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Since the first edition of this book was published in1995, it has been my intent to provide exam-like prob-lems that assess your knowledge of seismic design funda-mentals and the seismic code provisions for designingstructures. This book’s twelfth edition continues in thesame spirit as earlier editions.

In this edition, existing problems were updated to thelatest exam-adopted codes: the 2016 California BuildingCode (CBC), the 2015 International Building Code(IBC), and the 2010 Minimum Design Loads for Build-ings and Other Structures (ASCE/SEI7).

I continue to find great contentment in presenting theseismic design fundamentals and principles that safe-guard lives and minimize the economic loss and disrup-tion that follow an earthquake. Being a part of thispreventative effort and the role that California CivilSeismic Principles Solved Problems has played in thecareer advancement of many engineers have been, andwill continue to be, sources of great pleasure and satis-faction to me.

I also value your suggestions and would appreciate yourfeedback regarding any errors or ambiguities in thisbook. You can submit comments via PPI’s errata site atppi2pass.com/errata.

Majid Baradar, PE

Prefacep

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ABOUT THIS BOOK........................................................................................................................

California Civil Seismic Principles Solved Problems con-tains 360 problems that promote and reinforce yourknowledge of seismic principles and the fundamentalearthquake engineering of structures. Problems are mul-tiple-choice and categorized into chapters by topic, aslisted in Table 1. While each problem is based on seismicengineering fundamentals, some require more knowl-edge, judgment, and insight than others. Typically, eachchapter begins with simple problems and then progres-sively presents more difficult and complicated problems.Complete solutions are provided to explain key points,provide problem-solving techniques, and identify appro-priate code references. Where applicable, problems arepresented in customary U.S. units followed by SI unitsin parentheses, and solutions are solved using bothunits.

This book may be used to prepare for the CaliforniaCivil: Seismic Principles exam, which is administered bythe California Board for Professional Engineers, LandSurveyors and Geologists, and/or for seismic problemson the Structural Engineering (SE) exam, which isadministered by the National Council of Examiners forEngineering and Surveying (NCEES).

As you are working problems, be aware that this bookclearly differentiates between four usages of the term“rigidity” using consistent nomenclature and subscripts:absolute rigidity, Rabs; observed rigidity, Robs; relativerigidity, Rrel; and tabulated rigidity, Rtab. (See the “Def-initions of Rigidity Used in This Book” section for moreinformation.)

This book uses the 2015 International Building Code(IBC) and the 2010 Minimum Design Loads for Build-ings and Other Structures (ASCE/SEI7) when referenc-ing code provisions in problems and solutions, unless amore stringent statutory requirement exists. (Forexample, Title 24 of the California Code of Regulationsrequires that schools and hospitals be operational afteran earthquake, and this requirement supersedes lessercode requirements.) Since the 2015 IBC contains thesame material and section numbers as the 2016 Califor-nia Building Code (CBC), you may reference either the2015 IBC or the 2016 CBC.

ABOUT THE EXAMS........................................................................................................................

About the California Civil: Seismic PrinciplesExamThe California Civil: Seismic Principles exam is offeredon a continuous quarterly basis. The format of thisexam has evolved considerably. The current CaliforniaCivil: Seismic Principles exam is a computer–based test(CBT). It is 21

2 hours in length, which you take in a sin-gle sitting. The exam consists of 55 multiple-choiceproblems that each have four answer options. Some ofthe questions are conceptual, some are theoretical, someare practical, some require looking up answers, andsome require simple calculations. The average timeallowed per question is about two and a half minutes. Soyou can see, the level of difficulty cannot be insurmount-able. You just have to go, go, go. For most people, it’spretty easy to know when you have to guess at a ques-tion and then move on.

The total number of points on the exam and the mini-mum passing score are not public knowledge. The per-centage of people who pass varies considerably: between30% and 40%, typically. Many examinees receive spe-cialized instruction in seismic design (i.e., they take aspecialized course), and the reported passing percentagefactors in those “knowledgeable” examinees. There isonly a moderate correlation between the people whopass the NCEES PE Civil exam and the people whopass the California Civil: Seismic Principles exam or theCalifornia Civil: Engineering Surveying exam. The per-centage of people who pass all three exams at the sametime is not high.

The exam “test plan” that defines the fundamental principles,tasks, and elements of knowledge that you need to know hasbeen made public by the California Board for ProfessionalEngineers, Land Surveyors, and Geologists (referred to as“the Board”). If you want to know what you have to know inorder to pass, you can print out the test plan from theBoard’s website. A link to the test plan is also provided atppi2pass.com/CAspecial.

Introductionp

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The information that was used to write and update thisbook was based on the exam specifications at the timeof publication. However, as with engineering practiceitself, the California Civil: Seismic Principles exam andthe Structural Engineering Exam are not always basedon the most current codes or cutting-edge technology.Similarly, codes, standards, and regulations adopted bystate and local agencies often lag issuance by severalyears. It is likely that the codes that are most current,the codes that you use in practice, and the codes thatare the basis of your exam will all be different. It is yourresponsibility to find out which codes are relevant toyour exam. In the meantime, here are the codes andreferences that have been incorporated into this edition.

CODES........................................................................................................................

Building Code Requirements and Specification forMasonry Structures (ACI 530/530.1; TMS 402/602).American Concrete Institute, 2013.

Building Code Requirements for Structural Concrete(ACI 318). American Concrete Institute, 2014.

California Building Code (CBC). California BuildingStandards Commission, 2016.

International Building Code (IBC). International CodeCouncil, 2015.

Minimum Design Loads for Buildings and Other Struc-tures (ASCE/SEI7). American Society of Civil Engi-neers, 2010.

National Design Specification for Wood ConstructionASD/LRFD, including National Design SpecificationSupplement, 2012 (NDS). American Forest & PaperAssociation/American Wood Council, 2015.

Seismic Provisions for Structural Steel Buildings(ANSI/AISC 341). American Institute of Steel Con-struction, 2010.

Special Design Provisions for Wind and Seismic (AWCSDPWS). American Forest & Paper Association/Amer-ican Wood Council, 2015.

REFERENCES........................................................................................................................

The following references were used to prepare this book.You may also find them useful references when studyingfor your exam.

Ambrose, James, and Dimitry Vergun. Simplified Build-ing Design for Wind and Earthquake Forces. Hoboken,NJ: John Wiley & Sons, Inc.

Brandow, Gregg E., Chukwuma Ekwueme, and Gary C.Hart. Design of Reinforced Masonry Structures. Long-mont, CO: The Masonry Society.

Breyer, Donald E., Kenneth J. Fridley, Kelly E. Cobeen,and David G. Pollock, Jr. Design of Wood Structures—ASD/LRFD. New York, NY: McGraw-Hill.

California Board for Professional Engineers, Land Sur-veyors, and Geologists. Professional Engineers Act,Business and Professions Code, Sections 6700–6799.California Seismic Safety Commission. The CommercialProperty Owner’s Guide to Earthquake Safety.California Seismic Safety Commission. The Homeown-er’s Guide to Earthquake Safety.Faherty, Keith F., and Thomas G. Williamson. WoodEngineering and Construction Handbook. New York,NY: McGraw-Hill.

Naeim, Farzad, ed. The Seismic Design Handbook.Springer.

Pauley, T., and M. J. N. Priestley. Seismic Design ofReinforced Concrete and Masonry Buildings. Hoboken,NJ: John Wiley & Sons, Inc.

Structural Engineers Association of California(SEAOC). SEAOC Blue Book: Seismic DesignRecommendations.

U.S. Army Corps of Engineers. Seismic Design of Build-ings (UFC 3-310-04).

Codes and Referencesp

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becomes 1. Generally, the building acceleration is higher(not lower) than the ground acceleration.

The answer is (D).

SOLUTION 46........................................................................................................................

SI Solution

For the response spectrum provided, the spectral accel-eration, Sa, for a natural period of 0.3 s is 0.7 g. Thebase shear, V, is given by Newton’s second law.

= ===

V ma W0.7(0.7)(710†kN)

497†kN (500†kN)

The answer is (C).

Customary U.S. Solution

For the response spectrum provided, the spectral accel-eration, Sa, for a natural period of 0.3 sec is 0.7 g. Thebase shear, V, is given by Newton’s second law.

= ===

V ma W0.7(0.7)(160†kips)

112†kips (110†kips)

The answer is (C).

SOLUTION 47........................................................................................................................

SI Solution

Use Hooke’s law to determine the component’s stiffness,Kp.

= = =KF 4500†N

38†mm118.4†N/mmp

ASCE/SEI7 Eq. 13.6-1 is used to calculate the funda-mental period of vibration for mechanical components.

=

=

=

( )

TW

K g2

211000†N

118.4†N

mm9.81†

m

s1000†

mmm

0.61†s (0.60†s)

pp

p

2

The answer is (A).

Customary U.S. Solution

Use Hooke’s law to determine the component’sstiffness, Kp.

= = =KF 1000†lbf

1.5†in666.7†lbf/inp

ASCE/SEI7 Eq. 13.6-1 is used to calculate the funda-mental period of vibration for mechanical components.

=

=

=

( )

TW

K g2

22500†lbf

666.7†lbfin

32.2†ft

sec12†

inft

0.62†sec (0.60†sec)

pp

p

2

The answer is (A).

SOLUTION 48........................................................................................................................

A concentrically braced frame (CBF) is defined inASCE/SEI7 Sec. 11.2 as a braced frame where the mem-bers are subjected to primarily axial forces. Option A isa V-braced frame, a type of concentrically braced framewhere chevron braces each intersect a beam from above.Option B is a K-braced frame, where pairs of braces onone side of a column each terminate at an identicalpoint along the column height. Option D is an X-bracedsystem, where pairs of diagonal braces cross at or nearmid-length of the bracing members. Option C is aneccentrically braced frame, which is defined by ASCE/SEI7 Sec. 11.2 as a diagonally braced frame in which atleast one end of each bracing member connects to abeam on another brace a short distance from the beam-to-column or beam-to-brace connection.

The answer is (C).

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PROBLEM 1........................................................................................................................

