(Two marks ouestions and ansrvers)

I{NIT-I

l.

State any four losses that can take place in prestressed concrete. (A.U: APR/IVIAY

2008,

MAY/JITNE 2m9, 2012)

/

/

For pretensiooing and post tensioning: F Elastic deformation of concrete F Relaxation of sfess in steel Y gffinkage of concrete ! Creep ofconcrete For post-tensioning only

)

Anchorage slip

2. What !s meant by post tensioning? 1.1.u. i'tovloEc 2009) Post tensioning is a method of prestressing in which t}re tendon is tensioned has hardened. ln this method the prestress is imparted to concrete by bearing'

of concrete

3. Why high strength concrete is necessary for prestressed concrete? (A.U. NOV/DEC

2012,

NOV/DEC 2009)

F To withstand high compressive stress due to prestress at early stages F To offer higher iesistance to tension, shear, bond and bearing. P To have lesser shrinkage effect. F To have higher modulus of, elasticity and smaller creep strength and thus rezulting in lesser loss

l-a ( 4,!trt"

of prestress.

:

two advantages of prestress€d concreteover reinforced concrete. (A,U. NOv/DEc

"ny zooo Yotz, rulvaunr

F F F ) >

The technique df prestressing eliminates cracking of concrete under all.stages of loadirrg, the entirc section ofthe structure take part in resisting the extemal load' (ln RCC only the portion of the concrete above the neutral axis is effective. Absence of cracks results in higher capacity of the structure to bear reversal of stress. impact, vibration and shock. The use of curved tendons and the pre compression of the concrete helps to resist shear.

The quantity of steel required for prestressing is above.l/3'd of that required for reinforced concrete though the steel for the former should have high tensile strength. Prestress concrete beams have usually low deflection.

(;,rName any four systems or methods of prestressing? (A.u. MAY/JUNE Pretensioning systems I.

IL.-

Abutment method

2013)

Post tensioning svstem

L Freyssinet system

t_ ., l

2. Lee-Mccall sYstem 3. Magnet-Blaton system 3.Mould method 4. Prescon sYstem 5. Baur-Lcohharat sYstem 6' Gifford Udall sYstem concrete? 1e'U' pretensioning concrete oYer post tensioned of advantages the are What 6. ureyLrunr zorz, UAY/JUNE 2009) 2. Strut method

.

;r1c6;ffii6NrNG ING Suitable for large Suitable Ior mass Presuuuv, of small and r49iliu4 gn![.- construction Little or more

}D

ASPECT -:-...------.---

l. SuitabilitY ? Transoortahon l. End encno4g"s4 G,routing 5.

tnss of Preqllregr

^^--::^--l,Io

UntY serr wsrBul vau

6. Dead load counter action

L^ ew

Only stragnt or

cJool(cu

--^{:lyrvurv Reusable several times

8. Formwork or moulds

Any curved Profile feasible

Forms generallY

only

once

of a Prestressed

MAY/JI I{E 2012' 2or0)

:

used

Modest

High

invesment

ffi

dead loadi can be counteracted

^^,.-iara.ta.l

?. Cable Profile

9. Capital

Required Required

renrrired Nnt renrrired

]r.Tnt

--=.-

m-srre

concrete? (A-U.

the structure by primarily balancing a portion of the load on and ii'J;'ff"' "pptpriate ' to the moments due to dead weight

L,oad balancing concept is

choosing the proper prof'te applie
ioads.

flr

S.Whatlossduetoelasticshorteningcanbeignoretiforposttensionedbeam?.^ the loss due to elastic deformation is tensioned' simultaneously are wires the If all compared to that of post tensioned au. to creep is more for pretensioned beam

ffilo*,

member? (n-u. ePwMAY 2oro) creep than post tensioned pretensioned members have large magnitude of loss due to member' take"s placJ earlier in pretensioned over, as Eansfer of p,",*"" ot"Afy used in pre tensioning works? 10. Why is smaller diameter rvires

Theultimatetensilestrengthofwiresvarieswithitsdiameter.Thetensilestrength

AecreJ -ittt

fill \'/

increases in the diameter of wires'

concrete? tensile steel is used in the prestressed \ryhat are the three forms in which high High tensile steel wires

) ) >

Cables

Strads 2

t

"*ffi**

2,

o a

(A'u' MAY/JUNE 2009) Why high tensile steel is essential for prestressed concrete? to 240 N/nrm2 and it is apparent The normal loss of stress in steel is generally aboul 100 stress, the sg.ess in steel in the initial that ifthis toss of stress is to n" .*"li po6"on of thc initial ^ ranges are possible onlv ;ery hiCh, about 1200 to'2000 N/mm2. These high stiess ;;;;;;rG with the use ofhigh strength steel of steel? (A'U' Nov/DEc 2010) 13. What is meant by loss of prestress'due to relaxation 12.

