4b. Nonlinear Structural Analysis for Seismic Design_Spring 2018

CEE 243B – 243B – RESPONSE AND DESIGN OF RC STRUCTURAL SYSTEMS

4b. Nonlinear Structural Analysis Analysis for Seismic Design Lumped Plasticity models ➢

➢

Main Ma in Feat Featur ures es - Adva Advant ntag ages es – – Limit Limitati ations ons (Lectu (Lecture re 4a)

Implementation Implementa tion in PERFORM-3D

➢ Applications

of lumped lumped plasticity models for RC components NIST GCR 10-917-5

CEE 243B - Spring Spring 2018

Nonlinear Structural Analysis for Seismic Design Model Types Idealized structural component models

PEER ATC 72-1

Continuum (Finite Element) Model: Nonl Nonlin inea earr elem elemen ents ts expl explic icit itly ly mode modell the the unde underl rlyi ying ng phys physic icss of the the mate materi rial al respo espons nse, e, and and do not not enfo enforc rce e any any pred predef efin ined ed comp compon onen entt beha behavi vior oral al mode modes. s. Lumped Lumped Plast Plastici icity ty (Conce (Concentr ntrat ated ed Hinge Hinge)) Model Model:: Nonlinear elements represent nonlinear behavior vior in a phen pheno omen menolog ologic ical al way, with ith inelas elasti ticc deform ormation tion rul rules that that are are asso assocciat iated with with forc force-d e-def efor ormat mation ion behavi behavior or and hyst hyster ereti eticc respo response nse of comp compone onents nts obser observed ved in test tests. s.

Nonlinear Structural Analysis for Seismic Design Model Types Macro-scale phenomenological models (concentr (concentrated ated plasticity models) … simplified representation of overall force -deformation component response … based on observed behavior / test data Advan Advantag tages es : ➢ conceptually simple, easily parameterized ➢ easily calibrated to test data ➢ unia uniaxi xial al phen phenom omen enol olog ogic ical al hyst ystere eretic tic hing hinge e mode models ls have have been been a mainstay approach in seismic response analysis for many years, and have been developed to the point of capt captur urin ing g cycl cyclic ic str strengt ength h and and stif stiffn fnes esss degr degrad adat atio ion n fair fairly ly well well ➢ less computationally demanding than fiber and finite finite element models, relatively relatively robust. Limitations: ➢ Although such models are able to capture nonlinear cyclic degradation well, it is difficult response . to extend their rule-based formulations to multi-axial response. ➢ P-My-Mz and P-M-V interaction with cyclic degradation difficult to capture. ➢ Limitations associated with ASCE 41 force-displacement relationships commonly used in definition of concentrated hinge models.

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Nonlinear Structural Analysis for Seismic Design Model Types

Lumped Plasticity models ➢ Ma Main in Featu eature ress

- Adva Advant ntag ages es – – Limi Limita tati tion onss (Lec (Lectu ture re 4a) 4a)

➢

Implementation Implement ation in PERFORM-3D

➢

Appl Applic icat atio ions ns of lump lumped ed plas plasti tici city ty mode models ls for RC compo ompone nen nts

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship Almost all of PERFORM’s nonlinear components use the same F-Δ relationship:

"backbone YULRX curve”

The intent of the PERFORM actiondeformation relationship, with points Y, U, L and R, is to capture the main aspects of the behavior, namely the initial stiffness, strain hardening, ultimate strength and strength loss, as shown in the figure. The main intent of the PERFORM hysteresis loop is to capture the dissipated energy (the area of the loop). This area is affected by stiffness degradation under cyclic loading.

“Cyclic degradation” in PERFORM is essentially energy (stiffness) degradation.. If cyclic degradation is included, PERFORM adjusts the unloading and reloading stiffness to reduce the area under the loop.. 5

Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship Modeling Phase

Components

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship Modeling Phase

Components

Note: K0 (initial stiffness) not defined with the hinge properties

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: Rigid-plastic rotation hinge concept The hinge is initially rigid, and begins to rotate at the yield moment. Rotations DU, DL, DR are plastic rotations. From “Perform -3D Components and Elements Manual” Computers and Structures, Inc.

