PRACTICAL USES OF NONLINEAR PUSHOVER ANALYSIS

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1 PRACTICAL USES OF NONLINEAR PUSHOVER ANALYSIS Jerod G. Johnson, PhD, SE SEAU Education Conference February 22, 2017 Disclaimer This presentation is meant to neither explicitly endorse nor discourage the use of the nonlinear pushover analysis method for any given design scenario. As with any method, nonlinear pushover has its benefits and limitations. Whether nonlinear pushover analysis is appropriate lies at the discretion of the engineer in responsible charge. 1

2 Presentation Outline 1. What is Nonlinear Analysis? 2. What is Nonlinear Pushover Analysis? 3. Why Use Nonlinear Pushover Analysis? 4. What are the Common Perceptions? 5. Embracing Innovation. 6. Embracing Nonlinearity. 7. Nonlinear Pushover Analysis A Good First Step. 8. Nonlinear Element Modeling 9. Examples 10. Nonlinear Pushover Limitations 11. Time History Quick Summary 12. Software 1. What is Nonlinear Analysis? Simple Definition of Nonlinearity: An alteration of material, element or system modeling properties as a function of load (including direction of load), displacement, deformation or velocity. Wikipedia: In physical sciences, a nonlinear system is a system in which the output is not directly proportional to the input. Simple example a tension only element. 2

3 Types of Nonlinearity Geometric Nonlinearity Also known as P-Delta. Rate Dependent Nonlinearity Properties change as a function of rate (e.g. viscous damper) History Dependent Nonlinearity Properties change as a function of repeated load (cumulative ductility or fatigue). Cyclical Dependent Nonlinearity Change of hysteretic properties (e.g. tension only braces). Contact Nonlinearity (e.g. footing/soil interface, pounding) Material Nonlinearity e.g. yielding of steel. Geometric Nonlinearity This example is for illustrative purposes and assumes equal member lengths and section properties P P θ u θ 3 F 1 3 Axial loads in members (1, 3) change as a result of load F. Forces: Basic Stiffness Matrix: Stiffness reduction matrix due to geometric nonlinearity: Displacements: F 24EI/L 3 6EI/L 2 6EI/L 2-6P 1 /5L-6P 3 /5L -P 1 /10 -P 3 /10 u 1 0 = 6EI/L 2 8EI/L 2EI/L + -P 1 /10-2P 1 L/15-2P 2 L/15 -P 2 L/30 θ 2 0 6EI/L 2 2EI/L 8EI/L -P 3 /10 -P 2 L/30-2P 2 L/15-2P 3 L/15 θ 3 Note: The P 1, P 2 and P 3 forces are the developed frame forces which are resolved through iterative processes. 3

4 Rate Dependent Nonlinearity History/Cyclical Dependent Nonlinearity Slen der Intermediate Concentric Braces Stocky 4

5 Contact Nonlinearity 8 Footing Deflection Pounding Material Nonlinearity Some materials are more ductile than others. Some materials behave better when confined. Structural Steel Fy = 50ksi Rebar fy = 60ksi 5

6 Material Nonlinearity (cont.) Unconfined Concrete f c = 4000psi Some materials are less ductile than others. Some materials behave better when confined. Confined Concrete f c = 4000psi Mander Concrete Model Material Nonlinearity (cont.) Ductile systems are driven to enable material nonlinearity. This is the basis behind: Ties and confinement in Special reinforced concrete sections. Lateral bracing of moment frame beams in SRMF and OMF. Lateral bracing of beams in other BF systems. The casing and grout of a BRB. Definitions of seismic compactness. 6

7 Material Nonlinearity (cont.) Ductile systems are driven to enable: Element Nonlinearity Repeated cycles of stable (material) nonlinearity are preferred and even encouraged in the codes. This is reflected in the R factors. Let s observe F F F F Non-Degrading Stiffness Degrading Pinched Buckling R R R R R R R R R R R R?? BRB/SRMF SCSW OCBF 7

8 2. What is Nonlinear Pushover Analysis? Piecewise monotonically displacing a structure consistent with a rational loading pattern while explicitly accounting for nonlinearity of specific lateral force resisting elements (plastic hinges). The displacement magnitude of the structure is compared against the reactions that develop as nonlinear mechanisms develop. What is Nonlinear Pushover Analysis? C 0 SDOF to MDOF Modifier. C 1 Elastic to Inelastic Modifier. C 2 Pinched Hysteresis Modifier. C 3 P-Delta Modifier Base Shear vs. Displacement 1000 rxn rxn Base Shear Nonlinear Linear How is this performed? Rooftop Displacement 8

