Thomas F. Heausler, PE, SE Structural Engineer This ......• Ignores the most basic tenets of...
Transcript of Thomas F. Heausler, PE, SE Structural Engineer This ......• Ignores the most basic tenets of...
Seismic R = 1, 1.5, 3 with Low Seismic Design Example
Thomas F. Heausler, PE, SE Structural Engineer
This presentation will summarize and scrutinize the use of Seismic Response Modification Coefficient, R, equal to 1, 1.5 and 3 for Industrial/Nonbuilding Structures Similar to Buildings, and for Buildings located in Low Seismic Design Categories (SDC B, C). The benefits and disadvantages will be discussed, and Design Examples will compare Low and High R systems, and assess economics, complexity, reliability, and the potential for undesirable modes of failure.
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Indiana Structural Engineers Association2020 Spring Conference
Seismic R = 1, 1.5 and 3With Low Seismic Design Example
By:Thomas F. Heausler, PE, SEStructural EngineerKansas City
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Thomas F. Heausler, PE, SEStructural Engineer
• ASCE 7 Seismic Voting Member since 2006
• NCSEA Seismic Code Advisory Committee, Chair
• Provide Senior Review and Code Consulting to Engineering Firms
• 38 years experience
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Seismic R = 1, 1.5 and 3 – When and Where &Low Seismic Example
• What is R• Restrictions• Low Seismic, Industrial • Pros, Cons, Prudent
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R - Response Modification Coefficient
Base Shear - V
Sds = 1.0 San Francisco, SDC = D, PGA = 0.4Sds = 0.18 Stillwater, SDC B, PGA = 0.08
Table 12.2-1SCBF R = 6, Omega Ωo = 2, Cd = 5SMF R = 8, Omega Ωo = 3, Cd = 5.5Steel Systems Not Specifically Detailed for Seismic, R = 3, Omega Ωo = 3, Cd = 3
Each R value has strings attached.
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DetailingLimitations(height, permitted)
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R, Omega Ωo, Cd
• Not like Wind
• “R” is measure of effective ductility of system
• Ductility is range between yield and fracture
• R is composed of two components: • Omega Ωo : Overstrength
• Rd: inelastic behavior/energy dissipation
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R - Response Modification Coefficient
•Overstrength
•Ductility
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R - Response Modification CoefficientOverstrength - within the SFRS
• Material Strengths, φ, Utilization• Drift governed• First yield versus fully yield
The maximum strength developed along the curve is substantially higher than that at first significant yield,
and this margin is referred to as the system overstrengthcapacity.
The ratio of these strengths is denoted as Ω.
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R - Response Modification Coefficient
Ductility - within the SFRS
• Region after yield but before fracture
• Reliable, controlled fuse
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R - Response Modification CoefficientDuctility - within the SFRS
•Region after yield but before fracture
•Reliable, controlled fuse
•Moment Frame => Hinge in beam
•Braced Frame => Inelastic buckling of brace
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Strings Attached to High R Factor
•Collectors (ASCE 7 – SDC C, D, E, F) Ωo
•AISC 341 versus AISC 360
•ACI 318-14 Chapter 17, 18
•Masonry
•Wood
Ω is within fuse, Ωo is outside of fuse
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High R factors• AISC 341 Special Moment Frame, R = 8
• AISC 358 “prequalified” moment connections
• Develop expected strength of beam
• Demand Critical Weld, CJP welds
• Protected Zones
• AISC 341 Special Concentric Braced Frame, R = 6•Develop expected strength of brace
• Columns• Width/Thickness Ratios
• Develop expected strength of braces
• Anchor rods, Column splices
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Lower R factors
•AISC 341 Ordinary Moment Frame, R = 3.5
•AISC 341 Ordinary Concentric Braced Frame, R = 3.25
•Not very ordinary - Ωo is triggered for connections, braces, anchor rods etc.
