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Response of innovative high strength reinforced concrete encased-composite corbels
Structures 25 (2020) 798–809
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Response of innovative high strength reinforced concrete encased-composite corbels
T
Qasim M. Shakir Department of Civil Engineering, Faculty of Engineering, University of Kufa, Najaf, Iraq
ARTICLE INFO
ABSTRACT
Keywords: Encased composite corbels Shear-slenderness ratio Toughness Lateral buckling Horizontal shear Web openings Cracking
This work is devoted to discuss experimentally the behavior of high strength reinforced concrete (R.C.) encased corbels using the available commercial W-shape rolled steel. Eight specimens are tested and two shear slenderness ratio are considered, namely 0.70 and 1.00. The tested specimens are categorized in two groups according to (a/d) ratio. Each group included one conventional RC corbel and three composite corbels. Three configurations of composition are discussed, W-shape, WT shape and Tapered WT shape. Besides, two steel corbels have been tested, one W-shape while the other was WT-shape to get more understanding about the failure of composite corbels. The comparison between specimens is based on load-deflection curves, ductility, toughness, failure load, pattern of cracking propagation, failure mode and history of crack width development. Results revealed that the low properties commercial rolled steel can be used in composite corbels and such corbels could be adopted as a convenient alternative to the conventional RRC. In addition, it was found that the tested composite corbels yielded better behavior than the conventional ones, the composite corbels yielded toughness ranged from 120% to 170% from that of the RC conventional corbels with similar capacity for those composed using full W-shape with opening in webs. More ductile behavior is observed for corbels especially when shear force is dominant and low a/d ratio is adopted. Furthermore, Its found that that increasing a/d ratio from 0.7 to 1.0 for the control specimens, composite W-shaped and Tee-shaped encased beam result in reduction of capacity by 29%, 27% and 21%. Respectively. Moreover, a simple equation is suggested to estimate the composite corbels based on toughness and failure loads.
1. Introduction Reinforced concrete corbels (RCC) are defined as short cantilevers protrude from walls or columns having a shear slenderness, a v /d, normally less than 1, usually used to resist forces precast beams or floors at joints. Corbels are mainly designed to satisfy the requirements of resisting vertical loads and horizontal forces caused by shrinkage, thermal and creep effects of the beams, bridge crane or bridge piers. It became a common feature in the construction of buildings with increased use of precast concrete. Due to their small shear slenderness ratios, such elements are usually classified as a D-region, where there is considerable disturbance in the distribution of the strain through the depth of the cross-section, even in the elastic phase. The dominant behavior is controlled by shear rather than the bending moment. The ACI 318-14 [1] code stipulated that shear slenderness ratio a /d for corbels to be less than 2. Such element can be designed using the strutand-tie method and those with shear slenderness ratio less than 1 may be designed using the shear-friction approach. Many studies were published to study the behavior and
strengthening of RCCs. Different variables that may affect to behavior of such members were considered. Regarding the behavior of RCCs, Mattock et al. [2] then, Mattock [3] proposed several modified shearfriction models for design of corbels having shear slenderness ratios (a/ d) less than 1.0. Yong et al. [4] observed the validity of the ACI Code shear friction and truss analogy (STM) methods to RCCs having shear slenderness ratios of 0.39 with strength ranging between (41.4–82.7) MPa. In 1998, Torres [5] reported that RCCs may fail by one of six scenarios shown in Fig. 1. Such modes are: a) Yielding of the tension tie (Bending failure) which occur due to lack in main reinforcement (lightly reinforced section). b) Crushing or splitting of the compression strut (diagonal failure). This type of failure may occur due to excessive amount of main reinforcement (over reinforced section) c) Shear along the junction of the column with the corbel d) Loss of anchorage of the main steel when the development length is not enough to develop the required bond. e) Shearing failure under the loading plate
E-mail address: [email protected]. https://doi.org/10.1016/j.istruc.2020.03.056 Received 24 September 2019; Received in revised form 23 February 2020; Accepted 26 March 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Modes of Failure of RC corbels, adapted from Torres [1].
Regarding studies considered the strengthening of corbels, three main methods were adopted in the previous studies. These are external strengthening by FRP composites, external strengthening by steel plates and using posttensioned anchored bars. Heidayet et al. [16] through repairing several damaged RCCs by external plates found that the strength ratio of the (repaired/original) corbel ranged from 0.7 to 1.5. Ozden and Atalay [17] reported that wrapping RC beams with GFRP sheets with orientation of 45 degrees was more influential than other arrangements of wrapping. An improvement of (40%–200%) was obtained, depending on the reinforcement ratio, (a/d) ratio, and the characteristics of FRP layers. El-Maaddawy and El-Sayed [18] reported that strengthening by CFRP sheets yielded a strength enhancement in the range of (21–40)%. Mohammed and Hassan [19] through testing high strength concrete corbels wrapped with CFRP sheets obtained an enhancement in load capacity of 28.3%. Ivanova and Assih [20] studied strengthening of RCCs by carbon fiber fabrics. An increase in failure tensile strength more than 1.82 was obtained. The same authors [21] studied the static and dynamic response of RCC strengthened by using carbon fabrics. An improvement in the ultimate load by twice and stiffens less than a third was obtained. Urban and Krawczyk [22] investigated the use of post-installed threaded rods as additional reinforcement. An enhancement in capacity of about 64% was recorded. Mohammad and Al-Shamaa [23] examined the behavior of reactive powder concrete brackets, upgraded with Near Surface Mounted (NSM) CFRP strips. Average enhancement of 15% was obtained. Al-Kamaki et al. [24] studied the behavior of externally strengthened RCCs by CFRP fabrics. It is found that the diagonal configuration improved the ultimate strength by 27%. Shakir and Kamonna [25] studied experimentally the response of high strength self-consolidating RCCs upgraded with NSM steel bars.
f) Localized bearing when dimensions of the bearing plate not adequately distribute the point load. Mattock [6] reported that the equations of shear friction method assumed previously underestimate the shear transfer strength for ultrahigh strength RCCs Thus, some modifications are proposed relating with the upper limits for shear force to be applied on the corbel. Thus, the method. Russo et al. [7], proposed a model to determine the shear strength of RCCs, or brackets, by superimposing the strength contribution of the strut-and-tie mechanism due to the cracked concrete, principal reinforcement, and stirrups. Campione et al. [8] proposed a simplified model to calculate the shear strength of steel fiber RCCs including stirrups. Results showed the effectiveness in using fibrous RCCs. Lu and Lin [9] suggested a model to estimate the shear strengths of corbels with a/d ratios between 0.11 and 1.69. It was found that the shear strengths increase with increasing the grade of concrete and vertical stirrups and reducing (a/d) value. Khalifa [10] suggested a “macro-mechanical” strut and tie (STM) model to study the steel fiber high-strength RCCs. In this model, the fibers was adopted as a substitution of horizontal stirrups. Al-Shaarbaf et al. [11] studied the behavior of RCCs under repeated loadings, It was reported that the repeated load is more influential that monotonic loading. Wael Kassem [12] suggested a method for determining the capacity of RCCs based on the strut-and-tie (STM) and secant stiffness by combining strain compatibility and constitutive laws of cracked RC. Özkal and Uysal [13] discussed the optimum reinforcement layout of concrete corbels. Redha et al. [14] studied experimentally the response of ultra-high performance fibrous RCCs with concrete grade of 150 MPa. Wilson et al. [15] evaluated STM method to design corbels relative to the empirical design (Shear-Friction) method. 799
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Four different configurations of installations of strengthening bars were investigated. A maximum improvement in failure load of 57% and 41% for a/d of 0.85 and 1.25 respectively was obtained. The Upside down Vshaped“ strengthening system named is the most advisable for small values of shear slenderness ratio (a/d < 1). The horizontal bars arrangement is more recommended for large a/d values (a/d > 1). Chagas et al. [26] tested corbels that are precast separately of the column and then joined to it by means of socked and unbonded posttensioning. Results demonstrated that the proposed corbel presented strength 5% lower than the reference monolithic corbel. As it is shown above, that all studies that published to enhance the capacity of RC corbels were based either on improving the internal composition of the concrete by using high strength concrete, steel fiber concrete, reactive powder concrete, or externally installed strengthening elements. No study have been published that based on incorporation of steel sections to enhance the performance of RC corbels. This works aims to suggest a reinforced concrete composite encased corbels and investigating the performance against the well-Known conventional RCC. Moreover, explore if it can be adopted to develop higher capacities. In addition, a simple relation is suggested to estimate the capacity of composite corbels to show the advantage of using such type of corbels.
Table 2 Designation and characteristics of the tested specimens. Specimen
2.1. Materials The constituent materials of the concrete mix used in the present study was composed of Ordinary Portland Cement (Type I) manufactured by KAR Company, rounded coarse aggregate of max size of 19 mm, natural sand taken from Al-Najaf region, and GILENIUM ®54 as superplasticizer. Drinking water was used in preparing specimens, cubes and cylinders. Three sizes of steel reinforcement are used, ø8 and ø 16 as ties and longitudinal reinforcement for the column segment. Reinforcement of the corbel parts consist of bars of ø10 diameter except the main tension reinforcement for the control RCCs specimens in which ø 16 diameter was used. In addition, W-shape rolled steel sections are used in the six composite corbels. Material properties of concrete, steel bar are detailed in Table 1. The designations for the tested specimens are shown in Table 2. When the specimens gained the required strength (age of 28 days), the test is done. Besides, cubes of 150 mm and cylinders of (100 mm*200 mm) are tested to find the compressive and tensile strengths. Such strengths are found to be 57.1 MPa and 3.2 MPa respectively.
