Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1) Structural Engineering Review Course
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Lesson Overview Chapter 7: Lateral Forces •
Lateral Force Resisting Systems •
Bearing Wall Systems
•
Building Frame Systems
•
Dual Systems
•
Shear Wall-Frame Interaction Systems
•
Cantilevered Column Systems
•
Non-Seismic Steel Systems
•
Undefined Systems
•
Response Modification, Overstrength, and Redundancy Factors
•
Irregularities
•
Discontinuities
•
Shear Wall Design
•
Diaphragms
2
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Learning Objectives You will learn… •
•
•
•
how to distribute loads to structural sub-systems and components (e.g., diaphragms, chords, etc.) variables used in load distribution calculations use of sections, tables, and figures in relevant codebooks interpretation of code provisions
3
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Learning Objectives You should already be familiar with… •
layout of ASCE/SEI7 and IBC
•
load application by tributary areas
•
linear interpolation
•
calculating weighted averages
•
•
•
common terms from seismic and wind loading (e.g., center of mass, rigidity, windward, leeward, etc.)
•
•
typical lateral force-resisting systems (braced frames, moment frames, shear walls, etc.) typical building components (braces, beams, trusses, etc.) theory of earthquake forces (inertial forced induced by ground shaking) seismic and seismic loads concepts
4
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Referenced Codes and Standards •
International Building Code (IBC, 2012)
•
Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7, 2010)
•
Seismic Provisions for Structural Steel Buildings (AISC 341, 2010)
•
Specification for Structural Steel Buildings (AISC 360, 2010)
•
Special Design Provisions for Wind and Seismic with Commentary (SDPWS, 2008)
5
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Lateral Force-Resisting System lateral force-resisting system (LFRS) •
•
system with basic function of transferring lateral forces acting on structure to foundation vertical and horizontal resisting components used to provide a continuous and competent load path from top of structure to foundation •
system must maintain strength and stiffness across entire load path
•
strength and stiffness must be adequate for necessary design loads
6
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Lateral Force-Resisting System In Fig. 7.1, •
•
•
Figure 7.1Lateral Force-Resisting Components
loads transferred to diaphragm diaphragm transfers loads to LFRS (bracing) LFRS transfers lateral loads to foundation
7
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Seismic Design Category (SDC) seismic design category
description
A
building on good soils where expected ground shaking is minor
B
buildings of risk category I, II, III; expected ground shaking is moderate
C
building of risk category I, II, III with more severe ground shaking; building of risk category IV where expected ground shaking is moderate
D
buildings and structures in areas with severe and destructive earth shaking but not near a major fault
E
building of risk category I, II, III near active major fault
F
building of risk category IV near active major fault
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Lateral Force-Resisting System Requirements LFRS must conform to either •
•
one of the types in ASCE/SEI7 Table 12.2-1 a combination of systems as permitted in ASCE/SEI7 Sec. 12.2.2, Sec. 12.2.3, and Sec. 12.2.4
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Lateral Force-Resisting System Requirements LFRS listed in ASCE/SEI7 Table 12.2-1 must be designed in accordance with requirements from applicable reference documents listed in ASCE/SEI7 Table 12.2-1 •
•
any additional requirements in ASCE/SEI7 Chap. 14
LRFS not listed in ASCE/SEI7 Table 12.2-1 permitted if analytical and test data are submitted and approved. (See ASCE/SEI7 Sec. 12.2.1.)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Classification of LFRS ASCE/SEI7 Sec. 12.2.1 and ASCE/SEI7 Table 12.2-1 define eight major building types 6. shear wall-frame interactive system with ordinary reinforced concrete moment frames and ordinary reinforced concrete shear walls
1. bearing wall 2. building frame 3. moment-resisting frame 4. dual system with special momentresisting frames 5. dual system with intermediate moment frames
7. cantilevered column 8. steel systems not specifically detailed for seismic resistance, excluding cantilever column systems (undefined systems)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Bearing Wall Systems bearing wall system •
•
system with shear walls designed to resist vertical (gravity) loads and lateral loads shear walls transfer receive shear force from floor and roof diaphragms, transfer lateral force to foundation
•
typical bearing wall systems are •
•
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light-framed walls with shear panels, concrete or masonry walls light steel-framed bearing walls with tension-only braces
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Bearing Wall Systems Since bearing wall systems support both