ASCE/SEI7 uses the acronym MCER to mean themaximum

(A) considered earthquake ground motion

(B) credible earthquake ground motion

(C) considered design ground motion

(D) credible design ground motion

PROBLEM 2........................................................................................................................

According to ASCE/SEI7, what would be the seismicdesign category for a risk category III structure that hasa mapped spectral response acceleration parameter, S1,of 0.85 at 1 sec?

(A) B

(B) C

(C) D

(D) E

PROBLEM 3........................................................................................................................

Depending on the specifics of a structure, the systemoverstrength factor will vary between

(A) 1.0 and 1.3

(B) 1.3 and 1.6

(C) 1.3 and 3.0

(D) 1.6 and 2.0

PROBLEM 4........................................................................................................................

IBC seismic provisions are intended as minimumrequirements. The level of protection and safety can bemagnified by increasing which of the following?

I. seismic response coefficient

II. design lateral force

III. redundancy

(A) I only

(B) I and II only

(C) III only

(D) I, II, and III

PROBLEM 5........................................................................................................................

An engineering firm is designing a single family dwellingin a high seismic area that is also subject to very strongwinds. According to the IBC, which load will govern thedetailing of the dwelling’s lateral force-resistingsystems?

(A) Wind load governs over seismic load.

(B) Seismic load governs over wind load.

(C) The larger of the two loads governs.

(D) Not enough information is provided.

PROBLEM 6........................................................................................................................

Regarding the design of a structure, which statement isNOT correct?

(A) Wind loads may govern over seismic loads.

(B) Seismic loads may govern over wind loads.

(C) Seismic loads are inertial in nature.

(D) Wind loads are inertial in nature.

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PROBLEM 7........................................................................................................................

A site is subject to liquefaction and earthslides and islocated on an active major fault line. The IBC preventsconstruction on this site due to

(A) liquefaction

(B) earthslides

(C) fault lines

(D) none of the above

PROBLEM 8........................................................................................................................

According to the IBC, load combinations may beincreased by which percentage using the allowable stressdesign method (working stress design method)?

(A) 33%

(B) 66%

(C) no increase permitted

(D) not enough information

PROBLEM 9........................................................................................................................

For a structure assigned to seismic design category D,ASCE/SEI7 defines deformation compatibility in whichsection?

(A) Sec. 12.3

(B) Sec. 12.6

(C) Sec. 12.9

(D) Sec. 12.12

PROBLEM 10........................................................................................................................

Which facility is NOT an essential facility required toremain operational after an earthquake?

(A) aviation control towers

(B) jails

(C) water treatment facilities

(D) emergency rooms

PROBLEM 11........................................................................................................................

A small hospital is not equipped with a surgery room oran emergency room. Based on IBC requirements, thisfacility’s risk category is

(A) I

(B) II

(C) III

(D) IV

PROBLEM 12........................................................................................................................

Per ASCE/SEI7 requirements, which site class isassumed when soil properties are unknown?

(A) A

(B) B

(C) C

(D) D

PROBLEM 13........................................................................................................................

The response modification factor, R, accounts for astructural system’s

I. resistance

II. ductility

III. stiffness

(A) I only

(B) II only

(C) I and II only

(D) III only

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PROBLEM 14........................................................................................................................

According to ASCE/SEI7, the value of hn for the struc-tures shown is

structure I structure II

penthouse

level 6

level 5

level 4

level 3

level 2

level 1

level 5

level 4

level 3

level 2

level 1

(A) larger for structure I

(B) larger for structure II

(C) equal for structure I and structure II

(D) unable to be determined

PROBLEM 15........................................................................................................................

For steel eccentrically braced frames, what is the valueof Ct in customary U.S. units?

(A) 0.01

(B) 0.02

(C) 0.03

(D) 0.04

PROBLEM 16........................................................................................................................

The total seismic dead load should include

I. anything permanently suspended from the roofinside the building

II. anything mounted on the upper half of the walls

III. permanent equipment mounted on the roof

(A) I only

(B) III only

(C) II and III only

(D) I, II, and III

PROBLEM 17........................................................................................................................

Which statement is true for the effective seismic weightof a structure that has a flat roof snow load of 40 lbf/ft2?

(A) The snow load can be excluded.

(B) 20% of the uniform design snow load must beincluded.

(C) The snow load can be reduced by 25%.

(D) Only 30 lbf/ft2 of the snow load needs to beincluded.

PROBLEM 18........................................................................................................................

The weight, W, used in the base shear calculation for astorage area must include at least 25% of the floor

I. live load

II. dead load

(A) I only

(B) II only

(C) both I and II

(D) neither I nor II

PROBLEM 19........................................................................................................................

When designing a storage facility’s open parking struc-ture, what percentage of the live load must be includedin the value of total weight,W ?

(A) 0%

(B) 25%

(C) 75%

(D) 100%

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PROBLEM 20........................................................................................................................

The soil profile for a proposed building is hard rock. Theelastic fundamental period of vibration for the buildingis 1 sec. The mapped spectral accelerations are S1 = 0.4and SS= 1.0.

T0 Ts T (sec)

Sa =

sp

ectr

al a

ccel

erat

ion

(g

)

SD1/T

SDS

0.4SDS

Ts = SD1/SDS

Using the spectral shape shown, what will most nearlybe the corresponding value of the spectral acceleration?

(A) 0.2 g

(B) 0.5 g

(C) 0.8 g

(D) 1.0 g

PROBLEM 21........................................................................................................................

ASCE/SEI7 uses the formulas shown to determine thefundamental period, T, of a building with concreteshear walls.

=

=

+=

TC

h

CA

hh

A

hD

0.0019/ -

100

1 0.83

/

[ASCE SEI7†Eq.†12.8 9]

[ASCE SEI7†Eq.†12.8-10]

aw

n

wB i

xn

i

i

i

i

1

2

2

For shear wall i, the ratio hi/Di represents the

(A) length to height

(B) height to length

(C) depth to height

(D) height to depth

PROBLEM 22........................................................................................................................

Using ASCE/SEI7 to determine the fundamental frameperiod, T, for a steel moment-resisting frame, what isthe value of x in the equation shown?

=T C ha t nx

(A) 0.75

(B) 0.80

(C) 0.90

(D) 1.00

PROBLEM 23........................................................................................................................

The fundamental time period, T, of a high-rise buildingis larger than the long-period transition period, TL. Themaximum seismic response coefficient, Cs, is given by

(A) =CVWs

(B)=C

SRI

sDS

e

(C)=C

S

TRI

sD

e

1

(D)=C

S T

TRI

sD L

e

1

2

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PROBLEM 24........................................................................................................................

Which equation is the best for determining a structure’smaximum seismic base shear?

(A)=V

SRI

WDS

e

(B)=V

S

TRI

WD

e

1

(C) V = 0.01W

(D)=V

S T

TRI

WD L

e

1

2

PROBLEM 25........................................................................................................................

Which system lacks a complete vertical load-carryingspace frame?

(A) bearing wall systems

(B) moment-resisting frames

(C) building frame systems

(D) dual systems

PROBLEM 26........................................................................................................................

For a moment-resisting structural system, resistance tolateral load is provided by

(A) complete space frames

(B) shear walls

(C) braced frames

(D) flexural action of members

PROBLEM 27........................................................................................................................

For structures with three stories or fewer, which struc-tural system has the lowest ductility expected byASCE/SEI7?

(A) special reinforced concrete shear walls

(B) special reinforced masonry shear walls

(C) steel intermediate moment frames

(D) steel eccentrically braced frames

PROBLEM 28........................................................................................................................

What type of moment-resisting concrete frames shouldbe selected when designing a seven-story apartmentcomplex in Los Angeles (seismic design category D)?

(A) special steel moment-resisting frames

(B) intermediate reinforced concrete momentframes

(C) ordinary steel moment frames

(D) any of the above

PROBLEM 29........................................................................................................................

For a 200 ft (60 m) regular building in San Francisco(seismic design category D), different types of structuralsystems are being analyzed. Which systems are allowedby the IBC?

I. steel eccentrically braced frames

II. special steel truss moment-resisting frames

III. ordinary reinforced concrete shear walls

(A) I only

(B) I and II only

(C) I and III only

(D) I, II, and III

PROBLEM 30........................................................................................................................

A structure consists of composite steel and concrete con-centrically braced frames. According to ASCE/SEI7requirements, intermediate moment frames must becapable of resisting what minimum percentage of pre-scribed seismic forces?

(A) 0%

(B) 5%

(C) 15%

(D) 25%

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PROBLEM 31........................................................................................................................

Consider an 80 ft (25 m) building with a specialmoment-resisting steel frame. The building’s approxi-mate fundamental period is most nearly

(A) 0.4 sec (0.4 s)

(B) 0.5 sec (0.5 s)

(C) 0.8 sec (0.8 s)

(D) 0.9 sec (0.9 s)

PROBLEM 32........................................................................................................................

The three structures shown are located at a site in seis-mic design category C and underlain by the same siteclass. If an earthquake occurs with a predominantperiod of 0.6 sec, which of the buildings shown may bein resonance with the earthquake?

93 ft(28 m)

44 ft(14 m)

54 ft(17 m)

I

concreteshear wallsbearing wall

system

II

steelmoment-resisting

frame

III

concretemoment-resisting

frame

(A) I only

(B) I and III only

(C) II and III only

(D) I, II, and III

PROBLEM 33........................................................................................................................

A ten-story office building with site class B has aresponse modification factor, R, of 5.6; an effective seis-mic weight, W, of 2000 kips (8900 kN); and mappedacceleration parameters of SS= 1.25 and S1 = 0.45. Theseismic importance factor, Ie, is 1.0; the fundamentalperiod, T, is 2 sec; and the long-period transition period,

TL, is 3 sec. What is most nearly the seismic base shearfor the structure?

(A) 30 kips (120 kN)

(B) 50 kips (240 kN)

(C) 70 kips (320 kN)

(D) 100 kips (450 kN)

PROBLEM 34........................................................................................................................

A structure has a seismic base shear of 0.14W. The spec-tral response acceleration (expressed in percentage ofgravity) is most nearly

(A) 5.0%

(B) 10%

(C) 14%

(D) 25%

PROBLEM 35........................................................................................................................

