Chapter 4: Non-metallic Anchor System for Strengthening RC Beams
5.6. Analysis o f the Slabs 1. Flexural behaviour and the effect o f strengthening
The p erm issib le deflection lim its sugg ested by A C I-318 (2002) are from L /180 to T /480, or the m inim um thickness o f L I30, w here I. is a loading span, for a sim ply supported tw o- w ay slab. T herefore, the co rresponding d eflection lim its are 6 m m ~ 17 m m and the m inim um thickness o f 100 m m for the p re sen t slabs are obtained. A s the thickness o f the test slab (t = 90 m m ) is less th an the m inim um requirem ent, only the deflection lim it can be applicable for the current investigation, in a service state. T he load versus deflection responses o f each slab are show n in Fig. 5.3. N o te that the deflections w ere obtained at a distance o f 450 m m from the centre o f the slab due to m alfu n ctio n in g o f the centre p o ten tio m eter o f the control slab. T he cam ber effect by the prestressed C F R P sheets in strengthened slabs w as insig n ifican t (0.22 m m ) due to the narrow strengthened area, w hich is a d ifferent aspect w ith resp ect to beam applications (K im et al. 2006), as outlined in Ch. 2.
144 Y ail J. K im , P .E ng., P h.D . T hesis
C hapter 5: F lexure o f T w o-w ay Slabs S trengthened w ith P restre sse d C F R P Sheets
T he u n stren g th en ed slab indicated a very ductile response due to its h ig h ly u n d e r
rein fo rced nature (i.e., .0.62 % and 0.31 % in the colum n strip and o u ter strip, respectively). T he applied load w as u n lo ad ed at a load o f 132 kN as failure w as assum ed due to the excessive deflection and flexural cracking. T he FEA , con d u cted afte r the test, pred icted an ultim ate load o f 131 kN w hich w as sim ilar to the experim ental failure load.
T he load w here the cracking occu rred and the initial stiffness significantly degrad ed as a p ercentage o f the ultim ate load w as 25 % , 20 % , and 43 % for the u n stren g th en e d slab, the slab w ith non -p restressed C FR P sheets, and the slab w ith p re stressed C F R P sheets, respectively. N o te that the percen tag e o f B 2-S L 2 w as low er than that o f B 2-SL1 because the non-prestressed C FR P sheets contributed to an increase in the lo ad-carrying capacity;
w hile, the passive strengthening effect did not influence the cracking load. T he corresponding F E A p redictions on cracking loads w ere close to the experim ental findings, as show n in T able 5.2. N o te that the slab (B 2-S L 4) had already p re-crack ed in accident before the slab w as tested; thus, the slope change at a load level o f 100 kN o f B 2-S L 4, Fig. 5.3 (c), m ight be due to the opening o f a w ide crack spread along the tensile region o f the slab; ra th e r than due to the initial cracking. T he p o st cracking stiffness o f the slab w ith non-prestressed C FR P sheets (B 2-S L 2) w as alm ost identical to that o f the slab w ith prestressed C FR P sheets (B 2-SL3 and -SL4).