Figure 7.2Bearing Wall System
lateral and gravity loads, failure of lateral capacity will cause failure due to gravity loads. •
low response modification coefficient
•
high lateral design force
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Building Frame Systems building frame system •
•
structure with frame to carry (gravity) loads and separate system of nonbearing shear walls or braced frames to resist lateral loads
SEIS Figure 6.3Building Frame System
failure of the shear wall system does not compromise ability of structure to support gravity loads
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Building Frame Systems typical building frame systems •
steel eccentrically braced frames (EBF)
•
light-framed walls with shear panels
•
concrete or masonry shear walls
•
steel ordinary braced frames (OCBF)
SEIS Figure 6.3Building Frame System
•
special steel concentrically braced frames (SCBG)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Concentrically Braced Frames Figure 7.14Special Steel Concentrically Braced Frames
•
braces intersect frame at beam/column interface and/or other brace locations
•
lateral forces travel through braces and diaphragms only
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Eccentrically Braced Frames Figure 7.16Steel Eccentrically Braced Frames
•
high-shear “link” elements allow for concentrated areas of plasticity in shear
•
can dissipate considerable energy in shear yielding
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Moment-Resisting Frames moment-resisting frame systems •
•
•
•
•
resists forces in members and joints primarily by flexure
SEIS Figure 6.4Moment-Resisting Frame System
relies on frame to carry both gravity and lateral loads may be constructed of concrete or steel sufficient degree of redundancy, excellent inelastic capabilities require special detailing, can be costly STRC ©2015 Professional Publications, Inc.
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Moment-Resisting Frames typical moment-resisting frame systems •
•
•
•
steel and concrete special momentresisting frames (SMRF) concrete intermediate momentresisting frames (IMRF)
SEIS Figure 6.4Moment-Resisting Frame System
steel or concrete ordinary momentresisting frames (OMRF) special steel truss moment frames (STMF)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Dual Systems dual system •
•
•
essentially complete frames provide support for gravity loads
SE IS Fi gu re 6. 5Dual System
moment-resisting frames combined shear walls or braced frames to resist lateral loads often used in tall buildings; height limitations less restrictive than other LRFS
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Dual Systems •
ASCE/SEI7 defines two types of dual systems •
•
•
•
shear walls or braced frames, combined with special moment-resisting frames shear walls or braced frames, combined with intermediate moment-resisting frames
per ASCE/SEI7 Sec. 12.2.5.1, moment-resisting frames shall be capable of resisting ≥ 25% of design base shear at minimum design lateral forces for each system portioned based on relative rigidity
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Dual Systems Figure 7.17Dual System with Moment-Resisting Frames
braced frame with moment-resisting frame
shear wall with moment-resisting frame
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Shear Wall-Frame Interaction Systems shear wall-frame interaction system •
•
•
•
also called shear wall-frame interactive system
SEIS Figure 6.6Shear Wall-Frame Interaction System
combination of ordinary reinforced concrete shear walls and ordinary reinforced concrete moment frames (dual system) restricted to locations of low seismicity (categories A and B) special seismic detailing not required
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Shear Wall-Frame Interaction Systems •
components designed to resist lateral forces in proportion to their rigidities (consider interaction between shear walls and frames on all levels)
•
SEIS Figure 6.6Shear Wall-Frame Interaction System
ASCE/SEI7 Sec. 12.2.5.8: •
•
shear wall must resist ≥ 75% of design story shear at each level frames must resisting ≥ 25% of design story shear at each level
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Cantilevered Column Systems cantilevered column system •
•
•
•
also referred to as inverted pendulum systemsand cantilever column systems
Figure 7.18Cantilever Column System
structure supported on columns cantilevering from their base columns resist gravity and lateral loads typically, most of mass concentrated at or near top, fixed at their bases
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Cantilevered Column Systems •
columns designed for bending moments per procedures in ASCE/SEI7 Sec. 12.2.5.3
•
•
•
Figure 7.18Cantilever Column System
damage due to loading in one direction can compromise resistance capacity in the other (not desirable in high-seismicity areas) [ASCE/SEI7 Sec. 12.2.5.2] maximum height of 35 ft not permitted in SDC D, E, F unless special detailing is used STRC ©2015 Professional Publications, Inc.