Compound Component

The stiffness of the elastic beam segment defines the initial stiffness of the compound frame component. Total deformation = elastic + plastic deformations

K0

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship Non-degrading Loop for E-P-P Behavior

Non-Degrading Loop for Tri-linear Behavior

1

1

Degraded Loop for E-P-P Behavior

Degraded Loop for Tri-linear Behavior

From “Perform -3D Components and Elements M anual”

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship

The area of the loop is affected by stiffness degradation under cyclic loading. “Cyclic degradation” in PERFORM is essentially energy (stiffness) degradation.. If cyclic degradation is included (i.e., if the component properties include energy degradation factors), PERFORM adjusts the unloading and reloading stiffness to reduce the area under the loop.. The method is simple for EPP case, and rather more complicated for the tri-linear case.

Degraded Loop for E-P-P Behavior

Need to define energy factors in the cyclic “degradation tab”.. The energy factors control how much smaller the area of the degraded loop is..

Degraded Loop for Tri-linear Behavior 10

Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: General action-deformation (F- Δ) relationship Defining cyclic degradation parameters

Could

Area of degraded hysteresis loop divided by the area of the non-degraded loop

de different for different deformations (Y, U, L, R, X) Could be different for pos. / neg. deformations 11


Non-Degrading Loop after Strength Loss

1

Strength loss in one direction does not affect strength in the other direction Strength loss in one direction causes strength loss in the other direction 12




In Summary, when defining a moment-rotation hinge in PERFORM, we have control over:

-General shape of backbone curve: E-P-P or tri-linear. -Strength loss: Include or not include; if included strength loss in one direction may or may not affect strength in opposite direction (strength loss interaction). -Shape/area of hysteresis loops: energy factors can be defined in the “cyclic degradation” tab to control area of the degraded loop with respect to area of non-degraded loop. 13


Lumped Plasticity models ➢ Main Features ➢

- Advantages – Limitations (Lecture 4a)

Implementation in PERFORM-3D

➢ Applications

of lumped plasticity models for RC components

- RC beams in moment frames (HW2 …) - RC coupling beams - RC columns - RC Slab-wall and Slab-column connections

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Nonlinear Structural Analysis for Seismic Design Model Types HW2: Defining modeling parameters for RC beam in PERFORM-3D Elevation

Cross-Section at End Span b =24” ” 1

8#10

h =28” hslab = 12” 6#10

Longitudinal reinforcement: 8#10 top bars 6#10 bottom bars Clear cover (to ties)= 1.5” Clear distance between layers = 1.0” Transverse reinforcement: 6#4@6”

Show steps that you would use to model the RC beam in PERFORM-3D. Include (i) screenshots from PERFORM-3D with all appropriate input values , and (ii) calculations to justify ALL input values. ASCE 41

PERFORM-3D

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Nonlinear Structural Analysis for Seismic Design ASCE/SEI 41 Generalized Force-Deformation Curves

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Lumped Plasticity models ➢ Main Features ➢

- Advantages – Limitations (Lecture 4a)

Implementation in PERFORM-3D

➢ Applications

of lumped plasticity models for RC components

- RC beams in moment frames (HW2…) - RC coupling beams - RC columns - RC Slab-wall and Slab-column connections

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Nonlinear Structural Analysis for Seismic Design Model Types PERFORM-3D: Plastic hinge models Application in nonlinear modeling of RC coupling beams

Elevation A-A

Plan (gravity columns not shown)

Conventionally Reinforced RC Coupling Beams

Diagonally Reinforced

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Design of Coupling Beams (ACI 318-14)

Coupling Beam

Coupling Beams

- In many cases, geometric limits result in coupling beams that are deep in relation to their clear span. - Deep coupling beams may be controlled by shear and may be susceptible to strength and stiffness deterioration under earthquake loading. -Test results have shown that confined diagonal reinforcement provides adequate resistance in deep coupling beams. (ACI 318-14)

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Design of Coupling Beams (ACI 318-14) •

S18.10.7.1: Coupling beams with (ln /h) frames)

•



4 shall satisfy S18.6 (Beams of special moment

S18.10.7.2: ' 4 V   f Coupling beams with (ln /h) < 2 and with u c Acw shall be reinforced with two intersecting groups of diagonally placed bars symmetrical about the midspan.