9 3. Why Use Nonlinear Pushover Analysis? Explicit accounting of nonlinearity. More accurate prediction of member forces. More accurate prediction of base shear. More direct prediction of displacements. Offers consideration of multiple performance scenarios. Provides a rational methodology for higher ductility demand and/or irregular structures (per ASCE 41) Does not require input ground motions. Credit where credit is due (ASCE 41). Why Use Nonlinear Pushover Analysis? (cont.) Direct accounting of performance (as opposed to prescriptive design). Less conservative than ELF, Lower construction cost. Is the cost of construction proportional to the complexity of the design approach? $ Construction Design Complexity ($) 9

10 Performance can be better than expected: observed seismic performances of three existing buildings in Christchurch subjected to the 2011 Lyttleton event were compared to the predicted performance of the analytical nonlinear models of the subject buildings. In general, the observed performance of the buildings was found to be better than that predicted by the analytical models. Performance can be better than expected (cont.) If performance is better than predicted by the most sophisticated of nonlinear analysis procedures then how conservative are the provisions using equivalent lateral force static methods? 10

11 Performance can be better than expected (cont.) If performance is often better than expected, then the tools for analysis and design may be too conservative. Does it make sense to embrace a design methodology that is more complex but produces a less conservative design? A more complex design approach is more costly but can yield major savings in construction along with a more reliable (targeted) outcome. This is especially relevant in today s discussion regarding resiliency.. 4. What are the common perceptions? March 2014 Issue of Structure Magazine reported the following results of a survey of Academician/Research Engineers, Industry Professionals, Consultants and others More than 75% of respondents said that guidance for most of these topics [nonlinear analysis and design] was ambiguous. Claims of inadequate software (21%), too complicated (29%), not practical/time consuming (61%), lack of research (22%), lack of guidelines (43%). More guidance is needed for: Modeling NL Elements (42%), NL Procedures (18%), Benchmark problems with solutions (35%). Head, Dennis, Muthukumar, Nielson, Mackie Structure Magazine, March

12 What are the common perceptions? (cont.) there is a need to be able to communicate to the importance of doing nonlinear analysis to the owners, as the apparent gain to pay for a more extensive analysis is not always clear. Nonlinear analysis can be used when owners request ways to reduce costs (for new construction) by optimizing material use, more likely though as demonstrating a building retrofit is perhaps not even necessary (or if it is, that only minor changes/systems are needed rather than what the code would require), or even as a way of quantifying performance for owners, insurance and risk managers that may look at inventories of structures. So, the major question to the owner is whether they d prefer to pay now or pay later? From the Experts (March 2016 Structure Magazine) When to conduct NL Analysis Irregular building type Assumptions of code-based linear are not valid Retrofitting Viscous dampers, isolators or new type of LFRS 12

13 From the Experts (March 2016 Structure Magazine) NL Procedures are time consuming, computationally demanding and required added cost of a peer review Not to mention the added cost of design. Pushover analysis should not be used as the sole measure and not be needed if one is performing a nonlinear time history. Pushover is less useful for drift/ductility, but rather to help proportion the structure to activate any intended ductile mechanism. Pushover not appropriate for multi-mode buildings. the need for more education and training on advanced topics like nonlinear analysis cannot be overstated. Pay now or pay later? Head, Pathak, Muthukumar, Mackie Structure Magazine, March Embracing Innovation 13

14 A Tip Calculator? Much more than a tip calculator!... 14

15 What do we do fundamentally? Design Buildings? How? Mathematical Models 15

16 What was the basis of these equations?: Mathematical Models: 16

17 We Use Mathematical Models to: Predict behavior of structural systems with respect to theoretical load. Ensure structures are sufficiently strongto resistthe anticipated load. Reliably predict loads a structure may experience. Reliably predict the minimum strength of structural elements. Mathematical Models: M n =F y Z x M n =A s f y (d-a/2) T2 " # $%& '(%) '*%+,-. φp n,max = 0.80φ[0.85f c (A g -A st ) + f y (A st )] F 24EI/L 3 6EI/L 2 6EI/L 2 u 1 M 2 = 6EI/L 2 8EI/L 2EI/L θ 2 M 3 6EI/L 2 2EI/L 8EI/L θ 3 17