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Non-Seismic Steel Systems •
•
•
•
steel systems not specifically detailed for seismic loads designed and detailed according to AISC 360 not required to meet AISC 341 requirements intended for low-seismic applications; design based on response modification coefficient R ≤ 3 •
ensures nominally elastic response to applied loads
•
no special seismic detailing; may be less expensive to build
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Undefined Systems •
•
systems that do not fit into previous categories designer must determine appropriate design forces and submit rational basis for design forces used
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Example: Dual Systems A one-story structure is subjected to a design lateral force of 550 kips in one direction. The structure’s LFRS for forces in that direction is a dual system of two moment frames and four braced frames. The moment frames each have a rigidity of 150 kips/in, and the braced frames each have a rigidity of 200 kips/in. The system is designed per the requirements of ASCE/SEI7 Sec. 12.2.5.1. Does each set of frames meet the minimum design force requirement?
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Response Modification Factor •
represents inherent overstrength and global ductility capacity of structural
•
components determined from type of LFRS (ASCE/SEI7 Table 12.2-1)
•
•
reduces predicted elastic response to design loads, accounting for level of inelastic (plastic) response of LFRS If R = 1.0, structure responds purely elastically to seismic loading (lightly damped, brittle structures)
•
If R > 1.0, structure responds inelastically to seismic loading
•
higher R indicates higher damping and ductility (“better” seismic performance)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Poll Question: Response Modification Factor A steel moment-frame structure has a response modification factor of 8. Which statement about the structure can be inferred from this information? (A) The system must be detailed for high levels of inelastic deformation. (B) The system has a high cost of construction. (C) The system is brittle and will respond essentially to design level seismic forces. (D) The system has low redundancy. STRC ©2015 Professional Publications, Inc.
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Poll Question: Response Modification Factor A steel moment-frame structure has a
The high response modification factor of
response modification factor of 8. Which statement about the structure can be inferred from this information?
R = 8 reduces the seismic design force on the structure and is made possible by detailing that can withstand large inelastic deformations.
(A) The system must be detailed for high levels of inelastic deformation. (B) The system has a high cost of construction. (C) The system is brittle and will respond essentially to design level seismic forces. (D) The system has low redundancy.
Specially detailed structures typically have high costs, but this is not reflected in the R value. Brittle structures have low response modification factors. Redundancy is directly determined by response modification factor. The answer is (A).
