Chapter 1 Introduction
1.1 Abstract
Evaluation of seismic performance of moment-resisting (MR) steel frames is usually carried out assuming the elastic-perfectly-plastic type of hysteresis model for plastic zones (in particular for beam-to-column connections). This type of model is associated with a conventional available ductility, giving an indication of the maximum deformation beyond which strength degradation is likely to occur. This methodology leads to conservative results and is certainly adequate in obtaining reliable information on deformation when the above ductility is not exceeded. However, the safety of the frame at ‘collapse’ remains unknown. Safety margins against global collapse can be predicted only considering more realistic hysteresis behavior, i.e. using mathematical models able to take into account strength degradation and pinching phenomena.
A number of beam-to-column connection types are currently available in practice and their mechanical response is different from one type to another, both under monotonic and cyclic loading conditions. Connection exhibit hardening not only during monotonic loading, with increasing maximum deformations, but also during cyclic loading at a given deformation amplitude. Furthermore, under cyclic loading conditions, ‘geometrical damages’ result in a reduction in both stiffness and strength. In all types of connections, fatigue-related damage causes a reduction in the available ductility. So the first step to analyze the seismic performance of a MR frame is the development of a mathematical model able to capture correctly the connection hysteretic behavior, including both hardening, softening and pinching phenomena.
1.2 Objective and scope
This work of thesis starts from the previous considerations and the aim of it has been put on the different results that can derive from include, or neglect, deterioration in modeling steel details and structures. To realize that, different steel elements have been modeled and analyzed, both under monotonic and cyclic tests. These have been a cantilever column, several beam-to-column connections and finally a plane frame.
The need to use a model able to be used with all the steel cross-section, including semi-compact and slender sections (Eurocode class 3 and 4), has had a crucial importance in the thesis work. In fact the territory of Germany is characterized by a medium-low seismicity. Therefore these cross-section classes are of primary interest for Seismic Engineers.
The software used for that purpose has been OpenSees, a modern and powerful program developed in Berkeley University. Different combinations of materials, sections and element, already provided by the software, have been considered, both with or without a degrading and hysteretic behavior.
As a sophisticated model, the Ibarra-Medina-Krawinkler deterioration models with bilinear
1.3 Outline
In Chapter 2 some of the most interesting hysteresis models provided in literature have been taken into consideration and discussed. In fact, from the structural point of view, one major uncertainty is related to the type of hysteresis model to be used for performing numerical analyses. Looking at experimental results, it’s clear that usually assumed elastic-perfectly-plastic hysteresis model is far from being faithfully representative of the actual cyclic response of connections. The aim of the chapter has been focus on the three Ibarra-Medina-Krawinkler deterioration models (with bilinear hysteretic response, peak-oriented, with pinching).
An introduction of OpenSees software has been realized in Chapter 3. The Open System for
Earthquake Engineering Simulation is an object-orientated, open source framework which
allows users to develop sequential, parallel and grid-enabled finite element computer applications for simulating the response of structural and geotechnical systems subjected to earthquakes and other hazards. All the important steps for model definition and analysis have been explained in the chapter. Finally the OpenSees implementation of the pre-defined Ibarra-Medina-Krawinkler deterioration models has been discussed.
In Chapter 4 a steel cantilever column has been analyzed in order to take confidence with commands and possibilities provided by OpenSees. Different models have been considered, combining the possibilities, in terms of materials, sections and elements, provided by OpenSees. This include the Ibarra-Medina-Krawinkler deterioration model with bilinear hysteretic response. The results of the tests have been compared in order to underline the differences in the behavior.
