asce 41‐13 hands‐on approach analysis provisions part 02-asce_41_analysis... · asce 41‐13...

ASCE 41‐13 Hands‐On Approach Analysis Provisions

SEAU 5th Annual Education Conference 1

ASCE 41-13 Analysis ProvisionsRobert Pekelnicky, PE, SE

Principal, Degenkolb EngineersChair, ASCE 41 Committee*

*The view expressed represent those of the author, not the standard’s committee as a whole.

Identify the primary and secondary components

Displacement-based analysis provisions

Capacity-based design philosophy

Tie the building together

Three tiers of evaluation and retrofit

ASCE 41-13 Analysis Procedures

2

(not just the tables and equations)

Read the Standard!



Which elements are primary and which are secondary?

Primary & Secondary Elements

Main lateral force resisting system elements

Must be included in the analysis

Can be new or existing elements

Expected to sustain inelastic deformations (if possible)

Primary Components

Support gravity loads

Do not contribute significantly to the lateral strength and/or stiffness

Typically existing elements

Can yield provided gravity load support not lost

Can be left out of main linear analytical model

Must accommodate structures deformations – commonly using a separate model

Must be included in a nonlinear model

Secondary Components



“If the total initial lateral stiffness of secondary components in a building exceeds 25% of the total initial lateral stiffness of primary components, some secondary components shall be reclassified as primary to reduce the total stiffness of secondary components to less than 25% of the primary components.”

When is an element a primary or a secondary element?

Primary or Secondary

7-Story Concrete Building

Perimeter concrete moment frame

Flat-slab interior gravity framing

Primary or Secondary

Slab-column gravity systems resist 54% of longitudinal and 72% of transverse base shear!

Thus, slab-column frames must be considered primary elements.



Primary or Secondary – Concrete Buildings

Shear walls and associated collectors are primary elements.

Moment frames are typically primary elements.

Gravity moment frames and slab-column frames may be primary or secondary.

Primary or Secondary – Steel Buildings

Braced frames and moment frames, along with associated collectors, are primary elements.

Beam-column gravity framing is secondary.

Primary or Secondary – Wood Buildings

Plywood sheathed walls are primary elements.

Other sheathing material may or may not be primary.



Shall be considered structural elements if their stiffness exceeds 10% of the total stiffness of the primary system at that story

Precast concrete cladding in steel or concrete moment frame buildings is a common example

Nonstructural as Structural

Pseudo-lateral force displaces structure to an approximation of the maximum displacement envelope.

Displacement-Based Design

F5

F4

F3

F2

F1

VGround Moves

Ω0SaW/(R/I)

Displacement

Elastic Response

Inelastic Structural Response

SaW/(R/I)

For

ce

CdΔeΔe

ASCE 7 Design – Forced Based



CmSaW

Displacement

C1C2

V = C1C2CmSaWPseudo Lateral Force

Elastic Response

Inelastic Structural Response

Expected Maximum (Target) Displacement (t = C0C1C2Sd)

Yield Capacity, or QCE

For

ce

Sd

ASCE 41 - Displacement Based Design

5

F5

F4

F3

F2

F1

VGround Moves

If the pseudo-lateral force, V, displaces the structure to its maximum envelope, the demand on a deformation controlled action, Qud, predicts the maximum inelastic deformation of that component’s action.

t

V

u

Qud

Qce

y

Displacement / Rotation

For

ce /

Mom

ent

u

Qud

Qce

CP,sy LS,s

CP,pLS,pIO,p/s

CP,s= 0.75CP,s

CP,p= 0.75CP,p

IO,p= 0.67CP,p

mIO= 0.75IO,p/y

mLS,p= 0.75LS,p/y

mCP,p= 0.75CP,p/y

mLS,s= 0.75LS,s/y

mCP,s= 0.75CP,s/y

Displacement Based Design – Element Level



Secondary elements must be checked at maximum displacement of primary elements in linear procedures for earthquake induced deformations and gravity loads.

Different, larger, m-factors for secondary elements are provided.

Secondary elements MUST be modeled in nonlinear analysis per Section 7.2.3.3.

