Study of behaviour of reinforced concrete deep beam under two

points loading and the effect of shear reinforcement

Md M Sazzad*, Bangladesh Institute of Technology, Bangladesh M M Younus Ali, Bangladesh Institute of Technology Bangladesh

S M Nizamud-Ooulah, Bangladesh Institute of Technology Bangladesh

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27th Conference on OUR WORLD IN CONCRETE & STRUCTURES: 29 - 30 August 2002, Singapore

Study of behaviour of reinforced concrete deep beam under two points loading and the effect of shear reinforcement

Md M Sazzad, Bangladesh Institute of Technology, Bangladesh M M Younus Ali, Bangladesh Institute of Technology Bangladesh

S M Nizamud-Ooulah, Bangladesh Institute of Technology Bangladesh

Abstract

Many of the complex behaviors of reinforced cement concrete under shear and flexure are yet to be identified to employ this material advantageously and economically. The progress in the understanding and quantitative assessment of the behavior of member subjected to flexure and shear has been less spectacular. The fundamental nature of shear and diagonal tension strength is not yet clearly understood. So, further basic research should be encountered to determine the mechanism, which results in shear failure of reinforced concrete members. The paper presents the study of behavior of reinforced concrete deep beam under two-points loading and the effect of shear reinforcement. The influence of variation of web reinforcement spacing (both vertical and horizontal) on the shear strength of deep R.C. beam is investigated. The general trend in crack pattern, the load deflection characteristics and the mode of failure of deep R.C. beam under two-points loading are also investigated. Through the investigation, it is observed that under two-points loading system, diagonal cracks are usually the first cracks to be observed in the clear span of the deep beam. Diagonal cracks develop first in relatively deeper beams and flexural cracks develop first in shallower beam. The principal mode of failure in deep beams having adequate reinforcement is diagonal tension cracking. Different web reinforcement arrangements have no appreciable effect on the formation of initial diagonal cracks in deep beam.

Key Words: Deep Beams, Cracking Load, Crack Pattern, Shear strength, Ultimate Load, Two Point Loading.

1. Introduction

Deep beam can be defined as a beam having a ratio of span to depth of about 5 or less, or having a shear span less than about twice the depth and which are loaded at the top or compression face only (ACI-1989). They are encountered in multistory buildings to provide column offsets, in foundation walls, walls of rectangular tanks and bins, floor diaphragms and shear walls. Because of their properties deep beam are likely to have strength controlled by

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shear. On the other hand, their strength is likely to be significantly greater than predicted by the usual equations, because of a special capacity to redistribute internal forces before failure and to develop mechanisms of force transfer qUite different from beams of common proportions (Winter and Nilson-1989).

2. Mechanism of Shear Resistance in Reinforced Concrete Beams with Web Reinforcement

The inclusion of web reinforcement such as stirrup does not altogether change the fundamental mechanism of shear resistance. The stirrups rather act as the tie bars for the concrete cantilevers. The web reinforcement came into play either their role of transmitting the shear force only after the cracks have developed in the concrete beams. The web reinforcement adds strength to the shear mechanism by improving the condition of dowel action, suppresses initial tensile stresses in concrete cantilever by means of the diagonal compressive force, limits the crack openings and there by preserves the shear transfer by aggregate inter lock. In addition it carries the extra shear force (Vs) by truss mechanism.

3. Interaction of Flexure And Shear

Normally it has been observed that shear force does not affect significantly the development of flexure capacity of reinforced concrete beams with adequate web reinforcement. After the formation of a diagonal crack the internal tension in the flexure steel at a section away from it. Thus an intimate relation exists between flexure, shear, bond and anchorage in the shear span of a beam in which large shear forces are to be transmitted across a section at the ultimate moment, the distribution of the flexure strains in concrete and steel can be effected. In simply supported or continuous deep beams, where the external loads and reactions are applied to the top or bottom compression face of the beam, the mode of shear transfer after the formation of diagonal cracks is mainly arch action, shear forces in such beams can be so dominated that they govern the strength by inhibiting the development of full flexure capacity.

4. Laboratory Investigation

To attain the required goal, the following laboratory investigations were performed:

4.1 Fabrication and Casting of Test Beams

To cast the beams, Portland cement, Domar sand (FM=2.63), Brick khoa (0.75 in. down graded , FM=6.92) were used. The water-cement ratio of concrete was 0.55 and the concrete mix ratio was: Cement: Sand: Brick aggregate = 1:2:4(by weight). The physical properties of M.S. bar are given in the table-1 .

