Design Equations for Flexural Strengthening of Singly Reinforced RC Rectangular Section With Steel...

7/26/2019 Design Equations for Flexural Strengthening of Singly Reinforced RC Rectangular Section With Steel Plates

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Design Equations for Flexural Strengthening of Singly

Reinforced RC Rectangular Section with Steel Plates

Tamer Alafandy1 !agdy "a#ry$ Amr %afi$ Ayman Summra$

1&ousing and "uilding %ational Research Center Concrete Structures 'nstitute

$Ci(il Engineering De)artment Al*A+har ,ni(ersity

A-stract.

It is a common practice to strengthen and/or repair RC beam/slab with

bonded steel plate to increase/restore its carrying capacity in flexure. This method is

preferred than FRP application because of its low cost and higher ductility.

Howeer! scarce number of technical articles that gie closed form solution for

getting steel plate thic"ness and almost there is no aailable articles that gie

explicit e#uation for determining anchor bolts force and their method of design.

In this paper closed form closed form solutions for re#uired steel plate area

and anchor bolts force hae been gien $ll practical aspects of steep plate with!

thic"ness! plate width/ thic"ness ratio limits and also limit on neutral axis depth

hae been considered. %ethods of designing anchor bolts will be gien later on.Three design e#uations for getting steel plate area and two e#uations for getting

anchor bolts force are explicitly cited.

1* Analysis of steel )lated reinforced rectangular section.

$ccording to $CI &'( )'*! Ref. +',! the total amount of steel in a singly

reinforced section should not exceed /02 ! i.e.

3 4 5 /02

*1*


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Referring to Fig0 1

/062 a 3 Asfy 4 A) fy) 7$8

From 7$8

From 718 798

7:8

*$*


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Sol(ing 7:8 ;i(es AP

Su-stituting in 798 gi(es a

Ta#ing into consideration that

- implified 0#uation for $rea of teel Plate

$ simplified e#uation can be used for getting area of steel used for getting

area of steel plate as follows +panish practice! Ref. +-,,

& 1uctility Re#uirement for teel Plate

$ccording to Ref. +&, for ensuring ductile 2 flexural failure! the following

conditions should be satisfied

768

*9*


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c< 3 /0:

also

:* Anchor "olts Force

Ta"ing moment at the interface of anchor bolts with RC section

3 7

From forces e#uilibrium

From 71$8 in 7118

8

*:*


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71:8

8 4 8 3 / 71=8

A T$anchor 4" T anchor4 C 3 / 718

7168

2* Sim)lified Equation for Anchor "olts Force

The authors suggest the following simple e#uation for getting anchor bolts force

utili3ing panish practice Ref. +-,.

=* Exam)le

1ata from Ref. +',

b 4 -5 cm h 4 *5 cm

4 -65 "g/ cm- fy 4 *'5) "g/cm- fyp4 -*7) "g/cm

-

Coer 4 5 cm d' 4 *) cm d-4 *6 cm

%u 4 -'.(6 tm $s 4 8 cm-

*2*


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a, From ref. +', a 4 7.5 cm

4 '-.6' cm- Tanchor4 -'.8 ton

-8 "y )ro)osed equations

$4'7)5( 94 8)8'76 C4 ''-&&&6

From e#n. +*, 4 '-.6' cm-

from e#n. +&, a 4 7.5 cm

from e#n. +8, 4 '-.6(7 cm-

from e#n. +6,

cb 4

Ta"e c 4 ).&

a4 ).( : ).& 4 ).-* : *) 4 7.8 cm

4 '-.5& cm-

-&)/8 4 &(.& ; 5)

c, $nchor 9olts Force

From e#uations +'8, +'(,

areised4 &.)8 in 4 6.66-* cm +same as Ref. +',,

x 4 7.6'55 cm

From e#uation +'7,

*=*


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Conclusion uan Pere3 @alcarcel A Refuer3os %etalicos en Hormigon $rmadoB -)'*

3- $wadh 0 $eel et al AReplacing of Internal Tension 9ars by 0xternal 9onded

PlateB >n.! of 0ng. 2 1elop.! ol. '5! Do. &! ept -)''.

4- Rehabcon! $nnex E! A trengthening of Concrete tructures using

0xternally 9onded teel PlatesB! -))))

**


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5- $shrafA. $lfeehan, AtrengtheningfR.C. 9eams9y0xternalteelPlate

?sing %echanical Connection Techni#ueB >ournal of 0ngineering and

1eelopment, @ol. '(! Do.-! %arch -)'*

6-

Figure'< ultimate forces acting on plated beam section

*6*


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Figure - < condition of balanced loads

*>*

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