Rolled steel
8 10 16
500 521 510 285
593 647 682
0.7
Non W-shape with openings in web WT-shape with caps at ends Tapered W-shape with caps at ends As in CWF-GA As in CTE-GA
Group B
REF-GB CWF-GB CTE-GB CTP-GB
1.0
Non W-shape with openings in web WT-shape with caps at ends Tapered W-shape with caps at ends
Fig. 5 shows the effect of shear slenderness ratio on the response of RCCs. It can be seen that the specimen REF-GA yielded stiffer behavior than REF-GB. However, at 500KN, there was a partial failure due to the diagonal shear crack occurred causing rapid increase in deflection to up to a load of 550 kN. Then the corbel retire it’s stability and continues to resist load up to 760KN. Failure occurred suddenly and severe drop in capacity can be seen. Thus, a load level in the range (500–600)kN may be considered to be as the maximum capacity for safety aspects. Regarding the response of the specimen REF-GB, it can be seen that the behavior is more ductile referring that flexure effect is dominant. More cracks initiated, more deflection was recorded. Beyond the maximum load, it can be seen that there is a gradual reduction in capacity compared to specimen REF-GA. The safety aspect still, not satisfied as there is no enough warnings (gradual reduction in stiffness) before failure. The load-deflection curve for the specimen SWF-GA is shown in Fig. 6 for the sake of comparison with the composite corbel CWF-GA and to discuss the improvement in capacity due to encasing the steel section with concrete. Furthermore, investigation the behavior of the SWF-GA assist understanding the behavior of the composite corbels. It can be seen that specimen SWF-GA yielded a capacity of 180 kN corresponding to a capacity of specimen of CWF-GA of 750 kN. i.e. an
Table 1 Material properties of steel bars.
Bar dia. (mm)
REF-GA CWF-GA CTE-GA CTP-GA SWF-GA STE-GA
3.1. Load-deflection curves
Eight reinforced concrete corbels (RCC) with details shown in Fig. 2 have been tested experimentally in this work. Three forms of rolled steel section have been considered, I-shape with circular openings of 65 mm diameter in web with c/c distance of openings of 160 mm, Tshape with uniform depth and Tapered T-shape with depth at ends of 60 mm. Both of the T-shapes have end caps. Such caps and openings served as shear connectors to improve bond between steel section and the surrounding concrete. Each steel segment is of 820 mm length with flange and web thicknesses of 3 mm and 4 mm respectively. The flange
fu (MPa)
Group A
3. Results and discussion
2.2. Method of experimental work
f'y (MPa)
Shape of steel section
width of 75 mm and total depths of W-shape and T-shape of 130 mm and 120 mm respectively. The tested specimens are categorized into two groups based on shear slenderness ratio. Namely 0.7 and 1.0. In addition, two rolled steel segments of W-shape and WT-shape are tested with a/d = 0.7 to explore the behavior of steel corbel only. The weight of the steel segments are 6 kg, 7.5 kg and 8.5 kg for the Tapered Tee-, Tee- and W-shape respectively. Thus, the average percentage weight of steel segment to the weight of specimen is 5.5%. Two ø16 steel bars segments 100 mm long are welded to the top, bottom flanges are embedded on the top, and bottom column portions to fix a rolled steel section in place by using seem. Thus, there is no connection between the reinforcement of the corbel and the rolled steel segments. The two steel sections are tested using the same regime that adopted in testing the RC-composite corbels in which the specimen is subjected to a midspan point load that was gradually increased up to failure. Fig. 3 shows the scheme used in testing the rolled steel segments. The two steel beams SWF-GA and STE-GA are tested under the same loading setup used in testing the composite corbels. Thus is similar to the case when concrete in the composite corbel failed entirely when reaching its capacity. Then, the embedded rolled steel beam will resist the applied loading. The experimental tests are achieved in Structural Lab. of the college of Engineering/ university of Kufa. The universal machine shown in Fig. 4 with capacity of 200ton with a dial gauge of accuracy of 0,05 mm that is located at center of the column.
2. Materials and method
Steel
a/d ratio
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(A)RC corbels
(B)Composite corbels
Fig. 2. Detailing and dimensions of the tested specimens.
improvement in capacity of by 416%. It is expected that the steel and concrete constituting the sections worked together up to the point when slip occurred. Beyond this point, the full capacity of the steel section would be exhausted. This is represented by the horizontal part of the load deflection curve. Thus, it can be concluded that if slip is delayed or the strength against tearing failure is improved, higher capacity may be obtained. Fig. 6 shows the variation in response for the composite encased
corbels CWF-GA and CWF-GB. It can be seen that increasing (a/d) ratio from (0.7) to (1.0) results in reduction of ultimate load by (27%), with noticeable increase the ductility by 43% was observed. The stiff behavior for CWF-GA may be attributed to the dominance of shear force effect with small (a/d) values and effect of tearing failure between openings is small up to the final stages of loading. In contrast, flexural stresses is expected to control behavior of CWF-GB resulting in more ductile behavior.
(A)Specimen SWF-GA
(B)Specimen STE-GA Fig. 3. Loading setup of the specimens (A) SWF-GA (B) STE-GA. 801
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Fig. 7. Load deflection curves for the composite corbels with WT- section.
Taking another glance on Fig. 6, it can be seen there is no sudden drop in capacity for specimen CWF-GB. This can be recognized by the semi-flat curve close to the final stage and then, slip occurred gradually. Whilst, for specimen CWF-GA, there can be seen sudden change in slope near the failure instant. This may be simply realized if we remember that diagonal shear cracks occurred and crushing of concrete due to flexure may affect the bond between steel section and concrete. Thus, higher load capacity may be obtained by enhancing bond by different means such as adding caps at end, adding some shear studs at faces of the web or welding spiral steel bar on web sides or strengthening the zones between openings by steel plates to resist the horizontal shear in web. Fig. 7 shows the effect of shear slenderness ratio on the response of composite corbels CTE-GA and CTE-GB. The tee-section can be obtained by cutting the web of larger section. This may reduce the cost of the rolled section used. The web may be cut horizontally or as zigzag which may result in improving the bond resistance. Regarding the capacity, it is found that reducing a/d ratio from (1.0) to (0.7) improved capacity by (27%). In addition, it is clear that for specimen CTE-GB failure occurred gradually due to uniform reduction in bond between steel and concrete. However, due to the low moment of inertia, it can be seen that flexure effect is more obvious of specimen CTE-GB relative to CTE-GA. For specimen CTE-GA, it can be seen that the drop in bond occurred rapidly relative to CTE-GB. This may be because that CTE-GA, yielded higher stiffness in most of loading stages. Thus, the specimen yielded more brittle response than CTE-GB and few wide cracks occurred accompanied with crushing within the compression face at failure. Close to failure instant, the lateral support for the steel section deteriorated leading to rapid buckling of the steel section due to the excessive compression on the web. Fig. 7 shows also the response of the steel corbel of Tee shape only. It can been seen that the specimen yielded very soft behavior relative to specimen CTE-GA with failure load of about 75kN (11% of CTE-GA). Failure occurred in early stages by lateral buckling as in the figure. The low load capacity may be attributed to the low moment of inertia and removing the lateral support for the web when cutting the flange to build the tee-section. This can be realized easily when comparing the capacity of specimen STE-GA with the capacity of SWF-GA. It can be seen than the capacity of the Tee shape section is 42% of the wide flange section. Thus, it is expected that the concrete around concrete play as a lateral continuous support, then allowing the section to develop the full strength. Furthermore, if the difference between the capacities of the steel section is added to the capacity of specimen CTEGA, the capacity will be 765kN which very close to the capacity of CWF-GA. Thus, it is expected that the mode of failure of the rolled steel
Fig. 4. The universal machine used in testing specimens.
Fig. 5. Load deflection curves for the conventional R.C. corbels.
Fig. 6. Load deflection curves for the composite corbels with WF section.