The analysis of steel beam-to-column connections is the aim of Chapter 5. Several tests have been simulated. At first a beam-to-column connection has been extrapolated from the X-Z frame of Building 1 [see Chapter 7], and modeled using different possibilities provided by OpenSees, including the Ibarra-Medina-Krawinkler deterioration model with bilinear hysteretic response. Monotonic and cyclic plane analysis have been performed in X-Z plane. Then other connections have been modeled and analyzed, with the special aim of investigating the influence of material and geometrical parameters on the behavior of the connection itself. In Chapter 6 the pre-defined Ibarra-Medina-Krawinkler deteriorating model with bilinear response has been used to model several beam-to-column connection. In order to calibrate the deteriorating parameters that control the behavior of the model, both monotonic and cyclic analysis have been performed and the results have been compared with the ones obtained in real tests performed by the Department of Steel Construction of RWTH Aachen University within a research project for modern plastic design of steel structures, named PLASTOTOUGH [19].
As result of the experience collected in simpler analysis, in Chapter 7, a plane steel frame has been performed. The frame has been extrapolated from a building and analyzed using several combination of material, element and section provided by OpenSees. Both monotonic and cyclic displacement-controlled tests have been performed on the frame in order to better comprehend the behavior of the different models. Finally a simulated earthquake has been applied by imposing an acceleration pattern to the base nodes.
In Chapter 8 the main conclusions from the previous chapters of the work are summarized in order to have an overall review of it.
1.4 List of illustrations
1.4.1 Chapter 2 – Deteriorating hysteretic models
Figure 2.1 -qualitative picture of ‘performance curve’ [Ref. 5]
Figure 2.2 - reduction of bending strength owning to the activation of negative stiffness branches in the moment-rotation relationship [Ref. 5]
Figure 2.3 - simulation of pinching [Ref. 5]
Figure 2.4 - beam-to-column joint models [Ref. 5]
Figure 2.5 - effects of local softening phenomena on the seismic performance of the whole frame [Ref. 5]
Figure 2.6 - effect of cyclic fatigue-related strength degradation phenomena on the seismic performance of the whole frame [Ref. 5]
Figure 2.7 - Effect of pinching of hysteresis loops on the seismic performance of the whole frame [Ref. 5]
Figure 2.8 - a) specimen geometry; b) specimen instrumentation [Ref. 4]
Figure 2.9 - a) global rotation curves BCC5C, BCC6C and BCC8D tests b) Moment-beam plastic rotation and Moment-panel rotation curves [Ref. 4]
Figure 2.10 - example of multi-linear cyclic skeleton [Ref. 6] Figure 2.11 - typical cyclic skeleton [Ref. 6]
Figure 2.12 - general multi-linear reference skeleton [Ref. 6]
Figure 2.13 - modified Ibarra – Krawinkler (IK) deterioration model; (a) monotonic curve; (b) basic modes of cyclic deterioration and associated definitions [Ref. 7]
Figure 2.14 - Calibration examples of modified IK deterioration model - beam with RBS (no slab, data from Uang et al. 2000) [Ref. 7]
Figure 2.15 – cumulative distribution functions for (a) ; (b) ; (c) . Left: full data sets 1
and 2. Right: data sets 3 and 4, [Ref. 7]
