Professional Publications, Inc. • Belmont, California

Seismic DesignSolved ProblemsSixth Edition

Majid Baradar, PE

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1 Seismology Principles

PROBLEMS

1. The surface location of an earthquake is known as the

(A) epicenter

(B) focal depth

(C) dip angle

(D) focus

2. There is a footwall facing a hanging wall prior to anearthquake. The hanging wall moves up during the earth-quake. Which type of fault occurred?

(A) strike-slip fault

(B) reverse fault

(C) normal fault

(D) oblique fault

3. California’s San Andreas fault is a

(A) right-lateral fault

(B) left-lateral fault

(C) normal fault

(D) reverse fault

4. The process where an oceanic plate slides beneath acontinental plate is known as

(A) sea-floor spreading

(B) plate tectonics

(C) subduction

(D) strike-slip

5. Which statement is INCORRECT?

(A) Compression, shear, and surface waves are seis-mic waves.

(B) Shear waves are at right angles to compressionwaves.

(C) P-waves can be expressed as horizontal and ver-tical components.

(D) None of the above are incorrect.

6. Which statements are INCORRECT?

(A) S-waves travel more slowly than P-waves.

(B) S-waves transmit more energy than P-waves.

(C) S-waves cause less damage to structures thanP-waves.

(D) both A and C

7. Which activities occur as seismic sea waves approachland?

(A) wave velocity increases

(B) wave height decreases

(C) both wave velocity and height increase

(D) wave velocity decreases and wave heightincreases

8. Seismic waves are generated by

I. volcanic eruptions

II. deep, artificially induced explosions

III. sudden dislocations within the earth’s crust

(A) I and II

(B) II and III

(C) I and III

(D) I, II, and III

9. A tsunami is a

(A) seismic sea wave

(B) tidal wave

(C) surface-water wave

(D) all of the above

10. What does a seismometer measure?

(A) components of ground motion

(B) reference points

(C) attenuation

(D) actual displacement

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(A) frequencies

(B) periods

(C) acceleration

(D) stiffness

45. Consider the ratio of building acceleration to groundacceleration. Which statement is INCORRECT?

(A) The ratio depends on the building period.

(B) The ratio is equal to 1.0 for an infinitely stiffbuilding.

(C) The ratio is equal to 1.0 for buildings with zeronatural period.

(D) Building acceleration is typically lower thanground acceleration.

46. If W=160 kips (710 kN) and T=0.3 sec, what ismost nearly the base shear for the response spectrashown?

spec

tral

acc

eler

atio

n (

gs)

time (sec)

0.2 0.4 0.6 0.8

0.8

0.4

(A) 40 kips (180 kN)

(B) 70 kips (310 kN)

(C) 110 kips (500 kN)

(D) 140 kips (620 kN)

SOLUTIONS

1. The point on the earth’s surface directly above thefocus is the epicenter. The depth from the earth’s surfaceto the focus is the focal depth.

The answer is (A).

2. Since the hanging wall is thrust upward and over thefootwall, it is a reverse (thrust) fault.

fault line

before movement after movement

hanging wall

footwall

The answer is (B).

3. The sudden displacement, or slip, of the crust or rockalong California’s San Andreas fault is right-lateralmovement. When a person stands on either side of aright-lateral fault and looks across the fault, the faultmovement will be to that person’s right.

The answer is (A).

4. The term subduction refers to the process where anoceanic plate drops and slides beneath a continentalplate.

The answer is (C).

5. Compression, shear, and surface waves are all seismicwaves. Compression waves displace materials directlybehind or ahead of their path of travel, while shear waves(secondary waves or S-waves) displace material at rightangles to their line of travel and reach the surface later.S-waves (not P-waves) have horizontal and vertical com-ponents since their propagation path may be in anydirection from the source.

The answer is (C).

6. From the epicenter, compression waves (primarywaves or P-waves) travel through the earth’s interiorto reach the surface first. S-waves travel more slowlyand reach the surface after the P-waves. However,S-waves transmit more energy than the P-waves, thuscausing the bulk of damage to structures.

The answer is (C).

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1-6 S E I S M I C D E S I G N S O L V E D P R O B L E M S

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5 Design Problems

PROBLEMS

For Prob. 1 through Prob. 5, assume the followingscenario.