Table 1. The Physical Properties of Reinforcements Used in the Beams

A % Inch Nominal Diameter M.S. Bar Specimen

No. Actual

Diameter (inch)

Actual Area (in2

)

Yield Strength (psi)

Ultimate Strength (psi)

01 0.7322 0.420 50531 72187 02 0.7480 0.439 51133 73047 03 0.7640 0.458 50946 72780

Average 0.7480 0.439 50870 72671

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B. 114 Inch Nominal Diameter M 5 Bar Specimen

No. Actual

Diameter (inch)

Actual Area (in 2

)

Yield Strength (psi)

Ultimate Strength (psi)

01 0.2598 0.0530 58113 83019 02 0.2637 0.0546 60256 86080 03 0.2598 0.0530 58113 83019

Average 0.2611 0.0535 58827 84040

The total of six rectangular deep beams in two series were designed to fall in shear. Nominal cross section of the first series of beams were 6 inch x 12 inch and that for second series is 6 inch x18 inch. Span/depth ratio of the beam of first series was 2.5 and that for second series was 1. The total length of the beam was kept 36 inch for the first series and 27 inch for the second series. In all the beams, the longitudinal tension reinforcement was provided by two % inch diameter mild steel bars. Two ~ in . thick and 3 inch x 6 inch mild steel plates were welded to either end of the tension bars to prevent any premature bond failure. The centroid of the tension steel was maintained at 1.5 inch from the bottom face of the beams. Arrangement and the amount of web steel were the variables in each of test beams. The beams were designed with the tension to achieve either diagonal tension or shear compression failure. To accomplish this, the following procedures were adopted.

1. Steel ratio was kept well below the balanced condition to check against failure by crushing of concrete.

2. Adequate tension reinforcement was provided to guard against flexure tension failure prior to shear failure.

3. Anchor plates were provided to prevent any premature bond failure of the tension steel.

Design calculations were based on the ACI 318-77 code provisions. Six beams were fabricated. Wooden moulds were used to cast the test beams. Six standard size concrete cylinders were cast along with the test beam from the some batch of concrete as used in beams. % inch diameter mild steel bars bent in the form of closed rectangles were used as vertical web reinforcement. 3/4-inch clear concrete cover was provided at the top and bottom of the beam. The clear cover on two sides of the beam is % inch. Horizontal web reinforcements were also % inch diameter bars placed inside the vertical ones and tied to it by G.I. wires at every junction. In addition to the nominal web reinforcements a number of vertical and horizontal bars are placed near the supports of the beams to prevent bearing failure of concrete over supports. Details of reinforcement arrangement of beams are shown in the following figures.

/oading point":. Lifting hooks ~

I I I I

I I

"

I I I I

" 27 "

'll

1!.5" V. 5"

135"

r .....--t_--'1 /4"q>@3" c/c

~H-'-'-+-- 6-114" q>

4 5" ~ I~

2-3 /4"q>

Fig 1. Reinforcement Arrangement of Beam A1

361

ifting hooks

I I

I I 1

" 1II1II 4.5 " ~IIIIII

~oading point'-". ~

I I ! I I

~I 27 "

~

5" 1I4"<p @ 3"

14---"l'- ­ c/ c 4- 1/4"<p

2-3 /4"<p

Fig 2. Reinforcement Arrangement of Beam A2

1

"

~oading point~

27 " I'"

Lifting hooks "llV

14----4-=--~114" <p @ 3" c/c

~f+-!.'='--t--- 6-1 /4"<p

2-3 /4"<p

Fig 3. Reinforcement Arrangement of Beam A3

I I I I

1 I I

9"

~oading point~ t.. ........ I.

9"~I 18"

Lifting hooks "llV

j

3" ~ I

15"15"

15"

14--....:...j.:...-2114"<p@3" c/c

~-+-'-''-+--- 6- II4"<p

2-3 /4"<p

Fig 4. Reinforcement Arrangement of Beam 61

Lifting hooks

1

~oadi ng point~ V "ll

4" 1/4"<p @ 4.5"

14"

4"

4"

trJ+.~~- c/c

y J,,~:"'::"'-I--- 8- 114"<p

2-3/4"<p

9', 9" 18 "

~ I1II1II

Fig 5. Reinforcement Arrangement of Beam 62

362

Lifting hooks

,

3 " ,... 9 "

,...

~oading po int",

3 " ~,

18 " ,0IIII 9"

~,/

~,

15"15"

15"

~--+-_-,-,1I4" cp @ 3" c/c

,r.,.+-t---+-- 6 - 114"cp

2-3/4"cp

6"

Fig 6. Reinforcement Arrangement of Beam B3

On completion of the reinforcement assembly, the beams were cast control cylinder specimens were also cast. The beams were striped of the moulds after about 48 hours of casting. Two extended stirrups were provided near the ends of each beam and these were used as lifting hooks. The beam specimens and the control cylinders were then cured for 28 days by wrapping the beams with moist gunny bags. The beams were then air dried for the next three days.

