Exercises in Civil Engineering

From:

Ioannis Hadjiloizou(Dip1. Erg., Msc)

Member of scientific and technical chamber of Cyprus (A104931)

November 2013

"-u_,c L__D-E_P_ABr]\4EIIT_9J QLV I L & E N vl RO N M E NrA L_ru_ClU+liTNC

MSc in Civil Engineering

Test for 20A012007 applicants

\ 1,r'Structures/

Q/. Deterruine the magnitudes of the forces in members a, b. c in the simplest possible'// . \\'av.,.t *,t_

6 equal bays across the span

5

roof slope

1?\'H- { i. il*tz-'"

BRIDGE ELEVATION

T,-) fl..*oof',*l*" j 'iiEi ti:4o[*".sr-t "- i i1 -)

VBvt'a\:Ie*

15000 :

J :-ttT-- zone fcrstructure ofL - - f---- -varyinq depth

TUR}{ OVER

.r, C 5i, S."'

1i

r.Jti:

7

5 equal bays across the span

DECK CROSS SECTION

r t.

I

i

IIIIII

{=+c L.}2 A

m/s

Flui fMechan ics "f &*#mooring tou,er used for loading oi1 onto tankers at an offshore oi1 field corlprises

a vcrtical circular ser'tioned steel to\-er'7m in diameter. The u-ater deptli is l00rrrand the tourer is kept vertica,l by means of attached to the tou'er at aheight of 70m above the seabed. These cables are anchored to the bed at the fourcomers of a square which is centred on the tou'er and has a diagonal lcngth of 140m.

Local tidal currents have a maximum the u,ater surface andreduce approximateiy linearly to abo'ne the seabecl at thebase of the tou,er. Estimate the maximum tension the guy cables har.e to u,ithstanddue to this tidal current.

Also calculate the horizontal reaction fotce at the torver base to satisfy or.erall eclui-lihrirrm conditions.

The foliorving data should ].le used in your calculation: for seau'ater pt : 1.5 x10-3kgm-1s-1 and p:1025kg/m3: for a circular c5'linder, Co - 1.2 for Re1'nolcls

numberRea<3x105andCo:0.6forRc>3x105. " l\ \LtJe qsS**e*d t t-t;

Thelideck ;1 J-

", ) :

ur0,{t f Fsurface

4 guy cables in./ total atrl+./r intervals

tr t, ?.4

Q4. Ex rvhat is rneant by geornetlic, l:inernatic and d5-namic similaritr,.'"u/

A fluid florl,s uniformll. and stcndil-v- in a circular scctional pipc. Thc r.olurnc florvrate is to be measured b1, monitoring the lotational speed of a propeller situateclcoaxially in the ccntre of the piire using an ailpropriate calibration. Use the ntheorern method to clelive a set of dirnensionless groups to clescliJ:e this s\.stern.

TURN OVER

,//.//r'-/"

\F/\.

\.-

7m dia.

rI:

IiII

trts

Hou, u,ould 1,ou correlate experirnental data obtained from experiments u'ith pipes

of various sizes aitd carrS'ing fluids nith diffelerrt ph1'sica1 properties and at variotrs

florv rates.

A plopeiler of cliameter 80rnm is found to rotate at 3revs-1 rvhen installed in a

pipe of diameter 160rnm carrying u,at,er flowing at 5.2 x 10-3 m'/t. Stating 5'our

argutneut s clearll', deleltnine

(a) the rotational speed if the fluid is changed io g3*r*o:J-,qgp:e.=fl9ry11g at '1'46 x

10-2 m3/s. l: i(b) the florv rate if a gegm_e.!-f-t_S-qUy.similar propeiler of diameter 0.4rn rotates at

1.338rer.,/s in a pipe of diameter 0.8m carrf ing air. : "

Data: kinernatic r.iscosities : air, 1.45 x 10-5 -'/.; u'ater, 1.3 x 10-6 ^'1:,',

cai-llon

dioxide, 1.16 x 10-s m2/s.

3 Materials

Q5ri (a) Describe the principal processes involved in the mantrfacture of Portland ce-

V ment, r&.t:'," (b) Describe and explain the effect of

r Age

o water/cement ratio. curing temPerature

on the compressir,'e strength of Portland r:elnerrt concrete

Q6rl' (a) Deflne rrith the help of suitable graphs or- diagrams the terms

/,']1.,; o modulus of elasticitY-- . O.lTa ploof stloss r ' ,l l \ :.1 -!-..-\'i-, 3'^r-',{ r. ,1 1 l''.i; . ' 'l 12 i'o"t 'r-i {: ' r ]-

(U) expt'iin u'hy tggbrc;g is an importanflplopeltS' for stiuctural materials.