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Overstrength overstrength •
•
•
measure of structure’s actual strength compared to design strength in severe earthquakes, structures expected to deform beyond elastic load carrying capacities if effects of overstrength not considered, overloading of nonductile elements can occur
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Overstrength Factor overstrength factor, ΩO •
•
•
also known as seismic force amplification factor accounts for expected overstrength of structure in the inelastic range used to ensure inelastic behavior occurs in elements meant to provide ductility
•
values given in ASCE/SEI7 Table 12.2-1
•
calculated as VY
= base shear at formation of collapse mechanism
VS
= design base shear
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Redundancy Factor redundancy factor, ρ •
•
redundancy incorporated into structure designs to encourage multiple load paths and lateral loadresisting elements
•
•
penalizes structures with relatively few lateral load-resisting elements •
•
used to improve seismic performance of structures in seismic design categories D, E, and F
values specified in ASCE/SEI7 Sec. 12.3.4 Generally, ρ = 1.0 when yield of one element does not create unstable condition that may lead to collapse ρ = 1.3 when yield of one element will result in unstable condition
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Redundancy Factor ρ = 1.0 for the following cases. •
all structures in SDC B or C
•
drift calculations and P-delta effects
•
design of nonstructural components
•
•
•
design of nonbuilding structures (not similar to buildings) design of collector elements, splices, or connections where overstrength factor is required
•
•
•
design of members or connections where seismic load effects, including overstrength, required for design diaphragm loads from ASCE/SEI7 Eq. 12.10-1 structures with damping systems designed in accordance with ASCE/SEI7 Ch. 18 design of structural walls for out-ofplane forces, including anchorage
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Redundancy Factor For structures in SDC D, E, or F,ρ = 1.3, unless either •
•
each story resisting ≥ 35% base shear in direction of interest complies with ASCE/SEI7 Table 12.3-3 structures regular in plan at all levels •
•
provided that the seismic force-resisting systems consist of 2 or more bays of seismic force-resisting perimeter framing on each side of the structure (at each orthogonal direction at each story resisting ≥ 35% base shear number of bays for shear wall = length of shear wall divided by story height (twice the length of shear wall divided by story height for light-frame construction)
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: R, Ω0, and ρ SEIS Example 6.2
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: R, Ω0, and ρ SEIS Example 6.2
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Example: R, Ω0, and ρ SEIS Example 6.2
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Response Mo dification Factor SEIS Example 6.3
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Response Mo dification Factor SEIS Example 6.3
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Response Mo dification Factor
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Regular and Irregular Buildings •
selection of basic plan, shape, and configuration of structure is critical
•
decision influences ability of structure to withstand earthquake ground shaking
•
Previous earthquake performances of buildings clearly illustrates that, all other parameters being identical, the more regular the building, better the seismic performance will be.
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Regular Buildings regular building •
structure with continuous load path to transfer applied lateral forces to foundation
•
symmetric plan shape and similar LFRS strengths to minimize torsion
•
•
•
vertical and lateral force-resisting elements located to provide maximum torsional capacity uniformly distributed mass, stiffness and strength to minimize stress concentrations no geometric irregularities, discontinuities or reentrant corners that will produce stress concentrations
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Non-Regular Building non-regular building
building with one or more structural irregularity irregularities can produce •
stress concentrations
•
increased torsional effects
•
atypical behavior
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Non-Regular Building non-regular buildings penalized per ASCE/SEI7 Ch. 12 Penalties may include •
•
•
overstrength factor, ΩO, applied to design force in critical members prohibition of certain irregularities in buildings in SCD E and F: extreme soft stories, weak stories, extreme torsional irregularities
require dynamic analysis for buildings in SDC D, E, and F with irregularities such as soft stories, mass irregularities, vertical geometric irregularities, torsional irregularities exception: buildings no more than two stories in Risk Category I or II (three stories for light-frame construction)
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Structural Irregularities ASCE/SEI7 Table 12.3-1 and Table 12.3-2 list major irregularities and corresponding references.
SEIS Table 6.10: Plan and Vertical Structural Irregularities [ASCE/SEI7 Table 12.3-1 and Table 12.3-2] STRC ©2015 Professional Publications, Inc.
