structural analysis and design -...

Seminar on

Earthquake Resilient Design for School Buildings

Naveed Anwar, PhD

Post-earthquake School Reconstruction Project

Structural Analysis and DesignDay-2Session 1

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Structural Design Process

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Analysis and design

Phase I:

Structural System Development

• Review architectural drawings provided and other related documents as necessary.

• Develop structural concepts and the structural system with an objective to achieve good performance and cost effectiveness.

Phase II:

Detailed Structural Design

• Develop design criteria to be used for the structural design of the building.

• Create finite element models of the structure with varying complexities and refinements as suitable to understand the response.

• Carry out an analysis and design of the structure, progressively using linear -static, linear-dynamic, and other relevant techniques.

• Carry out detailed design and prepare structural design drawings.

Basis for Analysis

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The Structural System

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Dynamic Equibillirium

FFKuuCuM NL

Damping-Velocity

Mass-Acceleration Stiffness-Displacement

Nonlinearity

External Force

KuuCuM

The basic variable is displacement and its derivatives

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Nonlinearity

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Non Linear Equilibrium

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Stiffness and Nonlinearity

Section Stiffness

Member Stiffness

Structure Stiffness

Material Stiffness

Cross-section Geometry

Member Geometry

Structure GeometryLinear

Non-Linear

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Seismic Analysis from Dynamic Equilibrium

FFKuuCuM NL

Linear Time History Analysis

0KuuM

EQNL FFKu

Free Vibration

Pushover

Analysis

EQFKu Equivalent

Static Analysis

EQFKu

Response Spectrums

Response Spectrum

Analysis

Acceleration RecordsguMKuuCuM

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Free Vibration – Modal Analysis

Idealized SDOF system

Un-damped free vibrations of SDOF system Damped vibrations of SDOF system

0KuuM

No external loadsNo damping

Just mass and stiffness!

Significance of Modal Analysis

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• A mode shape is a set of relative (not absolute) nodal displacement for a particular mode of free vibration for a specific natural frequency

• There are as many modes as there are DOF in the system

• Not all of the modes are significant

• Local modes may disrupt the modal mass participation

Mode Shapes

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The Modal Analysis

• The modal analysis determines the inherent natural frequencies of vibration

• Each natural frequency is related to a time period and a mode shape

• Period is the time it takes to complete one cycle of vibration

• The Mode Shape is normalized deformation pattern

• The number of Modes is typically equal to the number of Degrees of Freedom

• The Time Period and Mode Shapes are inherent properties of the structure and donot depend on the applied loads

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• The Modal Analysis should be run before applying loads any other analysis to check the model and to understand the response of the structure.

• Modal analysis is precursor to most types of analysis including Response Spectrum, Time History, Push-over analysis, etc.

• Modal analysis is a useful tool even if full Dynamic Analysis is not performed.

• Modal analysis is easy to run and is fun to watch when animated.

The Modal Analysis

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• The Period and Mode Shapes, together with animation immediately exhibit the strengths and weaknesses of the structure.

• Modal analysis can be used to check the accuracy of the structural model• The Time Period should be within reasonable range,

• (Ex: 0.1 x number of stories seconds)

• The disconnected members are identified

• Local modes are identified that may need suppression

Application of Modal Analysis

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• Symmetry of the structure can be determined• For doubly symmetrical buildings, generally the first two modes are

translational and the third mode is rotational

• If the first mode is rotational, the structural is un-symmetrical

• The resonance with the applied loads or excitation can be avoided• The natural frequency of the structure should not be close to excitation

frequency

Application of Modal Analysis

Analysis Procedures and Aplication

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Analysis Procedures

• Code based, Static Equivalent (manual)

• Linear Static Procedure (LSP)

• Linear Response Spectrum Analysis (RS)

• Linear Time History Analysis (LTHA)

• Nonlinear Static Procedure (NSP)

• Nonlinear Time History Analysis (NLTHA)

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Linear Static Procedure (LSP)

• Captures First Mode response only

• Pseudo lateral force procedure will be used.

• Accidental torsion may be considered with 5% eccentricity.

• Concurrent multidirectional seismic effects can be considered, by combining the forces and deformations associated with 100% of the design forces in X-direction and the forces and deformations associated with 30% of the design forces in Y-direction and vice versa.

20Linear Static Procedure (LSP)

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• Captures “Spectrum” of several Modes

• Use linearly elastic response spectrum.• At least 90% of the participating mass can be considered.• Complete Quadratic Combination (CQC) rule can be used for combination

of responses from each mode. • Square Root of Sum of Squares (SRSS) rule can be used for combination of

multi-directional seismic effects.• 5% constant modal damping is recommended to be considered in the

analysis.• All forces and deformations can be modified by multiplying C1 and C2

coefficients.• Concurrent multidirectional seismic effects can be considered.

