

Remove the horizontal restrain on the support at the right, it becomes a simply support truss/frame, and find displacement of the upper right corner lower right support. Then place a dummy load at the upper right corner lower right support to close the gap. You can find example on indeterminate truss analysis, however I am not positive on pitched frame though.

 

[Tomfh]

I thought 2 as well.

 

[SKJ25POL]

Tomfh,
Thank you for your response too.
r13, dont mean to bug you so much but cant follow your instruction. The frame itself has rigid joints. The frame without the cable is one degree indeterminate (Do you agree with that?) Then cable ad one more unknown which makes it total of 2, doesnt it?

Hope somebody can explain or draw the reason that makes the answer one!!!

 

[r13]

My reasoning is that there is additional compatibility equation for the diagonal and the building frame, so globally you have 3 equations and 4 unknowns.

 

[SKJ25POL]

What if the right support was a roller instead, would then you call it a determinate system?

 

[r13]

Yes, but unstable, as the frame will move laterally.

 

[jayrod12]

I would agree that a roller on the right would make the system as a whole determinate. And therefore adding one more method of restraint would make it one degree indetermintate. If it was a roller, then the force in the right side column would be extremely easy to find using sum of moments about the left pin. The rest is just method of joints or sections.

 

[jayrod12]

Unstable to a point, that diagonal brace would restrain it quite well if you ask me. at least for loading applied towards the right of the page.

 

[SKJ25POL]

So my understanding from your replays is :

The questioned frame which has both of its supports as hinges or pinned and none are rollers.
Regardless of the applied load (P) as shown on the frame including the diagonal cable, the system is one degree indeterminate as r13 response.
However if the right support changes to a roller support the system will be determinate.

 

[rb1957]

so the structure is beams (EI) with simple supports (not fixed) ?

We need beams and fixed joints internally (at least at the peak).

if the upper joint of the LH vertical (where the load is applied) was fixed, then some of the load could the sheared into this vertical. If the joint is pinned then all the load has to travel over the peak and down the cable. There'd be uplift on the LH support and compression on the RH, and all the shear would be on the LH support ... or would it ? if the RH joint is fixed (upper joint, to the peak) the the RH vertical can react some shear, yes, and this is the single redundancy.

another day in paradise, or is paradise one day closer ?

 

[Tomfh]

If you turn the right roller to a support you still don’t know the internal forces in the trapezoid.

 

[hokie66]

The OP did say that the frame joints are rigid. If the right support changes to a roller, the frame is stable.

 

[r13]

Correction on my previous stated method:

Remove the horizontal restrain on the support at the right, it becomes a simply support truss/frame, and find displacement of the upper right corner lower right support. Then place a dummy load at the upper right corner lower right support to close the gap. You can find example on indeterminate truss analysis, however I am not positive on pitched frame though.

 

[r13]

Unstable to a point, that diagonal brace would restrain it quite well if you ask me. at least for loading applied towards the right of the page.

Correct. The amount of lateral displacement of the lower right roller support is depending on the strength of the brace.

 

[jayrod12]

I agree my initial response was in haste, and incorrect. With fixed joints It is indeterminate to the second degree. If you cut it through one of the eave beams and the brace you end up with

n=4(support reactions) + 4 (Internal reactions at the cuts) - 3 *2 (number of rigid body's remaining after the cut) = 2

 

[SKJ25POL]

The frame elements with EI are rigid connection to each.
The frame is pin supported on ground at each supports.
Cable is pined at each end to the frame.
Hope I am clear stating the problem.
However, confused as hell ...

 

[r13]

I think you need to review what is structural "external indeterminacy" and "internal indeterminacy" of frames. I afraid that am too far from that, thus could be on the wrong side.