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Vertical Irregularities •
ASCE/SEI7 Table 12.3-2 defines five
SEIS Figure 6.8Structural Configuration
types of vertical structural irregularities •
•
no irregularities need be considered for SDC A restrictions/remediation for each type of vertical irregularity can be found in ASCE/SEI7 Sec. 12.3.3 and Table 12.6-1
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Vertical Irregularities five types of vertical irregularities
1. soft/extreme soft story irregularity 2. mass (weight) irregularity 3. vertical geometric irregularity 4. in-plane discontinuity 5. weak/extreme weak story irregularity
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Soft Story Irregularity soft story irregularity
satisfies at least one of the following SEI S Fig ure 6.9Vertical Irregularities •
•
story stiffness < 70% of story immediately above story stiffness < 80% of average stiffness of three stories above
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Soft Story Irregularity extreme soft story irregularity
satisfies at least one of the following SEIS Figure 6.9Vertical Irregularities •
•
story stiffness < 60% of story immediately above story stiffness < 70% of average stiffness of three stories above
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Soft Story Irregularity can occur due to •
•
•
•
atypically large story height, especially in entryways and atria (leftmost figure)
SEIS Figure 6.9Vertical Irregularities
reduced number of LRFS on given floor (second figure) soft story at other location in structure (third figure) reduced size/amount of shear walls at given wall (fourth figure)
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Mass ( Weight) Irregularity mass (weight) irregularity •
•
story mass (weight) > 150% of effective mass (weight) of story above or below
SE IS Fi gu re 6. 9Vertical Irregularities
roofs lighter than floor immediately below are excluded
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Vertical Geometric Irregularity vertical geometric irregularity •
horizontal dimension of a story’s LFRS > 130% of that of an adjacent story
SEIS Figure 6.9Vertical Irregularities
(one-story penthouses excluded)
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In-Plane Discontinuity in-plane discontinuity
in-plane offset of a vertical seismic forceresisting element resulting in overturning demands on a supporting beam, column, truss, or slab
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Weak Story Irregularity weak story irregularity •
lateral strength of story < 80% of story immediately above
SEIS Figure 6.9Vertical Irregularities
extreme weak story irregularity •
lateral strength of story < 65% of story immediately above
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Distribution of Lateral Forces (Part 1)
Story Drift Ratio story drift ratio, ASCE/SEI7 Sec. 12.8.6 story drift ratio •
•
•
story drift relative to floor below floor-to-floor height
story drift ratio calculated from design lateral forces, neglecting torsion structure considered irregular due to soft story or mass (weight) irregularity can be considered regular if story drift ratio for each floor < 1.3 times story drift ratio for floor above top two stories need not meet criterion if all stories below satisfy STRC ©2015 Professional Publications, Inc.
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Distribution of Lateral Forces (Part 1)
Example: Mass Irregularities A ten-story office building, 100 ft x 50 ft, is analyzed to determine if it has a mass irregularity. All floors carry identical loads, except a mechanical floor at the fifth level. The nine non-mechanical floors carry a dead load of 60 lbf/ft2, including the allowance for moveable partitions, and a live load of 65 lbf/ft2. The mechanical floor carries a dead load of 125 lbf/ft2, including the allowance for moveable partitions, and a live load of 25 lbf/ft2. Is there a mass irregularity in the structure? STRC ©2015 Professional Publications, Inc.
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Distribution of Lateral Forces (Part 1)
Example: Mass Irregularities A ten-story office building is analyzed to
A mass (or weight) irregularity occurs
determine if it has a mass irregularity. All floors carry identical loads, except a mechanical floor at the fifth level. The nine non-mechanical floors carry a dead load of 60 lbf/ft2, including the allowance for moveable partitions, and a live load of 65 lbf/ft2. The mechanical floor carries a dead load of 125 lbf/ft2, including the allowance for moveable partitions, and a live load of 25 lbf/ft2. Is there a mass irregularity in the structure?
when one story’s effective mass (or weight) is more than 150% of the effective mass (or weight) of a story above or below it. Find the effective seismic weight of a non-mechanical floor. The building is not a warehouse or other storage facility, so live loads are not included. lbf Wnm 60 100 ft 50 ft ft 2 300 kips
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Distribution of Lateral Forces (Part 1)
Example: Mass Irregularities Find the effective weight of the
The effective weight of the mechanical
mechanical floor. lbf Wm 125 100 ft 50 ft ft 2 625 kips
floor is greater than 150% of the effective weight of both the story above and the story below it. There is a mass irregularity in the structure.
The ratio of the mechanical story’s effective mass to one of the stories above or below it is 625 kips 300 kips
2.08 1.5
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Horizontal Irregularities ASCE/SEI7 Table 12.3-1 lists and defines five types of horizontal structural irregularities 1. torsional irregularity •
torsional irregularity
•
extreme torsional irregularity
2. reentrant corner irregularity 3. out-of-plane offset 4. diaphragm discontinuity 5. nonparallel system irregularity
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Distribution of Lateral Forces (Part 1)
Horizontal Irregularities •
For SDC A, no irregularities need to be considered.