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S18.10.7.3: Coupling beams not governed by S18.10.7.1 or S18.10.7.2 shall be permitted to be reinforced either with two intersecting groups of diagonally placed bars symmetrical about the midspan or according to S18.6.3 through S18.6.5.

Experiments show that diagonally oriented reinforcement is effective only if the bars are placed with a large inclination. Therefore, diagonally reinforced coupling beams are restricted to beams having aspect ratio ln/h < 4. 20


•

Coupling beams with diagonally oriented reinforcement (S18.10.7.4) :

Confinement option 1 Each group of diagonal bars enclosed by rectilinear transverse reinforcement

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•

Coupling beams with diagonally oriented reinforcement (S18.10.7.4) :

Confinement option 2 Transverse reinforcement provided for the entire beam cross section

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•

Coupling beams with diagonally oriented reinforcement (S18.10.7.4) : Nominal shear capacity of coupling beam:

where = angle between the diagonal bars and the longitudinal axis of the coupling beam

Avd = total area of reinforcement in each group of diagonal bars Acw = area of concrete section of the coupling beam

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Test Setup 12 8

] % 4 [ n o 0 i t a t o R -4 -8 -12

Naish & Wallace

Loading Protocol 2 or 3 cycles at each rotation ( /l = θ ) 24

Research on RC Coupling Beams at UCLA (Naish & Wallace) CB24F - Rotation = 0.04

CB24F - Rotation = 0.04

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Rotation = 0.06

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Rotation = 0.08

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Rotation = 0.10

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Research on RC Coupling Beams at UCLA (Naish & Wallace) CB24D - Rotation = 0.04

Rotation = 0.04

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Rotation = 0.06

30


Rotation = 0.08

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Rotation = 0.10

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s t l u s e r t s e T

Naish & Wallace 1.6

PT Slab RC Slab No Slab ASCE 41-06

1.4 1.2

f . o t x n e o / i r t a u e b i h r s t , n p i o l C s , e e v r i t u a x l e e l f R

e d o c

1

n 0.8 V / V 0.6

½-scale (test)

0.4

Full scale

0.2 0 0

2

4

6

8

10

12

14

Beam Chord Rotation [%]

Cyclic envelope curves

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Naish & Wallace

Test PERFORM

Moment Hinge Model in PERFORM-3D - Elastic concrete beam cross-section (with EIeff ) - Concentrated plastic Mn-θ hinges (with cyclic degradation parameters)

Test PERFORM

Shear Hinge Model in PERFORM-3D - Elastic concrete beam cross-section (with EIeff ) - Concentrated plastic Vn-δ hinges (with cyclic degradation parameters) 34


Moment Hinge Model in PERFORM-3D - Elastic beam concrete cross-section (with EIeff ) - Concentrated plastic Mn-θ hinges (with cyclic degradation parameters) 35

Nonlinear Structural Analysis for Seismic Design Model Types Modeling of coupling beams using moment hinges in PERFORM-3D:

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Vn-δ hinge

Shear Hinge Model in PERFORM-3D - Elastic beam concrete cross-section (with EIeff ) - Concentrated plastic Vn-δ hinges (with cyclic degradation parameters) 37

Nonlinear Structural Analysis for Seismic Design Model Types Modeling of coupling beams using shear hinges in PERFORM-3D:

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Nonlinear Structural Analysis for Seismic Design Model Types Connecting a Beam Element to a Shear Wall Element in PERFORM-3D:

Coupling Beam

Wall Element

Horizontal Imbedded beam

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•

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Slender RC coupling beams can be modeled using beam elements with moment or shear hinges and horizontal imbedded beams. The coupling beam element must be connected to the walls by “imbedded” beam elements since shear wall elements have no in-plane rotational stiffness. If this is not done, the coupling beam will be effectively pin-connected to the wall. The imbedded beams must be stiff in bending, but should have very small axial and 41 torsional stiffness

4b. Nonlinear Structural Analysis for Seismic Design_Spring 2018

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