A structure with relatively rigid walls is being designedbelow grade using a gravel-sand mix backfill. Accordingto ASCE/SEI7, the design lateral soil load per squarefoot (meter) of depth should most nearly be

(A) 35 lbf/ft2 (5.5 kN/m2)

(B) 60 lbf/ft2 (9.4 kN/m2)

(C) 85 lbf/ft2 (12 kN/m2)

(D) 100 lbf/ft2 (16 kN/m2)

PROBLEM 36........................................................................................................................

A site has an SS value of 0.85 and is classified as siteclass D. The short period design spectral response accel-eration parameter is most nearly

(A) 0.60 g

(B) 0.70 g

(C) 0.80 g

(D) 0.90 g

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PROBLEM 37........................................................................................................................

The ASCE/SEI7 formula for horizontal seismic designforces, Fp= 1.6SDSIpWp, may NOT be used for

(A) penthouses

(B) self-supported water tanks

(C) braced parapet walls

(D) roof-mounted equipment

PROBLEM 38........................................................................................................................

A nonstructural component is anchored in masonry to astructure. Which of the following design concepts arevalid for the anchorage?

I. A steel anchor design must consider the anchor’stensile or shear yielding strength.

II. An anchor may be used if a bracket or otherattachment of the anchor has a ductile yieldingstrength less than the design strength of theanchor.

III. An anchor may be used if it has a design strength2.5 times higher than the factored loads transmit-ted by the component.

(A) I and II only

(B) I and III only

(C) II and III only

(D) I, II, and III

PROBLEM 39........................................................................................................................

For the design of the monument shown, what responsemodification factor, R, should be used?

(A) 2.0

(B) 2.2

(C) 2.9

(D) 3.6

PROBLEM 40........................................................................................................................

What are the amplification factor, ap, and the responsemodification factor, Rp, for an architectural componentpart of a structure’s ceiling?

(A) 1.0 and 2.5

(B) 1.0 and 3.0

(C) 2.5 and 3.5

(D) 2.5 and 4.0

PROBLEM 41........................................................................................................................

Which value of the seismic force overstrength factor,ΩO, should be used for a billboard?

(A) 1.75

(B) 2.00

(C) 2.50

(D) 3.00

PROBLEM 42........................................................................................................................

A nonbuilding structure has a response modificationfactor, R, of 1.25 and a mapped spectral response accel-eration parameter, S1, of 0.75 g. Assuming a seismicimportance factor of 1.0, the minimum value for theseismic response coefficient, Cs, is most nearly

(A) 0.01

(B) 0.03

(C) 0.10

(D) 0.50

PROBLEM 43........................................................................................................................

Which ASCE/SEI7 formula is used to obtain the lateralforce for a rigid nonbuilding structure with a funda-mental period, T, of 0.04 sec?

(A) V= 0.2SDSWIe

(B) V= 0.3SDSWIe

(C) V= 0.6SDSWIe

(D) V= 0.8SDSWIe

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The irregularity that the structure most likely possessesis a(n)

(A) in-plane discontinuity

(B) out-of-plane offset

(C) vertical geometric irregularity

(D) weight irregularity

SOLUTION 1........................................................................................................................

MCER stands for the maximum considered earthquakeground motion and is the most severe earthquake con-sidered in ASCE/SEI7 as defined in Sec. 11.4.

The answer is (A).

SOLUTION 2........................................................................................................................

According to ASCE/SEI7 Sec. 11.6, a structure withrisk category I, II, or III and a mapped spectral responseacceleration parameter greater than or equal to 0.75 at1 sec is given a seismic design category of E. All otherstructures must be determined in accordance withASCE/SEI7 Sec. 11.4.4 and Sec. 11.6.

The answer is (D).

SOLUTION 3........................................................................................................................

In a linear elastic structure, the force in the structurereaches R times the calculated design seismic force. R isthe response modification factor of the structure andhas a value between 1.0 and 8.0 depending on the struc-tural system. However, because of the inelastic behaviorof the actual structure, the fundamental period and thedamping ratio increase, and seismic energy is dissipated.This reduces the actual seismic force that can be devel-oped to ΩO times the design seismic force. ΩO is the sys-tem overstrength factor, which varies between 1.25 (1.3)and 3.0 depending on the structure.

The answer is (C).

SOLUTION 4........................................................................................................................

The level of protection and safety applies to the seismicresistance of the structures, which can be increased byincreasing the

• seismic response coefficient of the lateral force-resistingsystem

• design lateral force

• redundancy (i.e., two or more lateral load supportingsystems)

• quality of the construction materials and methods

The answer is (D).

SOLUTION 5........................................................................................................................

According to IBC Sec. 1604.10, lateral force-resistingsystems must meet seismic detailing requirements andlimitations prescribed in the IBC and ASCE/SEI7(excluding ASCE/SEI7 Chap. 14 and App. 11.A), evenwhen the code prescribed wind load effects are greater

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than seismic load effects. Therefore, the seismic designload requirements will govern over the wind load for thedetailing of the dwelling’s lateral force-resistingsystems.

The answer is (B).

SOLUTION 6........................................................................................................................

The larger load, wind or seismic, governs a structure’sdesign. (Unlike seismic detailing requirements, the seis-mic load requirements will govern over wind loadrequirements as prescribed by IBC Sec. 1604.10.) Windloads are applied over the exterior surface of the struc-ture, while the seismic loads are inertial in nature.

The answer is (D).

SOLUTION 7........................................................................................................................

The IBC does not prevent construction on a site subjectto liquefaction, earthslides, and major ground accelera-tion. As a minimum requirement, the IBC provisionsshould apply to the construction. To increase the levelof protection, R, the design lateral force, redundancy,and quality of the construction materials and construc-tion methods should be increased. Other state and localcodes may be applicable.

The answer is (D).

SOLUTION 8........................................................................................................................

IBC Sec. 1605.3.1 does not permit increases to allowablestresses using the basic load combinations. However,IBC Sec. 1605.3.2 does permit increases using the alter-native basic load combinations (e.g., load combinationsincluding wind or seismic loads may be increased wherepermitted by the code). Therefore, there is not enoughinformation to determine whether or not an increase tothe allowable stresses is permitted.

The answer is (D).

SOLUTION 9........................................................................................................................

For structures assigned to seismic design categories D,E, or F, deformation compatibility is defined in ASCE/SEI7 Sec. 12.12.5.

The answer is (D).

SOLUTION 10........................................................................................................................

Per IBC Sec. 202, all structures classified as essentialfacilities need to remain operational after an earth-quake. IBC Table 1604.5, risk category IV, lists essentialfacilities that must remain operational after an earth-quake. Hospitals with surgery or emergency facilities,

aviation control towers, and water treatment facilitiesrequired to maintain water pressure for fire suppressionare all essential facilities. Jails are listed as risk categoryIII and are not considered an essential facility.

The answer is (B).

SOLUTION 11........................................................................................................................

Per IBC Table 1604.5, hospitals without surgery or emer-gency treatment areas are considered risk category III.

The answer is (C).

SOLUTION 12........................................................................................................................

Site class designations A, B, C, D, E, and F are definedin ASCE/SEI7 Table 20.3-1. According to ASCE/SEI7Sec. 20.1, soil profile type D should be used for locationswith insufficient geotechnical details to determine thesoil profile type.

The answer is (D).

SOLUTION 13........................................................................................................................

A structure’s response modification factor, R, representsthe overstrength and global ductility of structuralcomponents.

R values are tabulated in ASCE/SEI7 Table 12.2-1 forvarious types of building structural systems and inTable 15.4-1 and Table 15.4-2 for nonbuilding struc-tures. A higher R value is indicative of a more ductilestructural system.

The answer is (B).

SOLUTION 14........................................................................................................................

ASCE/SEI7 Sec. 11.3 defines hn as the height in feet(meters) above the base to the nth level. The nth level isthe uppermost level in the main portion of the building.Generally, penthouses are considered more “elements”than structural systems. Therefore, they would not beconsidered part of the main portion of the structure. hnis larger for structure I.

The answer is (A).

SOLUTION 15........................................................................................................................

Ct is a coefficient used to determine the approximatefundamental period. ASCE/SEI7 Table 12.8-2 gives0.03 for the value of Ct for steel eccentrically bracedframes.

The answer is (C).

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SOLUTION 24........................................................................................................................

ASCE/SEI7 Sec. 12.8.1 gives the equations for deter-mining the seismic base shear of a structure. Any of thefour options can provide the maximum base shear for astructure, depending on the situation. However, optionA will always give the largest base shear value, regard-less of the building period. Therefore, it is the bestoption.

The answer is (A).

SOLUTION 25........................................................................................................................

ASCE/SEI7 Sec. 12.2 gives eight major types of struc-tural systems. Of these, bearing wall systems lack acomplete vertical load-carrying space frame. Instead,bearing walls or bracing systems are designed to supportall vertical loads [ASCE/SEI7 Sec. 11.2]. Lateral loadsare resisted by shear walls or braced frames.

The answer is (A).

SOLUTION 26........................................................................................................................

Moment-resisting structural systems have an essentiallycomplete frame that gives support to both vertical andlateral loads. According to ASCE/SEI7 Sec. 11.2, resist-ance to lateral loads is provided by flexural action ofmembers.

The answer is (D).

SOLUTION 27........................................................................................................................

The response modification factor, R, reflects the inher-ent overstrength and global ductility capacity of differ-ent lateral force-resisting systems. As the value of Rdecreases, the ductility of the structure decreases. R val-ues are given in ASCE/SEI7 Table 12.2-1. From thistable, the values of R for options A, B, C, and D are 6,5.5, 4.5, and 8, respectively. Therefore, steel intermedi-ate moment frames have the lowest ductility.

The answer is (C).

SOLUTION 28........................................................................................................................

There are three types of concrete moment-resistingframes: special, intermediate, and ordinary. These con-crete frames are required by design to be part of the seis-mic (lateral) force-resisting system. Referring to ASCE/SEI7 Table 12.2-1, use of ordinary or intermediate con-crete moment-resisting frames is not permitted for seis-mic design category D. So, the only choice is the specialsteel moment-resisting frames.

The answer is (A).

SOLUTION 29........................................................................................................................

