北海道地区自然災害科学資料センター報告
Vol.33, 47-58, 2020

Ultimate Deformation of Concrete Members and Suitable
Material Property for Strengthening("#+%&
Ueda Tamon1, 2 Tidarut Jirawattanasomkul3
1Professor Emeritus, Hokkaido University
2Distinguished Professor, Shenzhen University
3Assistant Professor, Kasetsart University! * 1, 2 ,Tidarut Jirawattanasomkul3)

'2,$

1,3Assistant Professor, Kasetsart University

Abstract  ! ! ! "!! !   !  ! & %"!!!"!   !!!!%"&! !!     !"  !   ! !  – ! ! "  !  $    ! !     $! &
! !  !$!!%!!
" !   !–!! !&!!  !! "!!!&  ! !" ! !!$!! !     $  #% !!$! "!&"&!&!!!
                 

1. Introduction
In order to have good seismic performance of structures, large enough ultimate
deformation is vital. Brittle member failure caused by shear failure or tension fracture ofreinforcement should be avoided to assure large ultimate deformation. The development ofestimation model for ultimate deformation (ultimate deformation model) is necessary topredict the ultimate deformation. The ultimate deformation model can also provide us theinformation on material property for reinforcement, which can enhance ultimate
deformation. This paper presents the generic model for prediction of ultimate deformation

47

for concrete members with various tension materials as embedded reinforcement for newstructures and externally bonded reinforcement for existing structures.

Based on thepresented model, the suitable material properties to achieve better ultimate deformation isillustrated.

2. Generic Ultimate Deformation Model
2-1 Definition of ultimate deformation

The ultimate deformation is usually defined as the point on the descending branch of theload (shear force) – deformation curve as shown in Fig.1. The curve I is the case of shear
failure before flexural yielding.

For the curve I, the ultimate deformation is thedeformation at the peak load, which is the ultimate shear strength.

The curves II, III andIV are the cases in which the ultimate deformation is reached after the flexural yielding
when the remaining load carrying capacity becomes equal to the yielding load, J . The
descending curve represent the reduction of load carrying capacity with increasing
deformation.

The curves II and III are the cases in which remaining shear strength

decreases with increasing deformation, while the curve IV is the case in which remaining
flexural strength decreases with increasing deformation. As shown in Fig.1, the remaining
flexural strength reduction shows the most ductile manner. On the other hand, when theremaining shear strength is smaller than that of flexural strength, the ultimate deformation
becomes smaller, meaning the less ductile behavior.
2-2 Remaining shear strength

Since the remaining shear strength determines the ultimate deformation, the estimationof the remaining shear strength is necessary. Figure 1 shows the remaining shear strengthwith the black solid/broken lines, which decreases with the deformation increase.

Theshear strength, which we usually talk about, is the remaining shear strength when thedeformation is zero.
The formulas to estimate the shear strength in design standards are usually experimentalones.

JSCE Standard Specifications for Concrete Structures 1) provide the following

equations for the shear strength, EAE7? , which is the summation of concrete contribution, 9and shear reinforcement contribution, D :
EAE7? k 9 i DQR9 k  r9A r(1)Rr#D vw

D k H HJ v  i  wv w

(2)
(3)

where 9A is concrete compressive strength (MPa),  and  is effective depth and widthof cross section, #D is tension reinforcement ratio, is, H , HJ ,  and  is cross-sectionalarea, yield strength, angle to member axis and spacing of shear reinforcement, and  istruss arm length. Equation (2) indicates that not only concrete strength but also amount oftension reinforcement affect the shear strength. The study on shear strength of memberswith FRP as tension reinforcement indicates that the greater the stiffness of tension

48

reinforcement is, the greater the shear strength is. The shear strength formula, therefore,should be dependent on the stiffness of tension reinforcement rather than the tension
reinforcement ratio.

In the case of steel shear reinforcement, the stress in shear

reinforcement at shear strength can be approximated by its yield strength, since the stressin shear reinforcement is almost constant after its yielding. However, the stress in shear
reinforcement cannot be estimated when the shear reinforcement is other than steel such asFRP which does not show yielding.

