BNSM inputs

The bnsm input dictionary controls the configuration of the nonlinear structural model, including the modelling strategy, load and mass assumptions, pushover analysis settings, and output format. The example below shows a complete bnsm configuration. All parameters are optional; default values are applied when not specified.

"bnsm": {
    "model": "CP01",
    "opensees": "py",

    "load_factors": {"G": 1.0, "Q": 0.3},
    "mass_factors": {"G": 1.0, "Q": 0.3},

    "scheme": "EQL",
    "max_drift": 0.05,
    "dincr": 0.001,

    "include_infills": True,
    "cyclic_model": False,
    "cracked_beam": None,
    "cracked_column": None,
    "infill_column_connection": "parallel",
    "beam_loads": "auto"
}

Model Selection

The model identifier selects one of several pre-calibrated nonlinear modelling strategies, all of which build on a shared base library (bnsm.baselib) that provides the common element-level formulation. In particular, every model inherits the same default treatment for the following components:

  • Beams are modelled with force-based beam-column elements (forceBeamColumn) using a HingeRadau plastic-hinge integration scheme. Inelasticity is concentrated within finite plastic-hinge lengths at the element ends, while the interior is represented by an elastic section (optionally using cracked-section flexural stiffness, see cracked_beam). End-hinge moment-curvature behaviour follows a Hysteretic uniaxial material with a trilinear backbone (yield, capping, residual). The yield moment and curvature follow the empirical expressions of Panagiotakos and Fardis (2001), or a simplified moment-curvature section analysis in the models noted below. The yield chord rotation follows EN 1998-3:2005 (Eq. A.10b), with the tension shift factor set from the shear cracking resistance of EN 1992-1-1:2004 (6.2.2); the capping moment, plastic rotation capacity and post-capping rotation capacity follow Haselton et al. (2008, 2016). The yield curvature of the hinges is adjusted so that the member yields at the yield chord rotation: the elastic interior gives the flexural part My·Ls/(3·EI) and the hinges carry the rest (tension shift, shear distortion and bond-slip) over the plastic hinge length, computed per Priestley et al. (2007). A bond-slip modification factor adjusts the hinge properties. By default, beam gravity loads are applied as point loads at the element ends when the joints are inelastic, as in O’Reilly and Sullivan (2019), and as uniformly distributed loads otherwise; see beam_loads.

  • Columns use the same forceBeamColumn / HingeRadau framework as beams, but with a P-Delta geometric transformation to capture second-order effects under gravity. Flexural behaviour about both local axes (My, Mz) is represented by Hysteretic materials assembled in an aggregated hinge section, with the same backbone and yield curvature adjustment as the beams (including the axial load). When capacity-design shear is not enforced, the aggregated section additionally includes Pinching4 shear hinges (Vy, Vz) wrapped with MinMax limiters, calibrated following Zimos et al. (2015) with input from Sezen and Moehle (2004), Priestley et al. (1994), Mergos and Kappos (2012), and O’Reilly (2016); the shear distortion term is then left out of the yield chord rotation, since the shear springs model it.

  • Beam-column joints are represented by rotational spring models that can be rigid, elastic, or inelastic.

  • Masonry infills are represented by an equivalent diagonal-strut macro-model: each infill panel is replaced by two compression-only diagonal truss elements with a nonlinear uniaxial material. The default panel properties for the three typologies ("Weak", "Medium", "Strong", corresponding to T1/T2/T3) follow Hak et al. (2012); concrete-equivalent Concrete01 material parameters (peak/residual strengths and strains) are derived from the same source.

  • Floor diaphragms are modelled as rigid via a retained node and multi-point constraints.

  • Foundations are lumped fixed support nodes.

Each model below either uses these defaults directly or replaces specific components with calibrated alternatives.

model (str, default: "CP01")

Identifier of the nonlinear modelling strategy to use. The following pre-defined models are currently available, organised by plasticity formulation.

Concentrated plasticity (CP) models

  • "CP01": Lumped-plasticity model using the base forceBeamColumn framework, with beam and column flexural hinges defined through the Hysteretic moment-rotation formulation calibrated by Haselton et al. (2008). Columns optionally include a degrading shear hinge using a LimitState material coupled with ThreePoint limit curves per Elwood and Moehle (2003). Beam-column joint springs follow O’Reilly (2016). Masonry infills use the equivalent diagonal-strut model calibrated within ESRM20 (Crowley et al., 2021): each strut is assigned a Concrete01 material whose peak compressive strength is obtained from a regression on Hak et al. (2012) data as a function of panel length and height.

  • "CP02": Extends CP01 by replacing the Hysteretic end-hinge material in both beams and columns with the energy-based HystereticSM formulation of Hasanoglu and O’Reilly (2026), which provides improved control of hysteretic energy dissipation under cyclic loading. Shear hinges, joints, infills (ESRM20-calibrated Concrete01 strut inherited from CP01), and assembly logic are inherited from CP01 unchanged.