•Ωo = 2, 3
Table 12.2-10BF R = 3.25, Omega Ωo = 2, Cd = 3.25OMF R = 3.5, Omega Ωo = 3, Cd =3Steel Systems Not Specifically Detailed for Seismic, R = 3, Omega Ωo = 3, Cd = 3
Each R value has strings attached.
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OMF R = 3.5 • Develop expected strength of beam• Demand Critical Weld, CJP welds
0BF R = 3.25• Ωo overstrength required• K-Brace prohibited• Beam Support DL+LL for inverted V bracing
Columns – (for both OMF and OBF)• Width/Thickness Ratios• Ωo overstrength required• Anchor rods, Column splices
“Ordinary” = not very ordinary!
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R = 3 for Steel Structures
• Not specifically detailed for seismic – AISC 360 only
• Not permitted in SDC D, E, F
• Ωo only required by ASCE 7 (e.g. collectors) and ACI Concrete anchorage.
• Rationale: Low ductility demand, mostly overstrength, accelerations are low.
• Frequently and economical to use where allowed.
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Industrial Structures
•Difficult or impossible to meet prescriptive requirements of high R factor.
R = 1.0 for Steel Moment Frames
R = 1.5 for Steel Braced Frames
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ASCE 7 Chapter 15Nonbuilding Structures Similar to Buildings
BUILDING: Any structure whose intended use includes shelter of human occupants.
NONBUILDING STRUCTURE: A structure, other than a building, constructed of a type included in Chapter 15 and within the limits of Section 15.1.1. (applicability).
11.1.3 Applicability. Structures and their nonstructural components shall be designed and constructed in accordance with the requirement of the following chapters based on the type of structure or component:
a. Buildings: Chapter 12;
b. Nonbuilding Structures: Chapter 15;
Buildings whose purpose is to enclose equipment or machinery and whose occupants are engaged in maintenance or monitoring of that equipment, machinery, or their associated processes shall be permitted to be classified as nonbuilding structures designed and detailed in accordance with Section 15.5 of this standard.
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Prescriptive requirements for High R Systems
• Brace Slenderness
• Develop full strength of brace
• Strong Column – Weak Beam
• AISC 358 Prequalified
• Weak axis bending, tube columns, discontinuous systems
• Protected Zones BF, MF
• Field Welding, CJP welds
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Chimney and Stacks – R = 2…ASCE 7 15.6.2, ACI 307
• Low ductility• Industry Standard
Nonbuilding not similar to buildings
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R – Tanks, SCR, HRSG, Soundwalls
Tanks on Grade, R = 3HRSG R = 8, 3.5, 3, 1.0Cantilevered fence, Wall >6’ R = 1.25
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ASCE 7 Nonbuilding
R = 1.5 BF, 1.0 MF
AISC 360
No proportioning
? R=1: Other than
Steel
UFC Essential
Facilities R = 1
Nuclear Plants
R = 1
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ASCE 7-16 Proposal – Essentially Elastic R = 1
• SIMPLIFY
• Limit Scope of Use
• Reduce Ductility Demand: R = 1
• Diaphragms, Non-Structural, Walls: Rp = 1
• Limit Irregularities, Simplify Drift
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High Lateral Resistant Buildings
Foundation Sliding – frost depth
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ASCE 7-16 Proposal – Essentially Elastic R = 1
Negative concerns:
•Magnitude of Earthquake not refined enough
•No ductility required is unsafe, backward direction, • 40 yrs, URM ?
• A second method, different than current
•Uneconomical, impractical
•Not correlated to Collapse Probability
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Negatives:• Need to substantiate R values for all types of structures• Ignores the most basic tenets of seismic performance: ductility,
continuity and capacity based design (acknowledging overstrength).
• Our codes and standards have never allowed unrestricted trade-off between strength and inelastic deformabilty or ductility in seismic design, which starts with what is now SDC B. There has always been a minimum set of detailing requirements specified, dependent solely on the SDC.