Therelaxationofprestressingsteel,definedasthereductionbfstressunderconstant strain, is due to creeP. 2009) What is meant by pretensioning? (A'u' Nov/DEc 2011' Nov/DEc before the-co-ncrete A method of pr-estressing concrete in which the tendons are tensioned between steel and bond by is imparted to conqete is placed. In this method, ti ;;;t 14.

concrete.

the principle of prestressing? (A-u' Nov/DEc 20rr) ' suitable The basic principle of presiressing is to produce bV 11Y 1:1"^t:^::T"i"n' whose tinsile stresses would occur, when' comoressive stressed in ,ff tn.r"'p*tr ut tt! .on"r"i" the extemal load i.e. dead and live loads are applied'

@Mention

and post tensioned woiks? What are grades of concrete to beused pre tensioned of 400 Mpa for The Indian code of practice suggests a minimum cube strength pretensioned and 300 Mpa for post tensioned system' (A'u' Nov/DEc 2009'2010) (A'u' APR/MAY 2010) 17. What is meant by pressure or thrust line? 16.

Atarrysectionofabeam,thecombinedeffectoftheprestressingforceandlheextemally into a single will result in a distribution of concrete stresse; that can be resolved called the -ri"l""r, or structure is or tr," poi.t.'oi upprication of this force in any beam Iii". 'pressure line'. moment on the pressure line? 18. What is the effect of increase in external O"'* A change in the extemal moments in the elastic ryC: of pT-t":T^"-d^^":":'-t:t:, torce ln the Dezrm. ,"rrlt. in ,rhidofthe pressure line rather than in an increase in the resultant pretensioned member compared to post f 9. Why loss due to shrinkage is mbre for tensioned member? (A-u. Nov/DEc 2010) applied load

Inthiscaseofpretensionedmembers,generallymoistcuringisresortedtoinorderto strain will

Cooi"queoily, t],e total residual shrinkage p'"st"'* in comparison with post tensioned be larger in pretensioned *"-b",, after transfer oi taken place by the time of transfer of *ffl ut'e members, where a portion "lieaay "i'.fu,ug"

p."r"nftr-irt ug",",1'*r" ti*"

oi

tr-rr"..

prestress.

20. What is meant by dxternal prestressing?

A member can be external Prestressing.

h*-

prestressed by extemal reaction ofiered

by rigid abutments is called

I!-Ita

b neant by loss of prestress due to slip in the anchorage?

*,rdoraselossesoccurduetoslipofwiresduringarrchorageorduetostrainat oi post tension.d system.

-I-;';;;

Such slips occur at both the jacking end and the

-d-inrage. ', Ia ofsaess due to anchorage slip = E, x strain / length' buded prestressed concrete and non-bonded prestressed concrete' pressed concrete: confiete in which prestress is. imparted to concrete through H ht8 Ae tendons and surrounding concrete. Pre tensioned members belong to this

ILl

A method of construction in which the tendon are not bonded concrete. ffr" t*ab"t may be placed in ducts fomred in the concrete

pcs*ressed concreie:

-;dngbe placed outside the concrete section. fl you improve the shear resistance of concrete D thircoral

beam using prestressing

or axial prestressing

> k*essing by inclined or sloping cable D Yrrtical or transverse prestressing

-

E tors which influence the

deflection of prestressing concrete beams. (a.u'

D Iryoced load and self weight D urgnitude of the presressing force D fre profile D Sr.o'rl moment or area of cross section D Hus of elasticity of concrete D 5tage, creep and relaxation of steel stress D $ dtte member. cable?

ft f t

(au. Nov/DEc 2orl)

cable is a tendon profile in which the eccentricity is proportional at all bcnding moment caused by any loading on a rigidly supported statically' or a profrle which does not induce any redundant reactions and hence

eficcting shrinkage of concrete? (A.U- NoviDEc

-d

quality

2010)

a

27. What is meant by loss of prestress?

The effective prestess in concrete undergoes a gradual reduction with time from the stages of transfer due to various causes..This is generally refened to as loss ofprestress. 28. What are the assumptions made in analysis of stresses in prestress concrete structural element? 1. Concrete is a homogeneous elastic material

2. Within the range ofworking stresses, both concrete and still behave elaltically. 3. A plane before after bending. 4. Linear strain distribution across the depth ofthe member.

rare the two methods to calculate @Wn \-/

loss due to creep of concrete? (A.u. NovlDEc 2010)

Ultimate creep strain method . 2. Creep coefficient method. 1.