Response Spectrum Analysis (RS)

22Response Spectrum Analysis (RS)

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• Captures all modes and step by step response history

• Use pairs of ground motion records, applied simultaneously along each principal direction of the building.

• If fewer than seven analyses, maximum response can be used for design.

• If seven or more are performed the average value of response can be used.

• Gravity loads from the previous analysis case are not included in the linear time history analysis case.

• Gravity loads can be combined with linear time history analysis results in the load combinations separately.

• 5% damping is recommended to be used in mass and stiffness proportional damping (Specify damping by period).

• P-∆ effects can be considered in both gravity and earthquake load cases. • All forces and deformations calculated from linear time history analysis can be

modified by multiplying C1 and C2 coefficients.

Linear Time History Analysis (LTHA)

24Linear Time History Analysis (LTHA)

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• Selected ground motion records should have magnitude, fault distances, and source mechanisms that are consistent with those that control the design earthquake ground motions.

• The sets of ground motion records can be scaled such that the average value of the SRSS spectra does not fall below 1.3 times the 5%-damped spectrum for the design earthquake for periods between 0.2 T and 1.5 T.

• The PEER Ground Motion Database (PGMD) web-based tool (PEER, 2011) may be used for linear scaling and selecting ground motions

• Scaling factor for each ground motion should not be greater than 8.

Selection of Ground Motions

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• Monotonically increasing lateral loading is applied on the building to represent the inertia forces generated by the earthquake.

• The lateral load pattern may be selected based on the fundamental mode shape of the building or lateral load specified in the standards and guidelines.

• The applied lateral load is increased until the target displacement of the control node, δt is exceeded, which represents the maximum displacement likely to be experienced during the earthquake.

• The performance of the building is checked at that probable maximum displacement of the building under earthquakes.

Nonlinear Static Procedure (NSP)

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• Target displacement is calculated by Coefficient Method.

• The relation between base shear and lateral displacement of the control node can be established for control node displacements ranging between zero and 150% of the target displacement.

• If the diaphragms are flexible, the target displacement can be amplified by the ratio of maximum displacement at any point on the roof to the displacement at the center of mass of the roof (δmax/ δ cm).

• δ max and δ cm can be based on a response spectrum analysis of a three-dimensional model of the building.


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• P-∆ effects can be considered in both gravity and lateral load cases.

• No line of vertical seismic framing can be evaluated for displacements small than the target displacement.

• Forces and deformations corresponding to the control node displacement equaling or exceeding the target displacement can be checked against the acceptance criteria.


29Nonlinear Static Procedure (NSP)

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Nonlinear Time History Analysis (NLTHA)

• Same procedure as LTHA, except nonlinear response is considered.

• Superposition of gravity loads and seismic loads will not be performed.

• NLTHA continues from end of gravity load case, considering both stiffness and loads from previous case.

• Direct integration technique can be used.

31Nonlinear Time History Analysis (NLTHA)

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Suggested Selection of Analysis Procedures

Building Type

Target

Performance

Levels

Analysis Procedures

10%/50

years

2%/50

yearsLSP RS LTHA NSP NLTHA

URM (≤ 3 stories) LS CP M P A N N

URM (> 3 stories) LS CP N M A P S

RC Building LS CP N M A P S

N = Need not be usedM = Minimum level to be usedP = Preferred level to be usedA = Alternative analysis if practical, for comparison and verificationS = Special analysis if possible

Finite Element Modeling

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• Building can be modeled, analyzed, and evaluated as a three-dimensional assembly of the components.

• Appropriate software having the required capability (such as SAP2000 or equivalent) can be used as analysis tool.

• Linear Analysis Procedures• Linear modeling, assuming force-deformation relationship is linear.

• Nonlinear Analysis Procedures• Deformation-controlled actions can be modeled as nonlinear while force-

controlled actions can be modeled as linear.

Finite Element Modeling

Linear Model

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Component Modeling

Component Element Type Stiffness ModifierModifiers in

SAP2000

Reinforced Concrete Building

Girders

Columns

Secondary beams

Slabs and diaphragms

Foundations

Masonry infill walls (Strut)

Shear walls

Buckling restrained braces

Frame

Frame

Frame

Thin shell

Thick or Thin shell

Frame

Shell

Multi-linear plastic link

0.35 Ig

0.7 Ig

1.0 Ig

1.0 Ig

1.0 Ig

1.0 Ig

0.5 Ig

1.0 Ig

I33 = 0.35

I33 = 0.7, I22 = 0.7

No modifier

No modifier

No modifier

No modifier

f22 = 0.5

No modifier

Unreinforced Masonry Building

Unreinforced masonry walls

Jacketed masonry walls

Slabs and diaphragms

Foundations

Thin shell

Layered shell

Thin shell

Thick or Thin shell

See Section 3.2.6

See Section 3.2.7

1.0 Ig

1.0 Ig

See Section 3.2.6

See Section 3.2.7

No modifier

No modifier

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Girders , Secondary Beams and Columns

• Frame elements can be used.

