Degree of indeterminacy 4

[SKJ25POL]

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

Thank you

 

[rb1957]

indeterminate, 'cause it's statically determinate without the diagonal.

if the corners were pinned then it'd be determinate (load in diagonal = 1.414k, zero load in LH vertical).

with fixed corners, and no diagonal, the shear in LH is 1k.

the diagonal gives two loadpaths for the load (LH and diagonal) ... solved by stiffness.

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

 

[r13]

rb,

Yes, when all corners pinned, the reactions as you've predicted, but instability was detected at the computer run.

 

[rb1957]

that's as maybe, but the structure is "stable"; the diagonal reacts the applied load. Maybe computer doesn't like the loaded point, being not well supported; or deflection out of plane ? does it say what is "unstable" ?

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

 

[r13]

rb,

Run a simple frame with all joints pinned, you will get the same warning. Actually, I think, it is nothing more than the program tells you that there are more equations than unknowns. If all members are assigned axial only, then the warning should go away.

 

[271828]

r13 wrote:

Yes, when all corners pinned, the reactions as you've predicted, but instability was detected at the computer run.

Run a simple frame with all joints pinned, you will get the warning.

What do you mean by "all joints pinned"?

Assuming your model has moment connections at N2 and N3, might the error be due to rotation of the entire frame? Depending on the 3D boundary conditions, it could rotate about a line passing through N1 and N4 or about a line passing through N1 and N2.

 

[Settingsun]

In the all-pin case, and with a tension-only diagonal, it can't resist load applied in the opposite direction that causes compression in the cable. The software would flag that as an unstable structure.

 

[r13]

Below are two simply supported frames. Instability were detected, and joint 3 is locked for both cases.

 

[hokie66]

r13,

Of course that is unstable. You have a hinge at joint 2, in addition to the hinge at 1 and the roller at 4. Two many moment releases.

 

[r13]

hokie,

The first frame is quite clear, but I am little puzzled on the second model (with diagonal brace). The only explanation is the lack of rotational restrain of member M2. Then I tried another two runs, first to make joint 2 rigid, and joint 3 remains hinge connected, the warning appeared again. On the following run, joint 2 returns to hinge connected, but members M2 and M3 are rigidly connected, the run went through without warning. Any suggestion?

 

[rb1957]

I didn't say all pinned and no diagonal.

I said pinned joints with a diagonal
or fixed joints without a diagonal
are both determinate (with a roller on the RH attmt).

pinned joints without a diagonal is, of course, a mechanism.
fixed joint without a diagonal allows the members to carry transverse load, so the RH support reactions is transverse shear on the cross member, and the LH reaction to the load is transverse shear on the LH member.

pinned joints with the diagonal is also stable, with the diagonal reacting the applied load. Note I also didn't say "tension only diagonal", tho' that is how the OP phrased his question.

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

 

[r13]

pinned joints with the diagonal is also stable.

That's what got me puzzled. See the second model and the warning in my response made in 29Nov20 00:59; also my latest response to hokie66. What causes the program to issue instability warning? Note that this is only a not-so-practical discussion on a gray area of the structural analysis/modeling, which was touched off by the OP.

 

[GregLocock]

Gray area? This is a 301 handcalc. I'd guess a virtual work solution might be the least boring.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[r13]

GregLocock,

Excuse my ignorance, can you elaborate the relevance between virtual work and structural determinacy? Thanks.

 

[GregLocock]

Fig 8.13 here

https://learnaboutstructures.com/Force-Method-using-an-Internal-Force-as-the-Redundant-Force

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[r13]

The thing puzzles me is the warning from the program on the models below. No warning on the last one.

 

[phamENG]

r13 - is that from RISA? That instability warning means one of two things - it's really unstable, or the way you modeled it is confusing the algorithm that builds the stiffness matrix. Try the first one again, but fix both ends of the columns, leaving the boundary condition (support) as a pin. The result will be a moment that is still released (because the boundary condition is released), but the program will be able to build an accurate matrix.

 

[r13]

This was the situation leads to conduct the subsequent runs at the first place. The moment looks scarily large, but really negligibly small. RISA, correct. I think STAAD will report the same too.

 

[rb1957]

to my mind the frame with pinned corners and the diagonal is maybe a 2nd year uni problem.

I don't see that any of those frames are unstable. Why would the RH vertical need to be fixed to the horizontal to solve the frame ?

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

 

[r13]

There must be a reason for the program to post such warning, so I am trying to find the answer, for fun obviously. Hope not to confuse those 2nd year students though.

 

[phamENG]

rb - if that question was directed at my comment, I'm not bringing up a theoretical issue, but a software issue. RISA (and likely others that use a similar method) have limitations on what they can do. Joint releases is one of those things that can create a difficult to diagnose "garbage in garbage out scenario". Although the input may appear to be theoretically correct, the software doesn't know how to interpret it and give reliable results.

I should have added to my last post that the beam ends have to remain released while the column end is "fixed". If both are fixed, you'll resist a moment in the joint.