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SIMPLIFICATION OF SEISMIC CODE
PROVISIONS
A WHITE PAPER Prepared under the BSSC Simplified Seismic Design Procedures
Development Program
William T. Holmes
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Reduce Material Detailing Requirements (to Achieve Ductility) with Use of Lower R Factors
The detailing requirements for systems with high R factors generally involve design checks to avoid
brittle limit states (e.g., tensile fracture of structural steel or compressive crushing of concrete) and to
avoid focusing the inelastic demand in a small portion of the system (e.g., the “strong-column, weak-
beam” rule for special moment frames). Many of these detailing rules are rooted in the concept of
“capacity design,” in which the structure is constrained by design to perform in certain desirable
manners. These detailing requirements can be very time consuming in engineering practice.
The NEHRP Provisions and ASCE/SEI 7-10 are written to exclude the most brittle systems, generally
those with the lower R factors, from use on the higher seismic design categories, generally in locations
with the potential for very large seismic ground motions. In some cases, the restrictions apply primarily
to tall structures whereas in others, the restrictions apply to all heights. Suggestions to relax these
restrictions by requiring higher loading (smaller R factors) have been made in the past. Since the design
procedures include a reduction in the MCE ground motion as a part of the basic equation for an
equivalent design force, even an R of 1.0 implies acceptable structural performance beyond the design
loading assumptions. Some individuals cognizant of this fact suggest a value of R equal to 2/3 as a safe
alternative. Given that the ground motions to be considered exhibit a significant variability in key
parameters and that the capacity of a structure is not known with certainty, a probabilistic approach is
probably needed when considering these marginal cases. The methodology of FEMA P-695 would
provide guidance in this regard, but the amount of work required to perform these analyses
systematically for a wide category of structural systems would be overwhelming. Therefore, this option
was not selected for consideration in this study.
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R = 1 Status:
• Limited Scope Proposal nearly passed ASCE 7-16• SDC B, C; Regular, 3 story max
• The proposal is currently shelved• Could be used as a design guide – meets Code• Grass roots demand could bring it forward
• Needs justification of R values
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Conclusions:
• R = 3, 1.5 and 1 are allowed in certain areas and with heavy restrictions.
• SDC B, C => R = 3 for steel is the norm.
• Nonbuilding Industrial structures benefit from R = 1 MF, 1.5 BF.
• Use judgement for each configuration and proportioning; and consider vulnerability to an overload.• Collapse, redundancy, robustness/utilization
Introduction to Seismic Design Low Seismic
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byThomas F. Heausler, PE, SEStructural Engineer
Agenda
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• Complete seismic load analysis of a simple building – Small Building
• Low Seismic Risk - Not optimized for Seismic
• Calculations as Flowchart
• Present the Underlying Theory
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Given: ASCE 7-10, AISC 340, ACI 318 [Note: ASCE 7-10 maps and Provisions are used, Accidental Torsion of ASCE 7-16 is described.]Location: Hardeeville, South CarolinaUse: Storage and office without partitions. See Section 4.3.2 and 12.7.2(2) for partition load requirements), Risk Category IIRoof dead load = 70 psfRoof Live Load = 20 psf, Ground and minimum Roof Snow Load = 20 psfSeismic Force Resisting System: Steel Braced FrameSoil Allowable Net Bearing Pressure = 2,000 psfMaterials: Concrete f’c = 4,000psi; Steel Shapes and Plates Grade 50; Welding E70 electrode, Bolts A325N, Snug tight.
Figure 1 Simple Building Perspective
Calculations:
Seismic Design :Determine SS and S1:Site Class D default as per 11.4.2From ASCE Hazards Tool or USGS Website SS = 0.31, S1 = 0.130, SDS = 0.356, SD1 = 0.198 Verify that exemptions do not apply (11.1.2) and (11.4.1).