18 Tools of the Trade Today: Evolution of Computer Power: Moore s Law: The number of transistors in a dense integrated circuit doubles approximately every two years. -Gordon E. Moore co-founder of Intel Corporation and Fairchild Semiconductor. This law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development. What does this say about the advancement of computer power over the last 20 years? Increase = 2 10 = 1,024 How about the last 40 years? Increase = 2 20 = 1,048,576 18

19 Moore s Law: Embracing Nonlinearity It can do more than equivalent lateral forces! 19

20 6. Embracing Nonlinearity Lumped Plasticity Models Re: ASCE 41, FEMA P695, Others Embracing Nonlinearity Professor Ed Wilson: The enormous increase in speed and memory capacity of inexpensive personal computers and the development of new numerical methods allow structural engineers to conduct earthquake response analysis of large and complex threedimensional structures. Therefore, I am optimistic many structural engineers will realize linear and non-linear time-history dynamic analysis of structures is not difficult and performance based design is now a reality. 20

21 Embracing Nonlinearity Professor Ed Wilson (cont.): After fifty years of conducting linear and non-linear earthquake analyses of many different types of structures, I am concerned with the increase in use of the approximate Response Spectrum Method. The fundamental equilibrium equations are not satisfied for systems over one-degree-of-freedom. In addition, the application of the method to nonlinear structural analysis has no theoretical or physical justification. So, what is Dr. Wilson Talking About? 21

22 Higher Mode Response Multi-Degree of Freedom Systems 1.4 Seconds 0.67 Seconds 91% Mass Activation 0.38 Seconds 0.28 Seconds Higher Mode Response Multi-Degree of Freedom 22

23 Higher Mode Response The simple calculation of story drifts is not appropriate when using dynamic response spectrum analyses because combined modal displacements can be less than the combined modal story drift (signs are lost). This is a consequence of simplified approaches...the application of the method to nonlinear structural analysis has no theoretical or physical justification. 1.4 Seconds 0.67 Seconds 0.38 Seconds 0.28 Seconds In other words, what happens to these mode shapes when yielding occurs? 91% Mass Activation 23

24 7. Nonlinear Pushover Analysis A Good First Step A good first step into the larger world of nonlinear analysis. A good first step into the advanced capabilities of the tools we use. A good tool for helping us understand the basis behind many code provisions. Primary Shortcoming; how to handle higher mode effects. A Nonlinear Model: Includes explicit modeling of mechanisms (ductile and brittle) that are likely to occur as material limit states are reached and surpassed. Remember, a material or element reaching to a limit state doesn t necessarily mean collapse. A system failure means collapse. What has been asked in regions of low seismicity? Why would you want something to yield? -Targeted nonlinearity, fuse, system control, reduction of forces. 24

25 A Nonlinear Model Nonlinear models explicitly include nonlinear mechanisms or nonlinear material behaviors that become activated upon reaching a theoretical load or displacement threshold. Nonlinear Linear Linear: σ = εe Nonlinear: σ =?? Consider a Beam Approaching it s Flexural Limit State: Stress Diagrams F b =M/S F y F y M n =F y Z x Elastic Elasto-Plastic Plastic 25

26 How do the strain diagrams correlate? Stress Diagrams Elastic Elasto-Plastic Plastic Strain Diagrams Consider a Concrete Beam: Stress Diagrams σ c σ c 0.85f c M n =A s f y (d-a/2) σ s f y f y Elastic Elasto-Plastic Plastic 26

27 How do the strain diagrams correlate? Stress Diagrams ε c ε c ε cu =0.003 ε s ε t > Elastic Elasto-Plastic Plastic Strain Diagrams ε t > Comparing Strain and Curvature N.A. d/2 Strain(ε) Curvature: φ= ε/(d/2) φ 27

28 Consider Load vs Curvature Diagram: Moment Curvature Chart M n Moment (k-ft) Curvature (1/in) Consider Load vs Curvature Diagram: Moment Curvature Chart Moment (k-ft) What if the beam is not ductile? e.g. an over-reinforced or under-reinforced concrete beam? e.g. a steel MF beam w/ lack of lateral bracing? Curvature (1/in) 28