  • "CP03": Extends CP01 by representing the plastic hinges explicitly as zeroLength (beams) and zeroLengthSection (columns) elements placed in series with an elastic interior beam-column element. Rigid joint offsets are modelled with rigid-like elasticBeamColumn elements rather than geomTransf joint offsets, which allows auxiliary plastic hinge nodes to be defined explicitly. The infill formulation (ESRM20 Concrete01 strut) is inherited from CP01, but CP03 additionally exposes a configurable series-or-parallel infill-column shear interaction (see infill_column_connection below).

Distributed plasticity (DP) models

  • "DP01": Direct use of the base distributed-plasticity formulation. Beams and columns are modelled with forceBeamColumn elements and a HingeRadau integration scheme over a finite plastic-hinge length computed per Priestley et al. (2007), with aggregated end-hinge sections combining flexural (Hysteretic) and optional degrading shear (Pinching4+MinMax) responses. Masonry infills use the base equivalent-strut macro-model directly, with Hak et al. (2012) panel properties. Suitable as a general-purpose baseline distributed-plasticity model.

  • "DP02": Extends DP01 by recalibrating the end-hinge flexural moment-curvature relationships using Pinching4 materials following O’Reilly (2016), offering refined cyclic energy dissipation, pinching, and strength/stiffness degradation behaviour. Masonry infill struts are recalibrated for Pinching4 behaviour with cracking, peak, and residual strength/drift parameters from O’Reilly (2016). The remaining components are inherited from the base library.

  • "DP03": Extends DP01 by replacing aggregated end-hinge sections with fiber-discretized sections at both ends of beams and columns, explicitly capturing axial-flexure interaction and the influence of reinforcement detailing. Concrete confinement follows Mander et al. (1988) with Concrete04 (default), or the modified Kent and Park model (Scott et al., 1982) with Concrete01, and reinforcing steel is wrapped with MinMax limiters enforcing strain bounds that approximate bar buckling or rupture per Priestley et al. (2007). The interior section of beams and columns can be defined as elastic or inelastic. Infills are inherited from the base library (Hak et al. 2012 diagonal strut).

  • "DP04": A DP03-derived variant intended for cases where fiber-level refinement is required only for columns. Column end-hinge sections retain the DP03 fiber formulation, but the interior column section is set to elastic by default. Beam modelling reverts to the DP01 aggregated-section formulation. Joints, base-library diagonal-strut infills, diaphragms, and foundations are inherited unchanged.

  • "DP05": DP03 with an axial release at one end of each beam. The rigid floor diaphragm forces zero axial strain in the beams, whereas the axis of a fiber-section RC beam elongates as it cracks and yields; DP03 beams therefore develop fictitious axial compression that raises their flexural strength and stiffness. In DP05, the end section of each beam frames into an auxiliary node connected to the joint by a zeroLength element that is free along the beam axis and rigid otherwise (OpenSees Wiki, Rigid Diaphragm Consequences), so the beams carry no axial force. Columns, joints, infills, diaphragms and foundations are as in DP03.

opensees ("py" or "tcl", default: "py")

Output format for the generated OpenSees model script.

  • "py": generates an OpenSeesPy-compatible Python script.

  • "tcl": generates an OpenSees Tcl script.

Load and Mass Parameters

load_factors (dict, default: {"G": 1.0, "Q": 0.3})

Load combination factors used to compute gravity loads applied to the model.

  • "G" (float): factor for permanent (dead) loads.

  • "Q" (float): factor for variable (live) loads.

mass_factors (dict, default: {"G": 1.0, "Q": 0.3})

Factors used to compute seismic masses from gravity loads.

  • "G" (float): factor for permanent (dead) loads.

  • "Q" (float): factor for variable (live) loads.

beam_loads ("auto", "uniform" or "point", default: "auto")

How the beam gravity loads are applied in the numerical model.

  • "uniform": uniformly distributed element loads (beamUniform); the load over the rigid joint regions at the beam ends is applied as point loads at the element ends.

  • "point": equivalent point loads at the beam element ends, i.e., half of the total beam load at each end, as in O’Reilly and Sullivan (2019). The beams (and thus the columns) then carry no gravity-induced moments.

  • "auto": "point" if the beam-column joints are modelled as inelastic, as in the original joint model of O’Reilly and Sullivan (2019), and "uniform" otherwise (elastic or rigid joints).

All options apply the total beam load over the beam length measured between the grid lines, as in the design.

Pushover Analysis Parameters

scheme (str, default: "EQL")

Lateral load distribution scheme used for nonlinear static (pushover) analysis.

  • "FMP": fundamental-mode proportional loading.

  • "EQL": equivalent lateral force distribution.

  • "MPP": mass-proportional loading.

  • "TRI": triangular (height-proportional) loading.

  • "UNI": uniform loading.

max_drift (float, default: 0.05)

Maximum inter-storey drift ratio used to define the target displacement of the control node.

dincr (float, default: 0.001)

First displacement increment applied at the control node during pushover analysis (in metres).

