behavior of corbels with external prestressing bars_experimental study

ACI Structural Journal/November-December 1999 1033

ACI Structural Journal, V. 96, No. 6, November-December 1999.Received August 7, 1998, and reviewed under Institute publication policies. Copyright

© 1999, American Concrete Institute. All rights reserved, including the making of copiesunless permission is obtained from the copyright proprietors. Pertinent discussionincluding author’s closure, if any, will be published in the September-October 2000 ACIStructural Journal if the discussion is received by May 1, 2000.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This study presents experimental data of the reinforced concretecorbels that, after cracking, were strengthened by externalprestressing or passive (nonprestressing) steel bars. The purposeof the experimental tests was to recognize the influence of externalbars on cracking and on the load-carrying capacity of the testedspecimens. Nine corbels with various shear span-effective depthratio (a/d) were tested. The degree of prestress determined by thevalue of the prestressing force was assumed constant for all threetested prestressed specimens. To recognize the effect ofprestressing, the test results of the prestressed corbels werecompared with test results of the ultimate load and cracking ofcorbels without strengthening, and also with corbels strengthenedby external bars—the same as the prestressing bars but withoutexternal prestressing. Such passive bars are often used tostrengthen overloaded and cracked reinforced concrete (RC)corbels. It turned out that the effectiveness of external prestressingbars was significant, particularly for corbels with greater valueratio (a/d ≈1.0). External prestressing is a useful solution forstrengthening corbels and reducing their crack widths. Until now,there has been no recognition of crack morphology and the load-carrying capacity of cracked corbels strengthened by externalprestressing bars. The results of the experimental tests also showthat the truss analogy, or shear-friction theory used for designing,in practice cannot be applied (without modification) to the properdetermination of the ultimate load of the RC corbels strengthenedby external bars.

Keywords: corbels; external prestressing; strengthening; ultimate load.

INTRODUCTIONThe experimental data indicate that crack pattern and the

load-carrying capacity of RC corbels depend on the shearspan-to-effective depth ratio (a/d), on the amount of the mainreinforcement, and on the shape and amount of the stirrups.The first vertical flexural crack (r1 in Fig. 1) appears at a veryearly stage. As shown in Fig. 1, in the corbel subjected to thevertical load, the first crack appears approximately at theload V ≈ 0.25Vu (where V is the applied load and Vu is thecollapse load). This first crack is situated at the face of thecolumn. Inclined cracks (rinc ) are developed later when thevertical load varies between 0.4Vu to 0.6Vu. The practiceproves that the strengthening of RC corbels should be donewhen inclined cracks start to develop, thus at load V in therange of 0.5Vu to 0.6Vu.

According to Chakrabarti et al.,1 and Tan et al.,2

prestressing can delay flexural and shear cracking, so thesame effect can be expected at external prestressing of RCcorbels. External prestressing is more easily executed incases where a need of strengthening corbels exists. Thismethod protects corbels from corrosion, improves theirserviceability, and enhances their load-carrying capacity. Inpractice, sometimes strengthening of even noncrackedcorbels is needed. The modernization of construction when

the external load will increase is a good example. Externalstrengthening is relatively simple to carry out, is cost effective,and is often used in practical cases.

The purpose of the experimental tests described in thispaper is to experimentally evaluate the real effectiveness ofthe external prestressing bars used in strengthening thecorbels.

TEST PROGRAMNine RC corbels (three sets of three corbels) with various

a/d (a/d = 1.0, 0.6, and 0.3) were tested. From each set oneof three corbels did not have external bars indicating that thecorbel was not strengthened. These three corbels were calledthe basic corbels and were described as No. 4. The next threecorbels (No. 2) were prestressed by two external bars (thediameter of each was db = 25 mm and the yield strength fpy= 396 MPa). The last three corbels (No. 3) had the sameexternal two bars as corbel No. 2 had, but these bars werepassive (they were nonprestressed during the test).

MaterialsAll the specimens were made from the same concrete

mixture. The average concrete cylinder compressive

Title no. 96-S115

Behavior of Corbels with External Prestressing Bars—Experimental Studyby Krystyna Nagrodzka-Godycka

Fig. 1—Typical crack pattern of double corbel.

ACI Structural Journal/November-December 19991034

strength was fc′ = 25 MPa (fc′ ube ≅ 30 MPa) at the time ofthe specimen test. Ordinary portland cement 35, naturalsand, and an aggregate of 35 mm maximum size were usedfor the concrete mixture (water-cement ratio [w/c] = 0.67).The wooden forms were placed horizontally when theconcrete was laid.

The yield strength of ribbed steel bars of the diameter db =10 mm(≈ No. 3) as the main reinforcement was fym = 493MPa, and for smooth steel bars (as the stirrups) db = 6 mmwas fys = 291.4 MPa. For the corner ribbed bars db = 8 mmand fycorn was 483 MPa. The yield strength of the longitu-dinal column bars was 390 MPa (db = 32 mm).

