Experimental behaviour of reinforcedconcrete continuous deep beams A.F. Ashour Department of Civil and Environmental Engineering, University of

Transcription

1 Experimental behaviour of reinforcedconcrete continuous deep beams A.F. Ashour Department of Civil and Environmental Engineering, University of Abstract Test results of eight reinforced concrete continuous deep beams are reported. The main parameters considered were the shear span to depth ratio, the amount and type of web reinforcement, and the amount of the main longitudinal reinforcement. The vertical web reinforcement had more influence on the shear capacity than the horizontal web reinforcement. The failure is initiated by a major diagonal crack in the intermediate shear span between the edges of the load and intermediate support plates. Comparisons between test results and the ACI building code (318-89) show little agreement. Introduction Reinforced concrete continuous deep beams are fairly common structural elements. They are used as load distribution elements such as transfer girders, pile caps, tanks, folded plates and foundation walls, often receiving many small loads and transferring them to a small number of reaction points. There have been extensive experimental investigations of simply supported deep beams [3,4,5], but very few tests of continuous reinforced concrete deep beams [4,5]. Seventeen two-span reinforced concrete deep beams have been tested by Rogowsky et al. [5], 16 with either vertical or horizontal web reinforcement. The current codes of practice for shear in reinforced concrete continuous deep beams are based entirely on tests of simply supported deep beams. It was found that the shear strength obtained from the ACI building code (318-83) formula [1] overestimates the measured shear capacity of half of the continuous deep beams tested by Rogowsky et al. [5].

2 268 Engineering Integrity The present paper reports test results of 8 two-span reinforced concrete deep beams. The shear span to depth ratio included two values. Three levels of horizontal and vertical web reinforcement have been chosen. Two main flexural reinforcement ratios were studied. Test results are compared to the predictions of the ACI building code (318-89). Test specimens Two series of two-span reinforced concrete deep beams were tested. The overall dimensions of each series are shown in Fig. 1. All tested beams had the same length and width: the length L was 3000 mm and the width b was 120 mm. The locations of center lines of loads and supports were the same for all test specimens. Only the beam depth h was varied to obtain two different shear span to depth ratios: for series / (CDB1,CDB2,CDB3,CDB4,CDB5), the depth was 6 mm to give a clear shear span to depth ratio of 0.8 and for series // (CDB6,,CDB8), the depth was 4 mm to give a clear shear span to depth ratio of The details of reinforcement for each beam are given in Table 1. The ingredients of the concrete were ordinary portland cement, irregular gravel of maximum size 10 mm and sand. The concrete properties are given in Table 2. The cube compressive strength /^ shown in Table 2 is obtained from the average of compressive strengths of tested cubes (100x100x100 mm): 8 cubes for beams in series / and 6 cubes for beams in series //. The cylinder compressive strength /J given in Table 2 is the average compressive strength of two cylinders (0x300 mm). Table 2 gives the modulus of rupture /, (obtained from testing one prism of 100x100x500mm under four point loading system) and fracture energy G/ (obtained from testing two prisms of 100x100x500mm with notch under three point loading system) of concrete for different beams. Test results The test specimens were tested in the Amsler compression machine of total capacity 500 tons. Special arrangements had been taken to obtain two point loads and three support reactions as shown in Fig. 2. A top steel spreader beam was used to divide the total applied load from the machine head into two equal point loads, one in each span. Another stiffer steel beam was placed underneath the tested specimens to collect the three support reactions to the other head of the machine as shown in Fig. 2. The load was applied in increments of 5 tons until failure occurred. After each increment, the load was kept constant to allow marking of the new cracks and running the data logger. The test was under load control until the specimen reached its peak strength. After the peak strength of the specimen and during softening, two more readings were recorded by the data logger (ORION 3530) whenever that was possible.