4.2 Testing of the Beams to Investigate the Relevant Behaviors

Six test beams were investigated in two series having span/depth (LID) ratio equal to 2.5 for the first series and LlD=1 for the second series.

4.3 Test Set Up

Each beam was tested under two- points concentrated load by 400 kips capacity universal testing machine (hydraulic type) . The load was applied on the top surface through a 1.5 in. thick and 6 in. long steel plate and the reactions were supported by two 1 in. thick and 3 in. long steel plates placed at the bottom of the beams. One of the reaction plate rested on a steel block and itself placed on the anvil of the testing machine. The other reaction plate was placed over a steel block supported by 5/8-in. diameter steel rollers . I-joists with rollers and rubber pads were employed as load transfer devices for two series of beams. The support lines were clearly marked on both sides of the beams. The loading blocks were also marked on both sides at their centers. A deflectometer graduated in 0.001 in . division was used to measure the mid span deflections of test beams at each load increment. The beam was then loaded and deflection readings were taken at regular interval of load increment. Test beams were white washed to facilitate visual observation of the propagation of cracks on the surface of beam . Cracks were deeply marked with a soft pencil upon their formation on the beam surface and the load intenSity at which it was formed was noted besides the crack. One of the cylinders cast along with each of the test beam was tested under axial compression to determine the ultimate compressive strength of concrete and the other was tested under diametrical compression to find the split cylinder tensile strength.

5. Test Result

A tota l of six deep reinforced concrete beams have been tested under static two point concentrated loading system. The special interest of the investigation is to study the effect of different web reinforcement arrangement on the ultimate shear strength of brick aggregate concrete beams under two series and as a whole the overall behavior of deep beams under two point concentrated loading. The specific observation of interest during the test has been recorded and is being presented in this chapter.

The critical load at tension cracking , the load at flexure cracking, the ultimate load and deflections under different load intensities are noted in a systematic manner during the test. For an easy

363

grasp of the overall performance of the beams, the test results are presented here in a tabular form. a general description of the contents of the different tables containing various test data seems necessary and is furnished below. In table 3, the typical beam properties of all the beams have been provided. This includes the actual overall depth, beam width, span to effective depth ratio, web steel ratio (both for vertical and horizontal web steel), cylinder crushing strength and split cylinder strength. The different steel ratios are computed on the basis of actual area of steel provided and mean of the measured width and effective depth after casting. Some of the basic properties of brick aggregate concrete like, compressive strength , split cylinder strength and the relation between them is given by Brazilian ratio and the unit weight of harden concrete is computed by dividing the weight of standard cylinder by its volume. Average of three such values is presented here. The critical load (Per) at diagonal tension cracking, the load (Pf) at the initiation of flexure crack , and the ultimate load (Pu) are listed in table 6. The ratio of flexure cracking load to ultimate load and the diagonal cracking load to ultimate load is computed for all the beams and are presented in this table.

Table 2. Sectional Area of Provided Tensile Steel in the Test Beam

Beam mark

Diameter (inch) Area of bar (inch<) Total sectional area of tension steel, As (inch2)Bar (1) Bar (2) Bar (1) Bar (2)

A1 0.7752 0.7742 0.472 0.471 0.943 A2 0.7626 0.7640 0.457 0.458 0.915 A3 0.7892 0.7862 0.489 0.485 0.974 B1 0.7762 0.7750 0.473 0.472 0.945 B2 0.7772 0.7760 0.474 0.473 0.947 B3 0.7690 0.7680 0.464 0.463 0.927

Table 3. The Typical Beam Properties of All the Beams.

First series: Nominal LID = 2.5 Beam mark

Measured overall depth,

D (in)

Beam width (in)

Span length

(in)

Nominal LID LID

A1 12 6.10 30 2.5 2.857 A2 12 6.25 30 2.5 2.857 A3 12 6.30 30 2.5 2.857

Second series: Nominal LlD=1 B1 18 6.2 18 1 1.091 B2 18 6.10 18 1 1.091 B3 18 6.25 18 1 1.091

Table 4. Some Properties of Concrete of the Test Beam.