Two structures, each with the same height and floorweight, are shown in elevation. Structure I has anoccupancy category of II and is located on a site wherethe mapped spectral acceleration parameters, S1 andSS, are 0.42 g and 1.06 g, respectively. Structure II hasan occupancy category of III and is located on a sitewhere the mapped spectral acceleration parameters,S1 and SS, are 0.30 g and 0.75 g, respectively. Thefundamental time period is 0.63 sec for structure I and0.43 sec for structure II. For both structures, it is lessthan the long-period transition period. The penthousein structure II is a special moment-resisting frame.

100 kips (445 kN)100 kips (445 kN)100 kips (445 kN)100 kips (445 kN)100 kips (445 kN)100 kips (445 kN)

30 kips (133 kN)penthouse

10 ft (3 m)

10 ft (3 m)

55 ft (16.8 m)

S1 = 0.42 gSS = 1.06 g

S1 = 0.30 gSS = 0.75 g

special moment-resistingreinforced concrete frame

structure I

special steel concentrically braced frame

structure II

soft clay

typical

hard rockmaterial

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)

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

(A) 80 kips (350 kN)

(B) 140 kips (620 kN)

(C) 200 kips (890 kN)

(D) 300 kips (1300 kN)

3. Based on ASCE/SEI7 requirements, the allowableelastic interstory displacement (drift) for structure I ismost nearly

(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)

4. Based on ASCE/SEI7 requirements, the allowableelastic interstory displacement (drift) for structure IIis 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. Determine the seismic loading, Fp, for the penthouse,which is rigidly attached to the main building.

(A) 10 kips (50 kN)

(B) 20 kips (70 kN)

(C) 40 kips (200 kN)

(D) 70 kips (300 kN)

For Prob. 6 through Prob. 10, assume the followingscenario.

For an office building in a high seismic area, an architec-tural firm proposes the special steel concentrically bracedframe structure shown. The SD1 and SDS values are givenas 1.04 g and 0.522 g, respectively. Ignore vertical struc-tural irregularities for this building. Use the equivalentlateral force procedure. The importance factor is 1.0.

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(A) 800 ft-kips (1100 kN�m)

(B) 1000 ft-kips (1300 kN�m)

(C) 1200 ft-kips (1600 kN�m)

(D) 1400 ft-kips (1900 kN�m)

SOLUTIONS

1. SI Solution

Structure I sits atop hard rock material. Therefore, fromASCE/SEI7 Table 20.3-1, the site class is A. The mappedMCE spectral response acceleration parameters aregiven. To convert these parameters into site-specific spec-tral response acceleration parameters, SMS and SM1, thevalues of the site coefficients, Fa and Fv, will need to bedetermined.

ASCE/SEI7 Table 11.4-1 provides the value of sitecoefficient Fa. For SS =1.06 and site class A, Fa=0.8.ASCE/SEI7 Table 11.4-2 provides the value of sitecoefficient Fv. For S1= 0.42 and site class A, Fv=0.8.

ASCE/SEI7 Sec. 11.4.3 gives the equations for SMS

and SM1.

SMS ¼ FaSS ¼ ð0:8Þð1:06Þ ¼ 0:848

SM1 ¼ FvS1 ¼ ð0:8Þð0:42Þ ¼ 0:336

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

SDS ¼ 23SMS ¼ 2

3

� �ð0:848Þ ¼ 0:565

SD1 ¼ 23SM1 ¼ 2

3

� �ð0:336Þ ¼ 0:224

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 factorgiven in Table 12.2-1. For a special moment-resistingconcrete frame, R is 8. The importance factor, I, foroccupancy category II is 1.0 [ASCE/SEI7 Table 11.5-1].

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

Cs ¼ SDS

RI

¼ 0:56581

¼ 0:071

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;max ¼ SD1

TRI

� � ¼ 0:224

ð0:63 sÞ 81

� � ¼ 0:044 ½governs�

Use ASCE/SEI7 Eq. 12.8-5 to check Cs against theminimum value.

Cs;min ¼ 0:01

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D E S I G N P R O B L E M S 5-9