30. What are the factors affecting creep coelficient? (A.U. NOv/DEc 2010) 1.

Humidity

2. Concrete quality 3. Duration of applied loading 4. Age ofthe concrete when loaded. 31. What is meant by

'wobble' or 'waves'? The loss oflstress due to friction between the cables and undulations in the duct termed 'wobble' or 'waves'.

as

32. Define prestressed concrete. (A.U. MAY/JUNE 2002, Nov/DEC 2009)

Prestressed concrete is basically concrete in which intemal stresses of a suitable magnitude and distribution are introduced so that the stresses resulting from extemal loads are counteracted to a desired degree. 33,

Differentiate reinforced' concrete and prestressed-concrete.

ln RCC members, the prestress is commonly introduced by tensioning the steel reinforcement. The tensile strength of plain concrete is only a fraction of its compressive strength and the problem of it being defrcient in tensile strength appears to have been the driving factor in the development of the composite material known as reinforced concrete Prestressed concrete is basically concrete in which intemal stresses of a suitable magnitude and distribution are introduced so that the stresses resulting &om extemal loads are counteracted to a desired degree. 34.

Write some need for high strength steel ard concrete material. (4.u, Nov/DEc 2orl)

l. Necessity ofusing high-strength steel and concrete 2. Recognition of losses of prestress due to various causes.

35. Define the terms: a) Ten'don, b) Anchorage, c)

Full prestressing, d) Partial prestressing

A sfretched element used in a concrete member of $rucnre to impart

d"*iJfy,

0.".L*

to lhe concrete-

frign ,ensile steel wires, bars cables or strands are used as tendons'

b)ANCHORAGE prestress in the concrete''

A device generally used to enable .the tendon to impart the maintain rr'""o*,o,ontyusedun"ho,ug"saretheFreyssinet,MaglelBlaton,Gifford-Udall,Leonhardt. Baur, LeeMcCall, Dywidag, Roebling, and BBRV systems' c)

FULL PRESTRESSING

prestressed concrete in which tensile stresses in the concrete are entirely obviated at working loads by having sufiiciently high presbess in-the members' d) LIMITED OR PARTIAL PRESTRESSING (A.U. NOV/DEC

2OO9}.

Thedegreeofprestressappliedtoconcreteinwhichtensilestressestoalimiteddegpeare perrnitted in concrete under working loads. 36. Define

ixial prestressing.

compressive prestress' In Members in which the entire cross-section of concrete has a uniform the concrete section. thi" typ" ofp.".t essing, the centroid, ofthe tendons coincides with that of 37. Define eccentric

prestressing.

section at which the tendons are eccentric trapezoidal compressive stress distribution'

A

:

to the centroid, resulting in a triangular or

38. Define Non-distortional prestressing' stress is such that ln this type, the combined effect of the degre" of p.estr"ss and the deadweight due to tte a"nection of the axis of the membei is preverted. In such cases, the moments in the member' prestress and deadweight exactly balance resulting only in an axial force

triaxial prestressing? where concrete is prestressed (i) in only one direction, (ii) in two

39. What is meant by Uniaxial, biaxial and

The terms refer to the cases *,rtuutty p"tp"naicular directions and (iii) in three mutually perpendicular directions' 40. Define circular Prestressing The term refers to prestressing in round members, such as tanks and pipes'

41. What is meent by moderate Prestressing?

form of No limit is imposed rpon the magnitude of the tensile stesses at working loads. This concrete with construction is not really protroin concrete but is to be regarded as reinforced of reinforced reduced cracking and tte sectioos should be analyzed according to the rules concrete.

42. Deline

or untensioned reinforcement,

Reinforcement in prestressed members not tensioned with respect to the surrounding concrete before the application of loads, these are gcncrally uscd in partial prestressed members. 43. Define the terms: Transmission length, cracking Ioad.

The length of the bond anchorage of the prestressing wire ftom the end of a pretensioned member to the point

offull

steel stress is called as transmission length.

The load on the structural elernent corresponding to the load. 44. What is meant by

frst visible crack is known

as cracking

proof stress?

The tensile stress in steel which produces a residual strain ctf 0.2 % ofthe original gauge length on unloading. 45, Define cap cable.