First series : Nominal LID = 2.5 Beam mark

Tension steel ratio,

As/bd

Web steel ratio Cylinder crushing strength (psi)

Split cylinder strength

(psi)Vertical, Pv=Av/bd

Horizontal, Ph=Avh/bd

A1 0.01472 0.0058 0.0041 3258 320 A2 0.01394 0.00582 0.0040 3260 325 A3 0.01472 0.00530 0.00373 3270 330

Second series: Nominal LlD=1 B1 0.00924 0.00323 0.00323 3340 320 B2 0.00941 0.00390 0.00410 3340 325 B3 0.00899 0.00762 0.00356 3350 330

364

Table 5. Some Properties of Concrete of the Test Beam

First series Beam Mark

Concrete crushing strength , f' e

.yf'e Split cylinder strength, f'sp

Brazilian ratio F'sp= f'sp/ .yf'e

Unit weight, pet

A1 3258 57.08 320 5.60 128.34 A2 3260 57.10 332 5.70 128.60 A3 3270 57 .18 330 5.77 127.32

Second series B1 3340 57.79 320 5.33 134.6 B2 3340 57.79 325 5.62 133.9 B3 3350 57 .88 330 5.70 132.5

Table 6. Observed Cracking and Ultimate Loads of the Test Beams

First series Beam mark

Concrete strength, f'c (psi)

Flexure cracking load,

Pr (kips)

Diagonal cracking load,

Per (kips)

Ultimate load, Pu

(kips)

Ratio PrtPu

Ratio Pe/Pu

A1 3258 65 70 105 0.62 0.67 A2 3260 75 80 103 0.73 0.77 A3 3270 70 75 95 0.73 0.78

Mean 0.69 0.74 C 9.22 8.22

Second series B1 3340 110 100 150 0.73 0.67 B2 3340 120 110 160 0.75 0.69 B3 3350 127 127 185 0.68 0.69

Mean 0.72 0.68 C 5 1.8

..C = Co-effiCient of variation in percent

6. Load Deflection Characteristics

While testing the deep beams, the corresponding deflections of the beams were computed and it was found that the actual observed deflections were significantly larger than the computed deflections. The deflection was lower for deep beams as compared to shallow beams. Load deflection curve of beam A3 is shown below.

Load Deflection Curve

0.14

0.12

€ 0 .1 c '; 0 .08 o 'U 0.06 Ql

'iii 0.04 o 0.02

o

~~ Computed Defiection ~ . _Observed Defiection . -r­~

.. --­-­..­~ II"

/ ---- c---.

/ ..&

lL I I I o 20 40 60 80 100 120 140

Load (kips)

Fig 7. Load Deflection Curve of Beam A3

365

7. Mode of Failure and Crack Pattern

The crack pattern and the mode of failure of all the test beams were almost similar despite the variations in web reinforcement arrangement. From the test it was observed that diagonal cracks develop first in relatively deeper beams and flexural cracks develop first in shallower beams provided the beams have sufficient reinforcement. The crack pattern of beam A2 is shown below:

Fig 8. Crack Pattern of Beam A2

8. Conclusion

The following conclusions can be drawn from the previous analysis.

1. Under concentrated loading system, diagonal cracks are usually the first cracks to be observed in the clear shear span of the deep beam.

2. It is observed from the investigation that under two-point loading diagonal cracks are the first crack to be developed in relatively deeper beams and flexural cracks are the first crack to be developed in the shallower beams.

3. The crack pattern and the mode of failure of all the test beams were almost similar despite the variations in web reinforcement arrangement.

4. Different web reinforcement arrangements have no appreciable effect on the formation of initial diagonal cracks in the deep beam.

5. For the test beams, difference in web reinforcement spacing is found to have no significant influence over the ultimate shear strength of the beams.

6. Due to inadequate support condition the beam may fail at support due to punching of the support.

7. It is found that the actual observed deflections are significantly larger than the computed deflections.

References

[1] Kabir, A. & Rashid, A. , , Behavior of Reinforced Concrete Deep Beam Under Uniform Loading' , Dhaka, Journal of Civil Engineering, (I EB) Vol. CE 24. No. 2 December,1996, page155-169

[2] Fergusen. P. M. , , Reinforced Concrete Fundamental', John Wiley& Son 's, New York, 3 rd edition.-1973

[3] Winter. G. , & Nilson, A. H, ' Design of Concrete Structure', McGraw-Hili Company, New York, 11 th edition-1989

[4] Kabir, A. , ' Shear Strength of Deep Reinforced Concrete Beam ', M. Sc. Thesis, Dept. of Civil Engg. BUET, Dhaka , October-1982.

[5] Ali, G., , Study of Stress Distribution in Deep Reinforced Concrete Beams', M. Sc.Thesis,Dept. of Civil Engg . BUET, Dhaka, September-1984.

[6] Aziz, M. A, ' A text Book of Engineering Materials', Hafiz Book Centre, Dhaka-1981.

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