29 Consider Load vs Curvature Diagram: Moment Curvature Chart Moment (k-ft) Some other unstable behavior may occur before stable hysteretic nonlinearity develops Curvature (1/in) 8. Nonlinear Element Modeling Lumped (Concentrated) Plasticity Distributed Plasticity (forced based fiber nonlinearity) 29

30 Nonlinear Building Modeling Lumped (Concentrated) Plasticity vs Distributed Plasticity (forced based fiber nonlinearity) + Nonlinear Static Analysis (Pushover) vs Nonlinear Dynamic Analysis Nonlinear Static vs. Nonlinear Dynamic? Base Force (kips) Nonlinear Static Pushover Curve Roof Displacement (inches) Key Differentiators: Geoseismic Input Time Complexity Project Needs $$ Software Beam Force (kip-in) Element Hysteretic Response Beam Rotation (rad) 30

31 Nonlinear Analysis Explicitly includes either lumped plasticity elements or distributed plasticity elements to predict a system s response to an input function. May use either piecewise static analysis (pushover) or a full response-history analysis. Lumped (Concentrated) Plasticity: F y 0.85f c M n =F y Z x M n =A s f y (d-a/2) f y These very familiar models represent the ultimate strength limit state of these beams. 31

32 Lumped Plasticity Example: Plastic flexural hinge will develop at the support W14x159 Lumped Plasticity Example Force 32

33 Nonlinear Pushover: Force Force Pattern Reaction Nonlinear Pushover: 33

34 Nonlinear Pushover: Nonlinear Pushover: The flat nonlinear region is simply a reflection of the flat hysteretic backbone of the input 34

35 Nonlinear Pushover: Why displacement vs. reaction and not moment vs. rotation or curvature? The flat nonlinear region is simply a reflection of the flat hysteretic backbone of the input Distributed Plasticity: Reinforcement Unconfined Concrete Confined Concrete Note: this column may require at least 7 layers of material to effectively model 35

36 Distributed Plasticity Example: Distributed Plasticity Example: 36

37 Distributed Plasticity Example: Distributed Plasticity Example Pushover: 37

38 Comparison: Distributed Plasticity Lumped Plasticity Strain Hardening? Distributed Lumped 38

39 Comparison 2 Min. 52 Sec Sec. Distributed Lumped Lumped Plasticity vs. Distributed? Key Differentiators: Time Complexity Project Needs $$ Accuracy Software 39

40 Nonlinear Dynamic Distributed Plasticity Nonlinear Pushover Can use either lumped (discrete) plasticity models, sometimes called links or hinges or the elements may be included with specific material nonlinearities with explicit modeling using nonlinear fiber or shell type elements. 40

41 Nonlinear Pushover Can, in more explicit terms than elastic analysis, identify and quantify specific mechanisms and the order in which they are expected to occur. Nonlinear Pushover Larger Application: 41

42 Nonlinear Static Analysis (Pushover) Roof Displacement Base Reaction Nonlinear Static Analysis (Pushover) 42

43 Nonlinear Static Analysis (Pushover) Nonlinear Static Analysis (Pushover) 43

44 Nonlinear Static Analysis (Pushover) Nonlinear Static Analysis (Pushover) 44

45 Nonlinear Static Analysis (Pushover) Knowing the order of hinge occurrence may or may not be important, but knowing that beam hinging is likely to dominate the nonlinear behavior is important Nonlinear Static Analysis (Pushover) Nonlinear Static Pushover Curve Base Force (kips) Roof Displacement (inches) 4 45

46 Nonlinear Static Analysis (Pushover) Nonlinear Static Pushover Curve Base Force (kips) Immediate Occupancy Damage Control Life Safety Roof Displacement (inches) Collapse Prevention Nonlinear Pushover Can help us understand the basis behind code provisions. Can help us understand the consequences of element failure (e.g. brace buckling). 46

47 Nonlinear Pushover Braced Frame Unbalanced Forces: AISC F1-4a, F2-3. In V and inverted V configurations, beams in braced frames must account for unbalanced effects of braces reaching full yield strength and post-buckled compression strength. Nonlinear Static Analysis (Pushover) Frame 1 Frame 2 Frame 3 Simple Frame Comparisons A case study in the consequences of buckling 47