A short curved tendon arranged at the interior supports of a continuous beam. The anchors are the compressiori zone, while the curv6d portioh is in the tensile zone. 46,

in

Write the definition about degree of prestressing.

measure of the magrritude of the prestressing force related to the resultant stress occurring in the structural member at working load.

A

47. Define Debonding. (A.u. Nov/DEc 200E) Prevention of bond between the steel wire and the surrounding concrete is known as debonding. 48. Write some applications of prestressed concrete.

The use of prestressed concrete has revolutionized the entire building industry in the erst while USSR, USA, UK, Japan and the continent. Some of the applications are thirteen storey apartnent building with precast post-tensioned in slab conskuction, 203mm thick light weight concrete slabs of 8-6 m span in San Francisco. 49, Mention some tensioning devices used in prestressed concrete.

/ / / / 50.

Mechanical

Hydraulic Electrical Chemical

Write thq principles of post-tensioning.

)

Wedge action producing the tendons

. ts Direct bearing from rivet or bolt heads formed at the end of the wires D Looping the wires arorind the concrete.

I&,,

't I

51. Write the applications of post tensioning. post tdnsioning is ideally suited for medium to long span in-situ work where the tensioning cost is only a small proportion of the cost ofthe whole job.

5L Define the term Tendon splices. (A.u. MAY/JUNE 2002,2003) In case of continuous prestressed concrete members involving long tendons, it is necessary t0 splice the tendons to achieve continuity. Several types of splices have been developed over the yiuts to t it th" dif[erent types of wiies and stands used as tendons. 53.

Briefly explain thermo elastic prestressing. 1e.u. ernnr'rAY

2008, MAY/JUNE 2002)

of prestressing by heat tendons, achieved by passing an electric current in the hightensile wires, ii generally ieferred to as 'thermo-electric prestressing'. The process consists of elecrically heatirig the bars to a temperanre of 3004000 c.

The method

54.

Explain Hoyer,s effect in prestressed concrete, (A,U. MAY/JIiNE

2009, NOViDEC 2010)

For mass production of pretensioned elem'ents, the long-line process developed by Hoyer is genaally used in a factory- In this method, the tendons are stretched betweeft tlvo bulk heads' several hundred meters apart so that a number of similar units may be cast along the same goup of tensioned wires. The wires or skands wher teosioned hydraulic jacks or by a move able stressing'machine. 55.

Explain Gifford-Udall system

The Gifford-Udall system developed cone anchorages

in UK consists of steel split-cone and cylindrical female

to house the high-tensile wires bearing against Steel plates.

56. Exptain the concept about

Lee+kCaD systeur and l\fiagnel-Blaton.

(A.U. MAY/JUNE 200q

In the Lee-McCall system the tendons comprise high-tensile bars of diameter varying from 1240 mm which are threaded at the ods ASer tensioning bach bar is anchored by screwing a nut and washer tightly against the eod plares-

post-tmiooirg syse.m adopts metallic sandwich plaJes, flat wedges, and a plate for ancbodng &e wfu€s. Each sandwich plate can house upto four pairs of distribution The Magrcl-Blaton

wircs. 57. Define the

term chemi,I prcstressing. (A.u. Nov/DEc

demi:al

2009)

of concrete was made possible by the development of Setf-stessing or consists of 75% Portland cement, 150 high alumina expanding c€ments- Erga@ cement md I (FZ gpm, rhich resrlt in the formation of, caicium sulpho aluminate.

ml

fm frors iLaciry d.flectiotrs. (A.u. NovlDEc 2011) members are influenced by the following The deflectioos of,prtsrnd m* 1. Imposed loed d sf ciiE 2. ivlapitude of thc pt*tsig 6rce 58.

List any

3. Cable

profile

4. Second

romear of rte of crrc section 8

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-

xlL

zx 8L ,

n-.

^ (4 toP 'fi bre

CN/mmL)

?reaErc ss

tooX to3

7 A

46400

- z.l5 e zv

q35 x to+

, -4,o Sell utt' -gtrut

t-t

E

8-1L ,r&

Zy

-

L.L' Swrt

t N/mmL )

?

toox

A

oj

t

4b+oo

= 2.15

loo x ro3r ,qr.

7

@3Y*"rnah*t e

nt5 xto+ l- 9+,

M9.