Y ielding o f the internal reinfo rcem en t occurred in the vicinity o f the m id -sp an and corresponding plastic hinges possibly form ed. A com prehensive sum m ary o f the flexural b ehaviour is given in T able 5.2. T he increases o f the yield load w ere 10 % , 20 % and 55
% for B 2-S L 2, -SL3, and -SL4, respectively, w ith respect to the u n stren g th en ed slab (B 2- SL1). T his increase o f the yield loads in the strengthened slab supports the load-sharing 145 Y ail J. K im , P .E ng., Ph.D . T hesis
d iscussed in detail later). T he ultim ate load-carrying capacities o f B 2-S L 2, -SL 3, and - SL4 increased by 25 % , 18 % , and 72 % , respectively, as com pared to that o f the control slab. N ote that the sm all in crease in the case o f B 2-SL3 was due to the p rem atu re failure induced by p o o r bo n d o f the C F R P sheets. T he d eflection lim it from the C ode (i.e., 17 m m ) w as found at a load level o f 56 kN , 61 kN , 92 kN , and 110 kN for B 2-S L 1, -SL2, - SL3, and -SL 4, respectively. F ro m this observation, one m ay conclu d e that prestressed C FR P sheets significantly con trib u ted to an increase o f allow able service loads. It is also noted that the F E A m odel slightly o v erestim ated the ultim ate loads since the debonding m echanism w as no t accounted fo r in the m odel; nevertheless, the prediction indicated an excellent ag reem ent in cluding a m ax im u m error o f 4.6 % in the p red ictio n o f the ultim ate loads, if the p rem ature failure o f B 2-S L 3 is ignored. U nlike the control slab, strengthened slabs exhibited a progressive failure after the p ea k loads. The step-w ise decrease o f the applied load is attributed to the p ro g ressiv e delam ination failure o f the C FR P sheets.
P o stpeak b eh a v io u r o f the F E A m odels w as not obtained due to n um erical divergence.
T ypical m id -sp an deflection profiles along the centre span are p rovided in Fig. 5.4.
C om puted deflections w ere com p ared w ith the experim ental findings at an arbitrarily selected service load level o f 75 kN and n ear the ultim ate load. A parab o lic-lik e p rofile w as o btained in all slabs. T he F E A pred ictio n s agreed very w ell w ith the experim ental results as show n in Fig. 5.4 w ith a m axim um error o f 12 % at m id -sp an n ear the ultim ate load. B ecause the slabs w ere loaded n ear the m id-span, curvature along the loading span w as no t constant. A n alm ost lin ear trend w as o b served outside o f the loading area; on the other hand, h ig h er curvature w as observed un d er the loading fram e, as show n in Fig. 5.4.
146 Yail J. K im , P .E ng., Ph.D . T hesis
C h ap ter 5: F lexure o f T w o-w ay Slabs S trengthened w ith P restressed C FR P Sheets
T he co n trib u tio n o f the strengthening effect w as investigated by com p arin g the d eflection o f each slab at a typical service load o f 75 kN , as show n in Fig. 5.4 (d). T he com puted deflections o f the strengthened slabs w ere 70 % and 52 % (86 % and 32 % in the experim ent) for the slab w ith non -p restressed C FR P sheets (B 2-N P R ) and the slab w ith prestressed C FR P sheets (B 2-P R E ), respectively, w ith relative to the u n stren g th en e d slab (B 2-C O N T ).
5.6.2. Failure mode and crack patterns
All o f the tested slabs show ed a ductile failure m ode such that the reb ar h ad y ield ed p rio r to the m ajo r failure o f the slabs (i.e., excessive cracking o f concrete or delam in atio n o f the C FR P sheets). T he unstren g th en ed slab (B 2-S L 1) exhibited excessive deflection and corresponding flexural cracks, as show n in Fig. 5.5 (a). N ote that the orthogonal cracking patterns w ere observed n ear the m id-span; on the o th er hand, diagonal crack patterns w ere developed outside o f the loading area as m ore loads w ere applied, as show n in Fig. 5.5 (a).
This diagonal pattern has fo n n e d yield lines. T he failure m ode o f the slab strengthened w ith non -p restressed C FR P sheets (B 2-S L 2) w as induced by the delam ination o f the C FR P sheets including excessive flexural cracks, as show n in Fig. 5.5 (b). T he initial flexural cracks w ere investigated u n d er the loading fram e; then p ro p a g ated tow ards the edges as the slab w as further loaded. S im ilar cracking patterns (i.e., orthogonal and diagonal) w ith re sp ect to the control slab w ere observed; w hile, the patterns w ere no t as d istinguishable as in the control. T he initial delam ination o f the C FR P sheets w as observed at a load o f 140 kN . T he delam in atio n w as m ost likely in duced by excessive shear stress concentrations at the c u t-o ff p o in t o f the C FR P sheets and a lack o f adequate anchorage. T he reg io n w here the d elam in atio n occurred exp erien ced m ore severe 147 Y ail J. K im , P .E ng., Ph.D . T hesis
5.5 (b). A s the slabs w ere further loaded, the delam in atio n o f the C FR P sheets w as m ore distinct and step-w ise failure w ith red u ced strength w as observed, as show n in Fig. 5.3 (b).