3 Specimen behavior Engineering Integrity 269 The first mid-span crack generally occurred at the same time as thefirstflexural crack over the intermediate support as shown in Table 3. Then, the first diagonal crack suddenly developed at mid-depth within the intermediate shear span between the applied load and the intermediate support. Significant redistribution of internal stresses clearly occurred after development of the first diagonal crack. As the load increased, more flexural and diagonal cracks were formed and a diagonal crack extended to join the edges of the applied load and intermediate support plates. As the reinforcement was yielding, cracks became wider and the deflection significantly increased. Just before failure, the two spans showed nearly the same crack patterns. At failure, an end block formed, because of the significant diagonal crack connecting the edges of the load and intermediate support plates, and rotated about the end support leaving the rest of the beam fixed over the other two supports. At the separation line between the end block and the rest of the beam, concrete crushing and concrete separation were observed at the top and bottom ends of that separation line respectively as shown in Fig. 3 (Fig. 3(a) for CDB5 (as an example of beams in series I) and Fig. 3(b) for (as an example of beams in series II)) End support reactions and failure loads Fig. 4 shows the amount of the load transferred to the end support against the total applied load. On the same figure, the end support reaction obtained from linear elastic finite element analysis (plane stress) is presented. Although the amount of the web reinforcement influences the maximum reaction at the end support, it has no effect on the total load-end support reaction gradient. The gradient is nearly the same as obtained from linear elastic analysis up to the first cracking load, and then the redistribution of stresses increases the end support reaction more than that predicted by the linear elastic finite element. Table 4 gives total failure loads P,, end support reactions R at failure, maximum shear forces Q within the intermediate shear span, non-dimensional shear strengths T = QI bhfl and non-dimensional failure loads in each span A= P, / 1bhf[. for tested beams. CDB3 that had only horizontal web reinforcement, showed the lowest capacity of beams in series /. Mid-Span deflections The mid-span deflections for different beams against the total applied loads are given in Fig. 5. The deflections given are calculated relative to the intermediate support movement. The mid-span deflections shown in Fig. 5 are those recorded for the failed span. At low load level (up to thefirstcracking load), the mid-span deflections for each series seem to be independent of the amount and type of web reinforcement. Formation of thefirstdiagonal crack significantly

4 270 Engineering Integrity reduced the beam stiffness. All tested specimens exhibited some ductility at failure. The degree of ductility varied depending on the shear span to depth ratio and the amount of reinforcement. CDB3 that had only horizontal web reinforcement, showed the lowest ductility at failure. Beams having higher shear span to depth ratio (beams in series II) produced more ductility. Steel strains The variation of strains in different reinforcing bars against the total applied load will be presented for CDB1 and the steel strain results for the rest of the tested beams can be found in reference [2]. CDB1 steel strains CDB1 had heavy horizontal and vertical web reinforcement. Fig. 6(a) shows the positions of different ERS gauges attached to the reinforcement. Fig. 6(b) presents the variation of steel strains with the total applied load. Major redistribution of strains occurred at the bottom reinforcement after the first diagonal crack (strains at 9 and 10). After this the bottom longitudinal reinforcement was in tension throughout the length of the beam (strains at points 9, 10 and 11, even over the intermediate support, gauge 8) and yielded at failure (point 9). The top reinforcement was in tension throughout the length of the interior shear span but did not yield and neither did the web reinforcement. The failure was not in the instrumented span. Test results compared to ACI building code Comparisons between test results and the predictions of the ACI building code (318-89) [1] are presented in the following. The ACI building code provides special provisions for shear strength of continuous deep beams of clear span to depth ratio less than 5. Table 5 shows the comparison between the total shear strength v, (= v^. + v^ + v^,) of the tested beams, predicted by the ACI building code (318-89) with all safety factors removed, and the test results T = Ql bhfl given in Table 4. The table shows the contribution from concrete v^ (= YC I bhfc, where V^ is the shear force resisted by concrete), vertical web reinforcement v^(= V^ Ibhf^, where V^ is the shear force resisted by vertical web reinforcement) and horizontal web reinforcement v^ (= Fy/, / bhf^, where V^ is the shear force resisted by horizontal web reinforcement). The ratio between the experimental and ACI building code shear strength for different beams ranges from to 1.750, with average 1.23, standard deviation 31% and coefficient of variation %. The ACI building code predicts that the amount of shear resisted by the horizontal reinforcement is higher than that resisted by the vertical web reinforcement (contrary to test results). The ACI