(r,) Describe ancl discuss a method ol irrclcasing tlre !-o-U.g]tttess.o[ (o]rcr('tq. ,

' r. \ ,j-. !E irlv.:1,:.,^,:.,.i 1-..\-*. *, ..rj;-,:,.-".

4 Soil Mechanics

Q7. (a) Shorv hor,v in clay peak states depend or stress level and qrlelconsolidation :

{'-i,r:r. _.ra!|o. 1'::'r:: i:"'.:'l ,.,'.. ,r, i i , , , ,., -

:-" (b)/Table 1 gives results frorn triaxial tests on trvo samples of clay. Samples A and '."' , t' '' .-

\/ B t'cre complessed isutlopicallS-1o lcach not ntalh- consolidated states ut lnean=ffi

fflg"1ltl"Wsi*Z'==*J,QQ]<Pa-artd / : l00liPa I'cst)ectivel)-. 'fhe5-u'cre thcttJ'-'

shearecl cirained at constanr cr:ll ltressure. The specrfic voiumes of the sampies

at tfte stzrrt of shearing u'ere recorded to be 1.99 for sample,4, and 1.90 for:

sample B.

Determine the critical stat,e paratneters (N[,1,,\) for the clal'.

--| * ,; [,--.^ J.*nn:*.r\-t: *' $' itt,t :" i {:_ [ L -*u ) *1' * ;ua1*' I

'e

-f - (; ' 134 '* s:*,rtqt A

p-frffi6*u*TURN OVER

Iti

TI!TIL[,

TFl,rTILltttLtth

v,'ith a specific rrolurre .1, : 1.99, and uras

Determine the finaI stress state (p'. q') an

,rl:: V cla1i Ttre sheal modulus G of the clay has treen rletelrnined :is 15N,IPa.

(a),=Dlas, a plofile of the immediate settlement for a section- centre of the tboting diagonally to one corner of the scluat:e.rnost selious riiflelentia,l sct

. calculate tire consolidatlon under the centre of the foundation. tratingthat beiorn' 10rn depth the contribution to that settlement is negligible. Thecoefficient of complessibilitv m, is 0.4rn2/NIN at the surface, clecreasing linearlyrvitlr depth to 0.1m2/\'IN at 10rn. You rnay use a ralue of A:0.4 to applySkernpton & Bjelrurrts collection. It is assurnecl that 1,iie influence factors tocalculate stresses under a square footing are equal to those under a circularfooting of satne area. Relevant tables trnd rjrarts for the influence factors are

LS :ire *{ i*"t;$;X'*st (* *5ofi Joi,.-. * prra\'a-

Sample A (drained)isotropicallv norrnally

consolidated to p' : 200kPabefore sliearing F-r.

Sarnple B (drained)isot,ropicallv norrnaJ.ll'

consoliclated to p' : 400LBAbefore shea,r'ing fA

axiai;istrairI.-"''- tc/.\ca \/t))

deviatoricstressi.l

q' (kPafi

r.olunretricstrain

/(v \ru \,/c/

axialstraint" (%)3,1

deviatoricstrcss

q' (kPa)

volumetricstrain€" (%)

0

1

2

,+

0 ^t39 or'

82"'"/-l48...

0

2.2

J..)

4.8

5.9

6.4

6.56.5

0

1

2

4

0 *T,/6.

163,06

0

2.5

3.9;t ,.

8

72

16

22

194".."211"v''//2lg"/

wle E

8

t216

22

388474A'N+J/

s{438l

6.36.76.86.8

$a*a 'Iable 1:FF*uin "st

(.) A third sample c rvas tested in the triaxial apparatus. Sarnplepressed isotropically to rea.ch a norrnally consolidated state at

i,€+t* .. c-""*"ml]_*l_J-,

.