Exceptions: Low seismic , one and two family dwellingsSeismic Design Category A
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Calculations:
Seismic Design Category A
• [11.4.1] [11.7] [1.4]• Don’t Use Chapter 12• [1.4] General Structural Integrity • 1% W, 5% beam connections, 20% wall
connections• Non-Structural Components Exempt
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Ground Motion
SMS = FaSS (11.4-1)SM1 = FvS1 (11.4-2)
SDS = 2/3 SMS (11.4-3)
SD1= 2/3 SM1 (11.4-4)
SDS = 2/3 FaSS
SD1 = 2/3 FvS1
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F = ma• Rock accelerates during an earthquake
• Soft soil above rock amplifies the acceleration
• Building amplifies that acceleration from its base to roof
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Site Class, Fa, Fv
• Rock displaces during earthquake
• A peak acceleration may be measured
• Soft soil above rock amplifies acceleration – Fa, Fv
• Resulting in the ground motion at your site
- at base of building
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Building Response to Ground Motion
• Ground motion is amplified through the structure
• This is called “Response”
• Up to 2.5 times acceleration at ground
• Response is a function of mass and stiffness => Period, T
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Period T
Moment Frames
1 story T = 0.1 second5 story T = 0.5 seconds20 story T = 2 seconds
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Response of Building – ASCE 7 Maps
• 0.2 second Map
• 1.0 second Map
• Calibrate a Response Spectrum for your site
• Apply Period T to determine Response acceleration
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Map: ASCE 7-10 Chapter 22
Response Accelerations
San Francisco, CA
Ss = 1.50S1 = 0.67
PGA = 0.6
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Black line in margin indicates change from previous edition.
2/3
• “2/3”
converts from
• Maximum Considered Earthquake (Collapse Prevention)
To
• Design Earthquake (Life Safety)
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Ground Motion
SMS = FaSS (11.4-1)SM1 = FvS1 (11.4-2)
SDS = 2/3 SMS (11.4-3)
SD1= 2/3 SM1 (11.4-4)
SDS = 2/3 FaSS
SD1 = 2/3 FvS1
SDS and SM1 are now calibrated for site Now use Period T, to determine Base Shear for our Building
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Figure 11.4-1 Design Response Spectrum
1-Story 5-Story 10-Story 20-StorySolidBlock of Concrete
80-Story
PGA = 0.4
SDS = 1.0
San Francisco
• Spectrum• Response• Design Level
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Create a Response Spectrum
Ground Acceleration measured during an earthquake
Sometime during the duration, a building will have a maximum response
could be here
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Creating a Response Spectrum
• One SDOF system is subjected to time history of earthquake ground acceleration record.
• The SDOF model responds to ground acceleration.
• Sometime during the earthquake a peak acceleration response is measured for that SDOF
• Not necessarily at same time as peak ground acceleration
• Analysis is repeated for various different SDOF models completing a spectrum of results
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Response Spectrum
Period
(seconds)1 Story CMU
1 Story Moment Frame
2 Story Building20 story Building
10 Story Building
Res
po
nse
Acc
eler
atio
n
Resonance to Rhythmic Forcing Function
SDS
SD1/T
Earthquake 1
Earthquake 2
Earthquake 3
Ruler with Erasers:• Short Period• Resonance• Long Period
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R – Response Modification Factor
Now we know the building’s response due to:
• Acceleration of Rock at our site
• Soil amplification
• Building Period, T (i.e. m,k) – Amplification/Response
• Now we modify it further – Ductility - R
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Table 12.2-1SCBF R = 6, Omega Ωo = 2, Cd = 5SMF R = 8, Omega Ωo = 3, Cd = 5.5Steel Systems Not Specifically Detailed for Seismic, R = 3, Omega Ωo = 3, Cd = 3
Each R value has strings attached.