If the shear strength is achieved when the shear

reinforcement fractures, the stress in shear reinforcement at shear strength is the tensile
strength of shear reinforcement.

If the shear strength is achieved without the tension

fracture of shear reinforcement, however, it is necessary to estimate the strain in shear
reinforcement at shear strength. Considering those points, Sato et al proposed the shear
strength model which can be applied to both members reinforced with steel internal
reinforcement and with FRP internal reinforcement 2). Sato et al’s model shows that theshear strength depends on not only tension reinforcement stiffness but also shear
reinforcement stiffness.

Sato et al’s model can also estimate the strain of shear

reinforcement at shear strength.
The concept of Sato et al’s model can be applied to estimate the remaining shear strength.
As estimated by Sato et al’s model, the remaining shear strength decreases after flexural
yielding and after shear reinforcement yielding (see Fig.1).

As deformation increases,

strains of tension reinforcement and shear reinforcement increase. After the yielding of
those reinforcement, the remaining stiffness continuously decrease with the increase instrains.

Therefore, the remaining shear strength continuously decreases as thedeformation increases. When the tension fracture of either tension or shear reinforcement
happens, there is a sudden reduction in the reinforcement stiffness, resulting in the sudden
reduction in the remaining shear strength.

On the other hand, the tension fracture oftension reinforcement causes almost the total loss of flexural strength.

   
Fig.1 Ultimate deformation on load (shear force) – deformation curve49

2-3 Generic model for ultimate deformation

In order to predict the ultimate deformation, the generic model for load – deformation
relationship including post-peal range has been proposed 3). This generic model consists of
two strength models for flexure and shear and two deformation models for flexure and shear.
The flexure model for both strength and deformation basically follows the section analysis
as shown in Fig.2. The effects of confinement by not only tie reinforcement but also jacket
on concrete strength in compression zone are considered by the following equations (seeFig.3):

?I< k v

w#< !< < , ?< k v;w#< !< < (jacket confinement)

?IH k H #H !H H , ?JH k H #H !H H (tie reinforcement confinement)

(4)
(5)

whereH kf` P
duduqx&/%* yx&/ y
SYf _fPY
P_o&/a`VO&/LZZ#< , !< and < is ratio, strain and elastic modulus of jacket. #H , !H and H is ratio, strainand elastic modulus of tie reinforcement.

Fig.2 Section analysis for flexure model

Fig.3 Confinement effects by jacket and tie reinforcement

50The shear strength model is the modified Sato et al’s model to predict more precisely thecases of concrete structures reinforced with steel internal reinforcement and FRP externalreinforcement (jacket). According to the model, the shear strength, DF isthe summationof concrete resisting shear force, 9 and shear strength resisted by steel and FRP shear
reinforcements, D.< as below (see Fig.4):
DF k 9 i D.<(6)9 k: B D H G9 (7)D.< k H;8 n#H $H i #< $< p(8)whereQH9 k  r9;t R: k r6B k s'*3 < u ^ ZbR

D k r#D D; H k r#H H; i #< <; R!H H;  $< k !hhh$H k hhh
H <; hhh!H k%%++r7 : .&

H;8 k5dec
201 K

I\k|I
`

&.('Muu%'z /%&'rLf4f\.L]4]\.n) rLd4d\ p/%'r<Z\ { l i x<ua yZ\mm

 DEC k  j ; &/; UNRPX [NRUNOPxgf Wf\ Tg] W]\ yMt} l i x<t a yZb%,ml g W
ONNN/%%-x d d\y is width of cross section,  is effective depth,  is shear span, H;8 is projected shear
crack length to member axis, #D , #H and #< is ratio of steel tension reinforcement, steel andFRP shear reinforcement, D; , H; and <; is effective elastic modulus of tension
reinforcement, steel and FRP shear reinforcement, 9A and 9; is unconfined and confinedconcrete compressive strength,  is axial force, = is area of gross cross section, and $@ isaxial compressive stress in concrete. Due to shear cracking the depth of compression zone
(or neutral axis depth), ; becomes smaller than the one. > obtained by the bending theory
as indicated by Eq.(10). " is strut angle (shear crack angle), which depends on various
factors 4).

