Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2) Structural Engineering Review Course
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Lesson Overview Chapter 7: Lateral Forces
Lateral‐Force Resisting Systems •
Diaphragm Loads
•
Story Drift
•
P‐Delta Effects
•
Simplified Lateral Force Procedure
•
Seismic Load on an Element of a of a Structure
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Lesson Overview Chapter 7: Lateral Forces
Lateral‐Force Resisting Systems •
Diaphragm Loads
•
Story Drift
•
P‐Delta Effects
•
Simplified Lateral Force Procedure
•
Seismic Load on an Element of a of a Structure
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Learning Objectives You will learn •
•
•
•
simple approximations for the fundamental period of vibration of vibration of typical structures how to calculate seismic loads how to distribute seismic loads to typical building structures
•
•
guidance on choosing variables use of tables of tables and figures
•
application of minimum of minimum load limits
•
interpretation of important of important text
tips on how to navigate ASCE/SEI7 2010 and the IBC 2012 design codes for seismic loads
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Prerequisite Knowledge You should already be familiar with •
layout of the of the referenced design codes
•
load application by tributary areas
•
linear interpolation
•
calculating weighted averages
•
common terms for seismic loading
•
•
•
typical building components (braces, beams, trusses, etc.) theory of earthquake of earthquake forces (inertial forced induced by ground shaking)
typical LFRS (braced frames, moment frames, shear walls, etc.)
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Referenced Codes and Standards •
Minimum Design Loads for Loads for Buildings Buildings and Other and Other Structures Structures (ASCE/SEI7, 2010)
•
International Building International Building Code (IBC, 2012)
•
Specification for Specification for Structural Structural Steel Steel Buildings Buildings (AISC 360, 2010)
•
Seismic Provisions for Structural for Structural Steel Steel Buildings Buildings (AISC 341, 2010)
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Diaphragm Loads Loads acting on horizontal diaphragms are given in ASCE/SEI7 Sec. 12.10.1.1.
Figure 7.25 Diaphragm Loads
ASCE/SEI7 Eq. 12.10 ‐1
w px = seismic dead load tributary to a diaphragm, not including walls parallel to the direction of the seismic load
∑ F i = total shear force at level i ∑W i = total seismic weight at level i and above STRC ©2015 Professional Publications, Inc.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Diaphragm Loads: Simplifications For single‐story structures and at the second‐level for multistory structures, use F px
Figure 7.25 Diaphragm Loads
F w
w px
i
i
Recall that V = C sW . Reduce the equation to
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Diaphragm Loads Example 7.16
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Diaphragm Loads
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Diaphragm Loads
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Story Drift story drift [ASCE/SEI7 Sec. 12.8.6] •
•
lateral displacement of one level of a multistory structure relative to the level below calculation for story drift indirectly accounts for inelastic effects through the use of the factor C d ASCE/SEI7 Eq. 12.8 ‐15
C d = deflection amplification factor in ASCE/SEI7 Table 12.2‐1 xe = elastic deflection
I e = seismic importance factor STRC ©2015 Professional Publications, Inc.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Story Drift •
P‐Delta (P‐∆) effects can be neglected when the stability coefficient, θ , defined in ASCE/SEI7 Sec. 12.8.7, is less than 0.10.