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from the economic view, it is recommended to use the tapered WTshape since there is about 25% steel saving in web of the corbels relative to the WT-shape. 3.2. Cracking patterns Fig. 7 shows the crack patterns at failure for the tested composite corbels. The impact of shear slenderness ratio on the crack propagation at failure for reinforced corbels REF-GA and REF-GB can be seen in Fig. 9a and b respectively. It is obvious that for smaller (a/d) ratio the failure is due to diagonal shear and specimen yielded brittle behavior and failed suddenly without enough warnings. It is worth to mention that this type of failure is non prohibited. Regarding to specimen REF-GB, Fig. 9b shows that the failure was by diagonal shear failure as in specimen REF-GA with more ductility and without fragmentation of concrete. Thus, ACI318-14 [1] imposed limits on the useful capacity of the corbel depending on strengths of steel and concrete. Comparing specimens CWF-GA and CWF-GB, Fig. 9c and d, it can be seen that no of cracks for specimen CWF-GA is more than CWF-GB and there are various types of cracks i.e. vertical at junction and under loading point, diagonal. Referring to a ductile behavior due to increase moment relative to specimen CWF-GB and failing by diagonal shear failure with some crushing at compression face and spalling of concrete out of web of steel section. Specimen CWF-GB yielded a more brittle behavior and the failure as diagonal shear with crushing of the compression zone. With less amount of spalling of concrete out of steel section. This may be caused due to the relative more effect of shear of the specimen CWF-GB leading to the lesser amount of curvature with load increase. Comparing cracking patterns for CWF-GA and CTE-GA corbels, Fig. 9e and f, it can be seen that the crack distribution of CWF-GA propagated towards the ends of the corbel with a vertical trend through most of the depth of the corbel. This is referring to the efficiency of bond provided by the holes introduced in the webs. Regarding specimen CTE-GA, It can be seen the cracks initiated at the tension face change its trend and tend to be horizontal and developed from point of reaction towards the junction between the corbel and column where buckling to occur. Thus, referring the compression effect of caps at ends of the steel section subjected increasing force leading to some crushing of the concrete within the junction zone. This crushing revealed that insufficient bond between the steel section and concrete that contribute in transferring compressive force resulted from the bending moment to the steel section. Thus, it is recommended to use some stiffeners at the mid-distance from the column face to reduce action of lateral buckling and to improve the bond action by welding some steel bars at the two faces of the web to serve as shear connectors. Regarding specimens CTE-GA and CTE-GB, the same can be said when comparing CTP-GA with CTP-GB, that the shear effect is very clear when a/d = 0.7. Less intensity of cracks (but wider) can be seen and failure was of the diagonal shear type. Comparing specimens CTP-GA and CTE-GA, it can be seen that no of
Fig. 8. Load deflection curves for the composite corbels with tapered steel section.
affect the capacity of the composite corbel. i.e. Buckling of segments WT-shapes occurs earlier than horizontal shear for segments of Wshapes. Fig. 8 shows the influence of a/d ratio on the performance of composite corbels CTP-GA and CTP-GB. It can be seen that reducing a/d ratio from (1.0) to (0.7) result in improving the capacity by (21%). Moreover, it is obvious that there is clear bifurcation between the responses of the two specimens at the early stages of loading. This may be due to the weakness caused by increased no of cracks occurred at early stages for specimen CTP-GB. Whereas, for specimen CTP-GA shear effect is more obvious, stiffer behavior can be seen at the final stages, it can be seen that the slip for specimen CTP-GA started at deflection record of (2.9)mm and ended at (3.5)mm when specimen failed. While, for Specimen CTP-GB the zone of slip was (3.5–5.1)mm. This reveals that the extent of slip effect for specimen CTP-GB is higher than CTP-GA and less slip is expected to occur if more stiffeners are added at the midspan of the corbel. The initial cracking load, failure load and the corresponding recorded deflections are listed in Table 3. It also shown the ductility index for each specimen. It can be seen that there is a slight increase in the ductility reduced relative to the control specimen for low a/d ratio. This may be attributed that such corbels yielded stiff behavior and cracks propagated gradually through the member causing gradual loss in bond and crashing in concrete at instant where lateral support for steel section become weak to resist the vertical load failure occurred rapidly. Whilst, ductility increased significantly when adopting large (a/d) value because that slip increases gradually and deflection increases with B.M increment. Thus, uniform failure occurs because concrete between webs of steel section prevented lateral buckling of the rolled steel section as shown in Fig. 9. It is clear from Figs. 7, 8 and Table 3 that the composite corbels with tapered WT-shape yielded the same capacity as that included WT-shape with higher ductility index. Thus,
Table 3 Cracking and failure loads with the corresponding deflections. Specimen
Cracking load
Failure load
Deflection at initial crack
Deflection at failure
Ductility index
Group A
REF-GA CWF-GA CTE-GA CTP-GA
140 120 100 100
760 750 660 660
0.92 0.81 0.95 0.85
3.5 3.25 4.02 3.49
3.8 4.01 4.23 4.11
Group B
REF-GB CWF-GB CTE-GB CTP-GB
90 80 70 60
540 550 520 520
0.90 0.79 0.84 0.84
3.8 4.5 4.24 5.38
4.2 5.70 5.04 6.40
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(b) Specimen REF-GB
(a) Specimen REF-GA
(c)Specimen CWF-GA
(d)Specimen CWF-GB
(e)Specimen CTE-GA
(f)Specimen CTE-GB
(h)Specimen CTP-GB
(g)Specimen CTP-GA
Fig. 9. Crack patterns for the composite corbel specimens.
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(A) Top view
(B) Side view
(C) View of the bottom flange Fig. 10. Specimen SWF-GA at failure.
cracks for CTE-GA is less than CTP-GA. this may be attributed to the higher bond effect between the steel section and concrete. This bond assist in transferring some of compression to the steel section. Thus, compression failure occurred within the final stages of loading at instant when bond violated. In addition, it can be seen clearly that in specimens CWF-GA and CWF-GB, the volume of concrete block that resisting the pressure at the compression face was more the composite corbels with Tee shapes, resulting in smaller cracks propagation. Whereas for specimen CTP-GA and CTE-GA there is, one major deep and wide crack occurred within earlier stages of loading. Comparing specimens CTE-GA and CTE-GB, it can be seen that specimen CTE-GA failed by diagonal cracking with some crushing at the compression face whereas for CTE-GB, the failure occurred by bond failure between steel and concrete leading to severe separation of the compression block. Fig. 10 shows the specimen (SWF-GA) at failure. The top view, Fig. 10a, shows the yielding of steel at compression face. Whereas, Fig. 10c demonstrated the yielding of the bottom flange by tensile stresses. However, Fig. 10b, showed that the corbel tend to fail by bucking along diagonal line passing through the void within the shear span. The deformed shape for the steel WT-rolled shape (STE-GA) is shown in Fig. 11, which revealed that the failure mode was lateral buckling within the shear span nearest to the column face.
(A) Side view
(B)Top view
Fig. 11. Specimen STE-GA at failure.
Fig. 12 shows the toughness values for the corbel specimens tested in the present work. It is obvious that although specimens REF-GA and REF-GB yielded the highest load capacity but they have the lowest toughness. This refers to the high stiff behavior up to the final stages of loading. This type of behavior and the sudden behavior caused from was controlled by ACI-318 by imposing the limitations discussed in Appendix A. Thus 75% of the failure load was considered as a useful service load. Regarding the composite corbels CWF-GA and CWF-GB, it can be seen that such specimens acquired toughness of about (155%–165%) of the control beam with similar capacity. This refers that higher service load can be adopted without serious risk as in the reference RC corbels. For the corbels CTE-GA and CTE-GB. It is found that this
3.3. Toughness values Toughness is a measure of the ability of the structure (or member) to adsorb strains (deformations) before failure. In addition, it provide good indication for warning that the structure yielded before full collapse. Toughness represent the area under the load deflection curve. 805
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2000 1800 1785 1752
TOUGHNESS(KN.MM)
1600
1835
1754
1706
1400 1368
1200 1000 800
1072
1138
600 400 200 CTP-GB
CTP-GA
CTE-GB
CTE-GA
CWF-GB
CWF-GA
REF-GB
REF-GA
0
Fig. 12. Toughness values for the tested composite corbels.
arrangement acquired a toughness ranges from 120% to 163% relative to the control corbels although they yielded smaller capacity. This refers that the lack in bond results in premature failure and more capacity can be obtained if the conditions of bond and the resistance against lateral buckling is enhanced. The specimens CTP-GA and CTP-GB yielded the highest toughness which ranged from 150% to 170% relative to the reference corbels.
800 700 Load, kN
600
3.4. Crack width
500 400
CWF-GA-Flexural CWF-GA-Diagonal CWF-GB-Flexural CWF-GB-Diagonal
300 200 100
Fig. 13 shows the history of initial cracks width development for the RCCs REF-GA and REF-Gb. It can be seen that first crack initiated at (140kN) and (90kN) for the two specimens respectively, and was of the flexure type at junction between corbel and column. Soon the diagonal crack toward support developed at (400kN) and (180kN) and widened rapidly causing the flexure to stagnate. In addition, it is clear that the diagonal crack for REF-GB developed with higher rate compared to REF-GA. This may be attributed to the difference in B.M. Fig. 14 shows the history of initial cracks development RCC CWFGA and CWF-GB. It is obvious that the flexural cracking developed early, followed by the diagonal crack but the rate of the widening still low up the final stage of loading at which a loss in bond between steel section and concrete occur. Figs. 15 and 16 show the rate of widening of cracks for the composite specimens with WT-shaped and tapered WT-shaped rolled steel. It can be seen that crack width increased more rapidly than the CWF-GA and CWF-GB specimens did. This may be caused by the smaller flexure
0
0
0.2
0.4 0.6 0.8 1 Initial Crack width, mm
1.2
Fig. 14. History of crack width development for composite corbels with WFshape.
800 700 600 Load, kN
500
400 300 200 100 0
Fig. 15. History of crack width development for composite corbels with WTshape.
