SEAU 5 th Annual Education Conference 1. Read the Standard! ASCE Analysis Provisions. (not just the tables and equations)

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1 ASCE Robert Pekelnicky, PE, SE Principal, Degenkolb Engineers Chair, ASCE 41 Committee* *The view expressed represent those of the author, not the standard s committee as a whole. ASCE Analysis Procedures Identify the primary and secondary components Displacement-based analysis provisions Capacity-based design philosophy Tie the building together Three tiers of evaluation and retrofit 2 Read the Standard! (not just the tables and equations) SEAU 5 th Annual Education Conference 1

2 Primary & Secondary Elements Which elements are primary and which are secondary? Primary Components 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) Secondary 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 SEAU 5 th Annual Education Conference 2

3 When is an element a primary or a secondary element? 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. 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. SEAU 5 th Annual Education Conference 3

4 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. SEAU 5 th Annual Education Conference 4

5 Nonstructural as Structural 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 Displacement-Based Design F 5 F4 F 3 F2 F 1 Ground Moves V Pseudo-lateral force displaces structure to an approximation of the maximum displacement envelope. ASCE 7 Design Forced Based Elastic Response Ω 0 S a W/(R/I) Inelastic Structural Response S a W/(R/I) Force Δ e C dδ e Displacement SEAU 5 th Annual Education Conference 5

6 ASCE 41 - Displacement Based Design V = C 1 C 2 C m S a W Pseudo Lateral Force Yield Capacity, or Q CE Elastic Response C 1 C 2 C m S a W Inelastic Structural Response Force Displacement S d Expected Maximum (Target) Displacement ( t = C 0 C 1 C 2 S d ) V If the pseudo-lateral force, V, displaces the structure to its maximum envelope, the demand on a deformation controlled action, Q ud, predicts the maximum inelastic deformation of that component s action. Ground Moves F 5 F4 F 3 F2 t F 1 Q ud V Q ce y u 5 Displacement Based Design Element Level Q ud CP,s=0.75 CP,s CP,p=0.75 CP,p IO,p=0.67 CP,p Force / Moment Q ce m IO=0.75 IO,p/ y m LS,p=0.75 LS,p/ y m CP,p=0.75 CP,p/ y m LS,s=0.75 LS,s/ y m CP,s=0.75 CP,s/ y y u LS,s CP,s Displacement / Rotation IO,p/s LS,p CP,p SEAU 5 th Annual Education Conference 6

7 Deformation Compatibility 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 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 F 5 F4 F 3 F2 F 1 V Determine displacements of primary elements from main model, then displace secondary elements in a separate model to same displacements Capacity-Based Design SEAU 5 th Annual Education Conference 7

8 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. SEAU 5 th Annual Education Conference 8

9 Capacity-Based Design Designate specific elements to yield, which are called deformation-controlled elements 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 deformationcontrolled elements No brittle failures in force-controlled elements occur which could lead to instability Capacity-Based Design Example Collector Beam Column Brace Capacity-Based Design Example Collectors can be def-cont. or force-cont. Connections almost always force-contr. Columns can be defcont. or force-cont. Foundation elements almost always force-contr. Brace Beam supporting V or chevron brace force-cont. Soil actions can be def-cont. or force-cont. SEAU 5 th Annual Education Conference 9

10 Capacity-Based Design Example Connections are almost always forcecontrolled 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. ASCE Analysis Provision 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 Linear Analysis Procedures Apply the psuedo-lateral force, F x, to each story to get the earthquake action demand, Q e. V = C 1 C 2 C m S a W V (same as ASCE 7) SEAU 5 th Annual Education Conference 10

11 Displacement Amplification Factors C 1 & C 2 DCR max = maximum Q ud/κq ce for every deformation controlled element in the direction of loading. Using the equations becomes an iterative process. Deformation-Controlled Action Demand Q ud Acceptance criteria for deformation controlled actions Q ce is the expected strength of the action using mean material properties, typically nominal material strength times a factor Acceptance criteria can also be written as Linear Analysis Procedures Q g Gravity loads are calculated different from ASCE Dead load, Q D, is defined similar to ASCE7. Live load, Q L, is 25% of the unreduced live load from ASCE 7. Roof live load is not included per most interpretations, but never clarified. Snow load, Q S, is 20% of the flat roof snow load from ASCE 7 if snow load is greater than 30 psf, otherwise zero. SEAU 5 th Annual Education Conference 11