\YAS COrl]-

-- 200kPaundrained. {ffi, %.} * {**t"*nnu

ttre {trng } -,

running fro* th"

**-1h3f,**: a*"* F-*p"-i*"Ee*

f+"

Cp'

girren in the Appendix. ( *_ 1't_i**]3*:*-* *t"i.a **-*;- 4

S** H -f:*--a(r+ e*)

ef,tlE

sample. You will assume that the pore water pressure at tle start of shearing { *A"t..*trl*,_ *o. eglal to zero. { ft*op;r*k*3iita:}H&*&#:*::,_. yjirx"*,r/EH;

es./n11YfrB-ffi;"?,."fi#rffi{iuouo, Lo a \ery deep rayer or ' Tq T

I

I

E

3"\ +n:a^fu*+e -'**:.e"-*'

t-

APPtrNDIX

fnfluence factors for rec ular loadin corner settlement

'l

114'rt.t

t.J14t.5

[.581[ 5BB

0.813O.E3E

O ESE

0.879

[.EgB0 7180.7340.r5

tl.7EE0.795

[.822[.835n.892[.s4[.9821.U s

1.[521 11

1.1591.201

1.2391.272

1.61.71.81.92

-) ')

Ft

Lr

7D

g

10

?.42.53

3.54

4.5

Elastic stress dlstribution below centre of uniform circular and strip loadi

't\

t' l9vttL ,i-

.*+\ i*1-I Lr-t€ L)LL,fl| 6^v

END OF THE PAPER

LTBUgL/E LTB

UCL DEPARTMENT OF CIVIL, ENVIRONMENTAL &GEOMATIC ENGINEERING

MSc in Civil Engineering

Test for aPPlicants |/ zo'+ - zooe)\-l

1 Structures

Q1. Determine the magnitudes of the forces in mernbers a. b, c in the sirnplest possiblewa),.

6 equal bays across the span

Q2. A concrete road bridge is proposed to have the plofile shon'n beIou,. Indicate t.ithdiagrams hsw ),ou might prestless this. Plovide in

"r,'our ans\\ier a list of the factors

influencing 1,our decisions

15000+-__+zone for structure of

L- - j-varying depth

5 equal bays across the span

BRIDGE ELEVATION

DECK CROSS SECTION

TURN OVER

I:

t\,5roof slope

35000

Fluid Mechanics

Q3. (u) A rn.ide rectanguiar channel has a slope 5 - 0.02. The ltecl and u,alls of tliechannel are par,'ed u.ith concrete. 'f he r.ahie of \Ianningt loughness coefficientis n : 0.014 and the discharge per unit r,idtli of tlie channel is q : 3rn2f s.

Specify if the flou. in the channel is sub- or supercritical and find the depthand r.elocity of the flou,.

(b) The flow from the charrnel entels a natural channel of a similar closs-section.A dou'nstream control is used to maintain the depth H : 1.2nt just upstreamof the entrv point (see figure). To prevent the erosion of the natural bed a

horizontal apron is used. Estinrate the minirnal required length of the apron Ito ensure that the h).drar-rlic jump occurs o\rer the parred surface.

Q4. A mooring torver used for loading oil onto tankers at an offshore oil field cornpi'isesa vertical circular sectioned steel tou,er 7m in diameter. The rn.ater clepth is 100rnand the tou,er is kcpt r,ertical b1- rneans of 4 guy cables attached to the tou-er at aheight of 70m above the seabecl. These cables are ancliored to the bed at the fourcomers of a square rn'hich is centred ori the tou,er and has a diagonal length of 1.10rn.

Local tidai currents have a rnaximum velocity of 1.2m/s at the water surface andreduce approximatel-v lineal1y to the value of 0.2 rn/s just above the seabed at the

Thelideck

TURN OVER,

IIIIItIth[rhttttthhhF

base of the tou'er' Estirtlate tlte maxirnurn tension tlle gu1' cables larre to rvithsta,dclue to this tidal current.

Also calcrilate the holizontal reaction force at the tou.er base to satisfl. or.erall eclui-libriurn conditions.

The follou'ing data shouid be usecl in 1'our calculation: for searvater p : 1.5 x10-skgm-ls-1^and_ 1.: l025kg/ni3; fo. u

"ircut"..rfira.., C,!D:1.2 for Rey,nolclsnumber Rea< 3 x 105 anrf Co:0.6 for fle > 3 x tb5.

3 Materials

Q5' Discuss the adrantages and disaclr'antages of usirrg each of the portland cernentsu'hose oxide composition ancl complessive strengthlroperties are gir.en in the tablebelow for:

(a) Precast preteiisioned concrete bearns in u,hich a concrete compressive stre,gthof 30N'{Pa at three clal's is r:equired for the transfcrr of the prestress.(b) A 15 mx8 mx5 tn cleep foundation of a cable stal,sal bridge in ri,hich concrete ofstrength class c25/30 (BS EN 206) has been splcifierl, and the sulfate contentof the grormdu.ater in contact *,ith the fo,ndation is 6.5gms/litre.