Ref-GA-Flexural Ref-GA-Diagonal Ref-GB- Flexural Ref-GB- Diagonal 0
0.2
0.4 Initial 0.6Crack0.8 1 width, mm
resistance resulted from the relatively low amount of moment of inertia for the tapered sections (smaller area of contact with concrete) that may cause slip occur more rapidly.
1.2
4. Theoretical analysis
Fig. 13. History of crack width development for R.C. corbels.
The shear friction method [3] for design of RC corbels is described 806
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800
(a/d) and dimensions. To and T1: are toughness value for RC and composite corbels. Based on the above equation the useful load capacity for the composite corbels as listed in Table 5. It can be seen that Pc/Pf for composite corbels are higher than the RC corbels. This is expected due to the difference in general performance for the tested specimens.
700
Load, kN
600 500 400 CTP-GA-Flexural CTP-GA-Diagonal CTP-GB-Flexural CTP-GB-Diagonal
300 200 100 0
0
0.2
0.4 0.6 0.8 Crack with, mm
1
5. Conclusions 1) It was found that the R.C. composite corbels using the commercial low properties rolled steel section might serve as an appropriate alternative for the R.C. corbels with better performance. 2) The corbels composed of W-shaped steel sections with enough no. of openings in webs yielded the same failure load capacity with better ductility than the R.C. corbels and that it is needed to use caps at ends to increase load capacity and reduce slip behavior. 3) The R.C. corbels composed with Tee and Tapered steel section yielded the same capacity but more ductility for tapered section. Failure occurred by bond failure followed by lateral the buckling of the rolled steel. 4) The R.C. composite corbels yielded some softening behavior within the early stages of loading up to the initial cracking load. Then, stiffness increases gradually up to failure. This can be recognized by the cracking load value, which is lower than the conventional RCC. This may be attributed to the concentration of steel area with in th steel section and the relatively smooth contact surfaces if compared with the steel bars. 5) Failure Modes of the R.C. corbels was by diagonal shear while for the composite corbels, the failure was firstly due to the loss in bond between concrete and steel section then upon failure mode of the steel section only. Thus, it is expected that higher load capacity can be obtained by adding stiffeners and some shear connectors for the steel shapes. 6) A drop in the load capacity for the R.C. by 29% when increasing a/d ratio from 0.7 to 1.0, whereas for the composite corbels with H-shape the reduction was 32%. for the R.C. composed with Tee or tapered sections, the reduction was 21%.this difference in composite corbels may be attributed to the higher slip effect and less stiffness against flexure for Tee and tapered composed corbels with a/d = 0.7. 7) According to the limits of ACI318M-14 [1], fy for the steel bars used in concrete design may not be more than 400 MPa. Thus the useful load capacity that allowed to be resisted by the R.C. corbels tested in the present work was 200kN for a/d = 1.0 and 290 kN for a/ d = 0.7 per one corbel. Whereas the useful capacity for the composite corbels (fy for steel section = 285 MPa) ranged between (260–275)kN for a/d = 1.0 and in range (330–375)kN for a/ d = 0.7. This conclusion is based on the behavior at final stages, history of crack width and possibility to improve the response of the composite corbels. 8) The WF-shape, WT-shapes and Tapered WT-shapes composite corbels yielded toughness ranged from 154% to 165%, 120%-163% and 150%-170% respectively relative to that of the RC conventional corbels. 9) It is found that the failure mode for the steel shape affect largely the mode of failure for the composite corbels. In addition, the failure of the steel shape within composite corbel occurs simultaneously at the instant of bond failure. Furthermore. The capacity of composite corbel is at least four times the WF-steel corbel alone.
1.2
Fig. 16. history of crack width development for composite corbels with Tapered WF- shape. Table 4 Cracking and design loads for the control corbels. Specimen
REF-GA
REF-GB
Design load (fy = 420 MPa) Design load (fy = 520 MPa) Cracking load Max. allowed shear force Failure load
290 355 140 319 380
200 250 90 319 270
in Appendix A. For the control specimen REF-GA, the design shear force was 290 kN when the limit of ACI318M-14 [1] of 420 MPa yield stress for steel is used and 355 kN if the measured value is adopted. The failure load obtained experimentally was 380 kN. Regarding specimen REF-GB, the design shear force for satisfying the upper limit of yield stress for steel was 200 kN and 250 kN if this limit is neglected. The failure load was 270kN. The results are listed in Table 4. Comparing results of the tested specimens, it can be seen that the corbels composed with I-shaped steel sections yielded capacity very close to the RCCs, with more toughness, less crack with and less shear reinforcement. Furthermore, it is clear that the specimens composed with tee-shaped and tapered steel sections yielded similar results but with more ductility for the Tee-shaped composite specimens. Moreover, since there is not theoretical procedure to estimate the capacity of composite encased corbels. A simple equation is suggested based on the toughness ratios as follows;
Pc = P0 + (Pf
P0 )
T1 T0
1
Pf Pf 0
(1)
The value obtained from Eq. (1) above should be imposed to the limits of cross section dimensions of ACI318-14 [1] given in Eq. (1A) Pc, Pf = Useful and failure load capacities of the composite corbel respectively. Po, Pf0 = Useful and failure load capacity for RC corbel with same Table 5 Values of useful load according to Eq. (1). Specimen
P0
Pf
T1/T0
Pc
Pc/pf
REF-GA CWF-GA CTE-GA CTP-GA REF-GB CWF-GB CTE-GB CTP-GB
290 290 290 290 200 200 200 200
380 375 330 330 270 275 260 260
1 1.665 1.636 1.711 1 1.54 1.2 1.5
290 340*(319) 274 276 200 244 204 221
0.76 0.85 0.83 0.84 0.74 0.88 0.78 0.85
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 807
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Appendix A For the reinforced concrete corbel shown in Fig. 1A; the maximum Nominal shear force to be adopted is given as follows: ACI318-14
Vn = Min (0.2f
c
bw
d ; (3.3 + 0.08f c )
bw
d ; 11
bw
(1A)
d)
The factored Moment is given by:
Mu = Vu
aV + Nuc
(d
(2A)
h)
Then, steel reinforcement needed to resist flexure can be calculated as:
Af =
fy
Mu (d
a /2)
(3A)
fy used should not be more than 420 MPa Area of reinforcement An needed to resist the horizontal force Nu is calculated as:
An =
Nu fy
(4A)
The area of reinforcement Avf needed across the shear plane to resist shear.
Avf =
Vu fy µ
(5A)
Area of primary tension reinforcement Asc, is the least of (a) through (c)
Asc = Min Af + An ;
f' 2 Avf + An ; 0.04 c bw d 3 fy
(6A)
The area of horizontal stirrup reinforcement is calculated as:
Ah = 0.5(Asc
(7A)
An )
Fig. 1A. Typical RC corbel.
[11] Al-Shaarbaf IA, Al-Azzawi AA, Farahan Raad Sh. Experimental investigation on the behavior of reinforced concrete corbels under repeated loadings. J Eng Develop 2015;19(4). [12] Kassem Wael. Strength prediction of corbels using strut-and-tie model analysis. Int J Concr Struct Mater 2015;9(2):255–66. [13] Özkal FM, Uysal H. Reinforcement detailing of a corbel via an integrated strut-andtie modeling approach. Comput Concr 2017;19(5):589–97. [14] Redha Maha MS, Al-Shafi'I Nagham TH, Hasan Milad M. Ultra-high performance steel fiber reinforced corbels: experimental investigation. Case Stud Constr Mater 2017;7:180–90. [15] Wilson HR, Yousefpour H, Brown MD, Bayrak O. Investigation of corbels designed according to strut-and-tie and empirical methods. ACI Struct J 2018. [16] Heidayet A, Ramadhan A, Qarani O. Repairing of damaged reinforced concrete corbels strengthened by externally bonded steel plates. Zanco J Pure Appl Sci 2004;16(1). [17] Ozden S, Atalay HM. Strengthening of reinforced concrete corbels with GFRP overlays. Sci Eng Compos Mater 2011;18:69–77. [18] El-Maaddawy TA, El-Sayed ISh. Response of concrete corbels reinforced with internal steel rebars and external composite sheets: experimental testing and finite element modeling. J Compos Constr 2014;18. https://doi.org/10.1061/(ASCE)CC. 1943-5614.0000403. American Society of Civil Engineers. [19] Mohammed AA, Hassan GB. Load capacity and deformation of high strength concrete corbels wrapped with CFRP sheets. In: The 2nd International Conference of Buildings, Construction and Environmental Engineering (BCEE2-2015); 2015. [20] Ivanova I, Assih J. Experimental Study of Local Behavior of Strengthened Reinforced Concrete Short Corbel by Bonding Carbon Fiber Fabrics; 2015. [21] Ivanova A, Assih A. Static and dynamic experimental study of strengthened
References [1] ACI Committee 318-14. Building code requirements for structural concrete. Farmington Hills, Michigan: American Concrete Institute; 2014. [2] Mattock Alan H, Chen KC, Soongswang K. The behavior of reinforced concrete corbels. PCI J 1976;21(2):52–77. https://doi.org/10.15554/pcij10.15554/pcij. 03011976. [3] Mattock Alan H. Design proposals for reinforced concrete corbels. PCI J 1976;21(3):18–42. [4] Yong YK, McCloskey DH, Nawy EG. Reinforced corbels of high-strength concrete. Int. Concr. Abstracts Portal 1985;87. [5] Torres FM. Theoretic-experimental analysis of reinforced concrete corbels. Dissertation (Master Science in Structural Engineering) - Engineering School of São Carlos, São Paulo University, São Carlos; 1998 (In Portuguese). [6] Mattock AH. Shear friction and high-strength concrete. ACI Struct J 2001;98(1):50–9. [7] Russo G, Venir R, Pauletta M, Somma G. Reinforced concrete corbels—shear strength model and design formula. ACI Struct J 2006. [8] Campione G, La Mendola L, Letizia Mangiavillano M. Steel fiber-reinforced concrete corbels: experimental behavior and shear strength prediction. Struct J 2007;104(5):570–9. [9] Lu Wen-Yao, Lin Ing-Jaung. Behavior of reinforced concrete corbels. Struct Eng Mech 2009;33(3):357–71. https://doi.org/10.12989/sem.2009.33.3.357. [10] Khalifa ES. Macro-mechanical strut and tie model for analysis of fibrous highstrength concrete corbels. Ain Shams Eng J 2012;3(4):359–65. https://doi.org/10. 1016/j.asej.2012.04.004.
