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Experimental and analytical study of shearing behavior of the deep reinforced beam with openings

Alireza M. Goltabar1, Danesh Riazi2 and Aref Sadeghi Nik3

1Faculty of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran.E-Mail: [email protected]

2Master of Science student of Babol Noshirvani University of Technology, Babol, Iran.3Young Researchers Club, Jouybar Branch, Islamic Azad University, Jouybar, Iran.

Abstract

It is inevitable to use deep beams in some certain structures and web openings are used for architectural reasons like doors, windows or facilities such as pipes, ducts and ventilation circuits. Very limited studies have been done on such beams with openings and no regulation has been prepared for their design so far. The purpose of this research is the experimental study of the behavior of such beams with circular openings. Nine same beams were made and statically loaded up to the rupture point. In shearing points of the beam circular openings were arranged in different sizes and positions, and the variation of shearing strength and beams’ behavior were verified regarding different sizes and positions of the openings, also shearing strength of the experimental samples was compared with the results from Kung empirical relations. Findings show that increasing the dimensions of the openings will result a decrease of the shearing capacity of the beam, also the strength of the samples depends on how much the natural load path is crossed. Further more, a comparison between the experimental results and those of Kung relations, shows that the relations are conservative for the samples in which the natural load path is not crossed, and not for those in which the path is crossed.

Key words: reinforced concrete, deep beam, circular opening, shearing, experimental and analytical behavior.

1. Introduction

Deep beams are considered by the researchers due to their wide range of use in civil engineering such as high rises, reservoirs, rectangular storage buildings and marine structures [1]. There is no clear definition of such beams because of their complicated behavior but most of the references consider a beam as a deep one when the span (L) - depth (D) ratio is less than 5, while in European regulations [2] the figure is less than 2.5 and in American regulations [3] the figure is 4

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and in Canadian regulation it is considered up to 5. In different structures web openings are used for architectural reasons like doors, windows or facilities such as pipes, ducts and ventilation circuits. In such cases their behavior and ultimate loading capacity is very important.

Many researchers have done researches on the behavior of ordinary beams based on ultimate loading capacity and have come up with some empirical and semi-empirical relations for their ultimate loading capacity which eventually led to be registered in different regulations (CEB-FIP(1970)[4] and ACI-318(1971) [5]) for the design of the deep beams. Nevertheless researches on such beams with openings have been limited and there has not been any regulation for designing them. Kung et al have recently come up with some semi-empirical formulations to get the ultimate strength of such beams with and without openings [6-9].

Kung et al [10] in Newcastle university have studied deep beams behavior and come up with semi-empirical formulas to predict ultimate loading capacity for those with and without openings. Behavior of beams with rectangular openings has been studied by Mansur [11]. The results show that the first diameter cracks happened when loaded by about 36 to 55 per cent of the ultimate load at the corner of the opening at bearing support points. When loaded by 50 to 90 per cent of the ultimate load, critical diameter cracks in shearing boundaries, happened around the openings and spread towards bearing support and loading points and eventually led up to rupture. Many researchers have done researches on the behavior of ordinary beams based on ultimate loading capacity and have come up with some empirical and semi-empirical relations for their ultimate load capacity which eventually led to be registered in different regulations (CEB-FIP(1970)[6] and ACI-318(1971) [7]) for the design of the deep beams. Nevertheless researches on such beams with openings have been limited and there has not been any regulation for designing them. Kung et al have recently come up with some semi-empirical formulations to get the ultimate strength of such beams with and without openings [8-11].

2. Beams’ specifications

In this research, 9 beams with openings with a length of 150 Cm, a width of 12 Cm and a height of 50 Cm were made. Shearing span-depth ratio in these beams is 0.95 and beams’ span-depth ratio is 2.7. Tension rods include 4 reinforcing bars, 14 millimeter in diameter with yielding strength of 400 Mpa. These bars are put in two layers and to get the required strength, they go through holes in a 10-mm thick end-plate and are welded all around, on the other side of the plate. Shearing bars make a network with 150-mm square openings with a diameter of 6 mm. bars’ specifications and their arrangement in beams are shown in figure 1. All the beams have two circular openings, symmetric to the middle, located at beam’s shearing span (figure2). Opening dimensions are 150mm, 200mm and 250mm in which related height-depth ratio is 0.3, 0.4, and 0.5 respectively. Three cubic samples (100*100) were filled with concrete in a horizontal position in order to identify concrete compressive strength which is 30 Mpa.