ASCE/SEI7 Table 12.2-1 does not permit the use ofordinary reinforced concrete shear walls in buildings ofseismic design category D. There is a limit of 160 ft(48.8 m) on the height of buildings supported by specialsteel truss moment-resisting or steel eccentrically bracedframes. However, footnote d refers to ASCE/SEI7Sec. 12.2.5.4, which permits the height limit for eccentri-cally braced frames to be increased to 240 ft (73.2 m) forregular buildings, which also satisfies item two of thatsection.

The answer is (A).

SOLUTION 30........................................................................................................................

The structure consists of composite steel and concreteconcentrically braced frames, which is defined byASCE/SEI7 Table 12.2-1, category D, as a dual system.Dual systems must have moment frames capable ofresisting at least 25% of prescribed seismic forces. Thebraced frame, which has no minimum prescribed force,will usually far exceed 25%.

The answer is (D).

SOLUTION 31........................................................................................................................

SI Solution

The approximate fundamental period is determined byASCE/SEI7 Eq. 12.8-7.

=T C ha t nx

Ct and x are approximate period parameters given inASCE/SEI7 Table 12.8-2. For special moment-resistingsteel frames, the values of Ct and x are 0.0724 and 0.8,respectively. The height of the building from the base tothe highest level, hn, is given as 25 m. Therefore, theapproximate fundamental period is

=

==

T C h

(0.0724)(25†m)

0.95†s (0.9†s)

a t nx

0.8

The answer is (D).

Customary U.S. Solution

The approximate fundamental period is determined byASCE/SEI7 Eq. 12.8-7.

=T C ha t nx

Ct and x are approximate period parameters given inASCE/SEI7 Table 12.8-2. For special moment-resistingsteel frames, the values of Ct and x are 0.028 and 0.8,

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To calculate the design spectral response accelerationparameter at short periods, SDS, the maximum consid-ered spectral acceleration parameter, SMS, must befound. SMS can be calculated using ASCE/SEI7Eq. 11.4-1. From ASCE/SEI7 Table 11.4-1, the site coef-ficient, Fa, for a building with site class B is 1.0.

= = =S F S (1.0)(1.25) 1.25MS a S

The maximum considered spectral response accelerationparameter is given by ASCE/SEI7 Eq. 11.4-3.

= = =( )S S23

(1.25) 0.833DS MS23

The minimum seismic coefficient is

===

C S I0.044 0.01

(0.044)(0.833)(1.0)

0.037 [ 0.01,OK]

s DS e

Use a seismic coefficient of 0.037.

The seismic base shear is

===

V C W† (0.037)(8830†kN)

† 323.77†kN (320†kN)

s

The answer is (C).

Customary U.S. Solution

The seismic base shear is calculated from ASCE/SEI7Eq. 12.8-1, V=CsW. The seismic response coefficient,Cs, is given in ASCE/SEI7 Sec. 12.8.1. Because thefundamental period, T, is less than the long-period tran-sition period, TL, use ASCE/SEI7 Eq. 12.8-3 to deter-mine Cs.

=CS

TRI

sD

e

1

The design spectral acceleration parameter, SD1, is givenby ASCE/SEI7 Eq. 11.4-4, where S1 is 0.45.

= = =

= = =

S S

CS

TRI

23

(0.45) 0.3

0.3

(2†sec)5.61.0

0.027

D

sD

e

123 1

1

The minimum seismic coefficient is given by ASCE/SEI7 Eq. 12.8-5.

=C S I0.044 0.01s DS e

To calculate the design spectral response accelerationparameter at short periods, SDS, the maximum consid-ered spectral acceleration parameter, SMS, must befound. SMS can be calculated using ASCE/SEI7Eq. 11.4-1. From ASCE/SEI7 Table 11.4-1, the site coef-ficient, Fa, for a building with site class B is 1.0.

= = =S F S (1.0)(1.25) 1.25MS a S

The maximum considered spectral response accelerationparameter is given by ASCE/SEI7 Eq. 11.4-3.

= = =S S23

(1.25) 0.833DS MS23

The minimum seismic coefficient is

===

C S I0.044 0.01

(0.044)(0.833)(1.0)

0.037 [ 0.01,OK]

s DS e

Use a seismic coefficient of 0.037.

The seismic base shear is

===

V C W† (0.037)(2000†kips)

† 74†kips (70†kips)

s

The answer is (C).

SOLUTION 34........................................................................................................................

The spectral response acceleration, Sa, is derived fromNewton’s second law, F=ma, where V= F.

=

=

VWS

g

SVgW

a

a

From the problem statement, the base shear is 0.14W.

=

=

=

SVgW

W gWg

†(0.14 )

† 0.14

a

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The spectral response acceleration in percentage ofgravities is 14%.

The answer is (C).

SOLUTION 35........................................................................................................................

ASCE/SEI7 Table 3.2-1 gives the design lateral soil loadsfor structures designed below grade. For gravel-sand mixbackfill material, the load is 35 lbf/ft2 (6 kN/m2). How-ever, for structures with rigid walls, the table’s footnote cincreases this load to 60 lbf/ft2 (9.4 kN/m2).

The answer is (B).

SOLUTION 36........................................................................................................................

The short period design spectral response accelerationparameter, SDS, is given by ASCE/SEI7 Eq. 11.4-3.

=S SDS MS2

3

SMS is the MCE spectral response acceleration for shortperiods and is given by ASCE/SEI7 Eq. 11.4-1, SMS=FaSS. The site coefficient, Fa, is given in ASCE/SEI7Table 11.4-1. Since the site class is D, and the SS value is0.85, linear interpolation will be required to determineFa. For SS= 0.75, Fa= 1.2, and for SS= 1.0, Fa= 1.1.Therefore, for SS= 0.85,

= =

= = =

F

S F S

1.21.2 1.11.0 0.75

(0.85 0.75) 1.16

(1.16)(0.85) 0.986

a

MS a S

The design spectral response acceleration parameter is

= = =( )S S23

(0.986) 0.66†g (0.70†g)DS MS23

The answer is (B).

SOLUTION 37........................................................................................................................

Seismic demands on nonstructural components are rep-resented by the horizontal seismic design force, Fp, asgiven in ASCE/SEI7 Sec. 13.3. Nonstructural compo-nents include structural elements that are permanentlyattached to structures, their supports, or their attach-ments (e.g., penthouses, braced parapet walls, and roof-mounted equipment).

A self-supported water tank would be classified as anonbuilding structure, which must carry gravity loadsand may be required to resist the effects of an earth-quake. Design criteria for nonbuilding structures aregiven in ASCE/SEI7 Chap. 15.

The answer is (B).

SOLUTION 38........................................................................................................................

Per ASCE/SEI7 Sec. 13.4.2.2, option I is always valid.This section also validates options II and III when theassembly members meet other requirements. All threeoptions are valid for this anchorage.

The answer is (D).

SOLUTION 39........................................................................................................................

A monument is considered a nonbuilding structure.From ASCE/SEI7 Table 15.4-2, monuments have an Rvalue of 2.0.

The answer is (A).

SOLUTION 40........................................................................................................................

ASCE/SEI7 Table 13.5-1 gives ap and Rp values forarchitectural components and their elements. Ceilingshave an ap value of 1.0 and an Rp value of 2.5.

The answer is (A).

SOLUTION 41........................................................................................................................

Billboards are nonbuilding structures. Per ASCE/SEI7Table 15.4-2, the seismic force overstrength factor, ΩO,is 1.75.

The answer is (A).

SOLUTION 42........................................................................................................................

ASCE/SEI7 Sec. 15.4 gives structural design require-ments for nonbuilding structures. For nonbuilding struc-tures where S1 is greater than or equal to 0.6, theseismic response coefficient, Cs, is found using ASCE/SEI7 Eq. 15.4-2.

=

=

=

CS

RI

0.8

(0.8)(0.75)1.251.0

0.48 (0.50)

s

e

1

The answer is (D).

SOLUTION 43........................................................................................................................

Rigid nonbuilding structures are covered in ASCE/SEI7Sec. 15.4.2. For nonbuilding structures with a

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SOLUTION 48........................................................................................................................

For special steel moment-resisting frames, ASCE/SEI7Table 12.2-1, item C.1, states that there is no limit forstructures braced using this lateral system for anydesign category.

The answer is (D).

SOLUTION 49........................................................................................................................

The seismic response history procedure is covered inASCE/SEI7 Chap. 16. The code covers story drift inSec. 16.2.4.3, which states the design story drift cannotexceed 125% of the drift limit specified by ASCE/SEI7Sec. 12.12.1.

The answer is (B).

SOLUTION 50........................................................................................................................

Ordinary steel concentrically braced frames are classi-fied as building frame systems. Based on ASCE/SEI7Table 12.2-1, a 35 ft (10 m) height limit is applicable tothose systems with steel in seismic design category D.This height is permitted up to 60 ft (18 m) in pent-houses and in single-story buildings where the roof deadload does not exceed 20 lbf/ft2 (0.96 kN/m2). However,these exceptions do not apply to this problem.

The answer is (A).

SOLUTION 51........................................................................................................................

ASCE/SEI7 gives structural system height limitationsin Table 12.2-1. For a regular structure of steel bracedframes and seismic design category E, the height limitsin ASCE/SEI7 Table 12.2-1 are permitted to beincreased from 160 ft (50 m) to 240 ft (75 m).

The answer is (C).

SOLUTION 52........................................................................................................................

ASCE/SEI7 Sec. 12.9.2 allows the reduction of theforce-related parameters, including story drifts, supportforces, and individual member forces, for each mode ofresponse by the quantity R/Ie.

The answer is (B).

SOLUTION 53........................................................................................................................

ASCE/SEI7 Sec. 12.9.1 requires careful consideration ofthe number of modes generated. In each orthogonaldirection, the combined modal mass participationshould be at least 90% of the actual mass for the analy-sis to be valid.

The answer is (A).

SOLUTION 54........................................................................................................................

SI Solution

ASCE/SEI7 gives period determination parameters inSec. 12.8.2. The fundamental period may not exceed theproduct of the coefficient for a calculated period’s upperlimit, Cu, and the approximate fundamental period. Cuis given in Table 12.8-1 and is 1.4 for SD1 values greaterthan 0.4. Ta is determined from ASCE/SEI7 Eq. 12.8-7.