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R, Omega Ωo, Cd
• Not like Wind
• “R” is measure of effective ductility of system
• Ductility is range between yield and fracture
• R is composed of two components: • Omega Ωo : Overstrength
• Rd: inelastic behavior/energy dissipation
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R, Omega Ωo, Cd
• Overstrength Omega Ωo : • Material overstrength
• Phi
• Conservative overdesign, min ratios, drift driven
•Rd, Inelastic Behavior: • Level of inelastic response capability
• Bend not break
• Period lengthens, energy dissipation/damping
• Observed System Performance
• Possibility of vertical load system failure
• Redundancy (rho) and Backup frames
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R, Omega Ωo, Cd
• See NEHRP FEMA 450-2/2003 pages 36 – 41
• Special detailing required to insure inelastic performance
• Omega is overstrength factor (e.g. collectors, connections, columns)
• Cd converts elastic analysis deflection to inelastic/actual
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Importance Factor
• [11.5.1] [Table 1.5-2] [Table 1.5-1] and
• [IBC Table 1604.5] • Risk Category • Hazard, Essential, • e.g. 300 people, storage Ie= 1.0, 1.25, 1.5 Ip = 1.0, 1.5 [13.1.3] Life Safety,
Essential, Hazardous
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Importance factor, Seismic Design Category
• “Ie” Importance Factor
• A method to increase safety by reducing ductility demand
• (R/Ie)
• “SDC” Seismic Design Category triggers provisions, restrictions and detailing
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Calculations:Determine Analysis Procedure Allowed:
See (12.6) and (Table 12.6-1).
Check 12.14 Simplified method (OK, but not used in this example).
Period (12.8.2.1): Ta = CT hnx ; CT = 0.02, x = 0.75; hn = 14’; Ta = 0.14
seconds
T = Ta (12.8.2 last sentence); T = 0.14 seconds; TS = SDS/SD 1 =
0.198/0.356 = 0.55 seconds
TL = 8 seconds (Figure 22-14)
Check for Irregularities (12.3):
Horizontal (Tables 12.3-1) = None (See accidental Torsion check below).
Vertical (Table 12.3-2) = None
Check T < 3.5TS; 0.14 seconds < (3.5) 0.55 seconds; OK (Table 12.6-1).
Therefore the Equivalent Lateral Force Procedure may be used and it is
not necessary to use Modal Response Spectrum method nor Seismic
Response History procedure.
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Calculations:
Determine Response Modification Factor, R:
As per Tables 11.6-1 and 11.6-2 Seismic Design Category (SDC) = C
Seismic Force Resisting System: Braced Frame as per Table 12.2-1 H.
Steel Systems Not Specifically Detailed for Seismic Resistance: R = 3,
ΩO = 3, Cd = 3,
Detailing required as per (14.1), and (14.1.2.2.1 Exception): Use AISC
360 (need not detail as per AISC 341 Seismic).
Determine Seismic Importance factor, Ie:
See (11.5.1) and Table 1.5-2. Risk Category II, Ie = 1.0
Effective Seismic Weight -W
• [12.7.2] Dead Load• No Live Load except:o 25% of Storageo Partitions 10 psf [4.3.2]o Industrial Operating Weight – Unbalancedo 20% of snow > 30psfo Roof Gardens
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Calculations:Determine Base Shear:
Effective Seismic Weight (12.7.2)
Roof = 70psf dead load (20’x20’) = 28.0k
Walls = Height tributary to roof = 14’/2 = 7’; Perimeter of building = 80’;
Wall weight = 10psf (7’x80’) = 5.6k
W= Effective Seismic Weight = 28.0k + 5.6k = 33.6k
Seismic Base Shear: V = CsW (Eq. 12.8.1)
CS = SDS/(R/Ie) = 0.356/(3/1.0) = 0.1187 (Eq. 12.8-2)
CS = SD1/(T(R/Ie)) = 0.198/(0.14 (3/1.0)) = 0.471 need not exceed (Eq. 12.8.3)
CS = 0.044 SDS Ie = 0.044(0.356)(1.0) = 0.0157 minimum (Eq. 12.8-5)
CS = 0.01 (Eq. 12.8-5) minimum
CS = 0.1187 governs
V = CSW = 0.1187(33.6k) = 4.0k
V = 4.0 kips
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Calculations:
Vertical Distribution of force (12.8.3) and Diaphragm forces
(12.10.1.1) yield same results for a one story structure: 100% of
base shear V is distributed to roof; and this applies to
diaphragm calculations as well as vertical bracing calculations.