12 Knowledge Factor - κ 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. Material Testing Requirements Specific requirements for testing are found in the material chapters for each element. Force-Controlled Action Demand Q f 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 Q cl is the lower-bound of the action using mean material properties, typically nominal material strengths. SEAU 5 th Annual Education Conference 12

13 ASCE Change Q f 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: = 1.3 for Life Safety and greater performance level = 1.0 for Collapse Prevention performance level Linear Analysis Procedures J factor J factor is intended to reduce Q e 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 Q e 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. 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 SEAU 5 th Annual Education Conference 13

14 Linear Analysis Procedures ASCE 7 2 story CBF Building W 1 = W 2 = 2,000k W = 4,000 k S DS = 1.0 T = 0.35 s R = 3.25 I = 1.25 V = 1.0*4,000 / (3.25/1.25) V = 1,500 kips Linear Analysis Procedures ASCE 41 2 story CBF Building W 1 = W 2 = 2,000k W = 4,000 k S DS = 1.0 T = 0.35 s C 1C 2 = 1.1 for older braces with m = 4 C m = 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 7 Brace F = 750k P u = 433k Brace HSS 9x9x1/2 Compression ϕp n = 443k DCR = 433/443 = 0.98 ASCE 41 Brace F = 2,200k Q ud = 1,300k Brace HSS 9x9x1/2 Compression Q ce = 1.1*P n = 541k DCR = 1,300/541 = 2.4 m = 3.1 > DCR ok Tension ϕt n = 633k DCR = 433/633 = 0.68 Tension Q uf = F yea g Q uf = 1.1*46*15.3 = 774k DCR = 1,300/774 = 1.7 m = 3.1 > DCR ok SEAU 5 th Annual Education Conference 14

15 Linear Analysis Procedures ASCE 7 vs. ASCE 41 F ASCE 7 Collector F = 750k P u = Ω 0F = 2*750 P u = 1,500 k Connection P u = Capacity of brace P u = R yf ya g P u = 1.1*46*15.3 = 774k Check against ϕp n ASCE 41 Collector F = 2,200k Q uf = Q e/(c 1*C 2*J) J = DCR min = 1,300/774 = 1.7 (note J = 2 could be used but would be UNCONSERVATIVE) Q uf = 2,200/(1.1*1.7) = 1,170k Connection Q uf = Capacity of brace Q uf = 774k Or Q uf = Q e/(c 1*C 2*J) Q uf = 1,300/(1.1*1.7) Q uf = 700 k Check against P n Less than capacity because of issue with C 1*C 2 being double counted Notes on Modal Analysis - LDP No floor on the force level as there is in ASCE 7 No limit on period like in ASCE 7 C 1 C 2 factors should be applied to all analysis results before checking component actions For LDP Q e = C 1 C 2 times analysis output force or Response spectra input into model should be multiplied by C 1 C 2 Limitations on Use of Linear Procedures 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 SEAU 5 th Annual Education Conference 15

16 Weak Story Top and middle stories (2.5*60k+1.5*60k)/120k = 2.0 Bottom Story (4.0*150k + 2.0*150k)/300k = 3.0 DCR Bot > 1.25*DCR Mid If all DCRs had been 50% of what was shown, linear procedures would have been ok 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 Limitations on Use of Linear Procedures Linear Static Procedure not permitted when: T greater than 3.5T s Abrupt changes in lateral system dimensions Soft story condition Story torsional stiffness irregularity Nonorthogonal lateral systems SEAU 5 th Annual Education Conference 16

17 Overturning 300k 200k 70k /floor M OT = 300*40+200*27+100*14 = 18,800 k-ft M s = 3*70*30 = 6,300 k-ft DCR = 18,800/(0.9*6,300) = 3.3 OT = 0.5*(4+8) = 6 > DCR 100k Foundation Provisions Strength capacities, not allowable capacities q c = 3q allow for shallow & 1.5q allow for deep Bearing capacity and pile plunging are deformation-controlled m factors IO=1.5, LS=3, CP=4 for fixed base m factors vary for flexible base (w/ soil springs) Physical foundation element (i.e. footing or pile) is force-controlled Foundation Provisions 300k 70k /floor Q ud = (300*40+200*27+100*14)/ *(3* *3*72) = 920 k 200k 100k 6 x6 footing q allow = 3,000 psf q c = 3*3,000 = 9,000 psf Q ce = 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 SEAU 5 th Annual Education Conference 17