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Q.M. Shakir reinforced short concrete corbel by using carbon fabrics, crack path in shear zone. Frattura ed Integrità Strutturale 2015;34:90–8. https://doi.org/10.3221/IGF-ESIS. 34.09. [22] Krawczyk Ł, Urban T. Experimental research and modelling of corbel strengthened by steel accessory. In: Nagrodzka fib_symposium_2017, 078, v2 (final); 2017. [23] Mohammad AQ, Kadhim Al-Shamaa MF. Experimental study of behaviour of reactive powder concrete strengthening by NSM-CFRP corbels. Civ Eng J 2018;4(5). [24] Al-Kamaki YSS, Hassan GB, Alsofi G. Experimental study of the behaviour of RC
corbels strengthened with CFRP sheets. Case Stud Constr Mater 2018;9:e00181. [25] Shakir QM, Kamonna HHH. The behavior of high strength self-compacting reinforced concrete corbels strengthened with NSM steel bars. Int J Adv Sci Eng Inform Technol 2018;8(4). [26] Chagas LGM, Nogueira IF, Júnior LÁO, Araújo DL. Strength assessment of concrete corbels cast in two steps using unbonded post-tensioning. 4REEC – Revista Eletrônica de Engenharia Civ 2019;15(1).
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Response of innovative high strength reinforced concrete encased-composite corbels
T
Qasim M. Shakir Department of Civil Engineering, Faculty of Engineering, University of Kufa, Najaf, Iraq
ARTICLE INFO
ABSTRACT
Keywords: Encased composite corbels Shear-slenderness ratio Toughness Lateral buckling Horizontal shear Web openings Cracking
This work is devoted to discuss experimentally the behavior of high strength reinforced concrete (R.C.) encased corbels using the available commercial W-shape rolled steel. Eight specimens are tested and two shear slenderness ratio are considered, namely 0.70 and 1.00. The tested specimens are categorized in two groups according to (a/d) ratio. Each group included one conventional RC corbel and three composite corbels. Three configurations of composition are discussed, W-shape, WT shape and Tapered WT shape. Besides, two steel corbels have been tested, one W-shape while the other was WT-shape to get more understanding about the failure of composite corbels. The comparison between specimens is based on load-deflection curves, ductility, toughness, failure load, pattern of cracking propagation, failure mode and history of crack width development. Results revealed that the low properties commercial rolled steel can be used in composite corbels and such corbels could be adopted as a convenient alternative to the conventional RRC. In addition, it was found that the tested composite corbels yielded better behavior than the conventional ones, the composite corbels yielded toughness ranged from 120% to 170% from that of the RC conventional corbels with similar capacity for those composed using full W-shape with opening in webs. More ductile behavior is observed for corbels especially when shear force is dominant and low a/d ratio is adopted. Furthermore, Its found that that increasing a/d ratio from 0.7 to 1.0 for the control specimens, composite W-shaped and Tee-shaped encased beam result in reduction of capacity by 29%, 27% and 21%. Respectively. Moreover, a simple equation is suggested to estimate the composite corbels based on toughness and failure loads.
1. Introduction Reinforced concrete corbels (RCC) are defined as short cantilevers protrude from walls or columns having a shear slenderness, a v /d, normally less than 1, usually used to resist forces precast beams or floors at joints. Corbels are mainly designed to satisfy the requirements of resisting vertical loads and horizontal forces caused by shrinkage, thermal and creep effects of the beams, bridge crane or bridge piers. It became a common feature in the construction of buildings with increased use of precast concrete. Due to their small shear slenderness ratios, such elements are usually classified as a D-region, where there is considerable disturbance in the distribution of the strain through the depth of the cross-section, even in the elastic phase. The dominant behavior is controlled by shear rather than the bending moment. The ACI 318-14 [1] code stipulated that shear slenderness ratio a /d for corbels to be less than 2. Such element can be designed using the strutand-tie method and those with shear slenderness ratio less than 1 may be designed using the shear-friction approach. Many studies were published to study the behavior and
strengthening of RCCs. Different variables that may affect to behavior of such members were considered. Regarding the behavior of RCCs, Mattock et al. [2] then, Mattock [3] proposed several modified shearfriction models for design of corbels having shear slenderness ratios (a/ d) less than 1.0. Yong et al. [4] observed the validity of the ACI Code shear friction and truss analogy (STM) methods to RCCs having shear slenderness ratios of 0.39 with strength ranging between (41.4–82.7) MPa. In 1998, Torres [5] reported that RCCs may fail by one of six scenarios shown in Fig. 1. Such modes are: a) Yielding of the tension tie (Bending failure) which occur due to lack in main reinforcement (lightly reinforced section). b) Crushing or splitting of the compression strut (diagonal failure). This type of failure may occur due to excessive amount of main reinforcement (over reinforced section) c) Shear along the junction of the column with the corbel d) Loss of anchorage of the main steel when the development length is not enough to develop the required bond. e) Shearing failure under the loading plate
E-mail address: [email protected]. https://doi.org/10.1016/j.istruc.2020.03.056 Received 24 September 2019; Received in revised form 23 February 2020; Accepted 26 March 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Modes of Failure of RC corbels, adapted from Torres [1].
Regarding studies considered the strengthening of corbels, three main methods were adopted in the previous studies. These are external strengthening by FRP composites, external strengthening by steel plates and using posttensioned anchored bars. Heidayet et al. [16] through repairing several damaged RCCs by external plates found that the strength ratio of the (repaired/original) corbel ranged from 0.7 to 1.5. Ozden and Atalay [17] reported that wrapping RC beams with GFRP sheets with orientation of 45 degrees was more influential than other arrangements of wrapping. An improvement of (40%–200%) was obtained, depending on the reinforcement ratio, (a/d) ratio, and the characteristics of FRP layers. El-Maaddawy and El-Sayed [18] reported that strengthening by CFRP sheets yielded a strength enhancement in the range of (21–40)%. Mohammed and Hassan [19] through testing high strength concrete corbels wrapped with CFRP sheets obtained an enhancement in load capacity of 28.3%. Ivanova and Assih [20] studied strengthening of RCCs by carbon fiber fabrics. An increase in failure tensile strength more than 1.82 was obtained. The same authors [21] studied the static and dynamic response of RCC strengthened by using carbon fabrics. An improvement in the ultimate load by twice and stiffens less than a third was obtained. Urban and Krawczyk [22] investigated the use of post-installed threaded rods as additional reinforcement. An enhancement in capacity of about 64% was recorded. Mohammad and Al-Shamaa [23] examined the behavior of reactive powder concrete brackets, upgraded with Near Surface Mounted (NSM) CFRP strips. Average enhancement of 15% was obtained. Al-Kamaki et al. [24] studied the behavior of externally strengthened RCCs by CFRP fabrics. It is found that the diagonal configuration improved the ultimate strength by 27%. Shakir and Kamonna [25] studied experimentally the response of high strength self-consolidating RCCs upgraded with NSM steel bars.