Details of specimensThe shapes of the tested corbels for each Set WI (a/d =

1.0), WII (a/d = 0.6), and WIII (a/d = 0.3), as well as thearrangement and amount of reinforcement in specimens, areshown in Fig. 2.

The reinforcement ratio for the main internal reinforce-ment was equal to ρ = 0.0104.

InstrumentationThe steel strains were measured with electrical resistance

gages for each load increment to the failure. The gage lengthwas 20 mm. The strain gages were placed on the main rein-forcement at the face of the column, and in the middle ofdistance a (where a is the distance between vertical load andthe column face). As for the stirrups, the strain gages weremounted at the supporting section (at the column face) and inthe half-length of each stirrup.

The concrete strains were measured with a mechanicalextensometer in the direction of the compressive principalstresses and along the slope edge of the corbel. The readingswere taken for each load increment until the failure occurred.The crack pattern was also recorded. Crack widths weremeasured with a crack detection microscope with a magnifi-cation of 40.

Test procedureFirst, basic corbels No. 4 from each set were tested. All the

specimens were tested in an inverted position. The corbelswere subjected to vertical load V applied symmetrically atthe upper edge. The load was increased from V = 0 to V =Vubc (where Vubc is the ultimate failure load for basic corbel).When the ultimate load for the basic corbels was determined,the next two corbels from each set (described as No. 2 or 3)were tested until their failure. The load increment was ≅0.1Vubc. When the load reached 60% of the ultimate load ofthe comparable basic corbel, the tested corbel was unloaded.Corbels No. 2 (one from each set) were prestressed by twoexternal bars (db = 25 mm) placed at the upper tension edgeof the corbel on both sides. Prestressing was conducted bymeans of special screws, as shown in Fig. 3. At the begin-ning, the prestressing force in each external bar was 80 kN.Therefore, the prestressing force was equal to PS = 0.53Py(where Py = Aps. fpy).

The No. 3 corbels were strengthened by the same two bars(db = 25 mm); however, they were passive. The tests wererun in the way previously described.

TEST RESULTSCrack morphology

The width of the first crack appearing at the tension junc-tion was in a range between 0.04 and 0.1 mm. It depended on

Krystyna Nagrodzka-Godycka is a lecturer in the faculty of civil engineering at theTechnical University of Gdan′sk, Poland. She received her PhD in 1988. Her researchinterests include reinforced concrete and prestressed structures, and behavior ofrepaired and strengthened concrete structures.

Fig. 2—Details of tested corbels (all dimensions in cm).


a/d. Inclined cracks developed in all the tested corbels underthe load V ≈ 0.6Vubc , and their maximum crack widths were 0.1mm for Corbels WI and approximately 0.2 mm for CorbelsWII or WIII.

External prestressing (applied for the cracked Corbels WI-2, WII-2, and WIII-2) caused the cracks to close. Later, whenthe load acting on prestressed corbels was increased, thecracks opened again. The crack widths were smaller,however, than the corresponding crack widths of the corbelsstrengthened by passive bars (WI-3, WII-3, and WIII-3). Thecrack patterns of Corbel WI-2(WPS) with a/d = 1.0 (WPS =corbel with prestressing bars) is shown in Fig. 4.

Figures 5 and 6 present the crack patterns of Corbel WII-2(WPS) with a/d = 0.6 and for Corbel WIII-2(WPS) with a/d= 0.3, respectively.

The maximum crack widths for Corbels WI-2, WI-3;Corbels WII-2, WII-3; and Corbels WIII-2, WIII-3 at thetwo levels of the load were V = 0.6Vu and V = 0.9Vu (whereVu is the ultimate failure load for the corbel with externalbars), are shown in Fig. 7.

Fig. 4—Scheme of crack propagation of WI-2(WPS): (a)at V = 0.6Vubc; and (b) at Vu.

Fig. 5—Scheme of crack propagation of WII-2(WPS): (a) atV = 0.6Vubc; and (b) at Vu.

Fig. 3—Anchorage of external bars for prestressing.

1036 ACI Structural Journal/November-December 1999

Stress-strain and load-carrying capacityThe reason for the failure of Corbel WI and WII sets (a/d

= 1.0 and 0.6) was diagonal splitting, independent from thetype of external bars (prestressing or passive). The mode ofthe failure for Corbels WIII (a/d = 0.3) can be described asthe mode between diagonal splitting and shear failure.

The stresses of the main reinforcement of corbels under theload V = 0.6Vubc were averaging between 0.6fym and 0.7fym.The stresses at the same load in stirrups were ≈ 0.8fys andcompressive strains of concrete (εc) were from 0.6 to 1.0%.