P x I e V x hsxC d
0.10
P xΔ = secondary moment V xh sxC d = primary moment •
Maximum allowable story drifts, ∆a, are specified in ASCE/SEI7 Table 12.12‐1.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Story Drift: Maximum Allowable Table 7.8 Maximum Allowable Story Drift, Δa
h sx = height of story x
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Story Drift Example 7.17
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Story Drift Example 7.17
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Story Drift
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
P ‐Delta Effects •
caused by the eccentricity of gravity loads due to story displacements, which induces secondary moments in a story •
•
•
secondary moment in a story: product of the total dead load, floor live load, and snow load above a story multiplied by the elastic drift of that story primary moment in a story: seismic shear in the story multiplied by the height of the story
calculated by using the design level seismic forces and elastic displacements determined in accordance with ASCE/SEI7 Sec. 12.8.1
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Stability Coefficient •
The stability coefficient, θ , is defined in ASCE/SEI7 Sec. 12.8.7
•
P x I e V x hsxCd
P x Cd xe x 1e Vx hsxCd
P x
xe
x 1 e
Vx hsx
The stability coefficient must not exceed the value max
0.5 C d
max
0.25
0.5 C d
0.25
β is the ratio of the shear demand to the shear capacity in a story, and may be conservatively taken as equal to 1.0. STRC ©2015 Professional Publications, Inc.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
P ‐Delta Effects •
If the stability coefficient exceeds 0.10 (secondary moments exceed 10% of primary moments), P‐Delta effects must be considered. (secondary moments must be considered in the analysis of the whole structure )
•
The revised story drift accounting for P‐Delta effects is obtained by scaling the result obtained from ASCE/SEI7 Eq. 12.8‐15 by 1/(1δ)
C d xe 1 I e 1
x
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
P ‐Delta Effects For Fig 2.26, •
•
the primary moment in the second story frame is P 2 F2 hs 2 the secondary moment in the second story is M S 2
•
Figure 7.26 P‐Delta Effects
P 2 2 C d
W 2 2 e 1e
combining both equations results in
M S 2 M P 2
W 2 2e 1e F2 hs 2
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Primary and Secondary Moments Calculate the primary and secondary moments at the first floor in the frame shown given the following. story forces:
F 1 = 100 kips F 2 = 150 kips
story heights:
h s1 = h s2 = 10 ft
story weights:
W 1 = W 2 = 800 kips
elastic drifts:
δ1e = 2.0 in δ2e = 0.65 in
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Primary and Secondary Moments Calculate the primary and secondary moments at the first floor in the frame shown given the following. story forces:
F 1 = 100 kips F 2 = 150 kips
story heights:
h s1 = h s2 = 10 ft
story weights:
W 1 = W 2 = 800 kips
elastic drifts:
δ1e = 2.0 in δ2e = 0.65 in
The primary moment for the first floor is M P1 F1 F2 hs1
100 kips 150 kips 10 ft 2500 ft-kips
The secondary moment for the first floor is P M S 1 1 1 W1 W 2 1e C d
800 kips 800 kips 2.0 in 12
in ft
266.67 ft-kips STRC ©2015 Professional Publications, Inc.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Calculate Stability Coefficient For the previous example, calculate the stability coefficient and determine if secondary moments need to be considered. The primary moment for the first floor is M P 1 = 2500 ft‐kips. The secondary moment for the first floor is M S 1 = 266.67 ft‐kips.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Calculate Stability Coefficient For the previous example, calculate the stability coefficient and determine if secondary moments need to be considered. The primary moment for the first floor is M P 1 = 2500 ft‐kips. The secondary moment for the first floor is M S 1 = 266.67 ft‐kips.
Calculate the stability coefficient.
M S 1 M P 1 266.67 ft-kips 2500 ft-kips
0.107 0.10 Therefore, secondary moments need to be considered.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Calculate Stability Coefficient Example 7.18
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Calculate Stability Coefficient
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Calculate Stability Coefficient
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Lateral Force Procedure: Limitations For some low‐rise structures, ASCE/SEI7 Sec. 12.14 permits an alternative, conservative, simplified design method, provided the following 12 limitations are met. 1. structure
≤ three
stories in height
Figure 7.27 Lines of Lateral Resistance
2. risk category I or II 3. site class A, B, C or D 4. LFRS either a bearing wall or a building frame 5. structure has ≥ two lines of lateral resistance in two major axis directions 6. at least one line of resistance provided on each side of the center of mass (CM) STRC ©2015 Professional Publications, Inc.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Lateral Force Procedure: Limitations For some low‐rise structures, ASCE/SEI7 Sec. 12.14 permits an alternative, conservative, simplified design method, provided the following 12 limitations are met. (continued ) 7. For structures with flexible diaphragms, overhangs beyond the outside line of LFRS (shear walls or braced frames) must satisfy ASCE/SEI7 Eq. 12.14‐1.
