Shear Behavior of Reinforced Concrete Varying Depth Beams

Ministry of High Education and Scientific Research University of Al-Mustansyriah

College of Engineering

Civil Engineering Department

Shear Behavior of Reinforced Concrete Varying

Depth Beams (Experimental Study)

PROJECT

SUBMITTED TO THE CIVIL ENGINEERING DEPARTMENT

COLLEGE OF ENGINEERING

UNIVERSITY OF AL-MUSTANSYRIAH

AS AFULFILLMENT FOR REQUIREMENTS TO DEGREE OF BACHELOR

IN CIVIL ENGINEERING

By

Mohammed Hussein Aysha Arkan

Supervised

Asst. Prof. Dr. Ali Hameed Aziz

AD 2016 Hijry 1437

المستخلصتص ظر للسل ه ت لي ال اس في التحر الع ني الد رس ئي للعتب ال الانش

ق تغير تأثير تحتمتغير الع ص. ا ال د الرئيسي ال عت ا في ال ق اله البحث ه تب من عع

تين تغيرا تم بي ،كلا الج ء عل ال بت الاب ل الاخر ث صه ل فح ن . العتب ال تض

تبر صب الجزء بع ال بع فحص أ نيه مسلحه ب للط ) ملم x1220140)عتب خرس

ص فح ل العتب ال ق متغير ل الي بي ك الع ئج .العر عل الت ت تبريه اش ال ال

ص أ ال مه ال دا قلتم يجي ( %50)ال %(6)ب طع تد دم تغير ال ن مع ع م

رجعيه نه . العتبه ال رس د من قبل ك ال عت ص ال لا التجريبيه لل ع نه مع ال تم اجراء م

ي ) ئجACI-318الامري ت قد اش ال ل الاق أ ( ي الح حس ه اقل من ال ال

تبريه .ال

Abstract

This study is concerned with the practical and theoretical investigation of

reinforced concrete beams with variable depth under the effect of shear

stress. The main variable is in this research is the depth of beam from

both sides, while, the other variables kept constant for all the tested

specimens. The experimental part including poured and test of four

reinforced concrete beams with dimension of (1220x140 mm) for length

and width, respectively, while the depth is considered to be variable all

tested beams. The experimental indicated that the shear strength

decreased for about (6%) to (50%) when the section gradually changed

compared with reference beam. Comparison with the empirical equations

of American concrete Code (ACI-318) is take place. The results indicated

that the ultimate calculated load is less than the experimental value.

List of Tables

Item Table No. Table Title Page No.

1 Table (2-1) Beams Designation and Details 7

2 Table (2-2) Description of Construction Materials 8

3 Table (2-3) Properties of Steel Bars 8

4 Table (2-4) Mix proportion 8

5 Table (2-5) Mechanical Properties of Concrete 12

6 Table (3-1) Shear and Ultimate Strength 16

7 Table (4-1) Ultimate Shear Strength of Tested Beams 20

8 Table (4-2) Experimental and Calculated Shear Strength 22

List of Figures

Item Figure No. Figure Title Page No.

1 Figure (1-1) Applications of varying Depth Beams 3

2 Figure (2-1) Details of Tested Beams (Prismatic Beam) 6

3 Figure (2-2) Details of Tested Beams (Varying Depth Beam) 7

4 Figure (2-3) Plywood Mold 9

5 Figure (2-4) Steel Reinforcement Inside the Mold 9

6 Figure (2-5) Universal Testing Machine 10

7 Figure (2-6) Concrete Mixer 10

8 Figure (2-7) Beam Specimen Stripping 11

9 Figure (2-8) Beam and Control Specimen curing 11

10 Figure (2-9) Beam Specimen setup 12

11 Figure (4-1) Crack Patterns of Tested Beams 19

12 Figure (4-2) Load-Deflection Relationship of Tested Beams 21

Chapter One Introduction

1

Chapter One

Introduction


2

Chapter One

Introduction

1-1-Introduction

The esthetic shape and substantial reduction of material quantities (the

materials required are usually much less than those needed for prismatic beams)

of varying depth RC beams leads to use such member extensively in several

structures, such as prestressed or nonprestressed beams of bridges and RC

trusses. The main feature of varying depth RC beams is saving in weight, which

affects especially the cost of transport, handling and erection for pre-cast cross

sections.