Mathematical models for use with nonlinear procedures shall include the stiffness and resistance of primary and secondary components. The strength and stiffness degradation of primary and secondary components shall be modeled explicitly.

Deformation Compatibility

Can include secondary elements in model or

Determine displacements of primary elements from main model, then displace secondary elements in a separate model to same displacements

V

F5

F4

F3

F2

F1

Deformation Compatibility

Capacity-Based Design



Capacity-Based Design – Desired Response

Compression brace buckles

Tension brace yields

Capacity-Based Design – Undesirable Response

Connection fractures

ASCE 41 aims to prevent brittle force-controlled elements from failing before ductile deformational-controlled elements yield.



Designate specific elements to yield, which are called deformation-controlledelements

Every other element of the structure should not yield, rupture, or otherwise fail, those are called force-controlled elements

Structure dissipates seismic energy through controlled yielding of deformation-controlled elements

No brittle failures in force-controlled elements occur which could lead to instability

Capacity-Based Design

Capacity-Based Design – Example

Column

Collector Beam

Brace


Columns can be def-cont. or force-cont.

Collectors can be def-cont. or force-cont.

Brace

Connections almost always force-contr.

Foundation elements almost always force-contr.

Soil actions can be def-cont. or force-cont.

Beam supporting “V” or chevron brace force-cont.




Connections are almost always force-controlled actions.

Steel moment frame construction and wood frame construction are the main exceptions, where connections are permitted be the yielding mechanism.

Another rare exception is in braced frames if there is explicit modeling and research to support ductile behavior.

Linear Static Procedure (LSP)

Linear Dynamic Procedure (LDP)

Modal response spectrum

Linear response history procedure

Nonlinear Static Procedure (NSP) –aka “pushover”

Nonlinear Dynamic Procedure –aka nonlinear response history

ASCE 41-13 Analysis Provision

Linear Analysis Procedures

V = C1C2CmSaW

Apply the psuedo-lateral force, Fx, to each story to get the earthquake action demand, Qe.

∑V (same as ASCE 7)



Displacement Amplification Factors – C1 & C2

DCRmax = maximum Qud/κQce for every deformation controlled element in the direction of loading.

Using the equations becomes an iterative process.

Deformation-Controlled Action Demand – Qud

Acceptance criteria for deformation controlled actions

Acceptance criteria can also be written as

Qce is the expected strength of the action using mean material properties, typically nominal material strength times a factor

Linear Analysis Procedures – Qg

Gravity loads are calculated different from ASCE 7.

1.1

Dead load, QD, is defined similar to ASCE7.

0.9

Live load, QL, is 25% of the unreduced live load from ASCE 7.Roof live load is not included per most interpretations, but never clarified.

Snow load, QS, is 20% of the flat roof snow load from ASCE 7 if snow load is greater than 30 psf, otherwise zero.



Factor to account for uncertainty in collection of as-built information.

κ = 0.75 or 1.0, depending on data collection requirements.

Additional value of κ = 0.90 for minimum data collection with material strengths listed in design documents, if:

Life Safety or lower performance level, and

Linear analysis procedures.

Knowledge Factor - κ

Specific requirements for testing are found in the material chapters for each element.

Material Testing Requirements

Force-Controlled Action Demand – Qf

Demands for force-controlled actions shall be taken as:

1. The maximum action that can be developed in a component based on a limit-state analysis considering expected strengths of the components delivering force or the maximum actions developed in a component as limited by nonlinear response of the building.

2. Alternatively, shall be calculated as

Acceptance criteria for deformation controlled actions

Qcl is the lower-bound of the action using mean material properties, typically nominal material strengths.



ASCE 41-17 Change – Qf

= 1.3 for Life Safety and greater performance level = 1.0 for Collapse Prevention performance level

Concern that the defined margin of safety provided by the Life Safety performance level was not being met with current procedures, because a there was no difference in force-controlled acceptance criteria led to:

J factor is intended to reduce Qe to the magnitude elements see while the structure is yielding.