Fig.4 Shear strength model51

The flexure deformation model considers the interaction effects with shear resistingmechanism. Once truss mechanism is formed after shear cracking, tension force in tension
reinforcement is increased (see Fig.5). In tension reinforcement additional force is caused
to balance the component in the longitudinal direction of diagonal compression force. Dueto this force, the flexure deformation is increased. It is called as tension shift (or momentshift).

The flexure deformation can be calculated by the ordinary method for flexure

deformation, however the flexure deformation induced by the additional force should beadded. The shear deformation model is based on truss mechanism, in which deformations
due to elongation of diagonal strut, D& and shortening of diagonal strut, D' are consideredas shown in Fig.6. The elongation and shortening of diagonal strut can be calculated as thedeformation under the shear force, D.< (see Eq.(8)).

Fig.5 Effect of shear cracking on flexure deformation

Fig.6 Shear deformation model

The model prediction results are compared with available experimental results. Figures
7 and 8 show the prediction results for the case with steel and FRP jacket, respectively. Thegeneric model can predict the load – deformation relationships very well for both pre- andpost-peak range. The FRP tension fracture predicted by the generic model (Eq.(9)) agree52well with the experimentally observed fracture. The predicted ultimate deformations forthe specimens in the past experimental studies agree very well with the experimentallyobserved ultimate deformation as shown in Fig.9.

Fig.7 Prediction results for steel jacket cases

Fig.8 Prediction results for FRP jacket cases

Fig.9 Comparison of ultimate deformation

53

3. Suitable Material Property for Shear Reinforcement/Jacket
3-1 Is high strength/stiffness always suitable property?

In order to achieve safety and serviceability, structural members need to possess required
strength and stiffness. Strength and stiffness of structural materials are chosen to achieve
the target member strength and stiffness. The higher strength and stiffness of material
can make structural member to gain the higher member strength and stiffness. Therefore,
it is quite natural to seek for structural material with higher strength and stiffness. Figure
10 shows the stress – strain relationships of various structural materials.

Steel is the mosttypical tension material, whose strength is lower than the other materials in Fig.10. This
fact clearly indicates that the materials with higher strength than steel have been sought
and accepted. The most successful one is carbon so far. The comparison in Fig.10 showsa very interesting fact. The higher the strength is, the higher the stiffness is. Since steel
is a unique material, which shows yielding, the stiffness here is the secant stiffness at thetension fracture. Another interesting fact is that the lower the strength is, the larger thefracturing strain is. Steel is an excellent material in terms of large fracturing strain.

Fig.10 Comparison of stress – strain relationships of various structural materials

As the generic model in 2.2 shows, the material with higher stiffness but larger fracturing
strain is a better option for shear reinforcement. From the experimental observation, thefracturing strain larger than 5% is large enough to avoid tension fracture of shear
reinforcement in the post-peak range of members which show great enough ultimate
deformation (high enough ductility).

The higher stiffness can be achieved even by amaterial with lower stiffness when providing the more amount of the material. However,the larger fracturing strain cannot be achieved with a material of smaller fracturing strain.
Therefore, it is practically difficult for carbon as shear reinforcement to achieve high ductility.
Steel as shear reinforcement is not a good option if it yields before reaching the ultimate
deformation.

54

It is because its secant stiffness decreases quickly, resulting in a quickreduction of the remaining shear strength, which means less ductile.

The best option,

therefore, is the structural material with a large fracturing strain (LFS) and a moderate
stiffness (see Fig.11).

Figure 10 shows that three materials; polyacetal, polyethylene

naphthalate (PEN) and polyethylene terephthalate (PET) are examples of the materials withsuch a property.

σ  ε εFig.11 Best option for shear reinforcement

3-2 Member behavior with LFS shear reinforcement

There have been many studies on behavior of members with shear reinforcement whose
fracturing strain is large (LFS shear reinforcement). Figure 12 shows the deformation ofcolumn specimen with steel internal shear reinforcement and PET jacket. PET jacket does
not show fracturing even after big plastic swelling deformation.