In the case o f the slab strengthened w ith prestressed C FR P sheets (B 2-S L 4), random directional cracks w ere observed, including localized delam ination o f the sheets. T he localized stress n ea r the anchorage induced partial ru pture o f the C F R P sheets, as show n in Fig. 5.5 (c). A s m ore loads w ere applied, m ore regio n s exhibited the localized failure and finally the strengthening system failed, Fig. 5.5 (c). A p ro g ressiv e step-w ise failure w ith reduced strength w as o b served as in the case o f the non -p restressed C FR P application (B 2-S L 2) as show n in Fig. 5.3 (c); nevertheless, the load level w as m uch higher. All o f the strengthened slabs show ed pseudo -d u ctility after the p eak loads since the failure o f the strengthening system did no t m ean the com plete failure o f the slab itself, as show n in Fig. 5.3.
T he failure criterion o f concrete in the F E A m odel is defined as follow s. I f the p rincipal stress state fu nction exceeds the failure surface function including the strength o f the concrete; th en the concrete elem ent fails (A N SY S 2004), as show n in A ppendix D. T he cracking philo so p h y is based on the o rthotropic nature: once the com puted principal stress in a direction exceeds the tensile lim it, th en the stiffness in the corresponding d irection is invalid and the o th er tw o d irectional stiffnesses can resist the applied load. I f all directional stiffness is rem oved, the elem ent com pletely loses its load-carrying capacity (A N SY S 2004). T herefore, the isotropic m aterial characteristic changes to an orthotropic nature after the cracking load is reached. T he initial cracking patterns o f the F E A m odels clearly indicated the d am aged regions and co rresponding reduced flexural stiffness, as 148 Y ail J. K im , P .E ng., P h.D . T hesis
C hapter 5: F lexure o f T w o-w ay Slabs S trengthened w ith P restressed C F R P Sheets
show n in Fig. 5.6. B ecause o f the ideal m o d ellin g characteristics th at w ere used, random ness o f cracking w as not observed. T he cracked area w as significantly red u ced as the strengthening effect increased. T he ratios o f the cracked versus u n crack ed areas, w hen the slabs experienced the initial cracking, are 85 %, 48 % , and 14 % fo r the unstren g th en ed slab, the slab w ith n o n -p restressed C FR Ps, and the slab w ith p restressed C FR Ps, respectively. C onsidering the d ifferent cracking loads o f each slab m odel, the crack resistin g capability o f the slab stren g th en ed w ith prestressed C FR P sheets has rem arkably increased. T he graphical com parisons o f each slab are available in Fig. 5.6.
Fig. 5.7 show s typical num erical crack pro p ag atio n s in the case o f the slab strengthened w ith p re stressed C FR P sheets. N ote that, in the prestressed C FR P application, d iscontinuity o f the num erical cracks w as o b served due to the presence o f the anchors, as show n in Fig. 5.7 (a). A s the applied loads increased, the d am aged area (o r the cracked area) expanded tow ards the edges by form ulating yield lines. N ote that the dam aged area rem ained alm ost the sam e after a certain load level (i.e., 60 kN ); h o w ev er the level o f dam age (i.e., losses o f o rthogonal stiffness) consid erab ly increased. T he elem ents located in the tensile region, especially un d er the loading fram e, experienced severe cracking as w id er cracks in this area w ere observed in the laboratory.
