Contests where researchers and practitioners blindly predict the response of structural systems have produced some rather interesting results. And by “interesting”, I mean “all over the place”. So much so, that in an effort to protect the contestants, the contest organizers rarely make the results publicly available.

Nonlinear structural analysis is hard though. Even with detailed structural drawings, material properties, and loading protocols, it’s easy to run into problems with units, dimensions, element formulations, constitutive models, numerical solution algorithms, and boundary conditions.

So, let’s take a step back and determine how well we can predict, or rather, agree upon, the linear response of a structural model that’s pretty well defined. A colleague in Eastchester studied the experimental behavior and numerical simulation of strongback frame systems during their Ph.D. Braced frames offer a multitude of teaching moments for linear and nonlinear structural analysis, so I’ve integrated my colleague’s strongback models in my courses. One such model is shown below.

The model shown here assumes infinitesimal joints, a simplification of the model with rigid offsets presented in this paper. All members are steel (=200,000 MPa), except the BRB, which we’ll assume has an effective of 300,000 MPa. Note that the column members on the right side of the frame are turned for weak axis bending. Also note that the left support is fixed while the right support is pinned.

So, what is the horizontal displacement (units=mm) of the joint indicated in the figure? The total horizontal load is only 1 kN, putting the frame response well within the linear-elastic, small displacement range.

E-mail me your answer, or if you are brave, post your answer in the comments section below. You don’t have to use OpenSees, use whatever software you want or whatever back of an envelope you can find. Let me know if you have any questions.

This will be fun! I look forward to your responses. I will share anonymized results in another post.

Update (March 6, 2020): The shear tabs are intended to be moment releases.

I have been involved in the development, maintenance, and growth of OpenSees since its early days. I am interested in learning Python and improving my academic writing.
View all posts by Michael H. Scott

It is an indication of the column orientation for bending in the plane of loading. On the left, the column will flex about its strong axis while the column on the right is turned to flex about its weak axis.

Hello MSB,
In the model, the BRB (and the HSS braces) have moment releases at each end, so you don’t really need the moment of inertia for these members.
PD

So, BRB should model using truss element and there is no need for modeling shear-tab using pinching04 model /zero-length rotational spring model (Liu & Astaneh-. Asl, 2004,2005) .

Hey,
I really like modeling challenges like this – I think it does a lot to help the the community learn.

I wonder if you could comment on (now or in your update) how best to model the releases, particularly for the mixed beam elements (W14x53) and the bottom pin connection.

For the bottom HSS member, it’s tempting to use a truss element for the member. However I think if you tried to connect a truss to your pinned foundation, your stiffness matrix would not invert.

Looking at the releases, for the “mixed” members (W14x53) and “double” pinned connection, I would resort to using zero length elements with rigid properties in the x / y directions, and flexible properties in the rotation direction. However this is a little involved – our problem jumps from using 7 to 11 nodes! Is there a cleaner solution I’m missing?

Hello C.,
Thanks for the questions. You should be able to connect truss and beam-column elements without getting a singular stiffness matrix. For the moment releases, you can use the equalDOF command in OpenSees. Unfortunately, there is not an elastic beam element in OpenSees with moment releases, at least not that I’m aware of. I will add that in some day!
PD

What’s the deadline?

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How about March 31?

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Hi,

What is the meaning of “strong” and “weak” for W10x54

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It is an indication of the column orientation for bending in the plane of loading. On the left, the column will flex about its strong axis while the column on the right is turned to flex about its weak axis.

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Hello P.D.,

I am not sure I read text carefully or not but I cannot find moment of inertia for BRB. I try to model BRB by elasticBeamColumn

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Hello MSB,

In the model, the BRB (and the HSS braces) have moment releases at each end, so you don’t really need the moment of inertia for these members.

PD

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So, BRB should model using truss element and there is no need for modeling shear-tab using pinching04 model /zero-length rotational spring model (Liu & Astaneh-. Asl, 2004,2005) .

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MSB,

Yes, the BRB can be a truss element and the shear tabs can be moment releases.

PD

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Hey,

I really like modeling challenges like this – I think it does a lot to help the the community learn.

I wonder if you could comment on (now or in your update) how best to model the releases, particularly for the mixed beam elements (W14x53) and the bottom pin connection.

For the bottom HSS member, it’s tempting to use a truss element for the member. However I think if you tried to connect a truss to your pinned foundation, your stiffness matrix would not invert.

Looking at the releases, for the “mixed” members (W14x53) and “double” pinned connection, I would resort to using zero length elements with rigid properties in the x / y directions, and flexible properties in the rotation direction. However this is a little involved – our problem jumps from using 7 to 11 nodes! Is there a cleaner solution I’m missing?

C.

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Hello C.,

Thanks for the questions. You should be able to connect truss and beam-column elements without getting a singular stiffness matrix. For the moment releases, you can use the equalDOF command in OpenSees. Unfortunately, there is not an elastic beam element in OpenSees with moment releases, at least not that I’m aware of. I will add that in some day!

PD

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