Figures 8 through 10 present the stresses of the maininternal reinforcement of the corbels and the stresses inexternal prestressing bars for prestressed corbels (WPS).

At the load V = 0.9Vu , the stresses of the internal mainreinforcement close to the tension zone almost reached the

Fig. 6—Scheme of crack propagation of WIII-2(WPS):(a) at V = 0.06Vubc ; and (b) at Vu.

Fig. 7—Crack widths of tested corbels: (a) atV = 0.6 Vu ; (b) at V = 0.9 Vu .

Fig. 8—Stresses of main internal reinforcement and externalprestressing bars for corbel WI-2(WPS).


Fig. 9—Stresses of main internal reinforcement and externalprestressing bars for Corbel WII-2(WPS).

Fig. 10—Stresses of main internal reinforcement andexternal prestressing bars for Corbel WIII-2(WPS).

Fig. 11—Stresses of stirrups for Corbel WII-2(WPS).

Fig. 12—Stresses of stirrups for Corbel WIII-2(WPS).

Fig. 13—Stresses of main internal reinforcement andexternal passive bars for Corbel WI-3(WPP).

yield stress while the stresses in the external prestressingbars reached approximately 280 MPa (70% fpy).

Figures 11 and 12 present the stresses of the stirrups forthe prestressed corbels: WII-2(WPS) and WIII-2(WPS). Thestresses in stirrups at the ultimate failure load reached theyield stress.

The stresses of the main internal reinforcement and theexternal strengthening passive bars of the corbels (WPP) areshown in Fig. 13 through 15. The test results indicated big

differences between the stresses for prestressing and passivebars. (70 MPa for the passive bars and 280 MPa for theprestressing bars).

1038 ACI Structural Journal/November-December 1999

Figure 16 presents the effectiveness of the corbels with theexternal bars, expressed as the ratio of the load-carryingcapacity of corbels with external bars to the load-carryingcapacity of basic corbels. Table 1 presents the ultimatefailure load for the tested corbels.

APPROXIMATE CALCULATIONOF LOAD-CARRYING CAPACITY OF

PRESTRESSED CORBELSComparing the author’s test results with the calculated

ultimate load obtained from a few well-known designmethods based on truss model or shear-friction theory, it wasfound that the ultimate load could not be properly estimated.The analysis results of the load-carrying capacity of theprestressed corbels with external bars based on a fewselected methods3-7 (the methods are summarized in theAppendix*) are given in Table 2. They prove the methodsoverestimate or underestimate the value of the load-carryingcapacity (Table 2).

The test results indicate that both the strain and the stressincrease were greater in the external prestressing bars incomparison with the external passive bars (Fig. 8 through 10and Fig. 13 through 15).

The stresses in external prestressing bars reached Vu ≈0.7fpy. These stresses were almost half as much as thestresses in the internal main reinforcement of the prestressedcorbels. At the same load, the stresses in the external passivebars reached only 0.17fpy, therefore, they were from six toseven times less than the stresses of the internal main rein-forcement of the corbels with external passive bars.

*The Appendix is available in xerographic or similar form from ACI headquarters,where it will be kept permanently on file, at a charge equal to the cost of reproductionplus handling at time of request.

Fig. 15—Stresses of main internal reinforcement andexternal passive bars for Corbel WIII-3(WPP).

Fig. 16—Effectiveness of external bars for tested corbels.

Table 1—Experimental ultimate load for tested corbels

Corbel a/d Load at failure Vu , exp , kN

WI-4 1.0 250

WI-2(WPS) 1.0 350

WI-3(WPP) 1.0 275

WII-4 0.6 475

WII-2(WPS) 0.6 525

WII-3(WPP) 0.6 500

WIII-4 0.3 650

WIII-2(WPS) 0.3 700

WIII-3(WPP) 0.3 650

Fig. 14—Stresses of main internal reinforcement andexternal passive bars for Corbel WII-3(WPP).


To obtain a reasonable agreement between calculated andexperimental load-carrying capacity, the differencesbetween the stresses of the internal main reinforcement andexternal strengthening reinforcement should be taken intoaccount. This agreement could be reached assuming a coef-ficient k = 0.5 reduces stresses in the external prestressingbars on the load-carrying capacity (Table 3).

Taking this assumption into account, it is possible to estimatethe ultimate load of corbels with a/d = 1.0 according to Krizand Raths’ method3 and for the shortest corbel (a/d = 0.3)using Walraven’s method.6 In both cases, for the satisfactoryagreement between the calculated and experimental ultimateload of the corbels, the coefficient k = 0.5, should beassumed.