=T C ha t nx

Ct and x are approximate period parameters given inASCE/SEI7 Table 12.8-2. For a concrete moment-resist-ing frame, Ct is 0.0466, and x is 0.9.

= = =T C h (0.0466)(30†m) 0.99†sa t nx 0.9

Therefore, the maximum fundamental period the struc-ture may have is

= = =T C T (1.4)(0.99†s) 1.4†su amax

The answer is (C).

Customary U.S. Solution

ASCE/SEI7 gives period determination parameters inSec. 12.8.2. The fundamental period may not exceed theproduct of the coefficient for a calculated period’s upperlimit, Cu, and the approximate fundamental period. Cuis given in Table 12.8-1 and is 1.4 for SD1 values greaterthan 0.4. Ta is determined from ASCE/SEI7 Eq. 12.8-7.

=T C ha t nx

Ct and x are approximate period parameters given inASCE/SEI7 Table 12.8-2. For a concrete moment-resistingframe, Ct is 0.016, and x is 0.9.

= = =T C h (0.016)(100†ft) 1.0†seca t nx 0.9

Therefore, the maximum fundamental period the struc-ture may have is

= = =T C T (1.4)(1.0†sec) 1.4†secu amax

The answer is (C).

SOLUTION 55........................................................................................................................

Per ASCE/SEI7 Table 12.3-2, item 5, vertical structuralirregularities of the weak story type exist where thestory strength is less than 80% of that in the storyabove, or Sn< 0.80Sn+1. Checking for each story showsthat S3 < 0.80S4. Therefore, the third story is weak.

The answer is (C).

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SOLUTION 62........................................................................................................................

SI Solution

Per ASCE/SEI7 Sec. 12.2.3.2, a two-stage equivalentlateral force procedure is permitted where the averagestory stiffness of the lower portion is at least 10 timesthe average story stiffness of the upper portion.

k k10average,rigid lowerportion average,flexibleupperportion

For structure I,

=

=

=

( )k

k

1400†kN/m

(3) 180†kNm

3180†kN/m

average,rigid lowerportion

average,flexibleupperportion

Since 1400 kN/m is not greater than or equal to 10 times180 kN/m, the criterion is not met, and a two-stage lateralforce procedure is not permitted.

For structure II,

=

=+

=

k

k

1900†kN/m

180†kNm

200†kNm

2190†kN/m

average,rigid lowerportion

average,flexibleupperportion

Since 1900 kN/m is equal to 10 times 190 kN/m, the cri-terion is met, and a two-stage lateral force procedure ispermitted.

The answer is (B).

Customary U.S. Solution

Per ASCE/SEI7 Sec. 12.2.3.2, a two-stage equivalentlateral force procedure is permitted where the averagestory stiffness of the lower portion is at least 10 timesthe average story stiffness of the upper portion.

k k10average,rigid lowerportion average,flexibleupperportion

For structure I,

=

=

=

( )k

k

8000†lbf/in

(3) 1000†lbfin

31000†lbf/in

average,rigid lowerportion

average,flexibleupperportion

Since 8000 lbf/in is not greater than or equal to 10 times1000 lbf/in, the criterion is not met, and a two-stage lat-eral force procedure is not permitted.

For structure II,

=

=+

=

k

k

11,000†lbf/in

1050†lbfin

1150†lbfin

21100†lbf/in

average,rigid lowerportion

average,flexibleupperportion

Since 11,000 lbf/in is equal to 10 times 1100 lbf/in, thecriterion is met, and a two-stage lateral force procedureis permitted.

The answer is (B).

SOLUTION 63........................................................................................................................

Per ASCE/SEI7 Sec. 12.2.3.1, where a combination ofdifferent structural systems is utilized to resist lateralforces in the same direction, the R value used for thedesign in that direction must not be greater than theleast R value for any of the systems utilized in thatdirection. The R value for a bearing special concreteshear wall is 5.0, and the R value for a special moment-resisting steel frame is 8.0. The R value of 5.0 should beused.

The answer is (A).

SOLUTION 64........................................................................................................................

IBC Sec. 1807.2.3 states a safety factor of 1.5 should beused when designing retaining walls against sliding oroverturning.

The answer is (C).

SOLUTION 65........................................................................................................................

For retaining walls, per IBC Sec. 1807.2.3, the minimumresisting force against sliding should be 1.5 times(150%) the lateral force.

The answer is (D).

SOLUTION 66........................................................................................................................

In designing interior walls, permanent partitions, andfabric partitions when the height exceeds 6 ft (2 m),IBC Sec. 1607.14 requires that they must resist

• all loads to which they are subjected

• a minimum force of 5 lbf/ft2 (0.25 kN/m2) appliedperpendicular to the walls

The answer is (B).

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response modification coefficient, R, for amusement struc-tures is 2. The importance factor, Ie, was given as 1.0.

= =

=

CS

TRI

0.55

(1.2†sec)2

1.0

0.23

sD

e

1

The roller coaster is a nonbuilding structure, and themapped spectral response parameter is less than 0.6.Therefore, per ASCE/SEI7 Sec. 15.4-1, item 2, the mini-mum seismic response coefficient is determined usingASCE/SEI7 Eq. 15.4-2.

= =

=

CS

RI

0.8 (0.8)(0.8)2

1.0

0.32 [controls]

s

e

,min1

The larger of the Cs values controls, so the minimumseismic response coefficient is 0.32.

The answer is (D).

SOLUTION 89........................................................................................................................

California Business and Professions Code Sec. 6735allows any licensed civil engineer, a licensed Californiasoils engineer, and an unlicensed civil engineer specializ-ing in structures who is under the responsible charge ofa licensed civil engineer to stamp structural drawings. Alicensed structural engineer (not one of the options)would also be allowed to stamp structural drawings.The code requires the individual to be proficient andexperienced in the field of work they complete, thussomeone with limited experience in structural design,such as a licensed architect, would not be qualified tostamp structural drawings for a bridge.

The answer is (D).

SOLUTION 90........................................................................................................................

SI Solution

ASCE/SEI7 Sec. 12.3.4.2 states that a structureassigned to seismic design category D has a redundancyfactor, ρ, of 1.3, unless the structure meets the require-ments of either ASCE/SEI7 Sec. 12.3.4.2 condition (a)or condition (b), whereby ρ is 1.0.

Condition (a) requires that every story resisting morethan 35% of the base shear meet the lateral-force resist-ing element requirements given in ASCE/SEI7Table 12.3-3. The problem states that the structuredoes not meet the requirements of Table 12.3-3, so con-dition (a) is not met.

Condition (b) requires that the structure be regular inplan at every level, and that every story resisting 35% ormore of the structure’s base shear have at least two baysof seismic-force resisting perimeter framing on each sideof the structure. The structure is regular in plan, andevery story except the top story has the required brac-ing. Check what percentage of the base shear the topstory resists by finding the ratio of the shear resistanceat the top story and the base shear.

= = ×

=

VFV

497†kN2162†kN

100%

23%

88

Since the top story does not resist more than 35% of thebase shear, ASCE/SEI7 Sec. 12.3.4.2 condition (b) ismet. The redundancy factor is 1.0.

The answer is (A).

Customary U.S. Solution

ASCE/SEI7 Sec. 12.3.4.2 states that a structureassigned to seismic design category D has a redundancyfactor, ρ, of 1.3, unless the structure meets the require-ments of either ASCE/SEI7 Sec. 12.3.4.2 condition (a)or condition (b), whereby ρ is 1.0.

Condition (a) requires that every story resisting morethan 35% of the base shear meet the lateral-force resist-ing element requirements given in ASCE/SEI7Table 12.3-3. The problem states that the structuredoes not meet the requirements of Table 12.3-3, so con-dition (a) is not met.

Condition (b) requires that the structure be regular inplan at every level, and that every story resisting 35% ormore of the structure’s base shear have at least two baysof seismic-force resisting perimeter framing on each sideof the structure. The structure is regular in plan, andevery story except the top story has the required brac-ing. Check what percentage of the base shear the topstory resists by finding the ratio of the shear resistanceat the top story and the base shear.

= = ×

=

VFV

111.8†kips

486.0†kips100%

23%

88

Since the top story does not resist more than 35% of thebase shear, ASCE/SEI7 Sec. 12.3.4.2 condition (b) ismet. The redundancy factor is 1.0.

The answer is (A).

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fundamental time period. Since the fundamental timeperiod does not exceed the long-period transitionperiod, use ASCE/SEI7 Eq. 12.8-3.

= = =CS

TRI

0.6

(1.3†sec)8.01.0

0.06sD

e

1

Since 0.09 exceeds 0.06, use 0.06 as the governing valueof Cs. Calculate the seismic base shear.

= =

=

( )V C W (0.06) (10†floors)(150,000†lbf)

90,000†lbf (90†kips)s

The answer is (B).

SOLUTION 12........................................................................................................................

SI Solution

The seismic load effects on structures are given inASCE/SEI7 Sec. 12.4. The vertical component of theearthquake load, Ev, is given by ASCE/SEI7 Eq. 12.4-4,where D is the dead load effect (i.e., the buildingweight).

= ==

E S D0.2 (0.2)(1.22)(6700†kN)

1635†kN (1600†kN)v DS

The answer is (C).

Customary U.S. Solution

The seismic load effects on structures are given inASCE/SEI7 Sec. 12.4. The vertical component of theearthquake load, Ev, is given by ASCE/SEI7 Eq. 12.4-2,where D is the dead load effect (i.e., the buildingweight).

===

E S D0.2

(0.2)(1.22)(1500†kips)

366†kips (400†kips)

v DS

The answer is (C).

SOLUTION 13........................................................................................................................

ASCE/SEI7 Sec. 12.10.1.1 discusses diaphragm designforces. The floor and roof diaphragms must be designedto resist seismic forces, not less than that determinedfrom ASCE/SEI7 Eq. 12.10-1. The force, Fpx, deter-mined from this equation need not exceed 0.4SDSIwepx. Ieis the importance factor determined from ASCE/SEI7Table 1.5-2, and wpx is the weight tributary to the

diaphragm at level x. In this problem, the weight isunknown. Therefore,

=

=

=

F S I w

ww

0.4

(0.4)(1.0)(1.25)

0.5

px DS e px

px

px

,max

The answer is (C).