I bxtob

Zt

1?5 xto'

?e 't'b

,oor,13x l?y

l;rox lo+

= 6.2" g."tb , Mq,- M x rob ------.9' -, zb 3to x to{. :

. **t-r-q Nw -Zb

t.

lbtto' alcxle'

StfiLt

?zuaty.*a

4. A

ula*

&eota^St

6oo

mm

HvsD

+ 6,N

ir

loo xl5^t,

Cr
?

h-a_o,

*lfie

lll ha4-

e.fle

g -he

6

s 4v

'tr't

ve .9trsn

rnar

Solr<"

Nirer

(aw

' b'la +h'}t

l+mn t

g-

t

ln - te

uimor* ttttttiry-

A.h+t lfed -b 4,e Sz*ior

ar -lhe 3oJ./ir

. mto.na bq () <-)

c+4

,;, tfre

unde q

,

-hon,

2 oomrn

+ o.35 il/rn-t.

p So mm.

rrt

y'.xutrtuea

/ocate"t

ba r-s

beam. -Il

&e

+L,L

Con

l-t-op ,

,

u

ba

{:eru f or

bt-an !

tvrrt.'

oo N/mnL' b ,25omm- ,' d " 6oomm ; 9w)24 '6 " 4 at h ho,4 t'ez 2oomm J-'1 orn bottorr'--' "d rd, lumrn ', € a

'

IOO tOrn

Sot-unou; iS At-o

= 9l - z|o ^ 600 = l5xtol ,n--

ib .lz,*f on tt

Hod LLILw

4xva-L

t)

4

frS lr) c1
P E.ltcoo M T ' = i5 xto4 -

vir

,6

M,

r. 1t.

- 4, vxr4L = + tr-ut y /rtq. =

'

zz=9!-'"25oxbooL_ 6 6

z,ilV N/wrnL

15, ,ob

^.!

6t6 mmL

+oo x 6, t = 4stzoo N i

f

e

+3 l2-ouN x toomrh

z.=----:--

xtob mm\ ?st ttrta . 2-37 + 2.3 + . 5.7t+ lmmL

,=:-i-t Pl =

15

5'r+ Xl5 lroo 4

t7 N/ - a.-------:rn*

F:a;"r-xNq

gbr

tuu-aatu, ,d

dte b"tt

^.

s/

bLto,{L 4ribre Gvep

Jorct

dlu

Strtlttt

roft', dqqft

oo

nulLp a,

woultt

loaafn*. I

b

t

b=-sooinn: d,36o*-,

= .d

J. &m)

.4KN/,yz;9=z+x^r7;

. Laox?oo = |stlotmm\

Ptodulu.r, Zo Zt = bd." _ Le,\BooL "

I

.hlt

uA"r/A*, X

- bxarf .

it) 5.tt. du<- +e gL z

.;.-l L

o,2

l-u T-z-tzti

t€ LL = t^tLL

den

le

7

.J

-- 3xtobmrnS

2 l. ++

o.3 X ,4

^

l'++x6L a

v1

/

-!.ae-oaea

he b-a.o*t uJfli(fu

e

g-z-am b

t-trfien the

/autratir|t

ze)

4.o x I L .--__-}

6,4

KN/r^._

e kN,*

!9 KNm

.

Y

tt-ttt @ brt-to* 4fi'b' 1 ,

Mg *

L4

gr

Z.

- &.+s+tyro6 <----

3 xtob

6= 8.tb

N

tb)

1

,-

. .-.'

f*

j.ora,

p - 8,!,1. g-3J.'*

,

te'f

.l

v btam" zfie co n cLntPi ceLl*

bX

rn

/ir.

; ur--

i t= 6m;P=)soKtL

4KN),m

.9otuTtou: .

il -ilr*-o , -d - lzoy3oo = J jxro?mtrlL iD .le.t&en r.todtLlur z , = kf . lzoxVoo L.=

6 "-_-?

ifis 3"n @ u, 4ntta f dpar, ,t) .Dfrrc* gtr_zrt

= 4?

.{tr-ut = kl =

.

+' * 1!!-'= ttllg

L.t

x

teo*tol =-l;;T *'N/'*^

'

t 8x to6

tpy to,

lo A/t ^ = ____:y-

Vi). SttuLtant Ab:_*arr @ cznt7-e *

@top

=

?

,1

+tlz = a +15 .= lg-

@wn-= i-;7 - n

I gx ttorfsn*V

=

_!lz,n, 1,,

'/ t f*rnpr*"r"nJ

5-*/o s -tV--.

flzrutorJ

.

lo t^r'eapon4

f

ry-

\"7: N

N,Ne

A

z: - 'r

P= r't ' /9o kM.