1-2-Beams with varying depth

Reinforced concrete members having varying depth are frequently used

in the form of haunched beams for bridges or portal frames as precast roof

girders or as cantilever slabs.

For beams with varying depth, the inclination of the internal compressive and

tensile stress resultants may significantly affect the shear for which the beam

should be design. In addition, the shear resistance of such members may differ

from that of prismatic beams

Beams must also have an adequate safety margin against other types of failure

such as shear, which may be more dangerous than flexural failure.

Shear stress happens when two forces affect the material in opposite directions

but do not affect the same place V tadian to move part of the material in the

direction of the other part in another direction

Shear failure of the concrete beam, is undesirable mode of failure because these

kinds of failure gives a few warnings, and have disastrous consequences.


3

Shear failure of reinforced concrete beam more properly called “diagonal

tension failure”, is difficult to predict accurately

With no shear reinforcement provided, the member failed immediately upon

formation of the critical crack in the high-shear region near the right support Shear strength is the maximum shear stress which a material can withstand

without rupture.

In engineering, shear strength is the strength of a material or component against

the type of yield or structural failure where the material or component fails in

shear. The shear strength is the load that an object is able to withstand in a

direction parallel to the face of the material, as opposed to perpendicular to the

surface.

Figure (1) Applications of varying depth Beams

1-3-Objectives of Project

In this project, the effect of shear force on the reinforced concrete beams of

varying depth will be study.

1-4- Project Layout

The present project is divided into five chapters as descripted below:-

1-Chapter One: Introduction.

2- Chapter two: Experimental work

3-Chapter three: Theoretical work


4

4-Chapter four: Discussion and Comparison of the Experimental

and Theoretical Results will be presented.

5- Chapter five:-Conclusions and Recommendations.

Chapter Two Experimental work

5

Chapter two

Experimental work


6

Chapter two

Experimental work

2-1-Experimental Program

Tests were carried out on four, varying section, simply supported beam

specimens under monotonically concentrated load. The tested beams are reinforced in

longitudinal direction (flexural reinforcement at the bottom) without shear

reinforcement to ensure failed in shear mode of failure. The varying in section is the

major adopted variable. The beam length, shear span-depth ratio (a/d) and

longitudinal reinforcement are kept constant for all tested beams. To evaluate the

compressive strength of concrete, the experimental program consists, also, cast and

test of a series of control specimens (cubes).

2-2- Beam Specimens Details

The nominal dimensions and the details of tested beams are shown in Figures

(2-1) and (2-2) and Table (2-1). The overall length was (1220 mm), while, the overall

width was (140mm). It may be noted that the depth of tested beams were kept

constant at the left side end (250mm) and varied from (150-250mm) at the right side

end. All beam specimens were reinforced with (2 16 mm) deformed bars as tension

(flexural) at the bottom.

Figure (2-1) Details of Tested Beams (Prismatic Beam)

1220 mm

1100mm

250 mm

2 16 mm 140 mm 2 16 mm


7

Figure (2-2) Details of Tested Beams (Varying Depth Beam)

The first beam specimen, (B-1), is poured with constant depth (Prismatic

Beam), while the beam specimens (B-2) is poured with varying depth of (250mm) at

right hand side and decreased gradually to (200mm) at left hand side. The beam

specimens (B-3) and (B-4) are poured with varying depth of (250mm) at right hand

side and decreased gradually to (175mm) and (150mm) at left hand side respectively,

Table (2-1) shows the details of tested beams.

Table (2-1) Beams Designation and Details

Beam Dimensions (mm) Reinforcement Depth (mm)

Designation bw h l Flexural Shear Left Right

(B-1)*

140 variable 1220 2 16 mm None

250 250

B-2 200 250

B-3 175 250

B-4 150 250

*Reference Beam

2-3- Materials

In manufacturing the test specimens, the properties and description of used materials

are reported and presented in Table (2-2).

Tensile test of steel reinforcement (manufactured in Ukraine) was carried out

on (ϕ16mm) hot rolled, deformed, mild steel bar employed as tension reinforcement.

Tables (2-3) show the results of tensile test for bars.