Figure 2.16 - Dependence of plastic rotation θp on beam depth d for beams other-than-RBS (a) full set of data; (b) d ≥ 533mm [Ref. 7]
Figure 2.17 - Dependence of plastic rotation θp on shear span to depth ratio L/d for beams
other-than-RBS - (a) full data set; (b) d ≥ 533mm [Ref. 7]
Figure 2.18 - Dependence of modeling parameters on h/tw ratio of beam web, [Ref. 7]
Figure 2.19 - Predicted versus calibrated values of θp [Ref. 7] Figure 2.20 - Predicted versus calibrated values of θpc [Ref. 7]
Figure 2.21 - Peak-orientated hysteretic model – basic model rules [Ref. 9]
1.2.2 Chapter 3 – Introduction on OpenSees
Figure 3.1 - a) simulation framework; b) comparison of codes [Ref. 1] Figure 3.2 - stress-strain diagram of elastic material [Ref. 1]
Figure 3.3 - stress-strain diagram of elastic-perfectly plastic material [Ref. 1] Figure 3.4 - stress-strain diagram of hardening material [Ref. 1]
Figure 3.6 - monotonic (a) and cyclic (b) stress-strain diagram of steel01 material [Ref. 1] Figure 3.7 - cyclic hysteretic stress-strain diagram of steel01 material with isotropic hardening in compression (a) and in tension (b) [Ref. 1]
Figure 3.8 - monotonic (a) and cyclic (b) stress-strain diagram of steel01 material [Ref. 1] Figure 3.9 - cyclic hysteretic stress-strain diagram of steel02 material with isotropic hardening in compression (a) and in tension (b) [Ref. 1]
Figure 3.10 - quadrilateral patch [Ref. 1]
Figure 3.11 - example of section aggregator [Ref. 1] Figure 3.12 - beam with hinges element [Ref. 1] Figure 3.13 - integration points distribution [Ref. 1]
Figure 3.14 - example of OpenSees implementation of hysteretic models [Ref. 8]
Figure 3.15 - moment-rotation relationship for a member based on the moment-rotation of the plastic hinge springs and elastic beam-column element [Ref. 10]
Figure 3.16 - Modified Ibarra-Medina-Krawinkler model – Moment-rotation curve [Ref. 3]
Figure 3.17 - Modified Ibarra-Medina-Krawinkler model with peak-oriented hysteretic response Moment-rotation curve [Ref. 3]
Figure 3.18 - Modified IMK model with Peak-Oriented hysteretic response – backbone curve [Ref. 11]
Figure 3.19 - Modified IMK model with Peak-Oriented hysteretic response – base case [Ref. 11] Figure 3.20 - Parameter variation on Modified IMK model with Peak-Oriented hysteretic response – a) Base case; b) Effect of residual strength; c) Effect of cyclic deterioration parameters; d) Effect of post-capping rotation [Ref. 11]
Figure 3.21 - Modified Ibarra-Medina-Krawinkler model with pinched responseMoment-rotation curve [Ref. 11]
Figure 3.22 - Modified IMK model with Pinched hysteretic response – backbone curve [Ref. 11] Figure 3.23 - Modified IMK model with Pinched hysteretic response – base case [Ref. 11] Figure 3.24 - Parameter variation on Modified IMK model with Pinched hysteretic response – a) Base case; b) Effect of residual strength; c) Effect of pinching parameters; d) Effect of post-capping rotation [Ref. 11]
1.2.3 Chapter 4 – Analysis of a cantilever column
Figure 4.1 - cantilever characteristics Figure 4.2 - Cantilever – Model 1 ; Model2
Figure 4.3 - Fiber section discretization of the HEB400 section Figure 4.4 - Cantilever column – Model 3
Figure 4.5 - Cantilever column – Model 4
Figure 4.6 - Cantilever column – Monotonic lateral force-controlled analysis - Quantities
Figure 4.7 Cantilever column – Reverse lateral force-controlled analysis - Quantities