SOLUTION 14........................................................................................................................

SI Solution

The approximate fundamental period, Ta, is given byASCE/SEI7 Eq. 12.8-7 as =T C ha t n

x. Ct and x areapproximate period parameters given in ASCE/SEI7Table 12.8-2. For a steel moment-resisting frame, theyare 0.0724 and 0.8. hn is the structure’s height.For structure I,

= = =T C h (0.0724)(9†m) 0.42†sa t nx

,10.8

For structure II,

= = =T C h (0.0724)(18†m) 0.73†sa t nx

,10.8

For structure III,

= = =T C h (0.0724)(27†m) 1.0†sa t nx

,10.8

Structure III has the largest approximate fundamentalperiod.

The answer is (C).

Customary U.S. Solution

The approximate fundamental period, Ta, is given byASCE/SEI7 Eq. 12.8-7 as =T C ha t n

x. Ct and x areapproximate period parameters given in ASCE/SEI7Table 12.8-2. For a steel moment-resisting frame, theyare 0.028 and 0.8. hn is the structure’s height.For structure I,

= = =T C h (0.028)(30†ft) 0.43†seca t nx

,10.8

For structure II,

= = =T C h (0.028)(60†ft) 0.74†seca t nx

,10.8

3-243-24 C A L I F O R N I A C I V I L S E I S M I C P R I N C I P L E S S O L V E D P R O B L E M S

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PROBLEM 30........................................................................................................................

According to ACI 318, cast-in-place concrete shouldprovide a minimum of how much concrete to protect thereinforcement?

(A) †in†(20†mm)3

4

(B) 1 †in†(38†mm)1

2

(C) 2 in (51 mm)

(D) 3 in (76 mm)

PROBLEM 31........................................................................................................................

Nonreinforced masonry walls are prohibited in struc-tures assigned to which seismic design category?

(A) A

(B) B

(C) E and F

(D) C, D, E, and F

PROBLEM 32........................................................................................................................

What is the direction of the shear reinforcement in amasonry shear wall? (Refer to ACI 530.)

(A) vertical

(B) horizontal

(C) diagonal at an angle of 30° from the horizontal

(D) diagonal at an angle of 45° from the horizontal

PROBLEM 33........................................................................................................................

Based on ACI 530, what should be the maximum allow-able shear stress for masonry walls when the ratioM/(Vd) is 0.5?

(A) f2.0 m g

(B) f2.3 m g

(C) f2.5 m g

(D) f3.0 m g

PROBLEM 34........................................................................................................................

A structure’s design spectral response accelerationparameters at short periods and 1 s are 0.32 and 0.12,respectively. The seismic importance factor is 1.25, andthe response modification coefficient is 3.5. The struc-ture is in seismic design category B. Most nearly,according to ASCE/SEI7, which seismic load should beused to determine the proper anchorage system for awall weighing 1000 lbf/ft (14.6 kN)?

(A) 45 lbf/ft (0.66 kN/m)

(B) 60 lbf/ft (0.88 kN/m)

(C) 100 lbf/ft (1.5 kN/m)

(D) 160 lbf/ft (2.3 kN/m)

PROBLEM 35........................................................................................................................

Per ASCE/SEI7 requirements, concrete or masonrywalls should be anchored to all floors, roofs, and otherstructural elements that provide lateral support for thewalls. Structural walls should be designed to resistbending between anchors where the anchor spacingexceeds

(A) 2 ft (0.6 m)

(B) 4 ft (1.2 m)

(C) 6 ft (1.8 m)

(D) 8 ft (2.4 m)

PROBLEM 36........................................................................................................................

The response modification factor, R, and the deflectionamplification factor, Cd, for a bearing special reinforcedmasonry wall are

(A) 2 and 2.5

(B) 2 and 3.5

(C) 5 and 3.5

(D) 5.5 and 2.5

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SOLUTION 24........................................................................................................................

Hoops/crossties (confinements) are loops of reinforcingbars enclosing longitudinal reinforcements. They applyto lateral reinforcement in compression members (col-umns). Provisions are stated in ACI 318 Sec. 18.7.5.

The answer is (A).

SOLUTION 25........................................................................................................................

Design yield hinging should occur in beams only; specialreinforcement is required at points where the yielding isexpected.

The answer is (A).

SOLUTION 26........................................................................................................................

Seismic hoops apply to lateral reinforcement in flexuralmembers. They should be placed where yielding isexpected. Yielding occurs at the ends of built-in beamsand at points where the moments are greatest (i.e., plas-tic hinges).

The answer is (D).

SOLUTION 27........................................................................................................................

According to ACI 318 Sec. 18.6.3.3, lap splices of flexu-ral reinforcement should be allowed only if hoop or spi-ral reinforcement is furnished over the lap length. Lapsplices cannot be used (1) within the joints, (2) within adistance of twice the member depth from the face ofjoint, and (3) at locations where analysis indicates flexu-ral yielding caused by inelastic lateral displacements ofthe frame.

The answer is (D).

SOLUTION 28........................................................................................................................

Based on the ACI 318 Sec. 18.6.3.3, lap splices of flexu-ral reinforcement can be used within the center half ofthe member length, but not less than twice the memberdepth from the face of the joint.

The answer is (D).

SOLUTION 29........................................................................................................................

Based on ACI 318 Sec. 2.2, plain reinforcement is rein-forcement that does not conform to the definition ofdeformed reinforcement.

Plain bars cannot be used for steel reinforcing in earth-quake resisting elements. In frame members and in wallboundary elements, low alloy A706 reinforcement bars

are required. Based on ACI 318 Sec. 20.2.2.4, billet steelA615 grades 40 and 60 reinforcement may be allowed ifcertain conditions are met.

The answer is (C).

SOLUTION 30........................................................................................................................

According to ACI 318 Sec. 20.6.1.1, item (c), cast-in-place concrete (nonprestressed) should provide a mini-mum of 3

4 in (20 mm) of concrete cover to protect thereinforcement for walls, slabs, and joists.

The answer is (A).

SOLUTION 31........................................................................................................................

ASCE/SEI7 Table 12.2-1 prohibits the use of plaindetailed or ordinary masonry walls in structuresassigned to seismic design categories C, D, E, and F.

The answer is (D).

SOLUTION 32........................................................................................................................

According to ACI 530 Sec. 8.3.5.2.1, the shear reinforce-ment must be provided parallel to the direction of theapplied shear force. Since the shears generated due toearthquake loads in a shear wall are generally horizon-tal, the shear reinforcement should be placed in the hori-zontal direction.

The answer is (B).

SOLUTION 33........................................................................................................................

ACI 530 Sec. 8.3.5.1.2 provides two equations for calcu-lating the maximum allowable shear stress in masonrystructures. If the ratio M/Vd is less than or equal to0.25, Eq. 8-26 is used.

F f3v m g

If the ratio M/Vd is greater than or equal to 1.0,Eq. 8-27 is used.

F f2v m g

The code allows interpolation for values of M/Vdbetween these two. Interpolate the two equations to findthe equation used whenM/Vd is equal to 0.5.

+ =f f20.250.75

2.3m g m g

The answer is (B).

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modification factor for the seventh floor must be lessthan or equal to 8.5. The response modification factorfor the sixth floor is 4.5, so the response modificationfactor for any floor below it must be less than or equalto 4.5. The response modification factor is not less than4.5 for any floor between the seventh and second floors,so the response modification factor for the second floormust be less than or equal to 4.5.

The answer is (B).

SOLUTION 47........................................................................................................................

According to ASCE/SEI7 Sec. 12.2.3.1, the responsemodification factor for the design of any story should beless than or equal to the response modification factorused for any story above that story. The response modi-fication factor for the sixth floor is 4.5, so the responsemodification factor for any floor below it must be 4.5.The response modification factor is not less than 4.5 forany floor between the seventh and fourth floors, so theresponse modification factor for the fourth floor must beless than or equal to 4.5, and the response modificationfactor is not less than 4.5 for the third floor, so theresponse modification factor for the second floor mustbe less than or equal to 4.5.

The answer is (A).

SOLUTION 48........................................................................................................................

Some structures (buildings and bridges) are not rigidlyanchored to their foundations but instead are equippedwith base isolators. In an earthquake, the ground movesindependently of buildings that are base isolated. As aresult, the acceleration of these structures will decrease.The isolation system should be designed and con-structed in accordance with the requirements of ASCE/SEI7 Chap. 17—Seismic Design Requirements for Seis-mically Isolated Structures.

The answer is (C).

SOLUTION 49........................................................................................................................

ASCE/SEI7 Sec. 17.1.2 defines an isolation system. Forstructures fitted with base isolation, the accelerationdecreases while the structure’s natural period increases.A structure is generally suitable for seismic base isola-tion where the site (soil) does not produce a long period.Base isolation is not suitable where the soil is soft,because the long period of soft soil may coincide withthe increased period of the structure and produce reso-nance. A structure that is rigidly anchored to its founda-tion is, by definition, not base isolated.

The answer is (A).

SOLUTION 50........................................................................................................................

SI Solution

According to ASCE/SEI7 Sec. 13.3.2.1, elements that areattached to the exterior should accommodate movementsof the structures based on the equation Dp=ΔxA− ΔxB.Dp is the relative displacement an element must bedesigned to accept, and Δx is the deflection of level x atthe center of mass of the level. Such elements are sup-ported by mechanical connections and fasteners as givenin the problem statement. Note that exterior nonbearing,nonshear wall panels can be supported by means of cast-in-place concrete.

ASCE/SEI7 Eq. 12.8-15 gives the story drift as

=C

Ixd xe

e

δx is the story drift at the center of the mass, δxe is thestory drift at the center of the mass found from linearelastic analysis, and Cd is the deflection amplificationfactor. From ASCE/SEI7 Table 12.2-1, for steel specialmoment frames, Cd= 5.5. Therefore,

= =

=

=

DCI

( )

5.51.0

(5†mm)

27.5†mm (30†mm)

p xA xBd

exeA xeB

Thus, the connections should allow for a relative move-ment of 30 mm between stories.