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Figure1:

arrangement of main reinforcing bars, horizontal and vertical network of the samples (in centimeter).

3. Experiment matrix

Categorization of the beams is presented in table 1. Samples were categorized into three main groups of A, B and C based on the openings’ location. In group A, openings are located in the middle of the shearing span (figure2) so that they intersect the path between loading and bearing support Point. In group B openings are located at the side with the loading plate, 75 Cm away from the top of the beam (figure3). The openings of group C are also located at the side with loading plate, 75 Cm away from the bottom of the beam (figure4).

Table1: categorization of the samples.

Opening diameter(mm)Opening locationsamplegroup

150Middle of the shearing spanB-150-CA



150Above shearing span near bearing support PointB-150-TB



150Under shearing span near loading pointB-150-BC



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Figure2: location of openings group A (a=150, 200, 250mm).

Figure3: location of openings group B (a=150,200,250mm).

Figure 4: location of openings group C (a=150,200,250mm).

4. Method of the experiment

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Loading method is shown in figure 5. All the samples were loaded by a hydraulic jack in a symmetric, 4-point loading system. Loading was done statically and on top. Strains in the middle of the samples were measured by an electrical strain gauge (LVDT). Loading and strain in the samples were recorded by a computer. Bearing supports were simple and 75mm away from each ends of the beam. 20-mm thick and 100-mm wide plates were used at the loading points to prevent crushing of the concrete. The development and spread of the cracks up to the rupture point were marked and rupture mode was recorded.

Figure 5: a typical loading system.

5. Experimental results

5.1. load-strain diagrams of the samples

In order to verify the rigidity and strain of the beams, load-strain diagram was studied. The diagram for groups A, B and C are presented in figures 6, 7 and 8 respectively. Basically beams’ behavior depends on the angle of intersection between openings and load path, as it is shown in the diagrams. samples B-150-T, B-200-T, B-150-B and B-200-B in which load path is not intersected by the openings, load-strain diagram is linear up to rupture while samples in which the path is partially or completely intersected by the openings, load-strain diagram is nonlinear up to rupture referring to greater pace for development, widening and spreading of the cracks in these samples. Also increasing the diameter of the opening from 150mm to 200mm and then to 250mm leads to a decrease of the rigidity of the beams and an increase of strain at the middle of the span for the corresponding load.

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Figure 6: load-strain diagram of the middle of the beam span-group A.

Figure 7: load-strain diagram of the middle of the beam span-group B.

Figure 8: load-strain diagram of the middle of the beam span-group C.

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5.2. Verification of the cracks

In general, studying the cracks developed in the samples and regarding table 2, the followings can be stated:

1. The first cracks which are shearing ones around the opening were developed when loaded by 39 percent of the ultimate load based on the average amount from table 2. Increasing the load the cracks will spread towards loading and webs. Increasing the load, new cracks were developed parallel to the existing ones and the ones along the diameter were widened. Flaking out, the cracks along the diameter were completely widened and finally rupture happened.

2. Bending cracks appear at the middle of the beam and at 0.3 of the height of the beam from the bottom. These cracks appear when loaded by 67 percent of the ultimate load, based on the average from table 2-4.

Table 2: first- ultimate load ratio.

Cracking load bending-rupture

load ratio

Cracking load shearing- rupture

load ratio

Rupture load (KN)

Cracking load bending

(KN)

Cracking load shearing

(KN)beam

0.780.3923118090B-150-C

0.770.3318014060B-200-C

0.910.4112011050B-250-C

0.580.36479280175B-150-T

0.500.35421210150B-200-T

0.780.49243190120B-250-T

0.560.35223240150B-150-B

0.570.41329190135B-200-B

0.590.45255150115B-250-B

0.670.39average

5.3. Rupture and shearing strength of deep beams with openings

Verifying how 9 samples of deep reinforced beams with openings it is concluded that there are two modes of ruptures for deep beams with openings based on dimensions and location of the openings. The first one occurs due to formation of two independent cracks along the diameter in the upper and lower chords of one of the openings and rupture occurs and divides it into two parts. The second one occurs because of a relative rotation

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of the three separate zones in shearing span of the beam. Rupture occurrence and the related loads for the 9 samples are presented in table 3 and figures 9 through 17.

