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FAQ

What is the difference between a Caltrans hinge and a fiber hinge?

Extended Question: It appears that the The Caltrans hinge and appears to be conceptually similar to the fiber hinge are conceptually similar. They are both in that both are based on strain compatibility and equilibrium of forces. The Caltrans hinge can be idealized as elastic-perfectly plastic as As shown in Figure 3.7 of the Caltrans Seismic Design Criteria version v. 1.4 - does the mean that when the user specifies auto Caltrans hinge, the program always uses the idealized moment curvature, which would be the main difference between the two types of hinges?

Answer: The Caltrans hinge is a PMM type of hinge based on an interactions surface. The only thing that makes it a Caltrans hinge rather than any other PMM hinge is the idealized elastic-perfectly plastic behavior and how it is calculated. Like all PMM hinges, once the hinge yields, it locks onto a moment rotation curve based on the yield point. This curve include axial and rotational deformation based on the normal to the yield surface. It is a phenomenological approach. It works best for static loading without significant hysteresis.

The fiber hinge uses multiple axial stress-strain curves. It is more "realistic". Each fiber has its own hysteresis behavior, so it can track any PMM variation. It is computationally more intensive.

How exactly is ICrack determined for Caltrans hinges?

Extended question: It is not clear how exactly is the ICrack determined. Is it the "traditional" Icr that neglects the contribution of concrete in tension that would be calculated at Mcr?

Answer: "Icr" represents the cracked moment of inertia and is calculated from the basic principles as follows:

    Icr = Mp / (Cp * E)

where, Cp = (Cy * Mp)/ My

Mp = Plastic moment (idealized)
Cp = Plastic curvarure
E = Modulus of elasticity
Cy = Yield curvature
My = Yield moment

See Also

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, the Caltrans hinge can be idealized as elastic-perfectly plastic. Does the software use this idealized model, and what are the main differences between the Caltrans and fiber hinge?

Answer: A comparison between these two hinge options is given as follows:

Caltrans hinge

The Caltrans hinge is a P-M2-M3 hinge based on the 3D interaction surface which defines coupling between axial and biaxial-bending behaviors. Its mathematical formulation and elastic perfectly plastic behavior distinguishes the Caltrans hinge from others. Similar to other P-M-M hinges, once loading conditions combine to induce yielding, plastic behavior follows an energy dependent moment-rotation curve which extends along the angle between M2 and M3, normal to its yield point on the interaction surface. Monotonic loading is best suited for this phenomenological approach. Significant hysteresis should be avoided in dynamic applications.

Fiber hinge

The fiber hinge is useful for defining coupled axial and biaxial-bending behavior in frame objects, though it follows a different approach. The cross section is discretized into a series of representative axial fibers which extend longitudinally along hinge length. Depending on the material in its tributary area, each fiber has a stress-strain relationship. Integrating behavior over the cross section, then multiplying by hinge length, provides axial force-deformation and biaxial moment-rotation relationships. The fiber hinge model is more accurate in that the nonlinear material relationship of each fiber automatically accounts for interaction, changes in along the moment-rotation curve, and plastic axial strain. A trade-off is that fiber application is more computationally intensive. Fiber hinges are ideal for dynamic behavior since they capture nonlinear hysteretic effects.

How is I _cr determined for Caltrans hinges?

Answer: I _cr represents the cracked moment of inertia, calculated through basic principles as follows:

I _cr = M _p / (C _p * E)

where:

C _p = (C _y * M _p) / M _y

and where:

M _p = Plastic moment (idealized)
C _p = Plastic curvature
E = Modulus of elasticity
C _y = Yield curvature
M _y = Yield moment

See Also

• P-M2-M3 hinges article