The answer is (D).

Customary U.S. Solution

According to ASCE/SEI7 Sec. 13.3.2.1, elements that areattached to the exterior should accommodate movementsof the structures based on the equation Dp=ΔxA− ΔxB.Dp is the relative displacement an element must bedesigned to accept, and Δx is the deflection of level x atthe center of mass of the level. Such elements are sup-ported by mechanical connections and fasteners as givenin the problem statement. Note that exterior nonbearing,nonshear wall panels can be supported by means of cast-in-place concrete.

ASCE/SEI7 Eq. 12.8-15 gives the story drift as

=C

Ixd xe

e

δx is the story drift at the center of the mass, δxe is thestory drift at the center of the mass found from linear

4-17D E T A I L S O F S T R U C T U R E S S O L U T I O N S 4-17

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diaphragm determines the spacing and size of the rein-forcing steel.

The answer is (A).

SOLUTION 63........................................................................................................................

SI Solution

AISC 341 Sec. F1 defines the requirements for ordinaryconcentrically braced steel frames. AISC 341 Sec. F1.5arequires that the brace satisfy the requirements ofAISC 341 Sec. D1.1 for moderately ductile members.AISC 341 Table D1.1 gives the limiting width-to-thickness(b/t) ratio for flanges of built-up box sections.

bt

EF

0.64

0.64

(210†GPa) 1000†MPaGPa

220†MPa19.8

y

AISC 341 Sec. F1.5b gives the requirements for the slen-derness of braces installed in V or inverted-Vconfigurations.

KLr

EF

4

4

(210†GPa) 1000†MPaGPa

220†MPa123.6

y

Find the minimum dimensions for the plate by checkingthe slenderness and width-to-thickness ratios againstAISC 341 specifications. The plate to use will be thelightest one that fulfills both the slenderness and width-to-thickness ratio requirements, so begin by checkingthe smallest plate given in the answer options.

A 150 mm× 6.0 mm plate has a width-to-thicknessratio of

= =

= >

bt

h tt2 150†mm (2)(6.0†mm)

6.0†mm23.0 19.8 [NG]

23.0 is greater than the maximum width-to-thicknessratio of 19.8, so try the next more substantial plategiven, the 150 mm× 10 mm plate. A 150 mm× 10 mmplate has a width-to-thickness ratio of

= =

= <

bt

h tt2 150†mm (2)(10†mm)

10†mm13.0 19.8 [OK]

A 150 mm×10 mm plate will meet the width-to-thicknessratio requirement. Check the slenderness ratio require-ment, KL/r. For a square, tubular brace made from150 mm×10 mm plates, the area moment of inertia aboutthe centroid is

= =

=

=

( )

I I Ih h t12

( 2 )

12

(150†mm)

12

150†mm (2)(10†mm)

1218386667†mm

t outer inner

4 4

44

4

The cross-sectional area of the brace is

=

=

=

( )

A h h t( 2 )

(150†mm) 150†mm (2)(10†mm)

5600†mm

2 2

2 2

2

The radius of gyration is

= =

=

rIA

18386667†mm

5600†mm57.3†mm

4

2

For a pin-connected brace, the effective length factor, K,is 1.0. The slenderness ratio is

=

= <

( )KLr

(1.0)(6.0†m) 1000†mmm

57.3†mm104.7 123.6 [OK]

104.7 is less than the maximum slenderness ratio of123.6, so a 150 mm× 10 mm plate will meet allAISC 341 requirements.

The answer is (B).

Customary U.S. Solution

AISC 341 Sec. F1 defines the requirements for ordinaryconcentrically braced steel frames. AISC 341 Sec. F1.5arequires that the brace satisfy the requirements of

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AISC 341 Sec. D1.1 for moderately ductile members.AISC 341 Table D1.1 gives the limiting width-to-thickness(b/t) ratio for flanges of built-up box sections.

bt

EF

0.64

0.6430,000†

kips

in

32†kips

in19.6

y

2

2

AISC 341 Sec. F1.5b gives the requirements for the slen-derness of braces installed in V or inverted-Vconfigurations.

KLr

EF

4

430,000†

kips

in

32†kips

in122.5

y

2

2

Find the minimum dimensions for the plate by checkingthe slenderness and width-to-thickness ratios againstAISC 341 specifications. The plate to use will be thelightest one that fulfills both the slenderness and width-to-thickness ratio requirements, so begin by checkingthe smallest plate given in the answer options.

A 6.0 in × 0.25 in plate has a width-to-thickness ratio of

= =

= >

bt

h tt2 6.0†in (2)(0.25†in)

0.25†in22 19.8 [NG]

22 is greater than the maximum width-to-thicknessratio of 19.8, so try the next more substantial plategiven, the 6.0 in × 0.38 in plate. A 6.0 in × 0.38 in platehas a width-to-thickness ratio of

= =

= <

bt

h tt2 6.0†in (2)(0.38†in)

0.38†in13.8 19.8 [OK]

A 6.0 in × 0.38 in plate will meet the width-to-thicknessratio requirement. Check the slenderness ratio

requirement, KL/r. For a square, tubular brace madefrom 6.0 in × 0.38 in plates, the area moment of inertiaabout the centroid is

= =

=

=

( )

I I Ih h t12

( 2 )

12

(6.0†in)

12

6.0†in (2)(0.38†in)

12

45.2†in

t outer inner

4 4

4 4

2

The cross-sectional area of the brace is

=

=

=

( )

A h h t( 2 )

(6.0†in) 6.0†in (2)(0.38†in)

8.54†in

2 2

2 2

2

The radius of gyration is

= =

=

rIA

45.2†in

8.54†in2.30†in

4

2

For a pin-connected brace, the effective length factor, K,is 1.0. The slenderness ratio is

=

= <

( )KLr

(1.0)(20†ft) 12†inft

2.3†in104.3 122.5 [OK]

104.3 is less than the maximum slenderness ratio of122.5, so a 6.0 in × 0.38 in plate will meet all AISC 341requirements.

The answer is (B).

SOLUTION 64........................................................................................................................

SI Solution

ACI 318 Sec. 18.7.5.3 specifies the maximum spacing of acolumn’s transverse reinforcement as the smallest of (a)one-quarter of the smallest member dimension, (b) sixtimes the diameter of the smallest longitudinal bar, and(c) so = 100 + (350 − hx)/3, where 100 mm≤ so≤152 mm. hx is the horizontal spacing of the crossties, not toexceed 350 mm. ACI equations assume customary U.S.units; criterion (c) is the customary U.S. equation con-verted for SI units.

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For Prob. 1. through Prob. 5., use the following scenario.Two structures, each with the same height and floorweight, are shown in elevation. Structure I has a risk cate-gory of II and is located on a site where the mapped spec-tral acceleration parameters, S1 and SS, are 0.42 and 1.06,respectively. Structure II has a risk category of III and islocated on a site where the mapped spectral accelerationparameters, S1 and SS, are 0.30 and 0.75, respectively. Thefundamental time period is 0.63 sec for structure I and0.43 sec for structure II. For both structures, it is less thanthe long-period transition period. The penthouse in struc-ture II is a special moment-resisting frame.

100 kips (450 kN)100 kips (450 kN)100 kips (450 kN)100 kips (450 kN)100 kips (450 kN)100 kips (450 kN)

30 kips (150 kN)penthouse

10 ft (3 m)

10 ft (3 m)

55 ft (17 m)

S1 = 0.42SS = 1.06

S1 = 0.30SS = 0.75

special moment-resistingreinforced concrete frame

structure I

special steel concentrically braced frame

structure II

soft clay

typical

hard rockmaterial

PROBLEM 1........................................................................................................................

For structure I, the seismic base shear required byASCE/SEI7 is most nearly

(A) 20 kips (100 kN)

(B) 30 kips (120 kN)

(C) 40 kips (190 kN)

(D) 50 kips (220 kN)

PROBLEM 2........................................................................................................................

For structure II, the seismic base shear required byASCE/SEI7 is most nearly

(A) 80 kips (360 kN)

(B) 140 kips (620 kN)

(C) 200 kips (890 kN)

(D) 300 kips (1300 kN)

PROBLEM 3........................................................................................................................

Based on ASCE/SEI7 requirements, the allowable elas-tic interstory displacement (drift) for structure I is mostnearly

(A) 0.30 in (8.0 mm)

(B) 0.40 in (11 mm)

(C) 0.50 in (13 mm)

(D) 0.60 in (15 mm)

PROBLEM 4........................................................................................................................

If structure II were an ordinary (instead of special) steelconcentrically braced frame, then, based on ASCE/SEI7 requirements, the allowable elastic interstory dis-placement (drift) for structure II would be most nearly

(A) 0.30 in (8.0 mm)

(B) 0.40 in (10 mm)

(C) 0.50 in (15 mm)

(D) 0.70 in (20 mm)

5 Design Problemsp

Desig

nProblem

s

P P I • p p i 2 p a s s . c o m

0.044 > 0.01, so the value of Cs is acceptable.

Using the Cs,max value, the base shear is

=

=

=

( )V C W

(0.044) (6†stories)(450†kN)

118.8†kN (120†kN)

s

The answer is (B).

Customary U.S. Solution

Structure I sits atop hard rock material. Therefore, fromASCE/SEI7 Table 20.3-1, the site class is A. Themapped MCER spectral response acceleration param-eters are given. To convert these parameters into site-specific spectral response acceleration parameters, SMSand SM1, the values of the site coefficients, Fa and Fv,will need to be determined.

ASCE/SEI7 Table 11.4-1 provides the value of site coeffi-cient Fa. For site class A, Fa=0.8. ASCE/SEI7Table 11.4-2 provides the value of site coefficient Fv. Forsite class A, Fv=0.8.

ASCE/SEI7 Sec. 11.4.3 gives the equations for SMS and SM1.

= = == = =

S F SS F S

(0.8)(1.06) 0.848

(0.8)(0.42) 0.336MS a S

M v1 1

ASCE/SEI7 Sec. 11.4.4 gives the equations for thedesign spectral acceleration parameters.