06. /a )Y \ ''/

4 Soil

q7. (u)

(b)

(b)

(")

It is often stated that the toughness of structural nraterial is definecl as thearea utrder the stres-q/strairi grapli. Exirltrin carefully ri-hy this is not strictj'

Explain u.hv toughness is an irnportatrt propertv for structural rl:lterials.Describe .nd discrrss a metrrocl of increasing the toughness of conc'ete.

Mechanics

Shou' horv in clay pea.k statc+s depencl on stress lerrel and oyerco,solidationratio.

Table 1 gi'es results from tt-iaxia,i tersts on tu.o samples of clau Sarnples ,4 andB tilere compressed isotropically to reacli uormtrllv coirsoliclated states at meaneffective stresses p' : 200kpa ancj p, : 400kpa iespectivell.. ,fhev were then

axide composition66

2L

7fJ

1-)

57

2t5

3

1

2

54

22

7

4

1

2compressive strength of mort"r iBsTNE

25.4MPa47.5MPa 37.5MPa

TURN OVER

LIrITTT

T

!T

T

T

T

II:

I

I

I

sliealed drained at constant ce1l pressule. The specific r,olumes of tlie samplesat the stalt of shearing u,ere lecoLded to be 1.99 for sanipie A, and 1.90 forsarnple B.

Determine the critical state p:rrameters (,l\.1. f, )) for the c'1arr..

Sample A (drained)isotropically normall,v-

consolidated to 'p' : 200kPabefole shearing

Sample B (drained)isotropicall)r normailJ..

consolidated to p' : 400kPabefore shearing

axialstrain^ /(a\aa \/c)

deviatoricstress

q' (kPa)

volurnetricstrain€, (%)

axialstraine" (%)

deviatoricstress

q'(kPa)

rrolumetricstraina,, (:'/,,)

0

1

2

,1

8

12

16

22

0

39

82

148

794217218

279

0

2.2DT.).r)

4.85.9

6.46.56.5

0

1

2

4

8

72

16

22

0

78

163

296388474n ,'7+dt

438

0ol:

3.95'6.3

6.76.86.8

Table 1

(.) A thircl sample C u'as tested in the tr:iaxial apparatus. Sample C r,as corn-pressed isotropicalll, to reach a norrna115, consoliclatecl state at p/ : 200kPawith a specific r.ohrme l,:1.99, and lr.as then sheared undrained.

Deternrine the final stress state (.p',q') ancl final pore u,ater pressrrre in thesample. You r.ill assume that the pore water pressure at ttre start of shearingwas equal to zero.

Q8. A flexible sqilare footing, .1m u.ide, applies a stress of 801iPa to a ver-v cleep laver ofc1a5,. 11r. sherar mociulus G of the clay has been deterrnined as 15\,1Pa.

(a) Drarv a plofile of the irnmediate settlement for a section nrnrring from tliecenti'e of the footing diagonal15, to one corner of the sqllale. \\rhat is the areaof most serious differeirtiai settlernent'7

(b) Calculate the consolidation under the centre of the foundation. demonstratingthat belorv 1Oin depth the contribution to tliat settlement is negligible. Tiiecoefficient of cornpressibility m.u is 0.4m2/N,IN at the sulface, decreasing linearlyu,ith depth to 0.1ur2/\IN at 10rn. You mary use a value of ,4 : 0.4 to applySkernpton & Bjelrums corlection. It is assurned that the influence factols tocalcnlate stresses under a squale footing ale equal to those under a circularfooting of same area. Reler.ant tables and charts for the influence factors aregiven in the Appenclix.

TURN OVER4

APPENDIX

Influence factors for rec ular loading: corner settlement

1

1.1

1.2

1.3

1.4

1.5

0.561

U.5EE

tl E13

tl.63Etl.E5BD.E7g

1.81.7t.o'l .9

2

2.7

?.4L.J

:1J

3.54

4.5

ff 822[.835[.892n940.9821.01 I

I EgB

u 71E

tl./340./5

N.7EE

il.7E15

5

E

7nn

1.t152

1.11

1.1591"2n1

1.23Et .

1.27?

loading

E

1tl

Elastic stress distribution below centre of uniform circular and stri

END OF THE PAPER