B,u-t- N= lCoxtd ,t

- l, t rf hrrt

; tl . S6 rto3 rnmL 2' le - loo

JAm^-

.

rram

)

tf N/mm L

-ft"* Z

9ireei

f

BeraTrytStresc

Stress

N/mmL

?-uultant 3tr-ou

?ttuua

liru

ln -----@

0.e, 11

r bv:":: -"%-.1y1y"" !!y !:__lyr*y'! _@ (t ley/tuatr aou) tI(o.)a^ moa<.1 probkn:

Psc bnom q

Jaltfon- tzomrt

uJed ovel an

eAf

udl ry 4 kN/r-, b

aarrt n

fc

r.q

e

mr,'

'

-Dt-tei rni

4 )olo+ )a

nr

by

6rD

inclu.ltt tle

&rhfLh

a 4loru Pl /8o rt

fg

iparu y

t*iuc

tt'q-raea

.utnde

by

a

'Ete

)ooriilon A

:, l-t c'i on' 29

lotati on

?uarrcr {

n

ee.p fi

b oorm

.

a 7y'u

Cetble Ca-ntqf ry

an , eccentri ed

d

h, Suppor-t /,U uf.

S*c,r6 hl

g locatea' at

soom

+h'

ory *-

,L+\rt-uJt

Cantra.l

'Pav"

l'"n"

[irrEN:

:--.=P

Ic )2omm ; d = Aoo mh /, ez somrt- ..

?walt

,''%; '

ln

f-l d.ru-o z. l2q xTo l'5ro

ii) Jz&ion tt,) 8;H

=

HoctL!,L,u.r)

z E ';tL .--._-;-uor*]-4^ ,-v o \3ooL 3oo z I b

1

-

a

l?X toJ rnly; m?ri

I

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it) Dfrz ot rJtr-t4 ? ,

A

.tT,.<-

H'*

Fi

Itoxp3,

z

,:i

go I )D l

=-;;;; *{fu, t

Uo

I.1

[::

Y) A,H @

$.-

r

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F

N.!-v

!_

ix

s

ll

I

vf) B'H @ top

:

YiD futuhant

bt-

'i

rdtrsua A Ap

Tuuuoot -t*r-Ad @ -Boxtorn.

viiil

6,275,

ii

r

/rlltaLl4r /f"t

ri

?x) B.H @

XNm

- u

-,1

1 zottotn . zH - *-trxtrs loA// /nDLtgrtos = =

I

. /8

=

E'P P- -r- Ft A =: --:- = ,-f +)o.lo N/ -
*n

n

+

*-'*.

5*s-io.

:lrr!.llo)1 p31, z loOmrn

ut |uer.te. apan 4e67on n ZyLL _=_

. ,_x4x6L

o)_ " -="

t) A2rd?Z- rtfria 6 tuP f botlotn" /ssxtolN. 4i1

Rta

ul ant

,E

lr_ztt

@ tot.Z-?. , n

O l.t7r_t_

x

.

tt:Z

!!f

>- *: p S_s+l.s = 7,s N/mmL .t. @ bo+so 7n = 5 *, 7.f .2,, L = ^J/mm /.'/ 13 ' a x toL , xiD Shitt q lurlt.ttt I fti.o -- -i'--== a6 rnn

,H

Sotwtott,.-il Clrr-c,, d =

-z5o x3oo

= +Sxto3 mmL

fi) ,lzc*tan HduLA, g:^ = - Z

9.r",x

aoo L

. z:el ,tZf?

iit s'N @ unter, H? - rye _ !!"!rs.-----!. 1 4:

a-H@vua*etim7"ry= it)

5

trtns dut te lrartr*si ? Z - 54axto3 t/ A

Pe

54oxtd x 6or#

z

u)

o?5 r tor

3,ttu4 dua- b

AnL€lf-a

rYlq,

luazte+-

'> ily

=

L ,nrt^=

8*r'ttt sm --* - E:z-t!y

6

Cforar.

7-'?

l5to3 rr>m. '

= 6] kNn

lbo'

8.6 N/ryoz_

e2ter.racll -led,r. -

Er xto6

N/

s+s xrot iiJ_

-

l5- b,....N/-^.

,t.r*,ol Ny 3+Sr,or rrV{,

oC

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+

t-

l,f.oort*

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): e

D d^^, d ,

(Jaoox tsoo)

ii) "fi+ autj,ht

,

t'

- Soomn

- Csoox thoo)

Ctaa

x

UnTt un-

- lo4o mm-x )4 ,-

I 7' (fiU n.o.Z -

,s tcutnl

Z.!!3 h-

F,:

L

9;

RNln,-

4ox,ot

ool I oo3\

-'

lPoo x t+oo3)

i

-*4

'. i

i

u) 4rN/

rylf 25 x 4oL

a.\.

a f"r

TI3. ,s 6rrrn.