= = =

= = =

( )( )

S S

S S

23

(0.848) 0.565

23

(0.336) 0.224

DS MS

D M

23

12

3 1

The design base shear, V, is determined by ASCE/SEI7Eq. 12.8-1: V=CsW. Cs is the seismic response coeffi-cient determined in accordance with ASCE/SEI7Sec. 12.8.1.1. R is the response modification factor givenin Table 12.2-1. For a special moment-resisting concreteframe, R is 8. The importance factor, Ie, for risk cate-gory II is 1.0 [ASCE/SEI7 Table 1.5-2].

Use ASCE/SEI7 Eq. 12.8-2 to compute Cs.

= = =CSRI

0.5658

1.0

0.071sDS

e

Check that this value is within the maximum and mini-mum allowed values. Use ASCE/SEI7 Eq. 12.8-3 to

check the maximum Cs value, as the fundamental timeperiod, T, does not exceed the long-period transitionperiod.

= = =CS

TRI

0.224

(0.63†sec)8

1.0

0.044 [governs]sD

e

,max1

Use ASCE/SEI7 Eq. 12.8-5 to check Cs against the min-imum value.

C 0.01s,min

0.044 > 0.01, so the value of Cs is acceptable.

Using the Cs,max value, the base shear is

= =

=

( )V C W (0.044) (6†stories)(100†kips)

26.4†kips (30†kips)s

The answer is (B).

SOLUTION 2........................................................................................................................

SI Solution

Structure II sits atop soft clay. Therefore, from ASCE/SEI7 Table 20.3-1, the site class is E. The mappedMCER spectral response acceleration parameters aregiven. To convert these parameters into site-specificspectral response acceleration parameters, SMS and SM1,the values of the site coefficients, Fa and Fv, will need tobe determined.

ASCE/SEI7 Table 11.4-1 provides the value of site coef-ficient Fa. For SS= 0.75 and site class E, Fa= 1.2.ASCE/SEI7 Table 11.4-2 provides the value of site coef-ficient Fv. For S1 = 0.30 and site class E, Fv= 2.8.

ASCE/SEI7 Sec. 11.4.3 gives the equations for SMS and SM1.

= = == = =

S F SS F S

(1.2)(0.75) 0.90

(2.8)(0.30) 0.84MS a S

M v1 1

ASCE/SEI7 Sec. 11.4.4 gives the equations for thedesign spectral acceleration parameters.

= = =

= = =

( )( )

S S

S S

23

(0.90) 0.60

23

(0.84) 0.56

DS MS

D M

23

12

3 1

The design base shear, V, is determined by ASCE/SEI7Eq. 12.8-1: V=CsW. Cs is the seismic response coeffi-cient determined in accordance with ASCE/SEI7Sec. 12.8.1.1. R is the response modification factor given

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in Table 12.2-1. For a special steel concentrically bracedframe, R is 6. The importance factor, Ie, for risk cate-gory III is 1.25 [ASCE/SEI7 Table 1.5-2].

Use ASCE/SEI7 Eq. 12.8-2 to compute Cs.

= = =CSRI

0.606

1.25

0.125 [governs]sDS

e

Check that this value is within the maximum and mini-mum allowed values. Use ASCE/SEI7 Eq. 12.8-3 tocheck the maximum Cs value, as the fundamental timeperiod, T, does not exceed the long-period transitionperiod.

= =

=

CS

TRI

0.56

(0.43†s)6

1.25

0.271

sD

e

,max1

Use ASCE/SEI7 Eq. 12.8-5 to check Cs against the min-imum value.

C 0.01s,min

0.125 > 0.01, so the value of Cs is acceptable.

The base shear is

=

= +

=

( )V C W

(0.125) (6†stories)(450†kN) 150†kN

356†kN (360†kN)

s

The answer is (A).

Customary U.S. Solution

Structure II sits atop soft clay. Therefore, from ASCE/SEI7 Table 20.3-1, the site class is E. The mappedMCER spectral response acceleration parameters aregiven. To convert these parameters into site-specificspectral response acceleration parameters, SMS and SM1,the values of the site coefficients, Fa and Fv, will need tobe determined.

ASCE/SEI7 Table 11.4-1 provides the value of site coef-ficient Fa. For SS= 0.75 and site class E, Fa= 1.2.ASCE/SEI7 Table 11.4-2 provides the value of site coef-ficient Fv. For S1 = 0.30 and site class E, Fv= 2.8.

ASCE/SEI7 Sec. 11.4.3 gives the equations for SMS and SM1.

= = == = =

S F SS F S

(1.2)(0.75) 0.90

(2.8)(0.30) 0.84MS a S

M v1 1

ASCE/SEI7 Sec. 11.4.4 gives the equations for thedesign spectral acceleration parameters.

= = =

= = =

S S

S S

23

(0.90) 0.60

23

(0.84) 0.56

DS MS

D M

23

12

3 1

The design base shear, V, is determined by ASCE/SEI7Eq. 12.8-1: V=CsW. Cs is the seismic response coeffi-cient determined in accordance with ASCE/SEI7Sec. 12.8.1.1. R is the response modification factor givenin Table 12.2-1. For a special steel concentrically bracedframe, R is 6. The importance factor, Ie, for risk cate-gory III is 1.25 [ASCE/SEI7 Table 1.5-2].

Use ASCE/SEI7 Eq. 12.8-2 to compute Cs.

= = =CSRI

0.606

1.25

0.125 [governs]sDS

e

Check that this value is within the maximum and mini-mum allowed values. Use ASCE/SEI7 Eq. 12.8-3 tocheck the maximum Cs value, as the fundamental timeperiod, T, does not exceed the long-period transitionperiod.

= = =CS

TRI

0.56

(0.43†sec)6

1.25

0.27sD

e

,max1

Use ASCE/SEI7 Eq. 12.8-5 to check Cs against the min-imum value.

C 0.01s,min

0.125 > 0.01, so the value of Cs is acceptable.

The base shear is

= = +

=

( )V C W (0.125) (6†stories)(100†kips) 30†kips

78.8†kips (80†kips)s

The answer is (A).

SOLUTION 3........................................................................................................................

SI Solution

Based on ASCE/SEI7 Table 12.12-1, the allowable storydrift for a risk category II, concrete moment framestructure (i.e., “all other structures” category) is

= = =( )h0.020 (0.020)(3†m) 1000†mmm

60†mma sx

5-13D E S I G N P R O B L E M S S O L U T I O N S 5-13

Desig

nProblem

s

P P I • p p i 2 p a s s . c o m

SOLUTION 22........................................................................................................................

SI Solution

ASCE/SEI7 Sec. 12.11 gives the requirements for thestructural walls and their anchorages. To determine theout-of-plane force anchorages of concrete structuralwalls to flexible diaphragms, ASCE/SEI7 Eq. 12.11-1 isused, Fp= 0.4SDSkaIeWp.

The flexible diaphragm factor, ka, is found from ASCE/SEI7 Eq. 12.11–2. Lf is the span of the diaphragm inmeters.

= +

= +

=

kL

1.031.3

1.018†m

31.3†m1.6

af

Determine SDS and Wp. The importance factor, Ie, isgiven in the problem statement as 1.0.

=S S [ASCE/SEI7†Eq.†11.4-3]DS MS2

3

For seismic design category D and an SS value of 1.41,the site coefficient, Fa, is 1.0 [ASCE/SEI7 Table 11.4-1].Therefore,

= = =S S23

(1.41) 0.94DS MS23

ASCE/SEI7 Sec. 13.3 governs the design of the nonstruc-tural components, and Sec. 13.4.2 gives force modificationsfor anchors in concrete or masonry. Footnote b in ASCE/SEI7 Table 13.5-1 requires that where flexible diaphragmsprovide lateral support for concrete or masonry walls andpartitions, the design forces for anchorage to the dia-phragm must be as specified in ASCE/SEI7 Sec. 12.11.For concrete anchorages assigned seismic design categoryD, use ASCE/SEI7 Eq. 12.11-1.

=

=

=

F S k I W0.4

(0.4)(0.94)(1.6)(1.0) 4800†N

m

2887.7†N/m

p DS a e p

2

2

The anchors should be designed to support the tributaryarea of the wall that needs to be anchored to thediaphragm.

+ = +

=

hh

2(1.2†m)

6†m2

1†m (1.2†m)

4.8†m

wallparapet

2

The required anchorage force at the roof line is

= =F 2887.7†N

m(4.8†m ) 13 861†Np 2

2

The minimum anchorage force required by ASCE/SEI7Sec. 12.11.2 is

=

=

==

=

=

F k I W

F W

0.2

(0.2)(1.6)(1.0) 2887.7†N

m(4.8†m )

4436†N0.10

(0.10) 2887.7†N

m(4.8†m )

1386†N

p a e p

p p

22

22

Since the largest value controls, the required anchorageforce is 13 861 N (14 000 N).

The answer is (B).

Customary U.S. Solution

ASCE/SEI7 Sec. 12.11 gives the requirements for thestructural walls and their anchorages. To determine theout-of-plane force anchorages of concrete structuralwalls to flexible diaphragms, ASCE/SEI7 Eq. 12.11-1 isused, Fp= 0.4SDSkaIeWp.

The flexible diaphragm factor, ka, is found from ASCE/SEI7 Eq. 12.11-2. Lf is the span of the diaphragm infeet.

= +

= +

=

kL

1.0100

1.060†ft100†ft

1.6

af

Determine SDS and Wp. The importance factor, Ie, isgiven in the problem statement as 1.0.

=S S 11.4[ASCE/SEI7†Eq.† -3]DS MS2

3

For seismic design category D and an SS value of 1.41,the site coefficient, Fa, is 1.0 [ASCE/SEI7 Table 11.4-1].Therefore,

= = =S S23

(1.41) 0.94DS MS23

ASCE/SEI7 Sec. 13.3 governs the design of the nonstruc-tural components, and Sec. 13.4.2 gives force modificationsfor anchors in concrete or masonry. Footnote b in ASCE/SEI7 Table 13.5-1 requires that where flexible diaphragmsprovide lateral support for concrete or masonry walls and

5-265-26 C A L I F O R N I A C I V I L S E I S M I C P R I N C I P L E S S O L V E D P R O B L E M S