Variable

2 16 mm 140 mm

1220 mm

2 16 mm

1100mm


8

Table (2-2) Description of Construction Materials

Material Descriptions

Cement* Ordinary Portland Cement (Type I)

Sand**

Natural sand from Al-Ukhaider region with maximum size of (4.75mm)

Gravel**

Crushed gravel with maximum size of (19mm)

Water Clean tap water (Used for Both Mixing and Curing)

* Conform to Iraqi specification No. 45/1989. ** Conform to Iraqi specification No. 45/1984.

Table (2-3) Properties of Steel Bars

Nominal Diameter

(mm) Bar Type

fy*

(MPa)

fu

(MPa)

Es**

(GPa)

Elongation

%

16 Deformed 491 653 200 16

*Each value is an average of three specimens (Each 40 cm length) **ACI 318-M08

2-4-Concrete Mix design

One concrete mix was used in this work; the concrete mix proportions are reported

and presented in Table (2-4) below. It was found that the used mix produces good

workability and uniform mixing of concrete without segregation.

Table (2-4) Mix Proportion

2-5- Molds

One wooden mold containing four boxes, (1220x140xvariable ) dimensions are

used to poured beam specimens, see Figure (2-5). The molds were manufactured with

(18mm) thick plywood base and four movable sides. The sides were fixed to the base

by screws. When the mixing process was completed, the beam and control

specimens were then cast in three layers and compacted by a table vibrator (external

vibrator) to shake the mix and consolidate it into the molds. The surface of the

concrete (top face of control specimen and side face of beam specimens) was leveled

Parameter Quantity

Water/cement ratio 0.4

Water (Liter/𝑚3) 140

Cement (kg/m3) 350

Fine Aggregate (kg/m3) 700

Coarse Aggregate (kg/m3) 1000


9

off and finished with a trowel. Then, the specimens were covered with a nylon sheet

to prevent evaporation of water. It may be noted that, to ensure that it would be easy

to remove the samples when the concrete hardened, the inner faces of molds was

oiled.

Figure (2-5) plywood Mold

Figure (2-6) Steel Reinforcement Inside the Mold

2-6- Test Measurements and Instrumentation

Hydraulic universal testing machine (MFL system) was used to test the beams

specimens as well as control specimens. Central deflection has been measured by

means of (0.01mm) accuracy dial gauge (ELE type) and (30mm) capacity. The dial

gauges were placed underneath the bottom face of each span at mid.


10

Figure (2-7) Universal Testing Machine

2-7- Concrete Mixing and Placing (Pouring)

2-7-1- Concrete Mixer and Vibrating Table

The concrete was mixed by using a horizontal rotary mixer with (0.19 m3)

capacity. The vibrating table consists of (1.0x1.5m) table made of (10mm) thick steel

plate. The source of vibration was a rapidly rotating eccentric weight which makes

the table vibrates with a simple harmonic motion. The vibrator was manufactured by

Marui Company, Japan. The frequency of vibration was (7000rpm).

Figure (2-8) Concrete Mixer


11

2-7-2- Curing and Age of testing

After (24) hours, the beam specimens and control specimens were stripped

from the molds and cured (kept) in water bath for (28) days with almost constant

laboratory temperature. Before (24) hours from the date of testing, they were taken

out of the water bath and tested in accordance with the standard specifications.

Figure (2-9) Beam Specimen Stripping

Figure (2-10) Beam and Control Specimen Curing

2-8-Test Results of Control Specimens

Test results of mechanical properties of control specimens (compressive

strength) are summarized in Table (2-5). Compressive strength for cubes ( fcu) was


12

carried out on concrete in accordance with BSI 881-116 with standard cubes

(150x150x150 mm). The cubes were loaded uniaxially by the universal compressive

machine up to failure.

Table (2-6) Mechanical Properties of Concrete

Property (MPa) Value (MPa)

Cube compressive strength (fcu) * 24

Cylinder compressive strength ( '

cf )**

20.4

*Average of three samples. **'

cf =0.85 fcu

2-9- Test Procedure

All beam specimens were tested using universal testing machine (MFL system)

with monotonic loading to ultimate states. The tested beams were simply supported

over an effective span of (1100mm) and loaded with a single-point load; Figure (2-

11) shows the setup of beam specimens. The beams have been tested at ages of (28)

days. The beam specimens were placed on the testing machine and adjusted so that

the centerline, supports, point load and dial gauge were in their correct or best

locations.

Figure (2-11) Beam Specimen Setup

Loading was applied slowly in successive increments. At the end of each load

increment, observations and measurements were recorded for the mid-span deflection

and crack development and propagation on the beam surface. When the beams

reached advanced stage of loading, smaller increments were applied until failure.

