Solution Manual for Principles of Soil Dynamics 3rd Edition (2025) - Braja Das & Luo | Complete Solutions All Chapters (Verified Version)

ALLl12lCHAPTERSlCOVERED




SOLUTIONS MANUAL
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2.................................................................................................................................. 1

4 9

5 25

6 41

8................................................................................................................................ 51

9................................................................................................................................ 61

10 ............................................................................................................................... 65

11 ............................................................................................................................... 79

12 ............................................................................................................................... 91




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, Chapter 2 l




Springlconstant,lkl l Thelchangelinlthelforcelperlunitllengthlchangeloflthelspring.

Coefficientloflsubgradelreaction,lk:
k
Springlconstantldividedlbylthelfoundationlcontactlarea, kl=l
A


Undampedlnaturallcircularlfrequency: nl = rad/s
W
wherelml=lmassl=l
g


Undampedlnaturallfrequency: flnl = (inlHz)
2 m

Note:l Circularlfrequencyldefineslthelratelofloscillationlinltermloflradianslperlunitlti
me;l2πlradianslbeinglequalltolonelcompletelcycleloflrotation.

Period,lT:l Theltimelrequiredlforlthelmotionltolbeginlrepeatinglitself.

nl
Resonance:l Resonanceloccurslwhenl =l1


Criticalldampinglcoefficient: ccl =l2 km
W
wherelkl=lspringlconstant;lml=lmassl=l
g

cl c
Dampinglratio:l Dl=l =
cc 2 km

wherelcl=lviscousldampinglcoefficient;lccl =lcriticalldampinglcoefficient

Dampedlnaturallfrequency:

dl =ln 1l−lD2

fdl = 1l−lD2 fn


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©l2017lCengagelLearning®.lMaylnotlbelscanned,lcopiedlorlduplicated,lorlpostedltolalpubliclylaccessiblelwebsite,linlwholelorlinlpart.

, Weightloflmachinel+lfoundation,lWl=l400lkNl
Springlconstant,lkl=l100,000lkN/m
Wl 400l kN
Massloflthelmachinel+lfoundation,lml= =l =l40.77
g 9.81 ml sl2

Naturallfrequencyloflundampedlfreelvibrationlisl[Eq.l(2.19)]

1 k
flnl = = =l
2 m 2 40.77

1l 1l l
FromlEq.l(2.18),lTl = = =l
fln 7.88


Weightloflmachinel+lfoundation,lWl=l400lkNl
Springlconstant,lkl=l100,000lkN/m

Staticldeflectionloflfoundationlisl[Eq.l(2.2)]
W
zl = l =
400
=l4l10−3lml=l
s
k 100,000


Externallforceltolwhichlthelfoundationlislsubjected,l Ql=l35.6sinltl kN
fl=l13.33lHz
Weightloflthelmachinel+lfoundation,lWl=l178lkNlSpri
nglconstant,lkl=l70,000lkN/m
Forlthislfoundation,lletltimeltl=l0,lzl=lz0l=l0,l zl=lv0l =l0

Wl 178l kN
Massloflthelmachinel+lfoundation,lml=l = =l18.145
g 9.81 ml sl2

k
nl = = =l62.11lrad/s
m
2l l 2 l l
Tl =l =l =l
n 62.11

Thelfrequencyloflloading,l fl=l13.33lHz

l=l2lfl =l2l(13.33)l=l83.75lrad/s




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©l2017lCengagelLearning®.lMaylnotlbelscanned,lcopiedlorlduplicated,lorlpostedltolalpubliclylaccessiblelwebsite,linlwholelorlinlpart.