48 Frame 1 Frame 1 48

49 Frame 1 Frame 1 49

50 Frame 1 Frame 1 50

51 Frame 2 Frame 2 51

52 Frame 2 Frame 2 52

53 Frame 2 Frame 3 53

54 Frame 3 Frame 3 54

55 Frame 3 Frame 3 55

56 Pushover Curves Superimposed Base Shear (kips) Frame 1 Frame 2 Frame Rooftop Displacement (inches) A Caveat While this example corroborates the requirements of AISC 341, research by Sen, Roeder, Lehman & Berman at University of Washington shows much better performance in braced frames when quasistaticallyloaded under a fully reversed increasing amplitude cyclical protocol See Structure Magazine July

57 Nonlinear Pushover Strong column/weak beam: AISC E3-4a Requires that the sum of nominal flexural strengths of columns at a joint must be greater than the sums of the flexural strengths of the beams (with over-strength included) at the same joint. Why? Beam mechanisms are preferred over column mechanisms. The Stability Issue P P θ 2 F 2 θ What happens if the geometric nonlinear stiffness matrix overpowers the initial matrix? -6P 24EI/L 3 6EI/L 2 6EI/L 2 1 /5L-6P 3 /5L -P 1 /10 -P 3 /10 6EI/L 2 8EI/L 2EI/L + -P 1 /10-2P 1 L/15-2P 2 L/15 -P 2 L/30 6EI/L 2 2EI/L 8EI/L -P 3 /10 -P 2 L/30-2P 2 L/15-2P 3 L/15 The effects of geometric nonlinearity can become greater than the effects of strain hardening. 57

58 Pushover Analysis: Roof Disp. 400 Base Shear vs. Displacement Base Shear Base Reaction Rooftop Displacement The Stability Issue What is happening here?: P P θ 2 F 2 θ Base Shear Rooftop Displacement Base Shear vs. Displacement W/O P-delta W/ P-delta Residual column forces create reduced stiffness which creates increased displacements which create even more residual column forces. Geometric nonlinearity controls over strain hardening This is a consequence of columns which yield in flexure before beams yield in flexure. 58

59 Problems with Beam/Column Strength Ratios Roof Disp. Base Shear Rooftop Displacement Base Reaction Base Shear vs. Displacement W/O P-delta W/ P-delta Nonlinear Pushover A more elaborate demonstration. Nonlinear Pushover can help us understand the effectiveness of a reinforcement scenario 59

60 North-South Pushover North-South Pushover 60

61 North-South Pushover North-South Pushover 61

62 North-South Pushover North-South Pushover 62

63 North-South Pushover Failure occurs at 38 inches rooftop displacement North-South Pushover Curve Pushover Curve Base Shear (kip) Approximated displacement for a quake can be calculated using classical methods, adjusted to account for altered stiffness (and other factors) Displacement (in) 63

64 Nonlinear Pushover Can help us understand alternate load paths that may develop as members are pushed to failure Nonlinear Pushover Consider a multi-tiered braced frame with pseudo-static lateral forces: 64

65 Nonlinear Pushover Member forces based strictly upon the input loads would be: Do these forces really reflect the design level earthquake? Nonlinear Pushover What are the consequences of braces buckling in compression? 65

66 Nonlinear Pushover A typical brace hysteretic backbone: Brace Hysteretic Backbone What happens in the frame as these axial mechanisms begin to form? Axial Force (kip) Axial Deformation (in) Nonlinear Pushover Axial Force (kip) Brace Hysteretic Backbone Axial Deformation (in) Concept courtesy of Brent Maxfield, SE 66

67 Nonlinear Pushover A pseudo nonlinear approach? Nonlinear Pushover Can help us demonstrate the validity of a new approach 67

68 Bennett Federal Building Salt Lake City 68

69 Buckling Restrained Brace Concept Images Courtesy of Corebrace Buckling Restrained Brace Concept Unbonded Brace Hysterisis Backbone Special Concentric Brace Hysterisis Backbone Fmax=68.8 ksi 60 Fye=51.7 ksi Fmax=62.8 ksi 60 Fye=55 ksi Stress (ksi) TENSION COMPRESSION -40 Fye=-51.7 ksi -60 Stress (ksi) TENSION 27.5 ksi ksi -20 COMPRESSION ksi Fmax=-65.2 ksi Strain (%) Strain (%) tension Intermediate typical buckling brace displacement Local buckling less critical than inelastic buckling unbonded brace compression Axial force-displacement behavior 69