Figure 4.8 - Lateral force-controlled test - loading pattern
Figure 4.9 - Cantilever column – Monotonic lateral pushover analysis - Quantities Figure 4.10: Fig. 4.10: Cyclic displacement-controlled test - Displacement pattern Figure 4.11: Cantilever column – Cyclic lateral pushover analysis - Quantities Figure 4.12: Cantilever model 1-2 – monotonic lateral load-controlled analysis
Figure 4.13: cantilever model 1-2 – monotonic lateral load-controlled analysis – influence of the vertical load
Figure 4.14: Cantilever model 3 – monotonic static lateral load-controlled analysis Figure 4.15: Cantilever model 1-2 – reverse static lateral load-controlled analysis Figure 4.16: Cantilever model 3 – reverse static lateral load-controlled analysis Figure 4.17: Cantilever model 2 – Capacity curve
Figure 4.18: Cantilever model 3 – Capacity curve
Figure 4.19: Cantilever Model 2 - Cyclic displacement-controlled test – capacity curve Figure 4.20: Displacement pattern applied to node 2
Figure 4.21: Cantilever – Model3 (base case) – Capacity curve Figure 4.22: Cantilever – Model 3A – Capacity curve
Figure 4.23: Cantilever – Model 3B – Capacity curve Figure 4.24: Cantilever – Model 3C – Capacity curve Figure 4.25: Cantilever – Model 3D – Capacity curve
Figure 4.26: Cantilever – model 4 – monotonic force-controlled analysis Figure 4.27: Lateral force-controlled test - loading pattern
Figure 4.28: Cantilever – model 4 – cycle force-controlled analysis -
Figure 4.29: Cantilever – model 4 – cycle force-controlled analysis -
1.2.4 Chapter 5 – Analysis of a beam-to-column connection
Figure 5.1 – Material S235 – stress-strain curve
Figure 5.2: Geometry of rotational test specimen with profile IPE 400 Figure 5.3: Beam to column connection - geometric characteristics Figure 5.4: Beam to column connection – 3D view [SAP2000] Figure 5.5: Beam to Column connection – Model 1 - Nodes Figure 5.6: Beam to Column connection – Model 1 - Elements
Figure 5.7: Fiber section discretization of the HEB400 and IPE 400 sections Figure 5.8: Beam to column connection – Model 2 – Nodes
Figure 5.9: Beam to column connection – Model 2 – Elements
Figure 5.10: Beam to column connection - model 1 - monotonic lateral load-controlled analysis Figure 5.11: Lateral force-controlled test - loading pattern
Figure 5.12: beam to column connection - model 1 - reverse static lateral load-controlled analysis
Figure 5.13: beam to column connection - model 1 - monotonic displacement controlled pushover analysis
Figure 5.14: Beam to column connection - model 2 - monotonic lateral load-controlled analysis Figure 5.15: Beam to column connection – monotonic load-controlled test - Model 1 – Model 2 Figure 5.16: Lateral force-controlled test - loading pattern
Figure 5.17: Model 2 - reverse load-controlled test
Figure 5.18: Beam to column connection – reverse load-controlled test - Model 1 – Model 2 Figure 5.19: beam to column connection – Model 2 – monotonic displacement-controlled pushover analysis
Figure 5.20: Displacement pattern [ECCS procedure]
Figure 5.21: beam to column connection – Model 2 – cyclic displacement-controlled pushover analysis
Figure 5.22: Displacement pattern [ECCS procedure]Figure 5.23: beam to column connection – Model 2A – cyclic displacement-controlled pushover analysis
Figure 5.24: beam to column connection – Model 2B – cyclic displacement-controlled pushover analysis