Table 3: rupture occurrence and related loads for experimental samples.

Type of ruptureUltimate

strain(mm)Ultimate load(KN)

Cracking load(KN)

Beam

Shearing span divides into three parts3.223190B-150-C

Shearing span divides into three parts4.318060B-200-C

Shearing span divides into three parts5.817555B-250-CCritical crack along the diameter between

loading and bearing points4479175B-150-T

Critical crack along the diameter between loading and bearing points

4.8421150B-200-T

Shearing span divides into three parts5.6243120B-250-TCritical crack along the diameter between

loading and bearing points4423150B-150-B

Critical crack along the diameter between loading and bearing points

4.4329135B-200-B

Shearing span divides into three parts5.8255115B-250-B

Figure 9: rupture in sample B-150-T.

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Figure 12: rupture in sample B-150-C.

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Figure 15: rupture in sample B-150-B.

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Regarding the results it is stated that increasing the diameter of the opening from 150mm to 200mm, with a/h equals to 0.3 and 0.4 respectively; shearing capacity will decrease up to 19 percent in average. Again increasing the diameter of the opening from 150mm to 250mm, there will be a decrease of 45 percent in shearing capacity.

6. Analytical method

In this section, analytical method based on semi-empirical relations for calculation of shearing capacity of deep beams with circular openings, made by Kung et al, is presented. Structural parameters of the beams with web openings are shown in figure 18. Shearing strength of the beams with web openings ( ) equals to:

(1)

Where is acquired shearing strength by concrete and is ultimate shearing strength acquired by tension bar. In relations 2 to 12 shearing capacity of the concrete and tension bars

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are calculated [8]. Since there are openings in web, cutting tension bars which go through them, is inevitable. That is why shearing strength of the shearing bars is ignored.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

- For the openings with their centers NOT located in loading area.

(9)

- For the openings with their centers located in loading area.

(10)

(11)

(12)

Where is the area of tension bars, is compressive strength of concrete, is tension strength of concrete (equals to ), is beam’s width, is beam’s height, is load angle to the horizon (figure18), is free shearing span, is nominal shearing span, is the opening's

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width, is the opening height, are off-center of the opening (figure18), are coefficients of the opening’s position (figure18), is for reinforcing bars and

is for plain bars and [11].

Figure18: structural parameters of beams with openings in web.

5.4. Comparison between results from analytical method to predict shearing capacity for reinforced beams with circular openings

In order to make a comparison between the results for experimental beams and to predict shearing capacity for reinforced beams based on existing regulations, it is necessary to calculate shearing capacity by means of different methods. Therefore semi-empirical formula made by Kung et al was used. A comparison between experimental results and those of predicted theory by Kung’s model is presented in table 4 and figure19.

Table 4: comparison between acquired experimental shearing capacity and that of Kung’s model.

Results from Kung’s theoretical modelExperimental results

Beam(kN)(kN))kN( )kN(

Ultimate load

0.92124.452.0672.3115.5231B-150-C0.82109.852.0657.890180B-200-C0.699.852.064760120B-250-C

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1.28181.3652.06129.3234.5479B-150-T1.37153.3652.06101.3210.5421B-200-T0.9134.852.0682.7121.5243B-250-T1.4150.452.0698.35211.5422B-150-B1.24132.052.0679.8164.5329B-200-B1.05120.652.0668.5127.5255B-250-B

Making a comparison between experimental results and those of Kung’s semi-empirical relations indicates that shearing strength capacity for beams in which load path is intersected by the openings (samples B-150-C ، B-200-C ، B-250-C ، B-250-T و B-250-B), is calculated in a none-conservative manner in Kung’s model (figure 19), because rupture suddenly occurs due to a rotation in three separate sections in shearing span, so not all the shearing capacity calculated in Kung’s model is used. For these samples the ratio of experimental shearing capacity to the analytical shearing capacity is in the range of 0.6 and 0.92. For the other samples in which openings do not intersect load path, calculated shearing capacity in Kung’s model, is conservative and the ratio is in the range of 1.05 and 1.37.