Modelling Settings

Note

The parameters below are available for all model types unless stated otherwise. Parameters not recognised by the selected model are silently ignored.

include_infills (bool, default: True)

If True, masonry infill panels are included in the structural model.

cyclic_model (bool, default: False)

If True, model parameters are adjusted for cyclic (as opposed to monotonic) analysis.

cracked_beam (None, bool or float, default: None)

Effective (cracked-section) flexural stiffness of the elastic beam sections:

  • None or False: gross-section properties.

  • True: EIeff = My / phi_y with the yield moment and curvature of the plastic hinges (Panagiotakos and Fardis, 2001, or the simplified section analysis, see the model descriptions above), averaged over both end sections and bending directions. Flexure only.

  • float: user-defined ratio of effective to gross flexural stiffness, 0 < EIeff / EIg <= 1 (e.g., 0.5 as in EN 1998-1 4.3.1(7)).

Note

CP01 and CP02 should keep gross sections: their ConcentratedPlasticity integration gives the hinges a weight of one length unit and reduces the elastic interior accordingly, so cracked interior sections give inconsistent results.

cracked_column (None, bool or float, default: None)

Same as cracked_beam, for the elastic column sections. With True, My / phi_y includes the effect of the gravity axial load.

infill_column_connection ("parallel" or "series", default: "parallel")

Note

This parameter is only applicable to "CP03".

Modelling assumption governing the interaction between masonry infill struts and column lateral response.

  • "parallel": the infill strut acts in parallel with the column, contributing directly to the global lateral strength of the frame.

  • "series": the column lateral response acts in series with the horizontal component of the infill strut. The effective lateral strength is governed solely by the column.

References

CEN (2004). Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings. EN 1992-1-1:2004. Brussels, Belgium.

CEN (2005). Eurocode 8: Design of structures for earthquake resistance - Part 3: Assessment and retrofitting of buildings. EN 1998-3:2005. Brussels, Belgium.

Crowley, H. M., Dabbeek, J., Despotaki, V., Rodrigues, D., Martins, L., Silva, V., Romão, X., Pereira, N., Weatherill, G. A., & Danciu, L. (2021). European Seismic Risk Model (ESRM20). EFEHR Technical Report 002. https://doi.org/10.7414/EUC-EFEHR-TR002-ESRM20

Elwood, K. J., & Moehle, J. P. (2003). Shake table tests and analytical studies on the gravity load collapse of reinforced concrete frames. PEER Report 2003/01. Pacific Earthquake Engineering Research Center, University of California, Berkeley.

Hak, S., Morandi, P., Magenes, G., & Sullivan, T. J. (2012). Damage control for clay masonry infills in the design of RC frame structures. Journal of Earthquake Engineering, 16(sup1), 1-35. https://doi.org/10.1080/13632469.2012.670575

Hasanoglu, S., & O’Reilly, G. J. (2026). A hysteretic energy-based framework for seismic fragility assessment of ductile reinforced concrete frame buildings. (in preparation)

Haselton, C. B., Liel, A. B., Lange, S. T., & Deierlein, G. G. (2008). Beam-column element model calibrated for predicting flexural response leading to global collapse of RC frame buildings. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.

Haselton, C. B., Liel, A. B., Taylor-Lange, S. C., & Deierlein, G. G. (2016). Calibration of model to simulate response of reinforced concrete beam-columns to collapse. ACI Structural Journal, 113(6).

Mander, J. B., Priestley, M. J. N., & Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of Structural Engineering, 114(8), 1804-1826. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804)

Mergos, P. E., & Kappos, A. J. (2012). A gradual spread inelasticity model for R/C beam-columns, accounting for flexure, shear and anchorage slip. Engineering Structures, 44, 94-106. https://doi.org/10.1016/j.engstruct.2012.05.035

O’Reilly, G. J. (2016). Performance-based seismic assessment and retrofit of existing RC frame buildings in Italy. Doctoral dissertation, IUSS Pavia.

O’Reilly, G. J., & Sullivan, T. J. (2019). Modeling techniques for the seismic assessment of the existing Italian RC frame structures. Journal of Earthquake Engineering, 23(8), 1262-1296.

Panagiotakos, T. B., & Fardis, M. N. (2001). Deformations of reinforced concrete members at yielding and ultimate. Structural Journal, 98(2), 135-148.

Priestley, M. N., Verma, R., & Xiao, Y. (1994). Seismic shear strength of reinforced concrete columns. Journal of Structural Engineering, 120(8), 2310-2329. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:8(2310)

Priestley, M. J. N., Calvi, G. M., & Kowalsky, M. J. (2007). Displacement-based seismic design of structures. IUSS Press, Pavia.

Scott, B. D., Park, R., & Priestley, M. J. N. (1982). Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. Journal of the American Concrete Institute, 79(1), 13-27.

Sezen, H., & Moehle, J. P. (2004). Shear strength model for lightly reinforced concrete columns. Journal of Structural Engineering, 130(11), 1692-1703. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:11(1692)

Zimos, D. K., Mergos, P. E., & Kappos, A. J. (2015). Shear hysteresis model for reinforced concrete elements including the post-peak range. Proceedings of COMPDYN 2015, Crete Island, Greece. https://doi.org/10.7712/120115.3565.1184