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+) A,,ro-imate Method of getting Equivalent fcu eq. Eeq/

or the shon |C olmn strengtheneq ith |C xaet, igre 1w anq noing that the

euisting olmn}s f~ 1 Pa

anq for the |C xaets f~ Pa,

rom En. 1 aw, f e is given as follos

f e ~ 1 . .w . .1w .1 .1w Q . .w~ 1. Pa 1 aw

e sggest another simple En. as follos

f e.~..

w....v1..

+

~ 1. Pa 1 w

rom En. 1 aw

Ee~ 11 cueqf ~ 11 .1 ~ 1 w

e sggest the folloing to Ens. for getting Ee.

rom f ~ 1 Pa

1111

.1= eqE

~ 1 qw

rom f ~ Pa

Ee~ 11

.1

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~ 1 ew

he ratio of the Eegiven y En. 1 ew to that given y 1 w is .1, so e an se also

En. 1 ew.

0) Strength of Materials 1rinci,les

e an get the eivalent Eeas follos

he strain in the |C aeteq olmn is eal to that of the euisting olmn anq |C aet.

Aorqing to |ef. w, see ig. w, e get

existAexistEexist

P

tAeqEtP =

existA

existE

tP

jacketA

jacketEexistAexistE

existAexistP

tAeqE

tP

+

=

jacketA

jacketEexistAexistE

tP

tAeqE

tP

+

=

tA

eqE

~ jacketA

jacket

E

exist

A

exist

E +

eqE ~tA

jacketA

jacketEexistAexistE +

w

or the previos euample

..

.11..111

+

+=eqE

pa1=

his eals to Pa for all pratial prposes.

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Also, the eivalent shear moqls e, an e given as

tA

jacketA

jacketGexistAexistG

eqG+

= w

t has to e noteq that in |ef.w a orretion oeffiient has to e introqeq sh that

.dmonol

R

drepR

Anq .monol

K

repK w

n or euample

|atio ~ .1

111= w

2) Conclusion/

A more rigoros anq pratial qerivation of the eivalent f eanq elasti moqlie of |C

olmn strengtheneq ith |C aet has een qone anq ompareq ith a ite gooq rogh

tehnie anq it is fonq that it qoes give an arate preqition of the vales of f e., Ee

anq e.

3) References/

1- Evalation qe Performane Para ismies qes Porties en A |enfores par

Chemisage en etonarme et par anqage en C |P, emoire qe agistere

Constantine, 1.

- P.. imosheno, ehanis of aterials, nqEq.

- amiqreza asersaeeq, Evalation of ehavior anq eismi |etrofitting of |C

trtres y Conrete xaet, Asian xn. of Applieq ienes w 11-, 11.