5.6.3. Strains in the reinforcem ent
Fig. 5.8 presen ts the strain v ariations in the reinforcem ent along the loading span. T he pred icted strains o f the reb ar in the vicin ity o f the loading fram e w ere m uch hig h er than those o f o th er regions (e.g., 355 % h ig h er in the control slab). T his strain variatio n is related to the orthogonal crack p ro p a g atio n m entioned previously. M uch h ig h er stresses in the re b ar exist in the w id ely -crack ed location because there is no stress sharing 149 Yail J. K im , P.E ng., Ph.D . T hesis
N otice that the experim ental strain at m id-span in B 2-S L 4 at a load o f 227 kN w as m uch low er th an p redicted m ost likely due to the m alfunctioning o f the strain gauge, as show n in Fig. 5.8 (c). C om prehensive com p ariso n s at a typical service load o f 75 kN am ong the slabs is show n in Fig. 5.8 (d). T h e strains u n d e r the loading fram e, w h ere the highest stress occurred, decreased by 76 % and 56 % for B 2 -N P R and B 2-P R E , respectively, w ith respect to B 2-C O N T . T his decrease o f the reb ar strains significantly contributed to the hig h er y ield loads that w ere attained in the strengthened slabs, as show n in T able 5.2.
Strains in the C FR P sheets w ere also investigated, as show n in Fig. 5.8 (e) and (f). T he strains u n d er the loading fram e w ere the h ig h est as in the case o f the internal reinforcem ent. G ood ag reem ent w as o b serv ed b etw een the FEA and the ex perim ent in the case o f the slab w ith non -p restressed C F R P sheets (B 2-S L 2) as g raphically com pared in Fig. 5.8 (e); how ever, the slab w ith p restressed C FR P sheets (B 2-P R E ) exhibited som e discrepancy n ear the distance o f 650 m m at a load o f 227 kN w here the experim ental strain w as 88 % h ig h er than that o f the F E A , as show n in Fig. 5.8 (f). T he h ig h er strains in the ex perim ent are p o ssib ly due to the opening o f a crack in that region. A s w as addressed in the p revious section, the localized failure o f the p restressed C FR P sheets w as initiated n ea r the anchorage, as show n in Fig. 5.5 (c); how ever, the localized prem atu re failure w as not represented in the F E A m odel due to the perfect bond assum ption. In the slab w ith prestressed C F R P sheets (B 2-P R E ), the m axim um strain in the C FR P w as 58 % o f the ru pture strain; how ever, only 33 % o f the ultim ate strain w as used at failure in the slab w ith non-prestressed C FR P sheets (B 2-N P R ). T his observation supports statem ents regarding the efficiency o f the p re stressed C FR P sheet application such as the hig h er 150 Yail J. K im , P .E ng., P h.D . T hesis
C h ap ter 5: F lexure o f T w o -w ay Slabs S trengthened w ith P restressed C F R P Sheets
ultim ate load and m ore efficient use o f m aterial. N ote that the initial prestress w as taken into account in m easuring the C FR P strains, Fig. 5.8 (f). T able 5.2 also show s the strains in the C FR P sheets below the loading fram e.