Figure 5.25: beam to column connection – Model 2C – cyclic displacement-controlled pushover analysis
Figure 5.26: beam to column connection – Model 2D – cyclic displacement-controlled pushover analysis
Figure 5.27: beam to column connection – Model 2E – cyclic displacement-controlled pushover analysis
Figure 5.28: beam to column connection – Model 2F – cyclic displacement-controlled pushover analysis
1.2.5 Chapter 6 – Calibration of deteriorating model with real tests
Figure 6.1: Geometry of rotation test – specimen with profiles HEA 300 [19] Figure 6.2: Geometry of rotation test – specimen with profiles IPE 500 [19]
Figure 6.3: Weld details – a) non sophisticated (fillet weld); b) sophisticated (butt weld) [19] Figure 6.4: Beam to column connection – Nodes
Figure 6.5: Beam to column connection – Elements
Figure 6.6: Load-displacement curves for profile HEA 300 [19]
Figure 6.7: OpenSees model – load-displacement curves for profile HEA 300 Figure 6.8: Load-displacement curves for profile IPE 500 [19]
Figure 6.9: OpenSees model – load-displacement curves for profile IPE 500 Figure 6.10: RT-HEA-355_ns-2 test – Displacement pattern
Figure 6.11: RT-HEA-355_s-2 test – Displacement pattern Figure 6.12: RT-HEA-355_ns-3 test – Displacement pattern Figure 6.13: RT-HEA-355_s-3 test – Displacement pattern Figure 6.14: RT-HEA-355_ns-4 test – Displacement pattern Figure 6.15: RT-HEA-355_s-4 test – Displacement pattern Figure 6.16: RT-HEA-355_ns-5 test – Displacement pattern Figure 6.17: RT-HEA-355_s-5 test – Displacement pattern Figure 6.18: RT-IPE-355_ns-2 test – Displacement pattern Figure 6.19: RT-IPE-355_s-2 test – Displacement pattern Figure 6.20: RT-IPE-355_ns-3 test – Displacement pattern Figure 6.21: RT-IPE-355_s-3 test – Displacement pattern Figure 6.22: RT-IPE-355_ns-4 test – Displacement pattern Figure 6.23: RT-IPE-355_s-4 test – Displacement pattern Figure 6.24: Quantities used in Moment-Rotation diagrams
Figure 6.25: RT-HEA-355_ns-2 test [ECCS PROCEDURE] – Moment-Rotation diagram Figure 6.26: RT-HEA-355_s-2 test [ECCS PROCEDURE] – Moment-Rotation diagram
Figure 6.27: RT-HEA-355_ns-3 test [95% FRACTILE PROCEDURE] – Moment-Rotation diagram Figure 6.28: RT-HEA-355_s-3 test [95% FRACTILE PROCEDURE] – Moment-Rotation diagram Figure 6.29: RT-HEA-355_ns-4 test [KOBE PROCEDURE] – Moment-Rotation diagram
Figure 6.30: RT-HEA-355_s-4 test [KOBE PROCEDURE] – Moment-Rotation diagram
Figure 6.31: RT-HEA-355_ns-5 test [CONSTANT AMPLITUDE PROCEDURE] – Moment-Rotation diagram
Figure 6.34: RT-IPE-355_s-2 test [ECCS PROCEDURE] – Moment-Rotation diagram
Figure 6.35: RT-IPE-355_ns-3 test [MEAN VALUE PROCEDURE] – Moment-Rotation diagram Figure 6.36: RT-IPE-355_s-3 test [MEAN VALUE PROCEDURE] – Moment-Rotation diagram Figure 6.37: RT-IPE-355_ns-4 test [CONSTANT AMPLITUDE PROCEDURE] – Moment-Rotation diagram
Figure 6.38: RT-IPE-355_s-4 test [CONSTANT AMPLITUDE PROCEDURE] – Moment-Rotation diagram
1.2.5 Chapter 7 – Analysis of a plane frame
Figure 7.1: Building 1 ; X-Y plane Figure 7.2: Building 1 ; X-Z plane Figure 7.3: Building 1 ; Y-Z plane Figure 7.4: Building 1 ; 3D view
Figure 7.5: Fiber section discretization of HEB400 and IPE 400 sections Figure 7.6: Plane frame – Nodes
Figure 7.7: Plane frame – Generic node Figure 7.8: Plane frame – Elements Figure 7.9: Plane frame – Generic node
Figure 7.10: RT Plane Frame – Seismic Masses Distribution