f) Localized bearing when dimensions of the bearing plate not adequately distribute the point load. Mattock [6] reported that the equations of shear friction method assumed previously underestimate the shear transfer strength for ultrahigh strength RCCs Thus, some modifications are proposed relating with the upper limits for shear force to be applied on the corbel. Thus, the method. Russo et al. [7], proposed a model to determine the shear strength of RCCs, or brackets, by superimposing the strength contribution of the strut-and-tie mechanism due to the cracked concrete, principal reinforcement, and stirrups. Campione et al. [8] proposed a simplified model to calculate the shear strength of steel fiber RCCs including stirrups. Results showed the effectiveness in using fibrous RCCs. Lu and Lin [9] suggested a model to estimate the shear strengths of corbels with a/d ratios between 0.11 and 1.69. It was found that the shear strengths increase with increasing the grade of concrete and vertical stirrups and reducing (a/d) value. Khalifa [10] suggested a “macro-mechanical” strut and tie (STM) model to study the steel fiber high-strength RCCs. In this model, the fibers was adopted as a substitution of horizontal stirrups. Al-Shaarbaf et al. [11] studied the behavior of RCCs under repeated loadings, It was reported that the repeated load is more influential that monotonic loading. Wael Kassem [12] suggested a method for determining the capacity of RCCs based on the strut-and-tie (STM) and secant stiffness by combining strain compatibility and constitutive laws of cracked RC. Özkal and Uysal [13] discussed the optimum reinforcement layout of concrete corbels. Redha et al. [14] studied experimentally the response of ultra-high performance fibrous RCCs with concrete grade of 150 MPa. Wilson et al. [15] evaluated STM method to design corbels relative to the empirical design (Shear-Friction) method. 799
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Four different configurations of installations of strengthening bars were investigated. A maximum improvement in failure load of 57% and 41% for a/d of 0.85 and 1.25 respectively was obtained. The Upside down Vshaped“ strengthening system named is the most advisable for small values of shear slenderness ratio (a/d < 1). The horizontal bars arrangement is more recommended for large a/d values (a/d > 1). Chagas et al. [26] tested corbels that are precast separately of the column and then joined to it by means of socked and unbonded posttensioning. Results demonstrated that the proposed corbel presented strength 5% lower than the reference monolithic corbel. As it is shown above, that all studies that published to enhance the capacity of RC corbels were based either on improving the internal composition of the concrete by using high strength concrete, steel fiber concrete, reactive powder concrete, or externally installed strengthening elements. No study have been published that based on incorporation of steel sections to enhance the performance of RC corbels. This works aims to suggest a reinforced concrete composite encased corbels and investigating the performance against the well-Known conventional RCC. Moreover, explore if it can be adopted to develop higher capacities. In addition, a simple relation is suggested to estimate the capacity of composite corbels to show the advantage of using such type of corbels.
Table 2 Designation and characteristics of the tested specimens. Specimen
2.1. Materials The constituent materials of the concrete mix used in the present study was composed of Ordinary Portland Cement (Type I) manufactured by KAR Company, rounded coarse aggregate of max size of 19 mm, natural sand taken from Al-Najaf region, and GILENIUM ®54 as superplasticizer. Drinking water was used in preparing specimens, cubes and cylinders. Three sizes of steel reinforcement are used, ø8 and ø 16 as ties and longitudinal reinforcement for the column segment. Reinforcement of the corbel parts consist of bars of ø10 diameter except the main tension reinforcement for the control RCCs specimens in which ø 16 diameter was used. In addition, W-shape rolled steel sections are used in the six composite corbels. Material properties of concrete, steel bar are detailed in Table 1. The designations for the tested specimens are shown in Table 2. When the specimens gained the required strength (age of 28 days), the test is done. Besides, cubes of 150 mm and cylinders of (100 mm*200 mm) are tested to find the compressive and tensile strengths. Such strengths are found to be 57.1 MPa and 3.2 MPa respectively.
Rolled steel
8 10 16
500 521 510 285
593 647 682
0.7
Non W-shape with openings in web WT-shape with caps at ends Tapered W-shape with caps at ends As in CWF-GA As in CTE-GA
Group B
REF-GB CWF-GB CTE-GB CTP-GB
1.0
Non W-shape with openings in web WT-shape with caps at ends Tapered W-shape with caps at ends
Fig. 5 shows the effect of shear slenderness ratio on the response of RCCs. It can be seen that the specimen REF-GA yielded stiffer behavior than REF-GB. However, at 500KN, there was a partial failure due to the diagonal shear crack occurred causing rapid increase in deflection to up to a load of 550 kN. Then the corbel retire it’s stability and continues to resist load up to 760KN. Failure occurred suddenly and severe drop in capacity can be seen. Thus, a load level in the range (500–600)kN may be considered to be as the maximum capacity for safety aspects. Regarding the response of the specimen REF-GB, it can be seen that the behavior is more ductile referring that flexure effect is dominant. More cracks initiated, more deflection was recorded. Beyond the maximum load, it can be seen that there is a gradual reduction in capacity compared to specimen REF-GA. The safety aspect still, not satisfied as there is no enough warnings (gradual reduction in stiffness) before failure. The load-deflection curve for the specimen SWF-GA is shown in Fig. 6 for the sake of comparison with the composite corbel CWF-GA and to discuss the improvement in capacity due to encasing the steel section with concrete. Furthermore, investigation the behavior of the SWF-GA assist understanding the behavior of the composite corbels. It can be seen that specimen SWF-GA yielded a capacity of 180 kN corresponding to a capacity of specimen of CWF-GA of 750 kN. i.e. an
Table 1 Material properties of steel bars.
Bar dia. (mm)
REF-GA CWF-GA CTE-GA CTP-GA SWF-GA STE-GA
3.1. Load-deflection curves
Eight reinforced concrete corbels (RCC) with details shown in Fig. 2 have been tested experimentally in this work. Three forms of rolled steel section have been considered, I-shape with circular openings of 65 mm diameter in web with c/c distance of openings of 160 mm, Tshape with uniform depth and Tapered T-shape with depth at ends of 60 mm. Both of the T-shapes have end caps. Such caps and openings served as shear connectors to improve bond between steel section and the surrounding concrete. Each steel segment is of 820 mm length with flange and web thicknesses of 3 mm and 4 mm respectively. The flange
fu (MPa)
Group A
3. Results and discussion
2.2. Method of experimental work
f'y (MPa)
Shape of steel section
width of 75 mm and total depths of W-shape and T-shape of 130 mm and 120 mm respectively. The tested specimens are categorized into two groups based on shear slenderness ratio. Namely 0.7 and 1.0. In addition, two rolled steel segments of W-shape and WT-shape are tested with a/d = 0.7 to explore the behavior of steel corbel only. The weight of the steel segments are 6 kg, 7.5 kg and 8.5 kg for the Tapered Tee-, Tee- and W-shape respectively. Thus, the average percentage weight of steel segment to the weight of specimen is 5.5%. Two ø16 steel bars segments 100 mm long are welded to the top, bottom flanges are embedded on the top, and bottom column portions to fix a rolled steel section in place by using seem. Thus, there is no connection between the reinforcement of the corbel and the rolled steel segments. The two steel sections are tested using the same regime that adopted in testing the RC-composite corbels in which the specimen is subjected to a midspan point load that was gradually increased up to failure. Fig. 3 shows the scheme used in testing the rolled steel segments. The two steel beams SWF-GA and STE-GA are tested under the same loading setup used in testing the composite corbels. Thus is similar to the case when concrete in the composite corbel failed entirely when reaching its capacity. Then, the embedded rolled steel beam will resist the applied loading. The experimental tests are achieved in Structural Lab. of the college of Engineering/ university of Kufa. The universal machine shown in Fig. 4 with capacity of 200ton with a dial gauge of accuracy of 0,05 mm that is located at center of the column.
2. Materials and method
Steel
a/d ratio
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(A)RC corbels
(B)Composite corbels
Fig. 2. Detailing and dimensions of the tested specimens.
improvement in capacity of by 416%. It is expected that the steel and concrete constituting the sections worked together up to the point when slip occurred. Beyond this point, the full capacity of the steel section would be exhausted. This is represented by the horizontal part of the load deflection curve. Thus, it can be concluded that if slip is delayed or the strength against tearing failure is improved, higher capacity may be obtained. Fig. 6 shows the variation in response for the composite encased
corbels CWF-GA and CWF-GB. It can be seen that increasing (a/d) ratio from (0.7) to (1.0) results in reduction of ultimate load by (27%), with noticeable increase the ductility by 43% was observed. The stiff behavior for CWF-GA may be attributed to the dominance of shear force effect with small (a/d) values and effect of tearing failure between openings is small up to the final stages of loading. In contrast, flexural stresses is expected to control behavior of CWF-GB resulting in more ductile behavior.
(A)Specimen SWF-GA
(B)Specimen STE-GA Fig. 3. Loading setup of the specimens (A) SWF-GA (B) STE-GA. 801
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Fig. 7. Load deflection curves for the composite corbels with WT- section.