• Rectangular beam sections are applicable in association with the slabs modeled as shell elements.

• Insertion points and end offsets can be applied to account for the finite size of beam and column intersections, if required.

• The end offsets may be made partially or fully rigid based on engineering judgment to model the stiffening effect that can occur when the ends of an element are embedded in beam and column intersections.

• End releases can be applied to model different fixity conditions at the ends of the element in accordance with the type of detailing.

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Slabs and Diaphragms

• Shell elements can be used in modeling of slabs which includes the membrane and plate bending behavior.

• Rigid diaphragm assumption should not be applied concrete slabs, especially in the buildings with plan irregularity.

• Actual in-plane stiffness of the diaphragm can be considered in the lateral load analysis.

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Foundations

• Shell elements can be used in modeling of foundation.

• Effect of soil structure interaction can be considered for the buildings in which an increase in fundamental period due to soil effects will result in an increase in spectral accelerations.

• Vertical springs and lateral springs are assigned respectively in order to consider the interaction effect of soil.

• The spring stiffness values can be calculated based on the sub-grade modulus values from geotechnical report if available.

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Masonry Infill Walls

• Frame elements can be used in modeling of struts to represent the infill walls.

• Equivalent frame section can be calculated in accordance with ASCE 41-06: Section 7.4.2.1.

• Both moment in local axis 2 and 3 directions can be released in the strut.

Compression Strut Analogy (Ref: FEMA 356)

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• Shell elements can be used.

• The wall elements can be meshed horizontally and vertically in adequate numbers.

• The orientation of local axis of the shear wall elements can be consistent in entire wall.

• In-plane stiffness of unreinforced masonry walls can be considered as uncracked section.

• The out-of-plane stiffness of jacketed masonry walls can be neglected in analytical model of the global structural system.

• URM may be checked to resist out-of-plane inertial forces as isolated components spanning between floor levels, and/or spanning horizontally between columns and pilasters.

Unreinforced Masonry Walls

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• Thin shell elements can be used.

• The elements can be meshed horizontally and vertically in adequate numbers.

• The orientation of local axis of the shear wall elements can be consistent in entire wall.

Reinforced Concrete Shear Walls

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• Multi-linear plastic link element may be used in modeling of buckling restrained braces.

• Effective axial stiffness of BRB for linear analysis is calculated based on the length, modulus of elasticity and steel area of yielding core (AE/L).

• Only stiffness of U1 direction is considered in the link element.

Buckling Restrained Braces (BRB)

Nonlinear Model

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• Nonlinear flexural hinges are assigned at the ends of primary girders to represent the nonlinear flexural response while shear response is modeled as linear.

• Auto-hinge assignment can be used to model the flexural hinge based on the provided longitudinal reinforcement ("Reinforcement Overrides for Ductile Beams" in Frame Section Definition).

• The secondary beams are modeled as linear.

Girders and Secondary Beams

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• Fiber P-M2-M3 hinges are recommended to model the nonlinear behavior of coupled axial force and bi-axial bending.

• Fiber hinges can be assigned both ends of the column.

• It is recommended to use User-defined fiber hinges, by generating the fiber layout from Section Designer. Rebar fibers should be lumped while generating the fiber layout to reduce the analysis time.

Columns

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Columns

Lp = 0.08 L + 0.022 fyedbl ≥ 0.044 fyedbl (MPa)where

Lp = plastic hinge length

H = section depth

L = critical distance from the critical section of plastic hinge to the point of contraflexure

fye = expected yield strength of longitudinal reinforcement

dbl = diameter of longitudinal reinforcement

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• Multi-linear plastic link element can be used in nonlinear modeling of buckling restrained braces.

• Force-deformation relationship of BRB is calculated based on the material of yielding core.

• Kinematic hysteresis type can be used for hysteresis behavior.