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Accidental Torsion:
• Required for non-flexible diaphragms only
• ASCE 7-16 has a significant change from ASCE 7-10 for
accidental torsion requirements.
• For many buildings, accidental torsion forces are now only
applied to verify if a horizontal torsional irregularity exists.
If it does not exist, then the earthquake forces may be
calculated without accidental torsion.
• See Section 12.8.4.2 for specifics.
For this building, earthquake and accidental torsion forces are
applied and the displacements at each corner are calculated.
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As per Table 12.3-1, torsional irregularity check, the following formula may
be created.
Torsional irregularity exists if drift at ends of building are as follows:
Δ1 max > 1.2 (Δ1 max + Δ1 min)/2
0.015” < 1.2 (0.015+0.013)/2 = 0.0168” OK – No torsional irregularity
exists.
Note that since this is a relative displacement check, it does not matter if
drift is calculated at the elastic or inelastic level.
Since no torsional irregularity exists, then as per Section 12.8.4.2, third
paragraph, accidental torsion moments need not be included when
determining the seismic forces E in the design of the structure and in
determination of the design story drifts. The applied loads, drift and
reactions may be calculated as shown in Figure 4b.
Calculations:
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Calculations:
Load Combinations:
See (12.4), (2.3.6); and (12.4.3) when ΩO overstrength factor is
specifically required.
Redundancy (12.3.4.1) ρ = 1.0 in SDC C.
Horizontal Seismic Load Effect (12.4.2.1) Eh = ρQE = 1.0QE = QE
Vertical Seismic Load Effect (12.4.2.2) Ev = 0.2SDS = 0.2(0.356) =
0.0712
Orthogonal Effects (12.5.3) 100% - 30% corner columns: SDC C
not required.
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Calculations:
Check Drift:
From elastic computer analysis, maximum roof displacement measured at the
center of rigidity (excluding accidental torsion) is 0.014 inches. As per (12.8.6):
δxe = 0.014”
δx = Cd(δxe)/Ie = 3.0(0.014”)/1.0 = 0.042”
Drift = Δ1 = δx = 0.042”
P-delta Effects as per (12.8.7) are inconsequential by inspection.
Allowable Drift (12.12) Table 12.12-1 Δa = 0.020hsx = 0.020(14’)(12”/’) = 3.36”
0.042” < 3.36” therefore OK.
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Member and Connection
Checks:
• Figure 5a and 5b display
roof framing plan forces with
and without accidental
torsion respectively.
• Figure 6 displays elevation
view forces without
accidental torsion.
The following checks will use
the forces without accidental
torsion for the reasons
mentioned above.
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Calculations:Diaphragm:
Diaphragm forces are outlined in Section 12.10.1.1.
wpx = 33.6 k
Fpx = [4.0k/(33.6k)] 33.6k = 4.0 k
(Eq. 12.10-1)
Fpx min = 0.2SDSIewpx = 0.2(0.356)(1.0)33.6k = 2.4 k min
(Eq. 12.10-2)
Fpx max = 0.4SDSIewpx = 0.4(0.356)(1.0)33.6k = 4.8 k max
(Eq. 12.10-3)
The diagram forces from equation Eq. 12.10-1 need not exceed Eq. 12.10-3, however,
Section 12.10.1.1 states that “Floor and roof diaphragms shall be designed to resist
design forces from structural analysis, but shall not be less than Eq. 12.10-1.” This
infers that the diaphragm forces shall not be less than those caused by the Base Shear,
V, Fx forces of Section 12.8, including accidental torsion Mta when applicable.
Thus: v = diaphragm shear = 2.0k/(20’) = 0.10 k/’ See Figure 5b.
Check concrete slab thickness and connection of diaphragm to collector beams for
this ultimate strength level force.