•
Restrictions/remediation for each type of horizontal irregularity can be found in •
ASCE/SEI7 Chapter 12, Sections 3.3, 5.3, 7.3, 8.4, and 12.1
•
ASCE/SEI7 Sec. 16.2.2
•
ASCE/SEI7 Table 12.6-1.
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Distribution of Lateral Forces (Part 1)
Torsional Irregularity torsional irregularity •
•
maximum story drift (caused by lateral load and accidental torsion) at one end of structure transverse to its axis > 1.2 times average story drift (calculated from both ends)
SEIS Figure 6.10Horizontal (Plan) Irregularities
only buildings with rigid diaphragms affected by torsional irregularities
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Distribution of Lateral Forces (Part 1)
Torsional Irregularity extreme torsional irregularity •
maximum story drift (caused by lateral load and accidental torsion) at one end of structure transverse to its axis > 1.4 times average story drift (calculated from both ends)
SEIS Figure 6.10Horizontal (Plan) Irregularities
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Reentrant Corner Irregularity reentrant corner irregularity •
•
parts of structure project beyond a reentrant corner a distance of greater than 15% of the plan dimension in the given direction
SEIS Figure 6.10Horizontal (Plan) Irregularities
SEIS Fig. 6.10(b) •
projecting wing 0.15
•
projecting wing 0.15
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Distribution of Lateral Forces (Part 1)
Out-of-plane Offset out-of-plane offset •
•
discontinuity in lateral force path (outof-plane offset of vertical elements)
SEIS Figure 6.10Horizontal (Plan) Irregularities
requires special consideration of load path to compensate
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Distribution of Lateral Forces (Part 1)
Diaphragm Discontinuity diaphragm discontinuity
diaphragms have abrupt discontinuities or variations in stiffness •
•
SEIS Figure 6.10Horizontal (Plan) Irregularities
cutout or open areas > 50% of gross diaphragm area stiffness of the diaphragm changes > 50% from story to adjacent story
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Distribution of Lateral Forces (Part 1)
Nonparallel System nonparallel system •
vertical lateral force-resisting elements not parallel to or symmetrical about major orthogonal axes of LFRS
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Distribution of Lateral Forces (Part 1)
Example: Torsional Irregularity The plan view of a single-story structure is shown. Does a torsional irregularity exist in the structure? If so, what type of torsional irregularity exists?
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Distribution of Lateral Forces (Part 1)
Example: Torsional Irregularity The plan view of a single-story structure
Check if a torsional irregularity exists in
is shown. Does a torsional irregularity exist in the structure? If so, what type of torsional irregularity exists?
the structure.
2 2 1.2 1 2 0.6 2 0.6in 1.0in 1.2 1.2 2 2 0.96 in 1.0 in There is a torsional irregularity in the structure.
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Torsional Irregularity The plan view of a single-story structure is shown. Does a torsional irregularity exist in the structure? If so, what type of torsional irregularity exists?
Check if the torsional irregularity is an extreme torsional irregularity. 2 2 1.4 1 2 0.6 2 0.6in 1.0in 1.4 1.4 2 2 1.12 in 1.0 in There is not an extreme torsional irregularity. The structure must be designed with consideration for a standard torsional irregularity.
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Distribution of Lateral Forces (Part 1)
Analysis of Shear Walls •
•
Hold-downs at each end of wall are
•
required to prevent overturning. Gravity loads atop flexible shear walls may provide restoring moment.
calculated using SDPWS Eq. 4.3-7. T C vh •
It is most conservative to assume no gravity loads provide restoring moment when designing hold-downs.
Tension force in hold-down is
•
•
•
T
= tension force
C
= compression force
v
= induced unit shear
h
= shear wall height
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings •
traditionally designed considering each full height segment of wall as individual shear wall
•
•
•
Figure 7.11Segmented Shear Wall
e.g., wall with single opening designed as two separate shear walls; total of four hold-downs, one at either end of each wall (see Fig. 7.11) sheathing above/below opening not considered to contribute to overall shear capacity shear capacity calculated as sum of capacities of individual segments STRC ©2015 Professional Publications, Inc.