Figure 7.28 Flexible Diaphragm Overhang
a d /5 as shown in Fig. 7.28
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Lateral Force Procedure: Limitations For some low‐rise structures, ASCE/SEI7 Sec. 12.14 permits an alternative, conservative, simplified design method, provided the following 12 limitations are met. (continued ) 8. For structures with non‐flexible diaphragms, distance between the center of rigidity (CR) and CM parallel to each other ≤ 15% width of the diaphragm parallel to that axis. The building layout shall also satisfy both of these equations.
Figure 7.29 Torsion Check for Nonflexible Diaphragms
ASCE/SEI7 Eq. 12.14‐2A
ASCE/SEI7 Eq. 12.14‐2B STRC ©2015 Professional Publications, Inc.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Lateral Force Procedure: Limitations For some low‐rise structures, ASCE/SEI7 Sec. 12.14 permits an alternative, conservative, simplified design method, provided the following 12 limitations are met. (continued ) 9. lines of resistance of the structure’s LFRS oriented at angles orthogonal axes of the building
≤ 15° from
major
10. simplified design procedure used for each major orthogonal horizontal axis direction of the structure (i.e., it must be used for analysis in both directions) 11. irregularities caused by in‐plane or out‐of ‐plane offsets of LFRS elements are not permitted (except in two‐story structures of light frame construction, provided the upper wall is designed for with a factor of safety of 2.5 against overturning) 12. lateral load resistance of any story must
≥ 80%
of the story above
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Lateral Force Procedure •
•
•
When using this simplified design procedure, ASCE/SEI7 Sec. 12.14.3.1.1 states that the redundancy factory may be taken as In accordance with ASCE/SEI7 Sec. 12.14.3.2.1, the overstrength factor may be take as structural drift need not be calculated [ASCE/SEI7 Sec. 12.14.8.5 ] If a drift value is required for design of cladding or to determine building separation, it may be assumed to be 1% of the building height.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Poll Question Is the simplified lateral force procedure permitted when lateral forces are resisted by three bays of braced frames? (A) The simplified lateral force procedure is permitted. (B) The simplified lateral force procedure is not permitted.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Poll Question Is the simplified lateral force procedure permitted when lateral forces are resisted by three bays of braced frames?
The following conditions required for the simplified lateral force procedure cannot be met.
(A) The simplified lateral force procedure is permitted.
5. The structure has at least two lines of lateral resistance in two major axis directions.
(B) The simplified lateral force procedure is not permitted.
6. At least one line of resistance is provided on each side of the center of mass (CM).
The answer is (B).
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Poll Question Is the simplified lateral force procedure permitted for a jail founded on soft soil? (A) The simplified lateral force procedure is permitted. (B) The simplified lateral force procedure is not permitted.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Poll Question Is the simplified lateral force procedure permitted for a jail founded on soft soil? (A) The simplified lateral force procedure is permitted. (B) The simplified lateral force procedure is not permitted.