Taking another glance on Fig. 6, it can be seen there is no sudden drop in capacity for specimen CWF-GB. This can be recognized by the semi-flat curve close to the final stage and then, slip occurred gradually. Whilst, for specimen CWF-GA, there can be seen sudden change in slope near the failure instant. This may be simply realized if we remember that diagonal shear cracks occurred and crushing of concrete due to flexure may affect the bond between steel section and concrete. Thus, higher load capacity may be obtained by enhancing bond by different means such as adding caps at end, adding some shear studs at faces of the web or welding spiral steel bar on web sides or strengthening the zones between openings by steel plates to resist the horizontal shear in web. Fig. 7 shows the effect of shear slenderness ratio on the response of composite corbels CTE-GA and CTE-GB. The tee-section can be obtained by cutting the web of larger section. This may reduce the cost of the rolled section used. The web may be cut horizontally or as zigzag which may result in improving the bond resistance. Regarding the capacity, it is found that reducing a/d ratio from (1.0) to (0.7) improved capacity by (27%). In addition, it is clear that for specimen CTE-GB failure occurred gradually due to uniform reduction in bond between steel and concrete. However, due to the low moment of inertia, it can be seen that flexure effect is more obvious of specimen CTE-GB relative to CTE-GA. For specimen CTE-GA, it can be seen that the drop in bond occurred rapidly relative to CTE-GB. This may be because that CTE-GA, yielded higher stiffness in most of loading stages. Thus, the specimen yielded more brittle response than CTE-GB and few wide cracks occurred accompanied with crushing within the compression face at failure. Close to failure instant, the lateral support for the steel section deteriorated leading to rapid buckling of the steel section due to the excessive compression on the web. Fig. 7 shows also the response of the steel corbel of Tee shape only. It can been seen that the specimen yielded very soft behavior relative to specimen CTE-GA with failure load of about 75kN (11% of CTE-GA). Failure occurred in early stages by lateral buckling as in the figure. The low load capacity may be attributed to the low moment of inertia and removing the lateral support for the web when cutting the flange to build the tee-section. This can be realized easily when comparing the capacity of specimen STE-GA with the capacity of SWF-GA. It can be seen than the capacity of the Tee shape section is 42% of the wide flange section. Thus, it is expected that the concrete around concrete play as a lateral continuous support, then allowing the section to develop the full strength. Furthermore, if the difference between the capacities of the steel section is added to the capacity of specimen CTEGA, the capacity will be 765kN which very close to the capacity of CWF-GA. Thus, it is expected that the mode of failure of the rolled steel
Fig. 4. The universal machine used in testing specimens.
Fig. 5. Load deflection curves for the conventional R.C. corbels.
Fig. 6. Load deflection curves for the composite corbels with WF section.
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from the economic view, it is recommended to use the tapered WTshape since there is about 25% steel saving in web of the corbels relative to the WT-shape. 3.2. Cracking patterns Fig. 7 shows the crack patterns at failure for the tested composite corbels. The impact of shear slenderness ratio on the crack propagation at failure for reinforced corbels REF-GA and REF-GB can be seen in Fig. 9a and b respectively. It is obvious that for smaller (a/d) ratio the failure is due to diagonal shear and specimen yielded brittle behavior and failed suddenly without enough warnings. It is worth to mention that this type of failure is non prohibited. Regarding to specimen REF-GB, Fig. 9b shows that the failure was by diagonal shear failure as in specimen REF-GA with more ductility and without fragmentation of concrete. Thus, ACI318-14 [1] imposed limits on the useful capacity of the corbel depending on strengths of steel and concrete. Comparing specimens CWF-GA and CWF-GB, Fig. 9c and d, it can be seen that no of cracks for specimen CWF-GA is more than CWF-GB and there are various types of cracks i.e. vertical at junction and under loading point, diagonal. Referring to a ductile behavior due to increase moment relative to specimen CWF-GB and failing by diagonal shear failure with some crushing at compression face and spalling of concrete out of web of steel section. Specimen CWF-GB yielded a more brittle behavior and the failure as diagonal shear with crushing of the compression zone. With less amount of spalling of concrete out of steel section. This may be caused due to the relative more effect of shear of the specimen CWF-GB leading to the lesser amount of curvature with load increase. Comparing cracking patterns for CWF-GA and CTE-GA corbels, Fig. 9e and f, it can be seen that the crack distribution of CWF-GA propagated towards the ends of the corbel with a vertical trend through most of the depth of the corbel. This is referring to the efficiency of bond provided by the holes introduced in the webs. Regarding specimen CTE-GA, It can be seen the cracks initiated at the tension face change its trend and tend to be horizontal and developed from point of reaction towards the junction between the corbel and column where buckling to occur. Thus, referring the compression effect of caps at ends of the steel section subjected increasing force leading to some crushing of the concrete within the junction zone. This crushing revealed that insufficient bond between the steel section and concrete that contribute in transferring compressive force resulted from the bending moment to the steel section. Thus, it is recommended to use some stiffeners at the mid-distance from the column face to reduce action of lateral buckling and to improve the bond action by welding some steel bars at the two faces of the web to serve as shear connectors. Regarding specimens CTE-GA and CTE-GB, the same can be said when comparing CTP-GA with CTP-GB, that the shear effect is very clear when a/d = 0.7. Less intensity of cracks (but wider) can be seen and failure was of the diagonal shear type. Comparing specimens CTP-GA and CTE-GA, it can be seen that no of
Fig. 8. Load deflection curves for the composite corbels with tapered steel section.
affect the capacity of the composite corbel. i.e. Buckling of segments WT-shapes occurs earlier than horizontal shear for segments of Wshapes. Fig. 8 shows the influence of a/d ratio on the performance of composite corbels CTP-GA and CTP-GB. It can be seen that reducing a/d ratio from (1.0) to (0.7) result in improving the capacity by (21%). Moreover, it is obvious that there is clear bifurcation between the responses of the two specimens at the early stages of loading. This may be due to the weakness caused by increased no of cracks occurred at early stages for specimen CTP-GB. Whereas, for specimen CTP-GA shear effect is more obvious, stiffer behavior can be seen at the final stages, it can be seen that the slip for specimen CTP-GA started at deflection record of (2.9)mm and ended at (3.5)mm when specimen failed. While, for Specimen CTP-GB the zone of slip was (3.5–5.1)mm. This reveals that the extent of slip effect for specimen CTP-GB is higher than CTP-GA and less slip is expected to occur if more stiffeners are added at the midspan of the corbel. The initial cracking load, failure load and the corresponding recorded deflections are listed in Table 3. It also shown the ductility index for each specimen. It can be seen that there is a slight increase in the ductility reduced relative to the control specimen for low a/d ratio. This may be attributed that such corbels yielded stiff behavior and cracks propagated gradually through the member causing gradual loss in bond and crashing in concrete at instant where lateral support for steel section become weak to resist the vertical load failure occurred rapidly. Whilst, ductility increased significantly when adopting large (a/d) value because that slip increases gradually and deflection increases with B.M increment. Thus, uniform failure occurs because concrete between webs of steel section prevented lateral buckling of the rolled steel section as shown in Fig. 9. It is clear from Figs. 7, 8 and Table 3 that the composite corbels with tapered WT-shape yielded the same capacity as that included WT-shape with higher ductility index. Thus,
Table 3 Cracking and failure loads with the corresponding deflections. Specimen
Cracking load
Failure load
Deflection at initial crack
Deflection at failure
Ductility index
Group A
REF-GA CWF-GA CTE-GA CTP-GA
140 120 100 100
760 750 660 660
0.92 0.81 0.95 0.85
3.5 3.25 4.02 3.49
3.8 4.01 4.23 4.11
Group B
REF-GB CWF-GB CTE-GB CTP-GB
90 80 70 60
540 550 520 520
0.90 0.79 0.84 0.84
3.8 4.5 4.24 5.38
4.2 5.70 5.04 6.40
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(b) Specimen REF-GB
(a) Specimen REF-GA
(c)Specimen CWF-GA
(d)Specimen CWF-GB
(e)Specimen CTE-GA
(f)Specimen CTE-GB
(h)Specimen CTP-GB
(g)Specimen CTP-GA
Fig. 9. Crack patterns for the composite corbel specimens.
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(A) Top view
(B) Side view
(C) View of the bottom flange Fig. 10. Specimen SWF-GA at failure.
cracks for CTE-GA is less than CTP-GA. this may be attributed to the higher bond effect between the steel section and concrete. This bond assist in transferring some of compression to the steel section. Thus, compression failure occurred within the final stages of loading at instant when bond violated. In addition, it can be seen clearly that in specimens CWF-GA and CWF-GB, the volume of concrete block that resisting the pressure at the compression face was more the composite corbels with Tee shapes, resulting in smaller cracks propagation. Whereas for specimen CTP-GA and CTE-GA there is, one major deep and wide crack occurred within earlier stages of loading. Comparing specimens CTE-GA and CTE-GB, it can be seen that specimen CTE-GA failed by diagonal cracking with some crushing at the compression face whereas for CTE-GB, the failure occurred by bond failure between steel and concrete leading to severe separation of the compression block. Fig. 10 shows the specimen (SWF-GA) at failure. The top view, Fig. 10a, shows the yielding of steel at compression face. Whereas, Fig. 10c demonstrated the yielding of the bottom flange by tensile stresses. However, Fig. 10b, showed that the corbel tend to fail by bucking along diagonal line passing through the void within the shear span. The deformed shape for the steel WT-rolled shape (STE-GA) is shown in Fig. 11, which revealed that the failure mode was lateral buckling within the shear span nearest to the column face.
(A) Side view
(B)Top view
Fig. 11. Specimen STE-GA at failure.