5 Engineering Integrity 271 building code predictions are unconservative for two beams (CDBl and CDB3). The discrepancy in the results predicted by ACI building code (318-89) may be attributed to the fact that the shear strength equations for continuous deep beams are derived from simple deep beam tests and they are not based on a rational theory. A theoretical analysis of tested beams based on the plasticity theory is given in reference [2]. Conclusions The parameters studied in this experimental investigation were the degree of vertical and horizontal web reinforcement, shear span to depth ratio and the amount of the main longitudinal reinforcement. The following behavior was observed: 1. All beams exhibited the same type of failure. A major diagonal crack in the intermediate shear span ran between the edges of the load and the intermediate support plates. An end block then formed and rotated about the end support leaving the rest of the beam fixed over the other two supports. 2. The shear capacity is influenced by the type of web reinforcement. For the tested beams presented in this investigation, the vertical web reinforcement had more influence on the shear capacity than the horizontal web reinforcement. 3. The comparison between test results and the ACI building code (318-89) shows poor agreement. The ACI building code (318-89) predictions are unconservative for two beams. Acknowledgments The assistance of the staff at Structures Research Laboratory (Cambridge University) and the financial support by Cambridge Overseas Trust are gratefully acknowledged. The author is deeply grateful to Dr. C. T. Morley at Cambridge University for his guidance throughout this project. References 1. ACI Committee 318. Building Code Requirements for Reinforced Concrete (ACI ), American Concrete Institute, Deteroit, Ashour, A. F. Behaviour and Strength of Reinforced Concrete Continuous Deep Beams, PhD thesis, University of Cambridge, Kong, F. K. Reinforced Concrete Deep Beams, Blackie and Son Ltd, Leonhardt, F., and Walther, R. Deep Beams, CIRIA English Translation, Jan Rogowsky, D. M., MacGregor, J. G. & Ong, S. Y. Tests of Reinforced Concrete Deep Beams, ACI Structural Journal, 1986, 4,

6 272 Engineering Integrity Table 1 Details of specimen reinforcement Main Longitudinal Reinforcement Web Reinforcement Beam No. CDB2 CDB3 CD24 CDB5 CDB6 CD47 CDB8 Bottom Total. No 4012 mm 4<j>12 mm 4^12 mm 4012 mm A;/y (kn) Top Total. No 4012 mm 4012 mm 4012 mm mm mm 2012mm A^' (kn) Horizontal Total. No 808 mm 408 mm 408 mm " 408 mm 406 mm 206 mm 206 mm A^ (kn) " Vertical Stirrup Total. No 2908 mm 08 mm " 08 mm 08 mm 2906 mm 06 mm mm A^' (kn) " is the yield force for a single reinforcing bar. Table 2 Concrete Properties Beam No. CD&2 CD#J CDB4 CDM CDM ODB& /, (N/mm^) /; (N/mm^) /, (N/mm^) G, (N/m)

7 Table 3 First flexural and diagonal cracking load Engineering Integrity 273 Beam No. CD22 CDBJ CD#4 CDBJ CDB6 CDB& First Flexural Cracking load at Mid-Span Over the int. Sup First Diagonal Cracking Load Table 4 Total failure load P,, end support reaction R, maximum shear force Q within the intermediate shear span, non-dimensional shear strength T and nondimensional failure load X in each span Beam No. CDB2 CDBJ CD&f CDBJ CDB6 CD#7 CD#<9 P, R Q T /t Table 5 Comparison between Test Results and ACI building code (318-89) Beam No. ODJ97 CDB2 CDB3 CDB4 CDB5 CDB6 OD^a v^ v* v^ v, exp./code

8 274 Engineering Integrity h=6 or 4 PT- 500 " 200 I 500 -J18o I / Fig. 1 Geometrical Dimensions of Test Specimens (All Dimensions in mm) Upper head of the machine Upper steel spreader beam '-Half cylinder Needle Roller Load celt ^te=j Cylinder Test specimen Packing Plates- Cylinder Lower steel spreader beam Lower head of the machine Fig. 2 Test set-up

9 Engineering Integrity 275 (a) CDB5 (b) Fig. 3 Crack Patterns and Failure Zones of Tested Beams

10 276 Engineering Integrity Finite Element Analysis 5 10 End Support Reaction Fig. 4 End-Support Reaction against Total Applied Load Mid-Span Deflection (mm) Fig. 5 Mid-span Deflection and Total Applied Load Relationship

11 Engineering Integrity ) 01 si CQ a: Cd 03. C co O 03 O cu 2 v: 3 U (suoi) o I