The efficiency of PET

jacket can be seen in both cases of specimens with high shear reinforcement ratio (flexurefailure dominant case) and with small shear reinforcement ratio (shear failure dominantcase) as shown in Fig.13 (a) and (b). The specimens with PET jacket (SP1, SP2, SP3 andSP4) show greater ultimate deformation than the reference specimen without PET jacket(SP5) as shown in Fig.13 (a). Comparing with the reference specimen (SC1s), which showed
shear failure, in Fig.13 (b), the specimen with carbon jacket (SC3s) shows greater peak loadand ultimate deformation. The ultimate deformation was determined by the fracture ofcarbon jacket. The specimens with PET jacket (SP2s and SP3s) show much greater peakload and ultimate deformation than the specimen with carbon jacket.

Fig.12 PET jacket performance after large plastic deformation55

       δδ   

 



   

   



Fig.13 Shear force – deformation relationships of columns with PET jacketing

The large fracturing strain of shear reinforcement is necessary only in plastic hinge zone.
For the other part, commonly accepted material for jacketing, such as carbon and aramid,
can be used to utilize its higher stiffness.

Considering this fact, a new seismic retrofit

method was developed in Japan, which is “Duplex Jacketing” (A-P Jacketing) in which PET
jacket is applied to plastic hinge zone and aramid jacket is applied to the other parts (seeFig.14).

Duplex Jacketing has been applied to real structures in Japan as shown in Fig.15.

       Fig.14 Duplex Jacketing                Fig.15 Real applications of Duplex Jacketing

56

The comparison presented in Fig.10 has a hidden fact. The higher the strength/stiffness
is, the higher the cost is. Generally, the cost of material amounts necessary to achieve thesame strength is less for the material with lower strength. The cost comparison between
Duplex Jacketing and jacketing with aramid is shown in Fig.16. In order to obtain the same
seismic performance, Duplex Jacketing is less expensive. The cost of jacketing with carbon
is also more expensive. In case when jacketing is only necessary in plastic hinge zone, thebenefit of using LFS materials is more significant.

       
    

Fig.16 Cost comparison of Duplex Jacketing

4. Concluding Remarks
The generic model to predict the load – deformation relationship of concrete members
reinforced with any tension material as tension and shear reinforcement, which can be either
internal or external reinforcement, is presented. The generic model consists of flexure model
for strength and deformation and shear model for strength and deformation. The model concept
is that the load for a given deformation is the remaining flexure or shear strength, whichever issmaller.

The generic model considers the interaction between flexure and shear resistingmechanisms.
Considering the prediction results by the generic model, it is concluded that the suitablematerial property for shear reinforcement to achieve large ultimate deformation is a large
fracturing strain together with a moderate elastic modulus.

The good examples of such amaterial are organic fiber material, such as polyacetal, polyethylene naphthalate (PEN) andpolyethylene terephthalate (PET).

5. Acknowledgements
The authors are grateful to all of the research team members for generic ultimate
deformation model and LFS (large fracture strain) shear reinforcement, especially, Prof Sato57

Yasuhiko, Prof Dai Jian-Guo, Mr Nakai Hiroshi and Mr Dhannyanto Anggawidjaja.
References

1) ConcreteCommittee(2017).

“STANDARDSPECIFICATIONSOFCONCRETESTRUCTURES”, JSCE. (in Japanese)2) Yasuhiko Sato, Tamon Ueda and Yoshio Kakuta (1997), “SHEAR STRENGTH OF
REINFORCEDANDPRESTRESSEDCONCRETE

BEAMS

WITH

SHEAR

REINFORCEMENT”, Concrete Library International of JSCE, No.29, pp.233-247.
3) Tidarut Jirawattanasomkul, Zhang Dawei, Tamon Ueda (2013), “PREDICTION OF THE
POST-PEAK BEHAVIOR OF REINFORCED CONCRETE COLUMNS WITH ANDWITHOUT FRP-JACKETING”, Engineering Structures, Vol.56, pp.1511-1526.
4) Tamon Ueda, Yasuhiko Sato, Tsunemasa Ito and Katsuhide Nishizono (2002), “SHEAR
DEFORMATION OF REINFORCED CONCRETE BEAM”, Journal of Materials,
Concrete Structures and Pavements, JSCE, No.711/V-56, pp.205-215.

58