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings perforated shear wall method •
shear capacity calculated as percentage of capacity of wall without openings
Figure 7.12Perforated Shear Wall
(method specified in SDPWS Sec. 4.3.3.5) •
advantage: only two hold-downs required
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings •
sheathed areas above and below openings not designed for force transfer (considered to provide only local restraint at ends)
•
Figure 7.12Perforated Shear Wall
shear capacity of perforated wall depends on maximum opening height and percentage of full height sheathing
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings SDPWS Sec. 4.3.5.3 requirements for perforated walls segment without openings must be located at each end of wall •
•
•
•
aspect ratio limitations of SDPWS Sec. 4.3.4.1 apply maximum required nominal unit shear capacity for single sided wall •
1740 lbf/ft for seismic
•
2435 lbf/ft for wind
•
•
•
where out-of-plane offsets occur, portions of wall on each side of the offset must be considered separate perforated shear walls collectors for shear transfer must be provided through full length of wall must have uniform top-of-wall and bottom-of-wall elevations height ≤ 20 ft
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings design shear capacity of perforated shear
Table 7.1Capacity Adjustment Factors
wall
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Distribution of Lateral Forces (Part 1)
Shear Walls with Openings •
force in a hold-down (also force in the end post) given by SDPWS Eq. 4.3-8
•
•
anchor bolts, in addition to resisting horizontal shear force, must also resist uniformly distributed uplift force given in SDPW Sec. 4.3.6.4.2.1
unit shear force in perforated shear wall is given in SDPWS Eq. 4.3-9
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Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall Example 7.4 Figure 7.12Perforated Shear Wall
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Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall Example 7.4
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall
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Lateral Forces: Distribution of Lateral Forces (Part 1)
Structural Engineering Exam Review Course
Distribution of Lateral Forces (Part 1)
Example: Perforated Shear Wall
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Wall Shear Stress •
shear walls on adjoining levels should
SEIS Figure 7.2Stacked Openings
be structurally continuous, should not be offset (where possible) •
•
•
should be complete transmission path from shear wall on one level to another below horizontally and vertically stacked openings need special attention (see SEIS Fig. 7.2) Vertical shears must be transferred to adjacent piers or boundary columns. STRC ©2015 Professional Publications, Inc.
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Wall Shear Stress required design shear stress •
•
150% of shear stress determined for base shear force of the building (for seismic design categories D, E, F) for masonry shear walls designed for in-plane shear forces by allowable stress procedures, see IBC Sec. 2106.1 (ACI 530 Sec. 1.18.3.2.6.1.2)
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Distribution of Lateral Forces (Part 1)
Wall Rigidity to determine total rigidity of wall with openings (observed or tabulated), divide wall into piers and beams
SEIS Figure 7.4Wall with Openings
pier
vertical portion of wall whose height is taken as smaller of heights of openings on either side (labeled P) beam
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Wall Rigidity relative rigidity •
•
•
rigidity of wall relative to other resisting walls in structure
SEIS Figure 7.4Wall with Openings
actual rigidity for any particular wall unimportant (relative rigidity is important) several methods of calculating wall rigidity from characteristics of piers and beams typically provide slightly different answers
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Wall Rigidity method A •
fastest method, simplest method, but less accurate
•
use only for preliminary analysis
•
rigidity of wall calculated as sum of rigidities of individual piers framed between openings in the wall
•
all piers assumed to be fixed
•
pier height = height of shortest adjacent opening
•
beams and wall portions above/below openings not considered
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Wall Rigidity method B •
•
•
•
deflection/force calculated from standardized values of force, thickness and modulus of elasticity wall rigidity = reciprocal of net deflection rigidity of wall calculated one opening at a time, considering fixed pier adjacent to opening and wall section below opening calculation of pier deflection correction becomes recursive when openings in walls are different heights (Method B is more accurate, but can take longer if wall is relatively complex.)