Omega Ωo Triggers
• [12.4 Load Combinations with Omega zero] • [12.2.5.2 Cantilever Columns] SDC B,C,D,E,F
• [12.10.2.1 Collectors – Light Frame, Wood excepted] SDC C,D,E,F
• [12.3.3.3 Columns, Beams Supporting Discontinuous Walls] SDC B,C,D,E,F
• [12.13.6.5 Pile Anchorage] SDC D,E,F
• [AISC where R>3, ACI 318-11Chapter 21, Appendix D, Etc.] SDC B,C,D,E,F
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Calculations:Collector:
Collector force requirements are outlined in Section 12.10.2.1. In
essence this section requires that collectors be designed for the
maximum of the following (paraphrasing):
1. Forces Fx in diaphragm due to Base Shear V, including accidental
torsion Mta, and including ΩO, but excluding redundancy ρ (12.3.4.1(5))
i.e. ρ = 1.0.
2. Forces Fpx in diaphragm due to Eq. 12.10-1 excluding accidental
torsion Mta, including ΩO, and excluding redundancy ρ.
3. Forces Fpx max from Eq. 12.10-2 excluding accidental torsion Mta,
excluding ΩO, but including redundancy ρ.
For this example however, accidental torsion Mta need not be included
in the above determination for collectors (Section 12.8.4.2 third
paragraph).
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Calculations:W12x26: Item 1 above governs thus:
v = diaphragm shear (including accidental torsion) = 0.10 k/’
T = tension (or compression force) = 0.10k/’(10’) = 1.0 kips axial load in beam.
Dead load = 1.75 k down
Live load = 0.50 k down
Check beam end connection for the following ultimate strength level loads as per
Section 2.3.6 (6)):
1.2D + Ev+ Eh + 1.0L + 0.2S (eqn. 2.3.6 (6))
Which as per eqn. 12.4-4a and eqn. 12.4-3 evolves to:
(1.2 + 0.2SDS)D + ρQE + 1.0L + 0.2S
and as per 12.10.2.1 SDC C use load combinations with overstrength as per 2.3.6(6):
1.2D + Ev+ Emh + 1.0L + 0.2S (eqn. 2.3.6 (6) with
overstrength)
Which as per eqn. 12.4-4a and eqn. 12.4-7 evolves to:
(1.2 + 0.2SDS)D + ΩOQE + 1.0L + 0.2S (note that r is not included)
(1.2+0.2(0.356))1.75k + 1.0(0.5k) = 2.72k vertical shear on connection
ΩOQE = 3.0(1.0k) = 3.0 kips axial/horizontal load on connection
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Collector, Continued:
Compare 2.72k vertical and 3.0 k axial to capacity of (3) 3/4”
diameter A325 N Bolts as per AISC ϕrn = 17.9 kips per bolt and
verify that all other limit states within connection do not govern.
Note that although this is a Seismic Design Category (SDC) = C,
and R = 3 was used, ASCE 7 Section 12.10.2.1 requires use of ΩO
for collectors, independent of AISC requirements.
Calculations:
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Brace:
E = 3.4 kips
Capacity of brace L = 17’ (approx./conservative)
From AISC Tables L= 17’, ϕcPn = 56.1 kips
3.4 kips < 56.1 kips therefore OK
See Figure 7.
Brace Connection:
E = 3.4 kips
Capacity of 1/4” fillet weld as per AISC ϕRn = 0.8(0.6)70ksi (0.707)(0.25”) = 5.56
kips/”.
Compare E = 3.4k to weld capacity and check other limit states within the connection
(e.g. gusset plate).
Note that this is a Braced Frame as per Table 12.2-1 H. Steel Systems Not Specifically
Detailed for Seismic Resistance, SDC C, and R = 3. AISC 360 is used and we need not
detail as per AISC 341 Seismic. Therefore, brace connections need not be designed for
ΩO, nor full strength of the brace, as would be required in AISC 341 and SDC D, E, and
F for higher R factor systems.