Figure19: comparison between experimental shearing capacity and analytical shearing capacity for beams with circular openings.

6. Conclusion

According to the experimental and analytical results obtained by conducting experiment on 9 beams with openings, the following conclusions are stated:

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1. Experiments show that the ratio of the load, for which the first bending crack appears, to the rupture load is 67% and the ratio of the load , for which the first shearing crack appears to the rupture load is 39%.

2. Bending cracks occur very little and usually appear under a load which is as much as 50 to 91 percent of the ultimate load. These cracks hardly develop at 0.3 of the depth from the bottom.

3. In beams B-150-T ، B-200-T ، B-150-B and B-200-B which openings do not intersect load path, rupture occurs due to formation of two independent cracks along the diameter in upper and lower chords of one of the openings and rupture occurs and divides it into two parts.

4. In all the samples in group A and also in B-250-T and B-250-B which the openings intersect the load path, rupture occurs in shearing span because of relative rotation of three independent sections.

5. Increasing the diameter of the opening from 150mm to 200mm, shearing capacity will decrease up to 19 percent in average and increasing the diameter of the opening from 150mm to 250mm, there will be a decrease of 45 percent in shearing capacity.

6. In Kung’s model, shearing strength capacity for beams in which load path is intersected by the openings (samples B-150-C ، B-200-C ، B-250-C ، B-250-T و B-250-B), is calculated in a none-conservative manner because rupture suddenly occurs due to a rotation in three separate sections in shearing span, so not all the shearing capacity calculated in Kung’s model is used.

7. For the samples in which openings do not intersect load path (samples B-150-T ، B-200-T ، B-150-B وB-200-B) calculated shearing capacity in Kung’s model, is conservative and the ratio is in the range of 1.05 and 1.37.

References

1. Subedi, N.K., Vardy, A.E., and Khota N. (1986), “Reinforced concrete deep beams- some test results” Magazine of concrete Research, vol. 38, No.137, December pp.206-219

2. CIRIA (1977), “CIRIA Guide 2: The Design of Deep Beams in Reinforced Concrete, Ode Arup and Partners” Construction Industry Research and Information Association, London.

3. ACI Committee 440.2R-02 (2002), “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-02)” American Concrete Institute, Farmington Hills, Michigan, 45 pp.

4. CEB-FIP Model code for concrete structure, (1990), “Cement and Convert Association (British Cement Association)” London.

5. ACI Committee 318. “Building code requirements for structural concrete (ACI 318-02)” American Concrete Institute, Detroit, p. 111.

6. Ray, S.P. and Reddy, C.S. (1979), "Strength of reinforced concrete deep beams with and without opening in web” Indian Concrete Journal, 53, No.9, Sept.: 242.

7. Ray, S.P. (1982), "Behavior and strength of deep beams with web openings” Further evidence, Bridge and Structure. Engr. (IABSE), India 12, No.1 March: 1.

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8. Ray, S.P. (1982b), "A short review of literature on reinforced concrete deep beams with and without opening in web” J. Structure. Eng., India 9, No.1, Apr.: 5.

9. Singh, R., Ray, S.P. and Reddy, C.S. (1980), "Some tests on reinforced concrete deep beams with and without opening in web”. Indian Concrete Journal, 54, No.7, July: 189

10. Kong, F.K., and Sharp, G.R. (1977), “Structural idealization for deep beams with web Openings,” Magazine of Concrete Research, Vol. 29, No. 99, pp. 81-91.

11. Mansur, M.A., and Alwist, W.A. (1984), “Reinforced concrete deep beams with web openings,” The International Journal of Cement Composites and Lightweight Concrete, Vol. 6, No. 4, pp. 263-271.

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