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

Design Equations for Flexural Strengthening of Singly Reinforced RC Rectangular Section with Steel Plates Tamer Tamer Alafandy1 !agdy "a#ry$ Amr %afi$ Ayman Ayman Summra Sum mra$ 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. Howeer! scarce number of technical articles that gie closed form solution for  getting steel plate thic"ness and almost there is no aailable articles that gie 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 hae been gien $ll practical aspects of steep plate with! thic"ness! plate width/ thic"ness ratio limits and also limit on neutral axis depth hae been considered. %ethods of designing anchor bolts will be gien 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 Analysis of steel steel )lated reinfor reinforced ced rect rectangu angular lar section section..

$ccording to $CI &'( )'*! Ref. +',! the total amount of steel in a singly reinforced section should not exceed /02 3

4

5 /02

*1*

! i.e.

Referring to Fig0 1

/062

a 3 Asf y 4 A) f y) y)

7$8

From 7$8

 From 718 798

7:8

*$*

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 $cco $ccord rdin ing g to Ref. Ref. +&, +&, for for ensur ensurin ing g ductil ductilee 2 flex flexur ural al failu failure re!! the follo followin wing g conditions should be satisfied

768

*9*

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

*:*

 

84

83/

A T$anchor 4 " T anchor 4 C 3 /

71:8

71=8

718

 

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 4 -65 "g/ cmCoer 4 5 cm

h 4 *5 cm f y 4 *'5) "g/cm-

f yp yp 4 -*7) "g/cm

d' 4 *) cm

d- 4 *6 cm $s 4 8 cm-

%u 4 -'.(6 tm

*2*

a, From ref. +',

a 4 7.5 cm

4 '-.6' cm-

Tanchor  4  4 -'.8 ton

-8 "y )ro)osed equations

$ 4'7)5( From e#n.

94 8)8'76

C4 ''-&&&6 4 '-.6' cm-

+*,

from e#n. +&,

a 4 7.5 cm 4 '-.6(7 cm-

from e#n. +8, from e#n. +6, c b 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,  +'(,

areised 4 &.)8 in 4 6.66-* cm +same as Ref. +',, x 4 7.6'55 cm From e#uation +'7,

*=*

Conclusion < eeral e#uations based on first principles of design of singly rectangular cross section hae been deeloped . 0#uations +*,!+8, and +6, can be used for getting area of steel plate and and gie  practically identical alues .while e#uations +'8,!+'(, and +'7, can be used be to gie shear force in anchor bolts and they also

practically gie identical alues.

ymbols< 4 actual reinforcement ratio 4 existing steel rebar ratio 4steel plate rein forcement ratio

* Refe Refere renc nces es.. foley et al.! al.! =tren =trengthe gthening ning existing existing reinfo reinforce rced d concre concrete te beams beams for  1- C % foley

flexure using bolted external structural steel channels! >an.! '77(.! %ar#uette ?niersity! ?$ alcarcel A Refuer3os %etalicos en Hormigon $rmadoB -)'* -)' * 2- - >uan Pere3 @alcarcel $wadh 0 $eel et al AReplacing of Internal Tension Tension 9ars by 0xternal 9onded 3- $wadh PlateB >n.! of 0ng. 2 1elop.! ol. '5! Do. &! ept -)''. Rehabc bcon on!! $nnex nnex E! A tre treng ngthe theni ning ng of Conc Concre rete te tru truct ctur ures es 4- Reha 0xternally 9onded teel PlatesB! -))))

**

using using

5- $shraf  A.  A. $lfeehan, Atrengthening f  R.C. 9eams 9y 0xternal teel Plate

?sing %echanical Connection Techni#ueB Techni#ueB >ournal of 0ngineering and 1eelopment, @ol. '(! Do.-! %arch -)'* 6-

Figure'< ultimate forces acting on plated beam section

*6*

Figure - < condition of balanced loads

*>*