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74 Nonlinear Pushover Bennett Federal Building N-S Push-over V vs Roof Displacement Base Shear - kips BRBF Braces Begin to Yield SCBF Braces Begin to Buckle SCBF Roof Displacement - Inches BRBF 74

75 Nonlinear Pushover Can help us understand what happens with combinations of systems in a more explicit manner Horizontal Combinations In the same direction, along the same line - Shear Wall and Moment frame: 100k w18x60 strut w14x120 w14x thick wall f c =4,000psi I= 0.35I g 0.98k 0.98k 98.04k w18x

76 Horizontal Combinations In the same direction, along the same line - Shear Wall and Heavy Moment frame: 100k w30x261 strut w24x370 w24x thick wall f c =4,000psi I= 0.35I g 7.69k 7.69k 84.62k Horizontal Combinations This demonstrates one immutable truth: Loads follow the path of most resistance Unless a stiffness compatibility exists, logic may predicate that the less rigid system be abandoned entirely. 76

77 Horizontal Combinations What happens if the stiffness of the load path changes as a result of loading (or deforming)? Dual System? Horizontal Combinations What does nonlinear pushover predict for this scenario? Let s use ρ = ρ min (0.0015) for vertical reinforcement Let s use lumped plasticity models 77

78 Horizontal Combinations Lumped Plasticity Approach: Horizontal Combinations 78

79 Horizontal Combinations Horizontal Combinations 79

80 Horizontal Combinations Horizontal Combinations 80

81 Horizontal Combinations Horizontal Combinations 81

82 Horizontal Combinations Horizontal Combinations 600 Pushover Curve 500 Base Shear (kip) Displacement (in) 82

83 Horizontal Combinations Nonlinear pushover demonstrates that the concrete wall does virtually all of the work and must literally become compromised before the steel frame begins to act. Unless a stiffness compatibility exists, logic may predicate that the less rigid system be abandoned entirely. Horizontal Combinations Another Approach? Use of distributed plasticity elements in lieu of lumped plasticity Account for nonlinearity of materials instead of nonlinearity of sections 83

84 Horizontal Combinations 12 thick wall with ρ vert = concrete reinforcement Horizontal Combinations Stress in Reinforcement Stress in Concrete 84

85 Horizontal Combinations Stress in Reinforcement Stress in Concrete Horizontal Combinations Stress in Reinforcement Stress in Concrete 85

86 Horizontal Combinations Stress in Reinforcement Stress in Concrete Horizontal Combinations Stress in Reinforcement Stress in Concrete 86

87 Horizontal Combinations Pushover Curves Base Shear (kip) Displacement (in) Nonlinear Pushover Can help us demonstrate that a system or geometry can work. Large scale example Combination of Systems 87

88 Nonlinear Pushover Seismic Retrofit Nonlinear Pushover Seismic Retrofit 88

89 Case Study College of Nursing Case Study College of Nursing 89

90 Case Study College of Nursing Nonlinear Pushover Seismic Retrofit Pushover demonstrated that the existing core walls could satisfy performance objectives while working in concert with new braced frames. 90

91 10. Nonlinear Pushover Analysis Limitations Does not directly account for cyclic behavior. Does not adequately capture higher mode effect. Does not have an explicit accounting for displacement. Does not account for highly transient effects (near field, unidirectional pulse). No accounting for cumulative ductility or cumulative 1 1 energy Acceleration (g) Acceleration (g) Time (sec) Time (sec) 10. Nonlinear Time History Quick Summary 91

92 Nonlinear Dynamic Analysis - MF Nonlinear Dynamic Analysis - MF Area within the enclosed force vs. displacement loop is energy dissipated Beam Force (kip-in) Beam Rotation (rad) 92

93 Nonlinear Dynamic Analysis BF/BRBF Red = Yielding and/or Buckling Keeping it Simple? Successful & efficient nonlinear modeling requires a targeted approach. 93

94 So, why not use Nonlinear Time History? Time $$ Ground Motions Owner Objectives Computing Power Review Software Hand 1.0 (by Ron Hamburger) SAP 2000 Ultimate ETABS Ultimate Perform 3D STAAD Pro Opensees(Open System for Earthquake Engineering Simulation, NEES) ANSYS LS Dyna ANSR (proprietary) RISA? 94

95 The End 95