The following conditions required for the simplified lateral force procedure cannot be met. 1. risk category I or II 2. site class A, B, C, or D
The answer is B.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Determination of Seismic Base Shear •
The simplified seismic base shear is ASCE/SEI7 Eq. 12.14‐11
•
The design spectral response acceleration at short periods, S DS , is given in ASCE/SEI7 Sec. 12.14.8.1 as
Per ASCE/SEI7 Sec. 11.4.1, •
The response modification factor, R, is given in ASCE/SEI7 Table 12.14‐1.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Response Modification Factor Table 7.9 Design Factors for Simplified Lateral Force Procedure (partial table)
Adapted with permission from Minimum Design Loads for Buildings and Other Structures, copyright © 2010, by the American Society of Civil Engineers. STRC ©2015 Professional Publications, Inc.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Seismic Base Shear | Simplified Procedure Example 7.20
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Seismic Base Shear | Simplified Procedure Example 7.20
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Seismic Base Shear | Simplified Procedure
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Vertical Distribution of Base Shear When using the simplified lateral force procedure, the calculated base shear must be distributed to floor levels as specified in ASCE/SEI7 Sec. 12.14.8.2. ASCE/SEI7 Eq. 12.14‐12
(equates to distributing the seismic base shear to floor levels based on their contribution to the seismic weight)
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Vertical Distribution of Base Shear Example 7.21
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Vertical Distribution of Base Shear Example 7.21
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Simplified Determination of Drift In accordance with ASCE/SEI7 Sec. 12.14.8.5, when using the simplified lateral force procedure the drift may be determined as 1% of the story height.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Seismic Load on an Element of a Structure •
Seismic load, E , is a function of both horizontal and vertical earthquake‐induced forces and is given in ASCE/SEI7 Sec. 12.4.2 as
vertical horizontal component component
•
The redundancy factor, ρ, as defined by ASCE/SEI7 Sec. 12.3.4, penalizes structures with relatively few lateral load‐resisting elements.
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Redundancy Factor •
•
•
Redundancy is incorporated in order to provide multiple load paths in a structure and multiple lateral load‐resisting elements. The redundancy factor, ρ, penalizes structures with relatively few lateral load‐ resisting elements. two cases in ASCE/SEI7
ρ = 1.0 where yield of one (or relatively few) element(s) will not result in an unstable condition that may lead to collapse ρ = 1.3 where yield of one (or relatively few) element(s) will result in an unstable condition that may lead to collapse
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Redundancy Factor Per ASCE/SEI7 Sec. 12.3.4.1, ρ = 1.0 for the following cases. 1. all structures in seismic design category B or C 2. drift calculations and P‐Delta effects 3. design of nonstructural components 4. design of nonbuilding structures that are not similar to buildings 5. design of collector elements, splices, and connections where overstrength factor of ASCE/SEI7 Sec. 12.4.3 is required
6. design of members or connections where seismic load effects including overstrength factor of ASCE/SEI7 Sec. 12.4.3 are required for design 7. diaphragm loads from ASCE/SEI7 Eq. 12.10‐1 8. structures with damping systems designed in accordance with ASCE/SEI7 Chap. 18 9. design of structural walls for out‐of ‐ plane forces including their anchorage
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Redundancy Factor Per ASCE/SEI7 Sec. 12.3.4.2, ρ = 1.3 for structures assigned to seismic design category D through F unless one of the following conditions are met. 1. Each story resisting ≥ 35% of the base shear in the direction of interest must comply with ASCE/SEI7 Table 12.3‐3. 2. Structures that are regular in plan at all levels (provided that the seismic force‐ resisting perimeter framing on each side of the structure in each orthogonal direction at each story resists ≥ 35% of the base shear. The number of bays for a shear wall must be calculated as the length of the wall divided by the story height, or two times the length of shear wall divided by the story height, h sx, for light‐frame construction.
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Redundancy Factor Example 7.23
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Redundancy Factor Example 7.23
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Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Redundancy Factor
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Redundancy Factor Example 7.24
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Example: Redundancy Factor Example 7.24
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Structural Engineering Exam Review Course
Lateral Forces: Seismic Loads (Part 2)
Seismic Loads (Part 2)
Learning Objectives You have learned •
•
•
•
simple approximations for the fundamental period of vibration of typical structures how to calculate seismic loads how to distribute seismic loads to typical building structures
•
•
guidance on choosing variables use of tables and figures
•
application of minimum load limits
•
interpretation of important text
tips on how to navigate ASCE/SEI7 2010 and the IBC 2012 design codes for seismic loads
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