Tbtoi

Moment ,

M-

'f =

vi) ltver \tiD

Shik

dr*, ^. + al-

=

Sooo + 2oo o

4ooo

f,,*

,et: &-e =

t?

aA-

-

,

:

I ooo mrn-

e .looo* goo =

N/mmu

Pet

7t

poomt^-

f * ?: {##r .X:fr

= 1.SC JF

Hr

loooxro3 NflL

/uu,auru ,ti

vi;i) lurlson* 6 truNo,

+

4++ xlob

. :, . .. -: :.:

.

],

]

t P*. b;d.q- deot comPr2Jom. Tne els q

a '])4

.

CaYry

of

aoi ru

fo't

otp|

2oo

rnm

iry? an

€-*f

ecti

l.o{Pit /i e* 8"

el

B'H

ma'a t'rq^'

ftal - fth-an 7{et*ion' Zf fic tota] Anffe -4 U

@)

Ettt-male *he *entre of .dPai y gfrae:' b Sboo KNm ' #u l<-.ttor* /Stzt*t clutlln@4 ab. Aw "Jettion- Luf rA'Couple- metaod' -bo fnternal td&dn9/tt

Il----r.f-/.I-- ---r----l

zt

&ryeu: .L. aon i

-*

t-zoohn

---------'--1---'

? = 6eo xlt

,.

r

uLc eboo ruluoonn t

iotuit ott;

ff,-e{. a,*a,{e, } Lr$

' fo? m!!t *-:......_,{

= ttzootz7o) * tzoa. YE?oo) t (5oo x+oo)

.l ,

6a

rtoi nz..

Jr"o*

I I

titY/tunt s

ultd

ef{eetiur r{pan y tom. Tne o

Catb

le

t

i tn

Z11O

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iar

rl {rc l-aad Count.n^*, +An funaf y e4feej ry +fit ls. ,Fqa q b) 4 -fr" /xttttt-te /fru y'oro- ArouX"l, Ar qr

I*Ft

ktt

tL tl drt .lzcfi on

gz-Ural .!)tad,

i+

LLnd

oL *.r,

ui*97 and

a*"on

oS ta,

rt-rultt"ttt.

&tveal:

6"

,iii

tsomm

,' d.3oomtn,'

.!-=

lom; e= Sohm ,.

P

" fiao kN ; e = l

:i

it, -^ot utt

ii;i

7)

o

u

,

dtua, ,l , tsomm x iootrrn = dfxto3_.,

il

il ff,l S"ns * ifi\6

Hodcoh.ot

t Z_, l,aL^ lSox 6 ---

,i

jpo2_

:

=

225 )( tofmm3

:!

': iii)- /iJ+ ttufq l.ut e/ it, fu,n'a L--"o *l* t,',, =dxf : o't5xo.JxL4 - t.orFN/,t. it ,..,r ^ :, '" ' )d tj'' incj-,'no.fron q -gu cabb b tfre horizon tal i, o, )i { & d-" (oncantra-&d 'Eqc' 2d (tE at ffie a (zn tre Y )Pan 6Por ' ii i; l-"a bahncing, Cal &'

zpgrn o =zparre=

9tloox ,ilooO

'o

- /D.kt/.

fgoox,o'^/ -t-_

L 4sxptnn"

6trlo @ bdha.ts,.Le

+

Soor rosx so7 ___.-l

Its

x

to*J

N/rrrmL

vi,t

z{pat1

-strez

. (&xto1 ,-.,2.f & 4

.fl,rg 7 .------- *,o{ / / L o^artot J

/,"ru

/tau Aaor"(

-d*uu @ = 22.)L

-fr.,-

L.p/aaL

.U^ Lotbtn glibre -= o,

,, :''::':":"' ,

t!

lr

.t ,

.1.

, ,

,

, t:

.,

I

il

rt.n7ut-n conatte h-zatrn- Soonn uLt1e f Soonm l) dpP ,,{ uPPort r il)re CDn tzntrdtect -/no& y a2 o kN ii dJ il ilt lalll ai fw Zra poirt*. y ct lpen Z 1-. il I il:t- a' a) SWAt a zlttitable abte /agli/e. q J*ut "runt ?r'y * 'I dl Ubte /uefte b toarnm. gar fr, bi,Ule 6.d porrTor. tie la4O't Stam , ealtulz're U- /l;
-ii d et n

tl-

r

;l

I

il

.