The author’s procedure,7 based on Mohr’s failure criterion,could be very useful in the case of strong main reinforce-ment, when the concrete strength determines the load-carryingcapacity of the corbel. To obtain the properly estimatedcalculated load-carrying capacity, the compression zone (c)should be limited. For example: for the ratio a/d = 1.0 →cmax = 0.4d; for a/d = 0.6 →cmax = 0.6d and for a/d = 0.3→cmax = 0.9d. For practical purposes, the load-carryingcapacity of the prestressed corbels can be calculated prop-erly by taking into account limited cmax and assuming k =0.5. The results of the calculation are given in Table 3.

CONCLUSIONSThe experimental test results indicate that the effectiveness

of the external prestressing depends on a/d. For a/d = 1.0, theultimate load due to prestressing increased by 40%. Thiseffectiveness decreased with the decrease of a/d. For a/d = 0.6or 0.3 (shorter corbels), the ultimate load increased by amaximum of only 12%.

The crack widths due to external prestressing also dependedon a/d. Crack widths decreased with the increase of a/d.

At the failure of the corbels, the yield stresses in each casewere reached in part of the internal main reinforcement, andhorizontal stirrups were placed inside the corbel. Themaximum stresses in external prestressing bars were approxi-mately 30% smaller than the yield stress (σps = 0.7fpy).

If, assuming for calculation purposes, that stresses in theinternal main reinforcement and external strengthening barsare equal to the yield stresses, the load-carrying capacity isoverestimated. These improper overestimates could beparticularly large when strengthening the corbels using thepassive bars. Thus, to calculate the load-carrying capacityof the corbels with external prestressing bars, the stress inthe prestressing bars might be approximately assumed σps= 0.5fpy.

ACKNOWLEDGMENTSThis research was supported by Grant No. 7-7233-92-03 from the Polish

State Research Committee (KBN), which is gratefully acknowledged.

REFERENCES1. Chakrabarti, P. R.; Farahani, D. J.; and Kashou, S. I., “Reinforced and

Precompressed Concrete Corbels—An Experimental Study,” ACI StructuralJournal, V. 86, No. 4, July-Aug. 1989, pp. 405-412.

2. Tan, K. H., and Mansur, M. A., “Partial Prestressing in Concrete Corbelsand Deep Beams,” ACI Structural Journal, V. 89, No. 3, May-June 1992,pp. 251-262.

3. Kriz, L. B., and Raths, C. H., “Connections in Precast ConcreteStructures—Strength of Corbels,” Journal of the Prestressed Concrete Institute,V. 10, No. 1, Feb. 1965, pp. 16-61.

4. Franz, G., “Column Corbels,” Beton und Stahlbetonbau, V. 71, No. 4, Apr.1976, pp. 93-102. (in German)

5. Hagberg, T., “Design of Concrete Brackets: On the Application of the TrussAnalogy,” ACI JOURNAL, Proceedings V. 80, No. 1, Jan.-Feb. 1983, pp. 3-12.

6. Walraven, J.; Frenay, J.; and Pruijssers, A., “Influence of Concrete Strengthand Load History on the Shear Friction Capacity of Concrete Members,” Journalof the Prestressed Concrete Institute, V. 32, No. 1, Jan.-Feb. 1987, pp. 66-84.

7. Nagrodzka-Godycka, K., “Contribution to Design of Reinforced ConcreteCorbels under Short-Term Load on Upper Edge,” Archives of Civil Engineering(Warsaw), V. 37, No. 2, 1991, pp. 221-248. (in Polish)

Table 2—Comparison of test results with the calculated ultimate load kN

Method corbel a/dKriz and Raths’3 Franz’s4

Hagberg’s5

Walraven’s6

Author’s7

Vu, expVu, steel Vu, concr Vu, steel Vu, concr

WI-4 1.0 205 308 287 210 — 288 288 250

WI-2 (WPS) 1.0 262 552 494 210 — 486 486 350

WII-4 0.6 287 471 444 326 471 432 432 475

WII-2 (WPS) 0.6 366 776 704 326 654 699 699 525

WIII-4 0.3 379 727 664 428 475 639 639 650

WIII-2 (WPS) 0.3 485 1246 1015 428 659 1246 712 700

Table 3—Ultimate load Vu with k = 0.5 assumption

Method corbel Kriz and Raths’3 Vu, calc /Vu, exp Walraven’s6 Vu, calc /Vu, exp Author’s7 Vu, calc /Vu, exp Vu, exp

WI-2(WPS)a/d = 1.0 237 0.68 — —

c = 0.4dVu,steel = 442Vu,concr = 298

0.85 350

WII-2(WPS)a/d = 0.6 331 0.63 571 1.09

c = 0.6dVu,steel = 644Vu,concr = 472

0.9 525

WIII-2(WPS)a/d = 0.3 438 0.63 576 0.82

c = 0.9dVu,steel = 1012Vu,concr =610

0.87 700

behavior of corbels with external prestressing bars_experimental study

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