5.6.4. Crack m outh opening displacem ent
T w o-w ay slabs u su ally exhibit a v ery ductile resp o n se un d er loads; thus, large deflections or excessive cracking m ay significantly influence the beh av io u r o f the slabs. T here are m any reasons w h y a slab m ay experien ce cracking such as the settlem en t o f plastic concrete, shrinkage, tem perature effects, and applied load. P ro p er vibration, go o d m ix design, and adequate p lacem en t o f rein fo rcem en t m ay m inim ize the o ccurrence o f cracking (P ark and G am ble 2000). M o st o f the b uilding codes suggest a perm issib le crack w idth or an equivalent crack control p aram eter (C S A A 23.3 1995; 2006), co nsidering durability characteristics. M any factors m ay affect the corrosion o f steel reb ars in a slab such as the thickness o f a con crete cover, soundness o f concrete (i.e., perm eab ility ), and duration o f sustained open-cracks (P ark and G am ble 2000). Fig. 5.9 show s the n o rm alized load versus norm alized crack m outh opening d isplacem ent (C M O D ) obtained at tw o d ifferent locations such as the m id-span and the C F R P -stren g th en ed location, based on the FEA . N otice that the C M O D w as assum ed as strain variatio n s in a finite elem ent located at a high curvature reg io n in the slab. C onsidering strain localization, this assum ption is reasonably accepted. C M O D s at the directly strengthened area w ere slightly lo w er than those at the m id-span. C M O D s at a typical service load (i.e., ap p roxim ately 40 % o f the ultim ate load) are g iven in Table 5.2. A s show n in Fig. 5.9, there existed no clear evidence o f red u ced C M O D s because o f the co n trib u tio n o f prestressed C FR P sheets. N ote that the sm all decrease o f the C M O D s, b etw een the m id- 151 Y ail J. K im , P .E ng., P h.D . T hesis
strengthened w ith prestressed C F R P s, the p re stressed C FR P sheets did no t con trib u te to the control o f C M O D s in the case o f a tw o -w ay slab. S ignificant reduction o f C M O D s in a b e a m ’s case is show n in K im et al. (2006), as o utlined in Ch. 2. T he reaso n is explained by the fact th at the stren g th en ed area o f the slab is m uch less than that o f the b eam application: only 15 % o f the tensile re g io n w as covered in the tested slabs; o n the o ther hand, 100 % o f coverage w as p ro v id ed in the b eam application.
5.6.5. Energy absorption and ductility
Structural ductility is a critical consid eratio n w hen a structure is strengthened w ith C FR P due to its b rittle and abru p t failure characteristic. S tructural ductility is d efined as an energy absorption ability o f a stru ctu re until its failure occurs. M any factors influence the ductility o f a structure; for instance, the rein fo rcem en t ratio, geom etry, strengthening schem es, concrete strength, and rate o f loading (K em p 1998, N ew hook et al. 2002).
Several m ethods to quantify the ductility are p ro p o sed such as displacem ent ductility, energy ductility, and curvature ductility (S pad ea et al. 2001, N ew hook et al. 2002, Z ou 2003). A m ong these m ethods, the energy ductility w as selected for this study. T he ductility index (jUe) is defined:
[5.1] M e =
^ y i e l d
w here E u\t and Ey-,eid are the energy ab sorbed until the ultim ate load and the yield load, respectively. N ote that the energy ab sorbed after the peak load o f the strengthened slabs
152 Y ail J. K im , P .E ng., P h.D . T hesis
C h ap ter 5: F lexure o f T w o-w ay Slabs S trengthened w ith P restressed C F R P Sheets
w as not acco u n ted for to give a fair com parison to the u n strengthened slab, despite being the p seu d o -d u ctility o f the strengthened slabs. T able 5.3 indicates the energy absorbed until the yield and the ultim ate loads as w ell as the calculated ductility indices. T he ductility indices obtained from the F E A w ere g reater than th o se from the ex perim ent including a m axim um erro r o f 32.5 %. N ote th at the slab strengthened w ith prestressed C FR P sheets exhibited alm ost the sam e level o f a ductility index w ith re sp ect to the unstren g th en ed slab: d espite the b rittle failure n ature o f the slab strengthened w ith prestressed C FR P sheets (B 2-S L 4), the h ig h er yield load and the asso ciated ultim ate load com pensated fo r the low er d eflection to achieve a sim ilar index (or slightly h igher) w ith respect to the control slab (B 2-S L 1). Flow ever, no significant im pro v em en t w as observed in the slab w ith non-prestressed C FR P sheets (B 2-S L 2). N ote that the ductility index o f B 2-SL3 w as very low (i.e., 44 % o f B 2-S L 4) due to its p rem ature failure.