18 Foundation Provisions 300k 200k 70k /floor Check punching shear Q uf = [(300*40+200*27+100*14)/30]/ *(3* *3*72) = 506 k Divided by 2.9 as C 1 C 2 J 100k Soil Structure Interaction 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, v s30, are know SEAU 5 th Annual Education Conference 18

19 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, v s30, are know Be wary of reductions that seem too big, i.e. 30% or more Nonlinear Analysis Procedures 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 μ strength < μ max and higher mode effects are not significant Deformation-controlled actions must be modeled Material chapters with modeling parameters and deformation limits Force-Controlled Actions Capacity based design (limit state analysis) or maximum force from model SEAU 5 th Annual Education Conference 19

20 Roof Disp = 9" Roof Disp. = 16" - G-Line Col. Flex. Yield Below Roof, - G-Line Col. Below 9th Pass LS Roof Disp. = th, & 8th Limit & Rest Form Flex Hinges. - Airshafts Pass LS Limit - Cont Stair Core Pass IO Limit - Cont Stair Pass LS Limit - Rest of G-Line Col. Pass LS Limit Interior Beams & - Discont. Stair Core Pass LS Limit Columns Passing LS - Interior Beam Flex Yielding Limt in This Region Roof Disp. = 7" - Col. Lap Splice Roof Disp. = 14" Roof Disp. = 31" Pass LS Limit - Col. Lap Splice Roof Disp. 24" - Coupling Beams Pass Roof Disp. = 10" Pass CP Limit - Elev. Core Pass CP Limit LS limit 4th - Roof. - Elev. Cores Pass IO Limit - Contin. Stair Passes CP Limit Roof Disp. = 11.5" - G-Line Col Flex. Yield - G-Ln Airshafts Pass CP Limit - G-Ln. Col. Pass LS Below 7th Limit Below Roof Roof Disp. = 18" - Discont. Stair Roof Disp. = 4" Core Passes CP Roof Disp. = 26" - Elev Cores Flex 3rd Fl. Limit - E-Ln. Airshafts - E-Line Flex Yield. Pass CP Limit BSE-1 Target = 10" Roof Disp. 17" Roof Disp. = 1.5" - Elev. Cores Pass LS Limit - Both Stair Walls Flex Base - G-Line Col. Below 8th Pss - All Elev. Core Coupling Beams Yield LS Limit - G-Line Flex. 2nd Fl. BSE-2 Target = 19" ASCE Hands On Approach Nonlinear Static Pushover Longitudinal Pushover Curve Base Shear [kips] Displacement [in.] Nonlinear Response Static Pushover History Tier 1 Screening 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. SEAU 5 th Annual Education Conference 20

21 Read the Standard! Always read the Checklist item s corresponding Appendix A statement. Tier 2 Evaluation 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. Read the Standard! Always read the pertinent Chapter 5 statement. SEAU 5 th Annual Education Conference 21

22 Tier 2 Deficiency-Based Retrofit 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) Deficiency-based vs. Systematic Example Tilt-up concrete building ASCE 41 would permit either T1/T2 or T3 Tilt-up Example Evaluation Wall in-plane Diaphragm Out-of-plane anchorage Cross ties Wall out-of-plane Deficiency-based Process Quick check on wall shear Check diaphragm aspect ratio and material Wall anchorage calculation No cross tie but no subdiaphragm calculations Wall aspect ratio check Systematic Process Minimum linear static calculation of shear in walls Calculation on diaphragm Wall anchorage calculation Cross tie and subdiaphragm calculation Wall out-of-plane calculation SEAU 5 th Annual Education Conference 22

23 Tilt-up Example Deficiencies Wall in-plane Diaphragm Out-of-plane anchorage Cross ties Wall out-of-plane Deficiency-based Process Shear ok Ok on aspect ratio and sheathing Wall anchorage no good Cross ties required Wall reinforcement ratio ok 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 Tilt-up Example Retrofit Wall in-plane Deficiency-based Process No retrofit Systematic Process Add inter-panel connections Diaphragm No retrofit Augment diaphragm nailing Out-of-plane anchorage Cross ties Wall out-of-plane Add wall to roof anchors Add cross-ties No retrofit Add wall to roof anchors Add cross-tie connections to framing and augment nailing for subdiaph. Add strong backs ASCE Robert Pekelnicky, PE, SE Principal, Degenkolb Engineers Chair, ASCE 41 Committee* *The view expressed represent those of the author, not the standard s committee as a whole. SEAU 5 th Annual Education Conference 23