Two options to determine J:1. Smallest DCR in the load path delivering force to the force-controlled element

2. Default values: 2.0 for High seismicity, 1.5 for Moderate seismicity, and 1.0 for Low seismicity.

Caveat on item 2 that defaults to J = 1.0 if the load path is elastic.

Linear Analysis Procedures – J factor

J factor is intended to reduce Qe to the magnitude elements see while the structure is yielding.

Two options to determine J:1. Smallest DCR in the load path delivering force to the force-controlled element

2. Default values: 2.0 for High seismicity, 1.5 for Moderate seismicity, and 1.0 for Low seismicity.

Caveat on item 2 that defaults to J = 1.0 if the load path is elastic.

Linear Analysis Procedures – J factor

IMPORTANT – If load path is elastic or if deformation-controlled elements DCRs or m-factors are less than 2.0, assuming J = 2.0 is UNCONSERVATIVE



Linear Analysis Procedures – ASCE 7

2 story CBF BuildingW1 = W2 = 2,000k W = 4,000 kSDS = 1.0T = 0.35 s

R = 3.25I = 1.25

V = 1.0*4,000 / (3.25/1.25)V = 1,500 kips

Linear Analysis Procedures – ASCE 41

2 story CBF BuildingW1 = W2 = 2,000k W = 4,000 kSDS = 1.0T = 0.35 s

C1C2 = 1.1 for older braces with m = 4

Cm = 1.0

V =1.1*1.0*1.0*4,000 V = 4,400 kips

ASCE 7 V = 1,500 kips

Linear Analysis Procedures – ASCE 7 vs. ASCE 41

F ASCE 7BraceF = 750kPu = 433k

Brace HSS 9x9x1/2

CompressionϕPn = 443k

DCR = 433/443 = 0.98

TensionϕTn = 633k

DCR = 433/633 = 0.68

ASCE 41BraceF = 2,200kQud = 1,300k

Brace HSS 9x9x1/2

Compression Qce = 1.1*Pn = 541k

DCR = 1,300/541 = 2.4

m = 3.1 > DCR ok

TensionQuf = FyeAg

Quf = 1.1*46*15.3 = 774k

DCR = 1,300/774 = 1.7

m = 3.1 > DCR ok



Linear Analysis Procedures – ASCE 7 vs. ASCE 41

F ASCE 7CollectorF = 750kPu = Ω0F = 2*750Pu = 1,500 k

ConnectionPu = Capacity of bracePu = RyFyAg

Pu = 1.1*46*15.3 = 774k

Check against ϕPn

ASCE 41CollectorF = 2,200kQuf = Qe/(C1*C2*J)J = DCRmin = 1,300/774 = 1.7(note J = 2 could be used but would be UNCONSERVATIVE)

Quf = 2,200/(1.1*1.7) = 1,170k

ConnectionQuf = Capacity of braceQuf = 774k

OrQuf = Qe/(C1*C2*J)Quf = 1,300/(1.1*1.7)Quf = 700 k

Check against Pn

Less than capacity because of issue with C1*C2 being double counted

No floor on the force level as there is in ASCE 7

No limit on period like in ASCE 7

C1C2 factors should be applied to all analysis results before checking component actions

For LDP Qe = C1C2 times analysis output force or

Response spectra input into model should be multiplied by C1C2

Notes on Modal Analysis - LDP

Not permitted for two defined types of irregularity

Weak Story – Total DCR above less than 125% Total DCR below

Torsion – Total DCR on one side of center of rigidity 150% Total DCR on the other side

Unless all DCR < 3.0 and associated component m-factor

Limitations on Use of Linear Procedures



Top and middle stories

(2.5*60k+1.5*60k)/120k = 2.0

Bottom Story

(4.0*150k + 2.0*150k)/300k = 3.0

DCRBot > 1.25*DCRMid

If all DCRs had been 50% of what was shown, linear procedures would have been ok

Weak Story

Torsion

Red Dot = Center of Rigidity

North frame DCR = 5.0

South Frame 1 DCR = 1.5

South Frame 2 DCR = 1.5

DCR North / South = 5/1.5 = 3.3

Torsional Irregularity Exists

Linear Static Procedure not permitted when:

T greater than 3.5Ts

Abrupt changes in lateral system dimensions

Soft story condition

Story torsional stiffness irregularity

Nonorthogonal lateral systems

Limitations on Use of Linear Procedures



MOT = 300*40+200*27+100*14 = 18,800 k-ft

Ms = 3*70*30 = 6,300 k-ft

DCR = 18,800/(0.9*6,300) = 3.3

OT = 0.5*(4+8) = 6 > DCR

300k

200k

100k

70k /floor

Overturning

Strength capacities, not allowable capacities

qc = 3qallow for shallow & 1.5qallow for deep

Bearing capacity and pile plunging are deformation-controlledm factors IO=1.5, LS=3, CP=4 for fixed basem factors vary for flexible base (w/ soil springs)

Physical foundation element (i.e. footing or pile) is force-controlled

Foundation Provisions

Qud = (300*40+200*27+100*14)/30 + 1.1*(3*70+0.25*3*72) = 920 k

6’x6’ footing

qallow = 3,000 psf

qc = 3*3,000 = 9,000 psf

Qce = 6*6*9 = 324 k

DCR = 920 / 320 = 2.9

m = 0.5*(1.5+3) = 2.3 < DCR => NG

Could revise model to include soil springs and get a larger m-factor or retrofit by tying footings together

300k

200k

100k

70k /floor




Check punching shear

Quf = [(300*40+200*27+100*14)/30]/2.9+ 1.1*(3*70+0.25*3*72) = 506 k

Divided by 2.9 as C1C2J

300k

200k

100k

70k /floor


SSI is a means by which the response spectrum parameters can be reduced because of properties of the foundation and soil affect the seismic response

Foundation Damping

Kinematic Interaction Effects

Base Slab Averaging

Embedment

Soil Structure Interaction

If SSI is used to reduce forces, the following conditions must be met

Horizontal and vertical soil springs are included in model

Foundation is tied together with mat or slab on grade that is not flexible compared to the vertical elements

Site parameters, vs30, are know




If SSI is used to reduce forces, the following conditions must be met

Horizontal and vertical soil springs are included in model

Foundation is tied together with mat or slab on grade that is not flexible compared to the vertical elements

Site parameters, vs30, are know


Be wary of reductions that seem too big, i.e. 30% or more

Nonlinear Static Procedure

Displace the structure to the maximum estimated roof displacement

Permit yielding and force redistribution

Evaluate nonlinear deformation of each component versus specified limits

Nonlinear Dynamic Procedure

Use actual or simulated EQ ground motions

Simulates structures response to the earthquake

Evaluate nonlinear deformation of each component versus specified limits

Nonlinear Analysis Procedures

NSP vs. NDP

NSP permitted to be used when μstrength < μmax and higher mode effects are not significant

Deformation-controlled actions must be modeled

Material chapters with modelingparameters and deformation limits

Force-Controlled Actions

Capacity based design (limit state analysis) or maximum force from model

Nonlinear Analysis Procedures



Nonlinear Static Pushover

Longitudinal Pushover Curve

0

500

1000

1500

2000

2500

3000

3500

4000

0.00 10.00 20.00 30.00 40.00

Displacement [in.]

Bas

e S

he

ar [

kip

s]

Roof Disp. = 1.5"- Both Stair Walls Flex Yield @ Base- All Elev. Core Coupling Beams Yield- Airshafts @ G-Line Flex. Yield @ 2nd Fl.

Roof Disp. = 4"- Elev Cores Flex Yield @ 3rd Fl.- Airshafts @ E-Line Flex Yield.