Figure 7.11: Plane frame – Displacement-controlled pushover analysis - Horizontal load pattern Figure 7.12: Ground Acceleration Displacement Pattern [Akz 1]
Figure 7.13: Acceleration Spectrum
Figure 7.14: Base Ground Acceleration Displacement Pattern [GMfacor=1,0] and Limit Ground Acceleration Displacement Pattern [GMfacor=8,0]
Figure 7.15: Plane frame – SAP2000 Deformed Shapes and Fundamental Periods
Figure 7.16: Plane frame – OpenSees Model 1 - Deformed Shapes and Fundamental Periods Figure 7.17: Plane frame – OpenSees Model 2 - Deformed Shapes and Fundamental Periods Figure 7.18: Plane frame – OpenSees Model 1 – Capacity curve 1
Figure 7.19: Plane frame – OpenSees Model 1 – Capacity curve 2 Figure 7.20: 7.20: Plane frame – OpenSees Model 2 – Capacity curve
Figure 7.21: Plane frame – Capacity curve of OpenSees Model 1 and Model 2
Figure 7.22: Plane frame –OpenSees Model 2 – Deformed shape of pushover analysis Figure 7.23: Ground Motion Simulation Analysis – Floor Number
Figure 7.24: Displacement Time History – Floor Number 5 Figure 7.25: Displacement Time History – Floor Number 4
Figure 7.27: Displacement Time History – Floor Number 2 Figure 7.28: Displacement Time History – Floor Number 1 Figure 7.29: Ground Motion Simulation Analysis – Floor Number Figure 7.30: Displacement Time History – Floor Number 5 Figure 7.31: RT Displacement Time History – Floor Number 4 Figure 7.32: Displacement Time History – Floor Number 3 Figure 7.33: Displacement Time History – Floor Number 2 Figure 7.34: Displacement Time History – Floor Number 1
Figure 7.35: IDA Curve – Max Interstorey Drift Ratio vs GMfactor
Figure 7.36: IDA Curve – Max Interstorey Drift Ratio vs Peak Applied Acceleration Figure 7.37: IDA Test – Model 2 - Maximum Recorded Moment for beam-hinges Figure 7.38: IDA Test – Model 2 - Maximum Required Rotation for beam-hinges Figure 7.39: IDA Test – Model 2 - Maximum Recorded Moment for beam-hinges
Figure 7.40: IDA Test – Model 2 - Maximum Required Rotation for ground column-hinges Figure 7.41: IDA Test – Residual displacement of roof storey
Figure 7.42: IDA Test – Evaluation of the behavior factor
Figure 7.43: IDA Test – GMfactor=4,0 – Floor 5 – Displacement Time History Figure 7.44: IDA Test – GMfactor=4,0 – Floor 4 – Displacement Time History Figure 7.45: IDA Test – GMfactor=4,0 – Floor 3 – Displacement Time History Figure 7.46: IDA Test – GMfactor=4,0 – Floor 2 – Displacement Time History Figure 7.47: IDA Test – GMfactor=4,0 – Floor 1 – Displacement Time History Figure 7.48: IDA Test – GMfactor=4,0 – Ground Nodes – Moment Time History Figure 7.49: IDA Test – GMfactor=4,0 – Nodes Storey 1 – Moment Time History Figure 7.50: IDA Test – GMfactor=4,0 – Nodes Storey 2 – Moment Time History Figure 7.51: IDA Test – GMfactor=4,0 – Nodes Storey 3 – Moment Time History Figure 7.52: IDA Test – GMfactor=4,0 – Nodes Storey 4 – Moment Time History Figure 7.53: IDA Test – GMfactor=4,0 – Nodes Storey 5 – Moment Time History Figure 7.54: IDA Test – GMfactor=4,0 – Ground Nodes – Rotation Time History Figure 7.55: IDA Test – GMfactor=4,0 – Nodes Storey 1 – Rotation Time History Figure 7.56: IDA Test – GMfactor=4,0 – Nodes Storey 2 – Rotation Time History Figure 7.57: IDA Test – GMfactor=4,0 – Nodes Storey 3 – Rotation Time History Figure 7.58: IDA Test – GMfactor=4,0 – Nodes Storey 4 – Rotation Time History Figure 7.59: IDA Test – GMfactor=4,0 – Nodes Storey 5 – Rotation Time History