Buckling Restrained Braces (BRB)

Acceptance Criteria

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Classification of Actions

ComponentDeformation-Controlled Force-Controlled

Action NL Response Action

RC girders Moment Hinge rotation ShearRC columns PMM Hinge rotation Axial compression

Shear

Secondary beams

- - Moment

Shear

RC slabs - - Out-of plane moment

Shear

RC diaphragms - - In-plane moment

Shear

Foundation - - Moment

Shear

Masonry infill walls

In-plane shear In-plane rotation (Drift)

Column shear adjacent to infill panels

Beam shear adjacent to infill panels

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Classification of Actions

ComponentDeformation-Controlled Force-Controlled

Action NL Response Action

Unreinforced masonry walls

In-plane shear

(if expected lateral rocking strength < lower bound lateral strength or shear strength based on toe compressive stress)

Rocking Axial compression

In-plane shear

(if expected lateral rocking strength < lower bound lateral strength or shear strength based on toe compressive stress)

RC shear walls Flexure Rotation

Axial strain

Axial compression

Shear

Buckling restrained braces

Axial Plastic deformation

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• Expected Strength• Evaluation of behavior of deformation-controlled actions• Expected material properties can be used to calculate the design strengths in

accordance with the code based procedures, except strength reduction factor, Φ can be taken equal to unity.

• Expected material properties may be calculated by multiplying lower-bound values by appropriate factors.

• Lower-bound Strength• Evaluation of behavior of force-controlled actions• Lower-bound material properties can be used to calculate the design

strengths in accordance with the code based procedures, except strength reduction factor, Φ can be taken equal to unity.

• Nominal material properties specified in construction documents may be used.

Component Strength

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Factors to Translate Lower-Bound Material Properties to Expected Strength Material Properties

Material Property Factor

Concrete compressive strength (f'c) 1.3

Reinforcing steel tensile and yield strength (fy) 1.25

Masonry compressive strength (fme) 1.3

Masonry flexural tensile strength 1.3

Masonry shear strength 1.3

Note: Factor of 1.3 is used for concrete compressive strength in lieu of factor of 1.5, mentioned in Table 6-4, ASCE 41-06.

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Design Code for Component Strength

Component Design Code

Masonry ACI 530

Reinforced concrete ACI 318, IS456

Structural steel AISC 360, IS 800

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Global Response

TypeSeismic Level

10%/50 years 2%/50 years

Reinforced Concrete Frame

Story drift (Permanent)

Story drift (Transient)

2%

1%

2%

1%

Unreinforced Masonry Building

Story drift (Permanent)

Story drift (Transient)

0.6%

0.6%

1%

1%

Foundation

Total settlement

Differential settlement in 30 ft

Sliding

Overturning

6 in.

0.5 in.

FS ≥ 1.5

FS ≥ 1.5

Major settlement

and tilting

FS ≥ 1.5

FS ≥ 1.5

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• Component response is checked based on the analysis procedures.

• Linear Analysis Procedures• ASCE 41-06: Section 3.4.2

• Nonlinear Analysis Procedures • ASCE 41-06 Section 3.4.3

Component Response

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Component Response from Linear Procedures

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Component Response from Nonlinear Procedures

• Deformation-Controlled Actions• The response of the components under deformation-controlled actions can

be checked in accordance with the acceptance criteria for nonlinear procedures mentioned through Chapters 4 through 8 of ASCE 41-06.

• Force-Controlled Actions• The response of the components under force-controlled actions can be

checked using the lower-bound strengths which can not be less than maximum design forces or maximum design forces developed as limited by the nonlinear response of the component.

Member Design Approach

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From Serviceability to Performance

Allowable material, control on deformation limits for design loads

Material failure criteria, section capacity for factored loads

Ductility considerations, deformation capacity, load capacity at large deformations. Extraordinary load considerations

Serviceability Design

Strength Design

Performance Design

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From Serviceability to Performance

• Satisfying one design level does not ensure that other design levels will be satisfied

– Serviceability design only ensures that deflections and vibrations, etc., for service loads are within limits but is irrelevant to strength.

– Strength design ensures that a certain factor of safety against overload is available within a member or a cross-section but is insignificant to what happens if the load exceeds the design level.

– Performance design ensures that the structure as a whole reaches a specified demand level. Performance design can include both service and strength design levels.

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Limit State Design Concept

Types of Limit State Description

Ultimate limit states -Loss of equilibrium -Rupture -Progressive collapse -Formation of plastic mechanism -Instability -Fatigue

Serviceability limit states -Excessive deflections -Excessive crack width -Undesirable vibration

Special limit states Due to abnormal conditions and abnormal loading such as: -Damage or collapse in extreme earthquakes -Structural effects of fire, explosion -Corrosion or deterioration

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• Limit state design involves:

– Identification of all potential modes of failure

(i.e. identify significant limit states)

– Determination of acceptable levels of safety against occurred each limit state

– Consideration by the designer of significant limit states

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Structural Design Considerations

Story Drift for Occupant Perception

Stability and Overturning

Axial Shortening of Columns

Transfer Girders and Deep Beams

Shear Wall Design and Detailing

Construction Sequence Analysis

Design for Lateral Loads

Seismic Performance

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