Roof Disp = 9"- G-Line Col. Flex. Yield Below Roof, 9th, & 8th- Cont Stair Core Pass IO Limit- Discont. Stair Core Pass LS Limit- Interior Beam Flex Yielding

Roof Disp. = 7"- Col. Lap Splice Pass LS Limit

Roof Disp. = 10"- Elev. Cores Pass IO Limit- G-Line Col Flex. Yield Below 7th

BSE-1 Target = 10"

BSE-2 Target = 19"

Roof Disp. = 11.5"- G-Ln. Col. Pass LS Limit Below Roof

Roof Disp. = 16"- G-Line Col. Below 9th Pass LS Limit & Rest Form Flex Hinges.- Cont Stair Pass LS Limit

Roof Disp. 17"- Elev. Cores Pass LS Limit- G-Line Col. Below 8th Pss LS Limit

Roof Disp. = 21.5- Airshafts Pass LS Limit- Rest of G-Line Col. Pass LS Limit

Roof Disp. = 31"- Coupling Beams Pass LS limit 4th - Roof.

Interior Beams & Columns Passing LS Limt in This Region

Roof Disp. = 14"- Col. Lap Splice Pass CP Limit

Roof Disp. = 18"- Discont. Stair Core Passes CP Limit

Roof Disp. 24"- Elev. Core Pass CP Limit- Contin. Stair Passes CP Limit- G-Ln Airshafts Pass CP Limit

Roof Disp. = 26"- E-Ln. Airshafts Pass CP Limit

Nonlinear Static PushoverNonlinear Response History

Screen for potential deficiencies based on checklist of observed deficiencies.

Target the scope of further evaluation.

Tier 1 was not originally intended to be a stand-alone evaluation.

Tier 1 Screening is intentionally conservative.

Tier 1 Screening



Always read the Checklist item’s corresponding Appendix A statement.

Read the Standard!

Evaluate the potential deficiencies flagged in the Tier 1 Screening.

Limited calculations

Tier 2 may require an analysis of the full building.

Some items can be assumed compliant during the evaluation, even if they are numerically noncompliant.

Requires judgement of how deep to dive when checking things.

Tier 2 Evaluation

Always read the pertinent Chapter 5 statement.

Read the Standard!



Correct the Tier 2 identified deficiencies using deficiency-based procedures

Does not trigger full systematic evaluation of building

Similar to Tier 2 Evaluation, may require modeling and/or assessment of the entire building

New elements must conform to the full requirements of ASCE 41

All Tier 2 limitations still apply

Only need to evaluate BSE-1E (in 41-13, -2E in 41-17)

Tier 2 Deficiency-Based Retrofit

Tilt-up concrete building

ASCE 41 would permit either T1/T2 or T3

Deficiency-based vs. Systematic Example

Deficiency-based Process

Quick check on wall shear

Check diaphragm aspect ratio and material

Wall anchorage calculation

No cross tie but no subdiaphragmcalculations

Wall aspect ratio check

Tilt-up Example – Evaluation

Systematic Process

Minimum linear static calculation of shear in walls

Calculation on diaphragm

Wall anchorage calculation

Cross tie and subdiaphragmcalculation

Wall out-of-plane calculation

Wall in-plane

Diaphragm

Out-of-plane anchorage

Cross ties

Wall out-of-plane




Shear ok

Ok on aspect ratio and sheathing

Wall anchorage no good

Cross ties required

Wall reinforcement ratio ok

Tilt-up Example – Deficiencies

Systematic Process

Wall panels not anchored to each other

Diaphragm nailing not sufficient

Wall anchorage no good

Cross ties required and subdiaphragm nailing augmentation

Wall under reinforced for out-of-plane forces

Wall in-plane

Diaphragm


Cross ties

Wall out-of-plane


No retrofit

No retrofit

Add wall to roof anchors

Add cross-ties

No retrofit

Tilt-up Example – Retrofit

Systematic Process

Add inter-panel connections

Augment diaphragm nailing

Add wall to roof anchors

Add cross-tie connections to framing and augment nailing for subdiaph.

Add strong backs

Wall in-plane

Diaphragm


Cross ties

Wall out-of-plane

ASCE 41-13 Analysis ProvisionsRobert Pekelnicky, PE, SE

Principal, Degenkolb EngineersChair, ASCE 41 Committee*

*The view expressed represent those of the author, not the standard’s committee as a whole.

asce 41‐13 hands‐on approach analysis provisions part 02-asce_41_analysis... · asce 41‐13...

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