Fig. 12 shows the toughness values for the corbel specimens tested in the present work. It is obvious that although specimens REF-GA and REF-GB yielded the highest load capacity but they have the lowest toughness. This refers to the high stiff behavior up to the final stages of loading. This type of behavior and the sudden behavior caused from was controlled by ACI-318 by imposing the limitations discussed in Appendix A. Thus 75% of the failure load was considered as a useful service load. Regarding the composite corbels CWF-GA and CWF-GB, it can be seen that such specimens acquired toughness of about (155%–165%) of the control beam with similar capacity. This refers that higher service load can be adopted without serious risk as in the reference RC corbels. For the corbels CTE-GA and CTE-GB. It is found that this
3.3. Toughness values Toughness is a measure of the ability of the structure (or member) to adsorb strains (deformations) before failure. In addition, it provide good indication for warning that the structure yielded before full collapse. Toughness represent the area under the load deflection curve. 805
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2000 1800 1785 1752
TOUGHNESS(KN.MM)
1600
1835
1754
1706
1400 1368
1200 1000 800
1072
1138
600 400 200 CTP-GB
CTP-GA
CTE-GB
CTE-GA
CWF-GB
CWF-GA
REF-GB
REF-GA
0
Fig. 12. Toughness values for the tested composite corbels.
arrangement acquired a toughness ranges from 120% to 163% relative to the control corbels although they yielded smaller capacity. This refers that the lack in bond results in premature failure and more capacity can be obtained if the conditions of bond and the resistance against lateral buckling is enhanced. The specimens CTP-GA and CTP-GB yielded the highest toughness which ranged from 150% to 170% relative to the reference corbels.
800 700 Load, kN
600
3.4. Crack width
500 400
CWF-GA-Flexural CWF-GA-Diagonal CWF-GB-Flexural CWF-GB-Diagonal
300 200 100
Fig. 13 shows the history of initial cracks width development for the RCCs REF-GA and REF-Gb. It can be seen that first crack initiated at (140kN) and (90kN) for the two specimens respectively, and was of the flexure type at junction between corbel and column. Soon the diagonal crack toward support developed at (400kN) and (180kN) and widened rapidly causing the flexure to stagnate. In addition, it is clear that the diagonal crack for REF-GB developed with higher rate compared to REF-GA. This may be attributed to the difference in B.M. Fig. 14 shows the history of initial cracks development RCC CWFGA and CWF-GB. It is obvious that the flexural cracking developed early, followed by the diagonal crack but the rate of the widening still low up the final stage of loading at which a loss in bond between steel section and concrete occur. Figs. 15 and 16 show the rate of widening of cracks for the composite specimens with WT-shaped and tapered WT-shaped rolled steel. It can be seen that crack width increased more rapidly than the CWF-GA and CWF-GB specimens did. This may be caused by the smaller flexure
0
0
0.2
0.4 0.6 0.8 1 Initial Crack width, mm
1.2
Fig. 14. History of crack width development for composite corbels with WFshape.
800 700 600 Load, kN
500
400 300 200 100 0
Fig. 15. History of crack width development for composite corbels with WTshape.
Ref-GA-Flexural Ref-GA-Diagonal Ref-GB- Flexural Ref-GB- Diagonal 0
0.2
0.4 Initial 0.6Crack0.8 1 width, mm
resistance resulted from the relatively low amount of moment of inertia for the tapered sections (smaller area of contact with concrete) that may cause slip occur more rapidly.
1.2
4. Theoretical analysis
Fig. 13. History of crack width development for R.C. corbels.
The shear friction method [3] for design of RC corbels is described 806
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800
(a/d) and dimensions. To and T1: are toughness value for RC and composite corbels. Based on the above equation the useful load capacity for the composite corbels as listed in Table 5. It can be seen that Pc/Pf for composite corbels are higher than the RC corbels. This is expected due to the difference in general performance for the tested specimens.
700
Load, kN
600 500 400 CTP-GA-Flexural CTP-GA-Diagonal CTP-GB-Flexural CTP-GB-Diagonal
300 200 100 0
0
0.2
0.4 0.6 0.8 Crack with, mm
1
5. Conclusions 1) It was found that the R.C. composite corbels using the commercial low properties rolled steel section might serve as an appropriate alternative for the R.C. corbels with better performance. 2) The corbels composed of W-shaped steel sections with enough no. of openings in webs yielded the same failure load capacity with better ductility than the R.C. corbels and that it is needed to use caps at ends to increase load capacity and reduce slip behavior. 3) The R.C. corbels composed with Tee and Tapered steel section yielded the same capacity but more ductility for tapered section. Failure occurred by bond failure followed by lateral the buckling of the rolled steel. 4) The R.C. composite corbels yielded some softening behavior within the early stages of loading up to the initial cracking load. Then, stiffness increases gradually up to failure. This can be recognized by the cracking load value, which is lower than the conventional RCC. This may be attributed to the concentration of steel area with in th steel section and the relatively smooth contact surfaces if compared with the steel bars. 5) Failure Modes of the R.C. corbels was by diagonal shear while for the composite corbels, the failure was firstly due to the loss in bond between concrete and steel section then upon failure mode of the steel section only. Thus, it is expected that higher load capacity can be obtained by adding stiffeners and some shear connectors for the steel shapes. 6) A drop in the load capacity for the R.C. by 29% when increasing a/d ratio from 0.7 to 1.0, whereas for the composite corbels with H-shape the reduction was 32%. for the R.C. composed with Tee or tapered sections, the reduction was 21%.this difference in composite corbels may be attributed to the higher slip effect and less stiffness against flexure for Tee and tapered composed corbels with a/d = 0.7. 7) According to the limits of ACI318M-14 [1], fy for the steel bars used in concrete design may not be more than 400 MPa. Thus the useful load capacity that allowed to be resisted by the R.C. corbels tested in the present work was 200kN for a/d = 1.0 and 290 kN for a/ d = 0.7 per one corbel. Whereas the useful capacity for the composite corbels (fy for steel section = 285 MPa) ranged between (260–275)kN for a/d = 1.0 and in range (330–375)kN for a/ d = 0.7. This conclusion is based on the behavior at final stages, history of crack width and possibility to improve the response of the composite corbels. 8) The WF-shape, WT-shapes and Tapered WT-shapes composite corbels yielded toughness ranged from 154% to 165%, 120%-163% and 150%-170% respectively relative to that of the RC conventional corbels. 9) It is found that the failure mode for the steel shape affect largely the mode of failure for the composite corbels. In addition, the failure of the steel shape within composite corbel occurs simultaneously at the instant of bond failure. Furthermore. The capacity of composite corbel is at least four times the WF-steel corbel alone.
1.2
Fig. 16. history of crack width development for composite corbels with Tapered WF- shape. Table 4 Cracking and design loads for the control corbels. Specimen
REF-GA
REF-GB
Design load (fy = 420 MPa) Design load (fy = 520 MPa) Cracking load Max. allowed shear force Failure load
290 355 140 319 380
200 250 90 319 270
in Appendix A. For the control specimen REF-GA, the design shear force was 290 kN when the limit of ACI318M-14 [1] of 420 MPa yield stress for steel is used and 355 kN if the measured value is adopted. The failure load obtained experimentally was 380 kN. Regarding specimen REF-GB, the design shear force for satisfying the upper limit of yield stress for steel was 200 kN and 250 kN if this limit is neglected. The failure load was 270kN. The results are listed in Table 4. Comparing results of the tested specimens, it can be seen that the corbels composed with I-shaped steel sections yielded capacity very close to the RCCs, with more toughness, less crack with and less shear reinforcement. Furthermore, it is clear that the specimens composed with tee-shaped and tapered steel sections yielded similar results but with more ductility for the Tee-shaped composite specimens. Moreover, since there is not theoretical procedure to estimate the capacity of composite encased corbels. A simple equation is suggested based on the toughness ratios as follows;
Pc = P0 + (Pf
P0 )
T1 T0
1
Pf Pf 0
(1)
The value obtained from Eq. (1) above should be imposed to the limits of cross section dimensions of ACI318-14 [1] given in Eq. (1A) Pc, Pf = Useful and failure load capacities of the composite corbel respectively. Po, Pf0 = Useful and failure load capacity for RC corbel with same Table 5 Values of useful load according to Eq. (1). Specimen
P0
Pf
T1/T0
Pc
Pc/pf
REF-GA CWF-GA CTE-GA CTP-GA REF-GB CWF-GB CTE-GB CTP-GB
290 290 290 290 200 200 200 200
380 375 330 330 270 275 260 260
1 1.665 1.636 1.711 1 1.54 1.2 1.5
290 340*(319) 274 276 200 244 204 221
0.76 0.85 0.83 0.84 0.74 0.88 0.78 0.85
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 807
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Appendix A For the reinforced concrete corbel shown in Fig. 1A; the maximum Nominal shear force to be adopted is given as follows: ACI318-14
Vn = Min (0.2f
c
bw
d ; (3.3 + 0.08f c )
bw
d ; 11
bw
(1A)
d)
The factored Moment is given by:
Mu = Vu
aV + Nuc
(d
(2A)
h)
Then, steel reinforcement needed to resist flexure can be calculated as:
Af =
fy
Mu (d
a /2)
(3A)
fy used should not be more than 420 MPa Area of reinforcement An needed to resist the horizontal force Nu is calculated as:
An =
Nu fy
(4A)
The area of reinforcement Avf needed across the shear plane to resist shear.
Avf =
Vu fy µ
(5A)
Area of primary tension reinforcement Asc, is the least of (a) through (c)
Asc = Min Af + An ;
f' 2 Avf + An ; 0.04 c bw d 3 fy
(6A)
The area of horizontal stirrup reinforcement is calculated as:
Ah = 0.5(Asc
(7A)
An )
Fig. 1A. Typical RC corbel.
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