I

-tt i+t

bat-an

I

.!

,i)/oad,t !

:I

a #te

b-z

nafnq /t

e,/{e

c.( q

-lh

e

b) Vor -tnt rdame corbre fuik

Con

antt otte'l

t *nd Jlrn ?l{' fuo'

t L' ii

,16 &tyeN:

;l b" 3oomm; d, Soomh ) il, Je kN I l'' 1n SouDtoat

e z loanln

i

Dc.

z 24 Ki//m3,,

:

i2 i

ii/ ;tU d'r.*, d. soo.n * ;

--

I

if) i lt. !

goomn

Jteion HdutuJ, Z:

E_

..

2_+x tommL Joox gooL ..'--l'

t 32 x ro -mtn'

'

I! tt t )LaJ 't

9( frz-aVuoiaa| ab/e /uyi/e & .rt/ectel _ifn tt *u BtoD ,i ,, \a dut b #t tt/n conctntrded _bad; n tta/u-z.oiaq_0 ,% AA^l J

i

:

i

:i i

i, l

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r"* ud- trtomtnt, Ha =

l 1

v) -b*ndlnfl-

,.^.h .

d

.-f

tt--ttt - !

.?-_

ii

MornrtLt @

c-pn.h,e

ry" =

)*

u.

_

f,"Ja

---:-

kNm

ge.g-z x1o6

-a,I7;T_ - !:Z:_%^.

t- ,t-ead,t . 4./ - !"-? rf It

2r

ll:, l\=

6oo tet{

---=-3

"

!'I l'l

'

6o k

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N-lt

"'e'P

yii)

?-xutr-ad

f.y> Forct , Ffrtd : p.

.:

?. io+ ytoS N

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q dPan f

q Sonm Zonaanln'" @ *An dupporu

4ol7. /oadfy ton.tftioru . e,qe& V /tnttb.rt?n6, 2L 4o,

tft

in fie

tnfa-tpart

dbtc, b

rlecfiotw _

ilA/

nutr-trrtfea

Lrt u/*in*

b 5- -,, LL , 2l
_

-{z

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D d-,,nn,

/i) icca"* Hdyhu , 2 . t!-" 6 -

toox boo 1

--- -:-- 1>

to

xrolra

3

;ii) &b cur2/ btam'fr = o'pto-6xt4

tr)

^r?atttr.tavry

4lora

I xgL ? -- 7t' . = g x o.. la ---o

.lt

;t

hrLz ?

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tb)

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beztn -. .2,ga * ?,oo H - /o,r" lcN/7,

.

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l

:

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b

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tn-

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9-

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&ueu;

f =lrn;,, b . 25omm ) 4" t*So mm g- tSonm ) LL -- 2's X N/m 3o t-s71911; r:::+=<.

) 4A. a Somn qb 9_

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ld , ii) Pt.u.\7,

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Q

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4-q'

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f"uo* sil xH * ewlJ +

fn,nonp'* r^

r"]1 +

I

I J

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{g=

t;-)

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uu\,)

Y-\+5b

32

'J

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fY)

.1, cti

on-

H odu-&,q

I

- =

l' f1a xoTn nf

o

7-

6.1 xtobrnm3

Nx-L" , Hqt u^4--=

v) B"H 6)

t"r+xgz

le.f 6 kMt*

d',

I'l

Total

p z. .8

Inx.-0L

2-eok s L i-= --

20 kNm

-

l-lorntrd, H =.tr t4g * Hs- r 12.56 *zo 32-f B Ki/m

vt

P= n

)-

3p,;b x tal

e

rfl,

- 2t7 ktJ

r--=-=--_

l?= "t+K^Jl L_..--.---./ vr

D

oLrzte

r -g/ - ) pqrl rlectiort

9-t+xbl N

D

632oo tnm o

^

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bincidet.

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4

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tpttt

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Ttte.

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ufia"

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loctea at a torutant euen*ici

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I

ryat rltrttt

'r-

bIrL U

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frti lrndoru

in

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/ooo N//n

m:

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in

,l"pporA /, q 4ht/m- f-Jgfrrh) At"r* b . loornyl I

il -

toommL

D -ilrus, g/ =

fD

i too

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:

goooornm L

, 7

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bd3

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3

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litt tal - ?. i!^//ry O.

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f / ong,aa-on.

4

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2.r

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