Calculations:
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Calculations:Column:
Axial Loads Dead Load = 7.0k; Live Load = 2.0 kips; E = 2.8 k
Orthogonal Effects (12.5.3) does not apply (SDC C – parallel system)
Section 2.3.6 (6)):
1.2D + Ev+ Eh + 1.0L + 0.2S
Which as per eqn. 12.4-4a and eqn. 12.4-3 evolves to:
(1.2 + 0.2SDS)D + ρQE + 1.0L + 0.2S
Pu = (1.2 + 0.2(0.356))D + 1.0E + 1.0L + 0.2S
Pu = 1.27(7.0k) + 1.0(2.8) + 1.0(2.0) + 0.2(0.0)
Pu = 13.7 k
As per AISC Tables L = 14’; W10x33 col; ϕcPn = 248 kips
13.7k < 248k therefore OK.
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Calculations:Column Base Connection:
Uplift case governs by inspection
Horizontal Shear = 2.0 k
Dead Load = 2.4 kips
Seismic = 2.8 kips
Section 2.3.6 (7)):
0.9D – Ev + Eh (eqn. 2.3.6 (7))
Which as per eqn. 12.4-4a and eqn. 12.4-3 evolves to:
(0.9 – 0.2SDS)D + ρQE
Tu = (0.9-0.2(0.356))D - 1.0E
Tu = (0.829)2.4k - 1.0(2.8k)
Tu = 0.82 kip net uplift
Vu = 2.0 kip horizontal shear
Compare to anchor bolt ultimate capacities for combined tension and shear
(See AISC Design Guide Number 1). See Figure 8.
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Calculations:Footing Loads:
Uplift: Verify weight of footing multiplied by 0.9 exceeds Tu = 0.89 kips.
Tprovided = Footing weight x (0.9) = 0.9(0.150kcf)(3’x3’x2’) = 2.4kips
0.89k < 2.4k therefore no net uplift, OK
Bearing Pressure:
New to ASCE 7-16, there is no need to include Ev in bearing pressure calculations. See
Section 12.4.2.2 for specifics.
Allowable Net Bearing Pressure = 2000 psf.
Dead Load = 7.0 kips
Live Load = 2.0 kips
Seismic = 2.8 kips
Convert Seismic load to Allowable strength level by multiplying by 0.7 as permitted by
Allowable Stress Design Load Combinations Section 2.4.5(8) and (9).
1.0D + 0.7Ev+0.7Eh (eqn. 2.4.5(8))
Which as per 12.4.2.2 Exception 2, eqn. 12.4-4a and eqn. 12.4-3 evolves to:
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Calculations:1.0D + 0.7ρQE
P = (1.0D + 0.7(1.0)E
P = (1.0(7.0k)) + 0.7(1.0)2.8k
P = 9.0 kips
And
1.0D + 0.525Ev + 0.525Eh + 0.75L + 0.75S (eqn. 2.4.5(9))
Which as per 12.4.2.2 Exception 2, eqn. 12.4-4a and eqn. 12.4-3 evolves to:
1.0D + 0.525ρQe + 0.75L + 0.75S
P = 1.0D + 0.525(1.0)E + 0.75L + 0.75S
P = (1.0(7.0k)) + 0.525(1.0)2.8k + 0.75(2.0) + 0.75(0.0)
P = 9.97 kips
P = 9.97 kips governs maximum downward ASD Force on footing.
fbrg = applied bearing pressure = 9.97k/(3’x3’) = 1.108 psf
1,108 psf < 2,000psf therefore 3’ x 3’ Footing is OK
Note that a reduction of applied bearing pressure could be implemented as per (12.13.4),
but was not used in this example.
2019 Structural Engineering Summit – Anaheim
Questions?
Thomas F. Heausler, PE, SE
(913) 963-1180
2019 Structural Engineering Summit – Anaheim
Questions? DiscussionElaboration
Thomas F. Heausler, PE, SE
(913) 963-1180
2019 Structural Engineering Summit – Anaheim
Questions? DiscussionElaboration
I have a friend who...
Thomas F. Heausler, PE, SE
(913) 963-1180