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Wall Rigidity method B
1. gross deflection of solid wall calculated, ignoring all openings and assuming cantilever action 2. strip deflection of an interior strip with length equal to wall length and height equal to height of tallest opening calculated, assuming cantilever action 3. strip deflection subtracted from gross deflection of solid wall
4. rigidities (not deflections) of all pi ers (assuming fixed ends) within removed strip are summed; pier deflection correction is calculated as reciprocal of sum 5. pier deflection correction added to difference in gross and strip deflections to give net deflection 6. wall rigidity = reciprocal of net deflection
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity SEIS Example 7.2
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity SEIS Example 7.2
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Lateral Forces: Distribution of Lateral Forces (Part 1)
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Example: Wall Rigidity
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Distribution of Lateral Forces (Part 1)
Flexible Diaphragms •
typically constructed from concrete composite and non-composite formed deck or wood structural panels
•
•
Figure 7.1Lateral Force-Resisting Components
must be designed with capacity to resist maximum shear at ends and smaller shears nearer midspan horizontal bracing may be used to resist lateral load in place of diaphragm
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Flexible Diaphragms In Fig. 7.1, •
•
•
diaphragm behaves like simplysupported beam
Figure 7.1Lateral Force-Resisting Components
maximum shear in diaphragm occurs at ends maximum moment in diaphragm occurs at midspan (moment carried by chords at edges of the diaphragm)
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Flexible Diaphragms •
maximum total shear in diaphragm (end reactions)
•
Figure 7.1Lateral Force-Resisting Components
maximum unit shear in diaphragm
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Chords •
•
•
edges of diaphragm normal to the lateral force are chords chord forces calculated from idealized moment in the diaphragm (assuming the diaphragm acts as a simply supported beam)
Figure 7.1Lateral Force-Resisting Components
maximum chord force calculated as
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Chord Size •
•
chord size controlled by chord forces required chord size (cross-sectional area) can be determined from allowable stress (similar for LRFD)
SEIS Figure 7.9Chords
SEIS Eq. 7.13 •
•
can also be calculated for tension, T chord area may be reduced near ends of chord (but reduction must be in accordance with actual moment distribution)
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Example: Chords The rectangular diaphragm shown is subjected to a distributed lateral seismic force of 250 lbf/ft along the long edge. The chord member is made of wood with an allowable stress of 250 lbf/ft 2, and is continuously braced such that the allowable compressive stress is equal to the allowable tensile stress. What chord area is required to resist the lateral seismic force?
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Example: Chords The rectangular diaphragm shown is
The maximum moment for the
subjected to a distributed lateral seismic force of 250 lbf/ft along the long edge. The chord member is made of wood with an allowable stress of 250 lbf/ft 2, and is continuously braced such that the allowable compressive stress is equal to the allowable tensile stress. What chord area is required to resist the lateral seismic force?
diaphragm is 250 lbf 60 ft 2 2 wL ft M 8
8
112,500 lbf/ft The maximum chord force is
C
MD B
112,500
lbf ft
30 ft
3750 lbf
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Distribution of Lateral Forces (Part 1)
Example: Chords The minimum chord area required is Achord
C
allowable stress
3750 lbf lbf 250 2 in
15 in2
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Learning Objectives You will learn… •
•
•
•
how to distribute loads to structural sub-systems and components (e.g., diaphragms, chords, etc.) variables used in load distribution calculations use of sections, tables, and figures in relevant codebooks interpretation of code provisions
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Lesson Overview Chapter 7: Lateral Forces •
Lateral Force Resisting Systems •
Bearing Wall Systems
•
Building Frame Systems
•
Dual Systems
•
Shear Wall-Frame Interaction Systems
•
Cantilevered Column Systems
•
Non-Seismic Steel Systems
•
Undefined Systems
•
Response Modification, Overstrength, and Redundancy Factors
•
Irregularities
•
Discontinuities
•
Shear Wall Design
•
Diaphragms
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