They fail abruptly without warning (sudden failure) and the diagonal cracks that


13

develop becomes wider and as a result, the load indicator stopped recording anymore

and the deflections increased very fast without any increase in applied load. The

developments of cracks (crack pattern) were marked with a pencil at each load

increment.

Chapter three Theoretical work

14

Chapter three

Theoretical work


15

Chapter three

Theoretical Work

3-1-Shear Strength of RC Sections Based on ACI-318 Code

According to ACI-318 Code, the nominal shear strength of RC members can be

calculated by using the following equation:-

Vn=Vu/ϕ=Vc+Vs ……………..Eq.(1)

Where

Vu = ultimate shear strength.

Vc= shear strength of concrete.

Vs= shear strength of transverse reinforcement

ϕ = shear reduction factor

3-2-Shear Strength of Concrete Solid Sections (Vc)

According to ACI-318 Code, the shear strength of solid concrete member can be

calculated by using the following equation:- 𝑉c = 𝜆 16 √𝑓𝑐′ 𝑏𝑤. 𝑑 ……………..Eq.(2)

Where:

= Cylinder Compressive Strength of Concrete=20.4 MPa

bw = Beam Width=140 mm

d = Effective depth of Beam

λ = Modification factor

=1.0 (For normal strength concrete)

=0.85 (For sand lightweight concrete)

=0.75 (For lightweight concrete)

For beam specimen (B-1)(Prismatic beam), the shear strength is:- 𝑉c = ∗ √ . ∗ −3 = . 𝑘𝑁

'cf


16

For beam specimen (B-2), daverage=250mm, the shear strength is:- 𝑉c = ∗ √ . ∗ −3 = . 𝑘𝑁



Table (3-1) Shear and Ultimate Strength

Beam Designation Shear Strength (kN) Ultimate Capacity (kN)

B-1 27.4 54.8

B-2 26.35 52.7

B-3 21.08 42.16

B-4 17.92 35.84

Chapter four Results and Discussion

17

Chapter four

Results and Discussion


18

Chapter four

Results and Discussion

4-1- Introduction

As mentioned before, the main objective of this project is to examine or assess

the structural behavior of reinforced concrete varying depth beams.

During the experimental work, ultimate loads, load versus deflection at

mid-span for each beam were recorded. Photographs for the tested beams are

taken to show the crack pattern and some other details. The recorded data,

general behavior and test observations are reported to analyze and understand

the effects of adopted parameters on behavior.

4-2- General Behavior

Photographs of the tested beams are shown in Figure (4-1) and test results

are given in Table (4-1). All beams were designed to fail in shear, which was

characterized by sudden failure and diagonal wide cracks which extended from

supports towards the load or openings locations.

The general behavior of the tested beams can be described as follows; at

early stages of loading, small vertical deflection initiated in the mid span of

tested beams, with further loading, diagonal cracks extended upwards and

became wider in shear span. One or more cracks propagated faster than the

others and extend through weak locations in the beam (little depth) and reached

the compression face (near applied load), where crushing of the concrete near

the positions of applied loads had occurred due to high concentrated stresses

under load.


19

Figure (4-1) Crack Patterns of Tested Beams

B-1

B-2

B-3

B-4


20

4-3- Mode of Failure

The appearance of the cracks reflects the failure mode for the tested

beams. The experimental evidences show that the diagonal cracks extended

from supports towards the load, the failure take place due to diagonal tension

cracks were formed diagonally and moved up and towards the position of load,

this crack is associated with crushing of the concrete near the positions of

applied loads, this mode of failure is called “Shear-Compression” failure, as

shown in Figure (4-1).

4-4- Ultimate Shear Strength (Vu)

The recorded ultimate loads of the tested beams are presented in Table (4-1). As

expected, test results show that the reference beam (B-1) has the maximum

ultimate strength in comparison with the rest beams.

Table (4-1) Ultimate Shear Strength of Tested Beams

Beam

Designation

Pu

(kN)

Pc

(kN)

Vu *

(kN)

Pc/Pu

(%)

Pu/PuR

(%) Mode of Failure

B-1 80 32 40 40 1.00 Shear-Compression

B-2 75 26 37.5 35 0.94 Shear-Compression

B-3 62.5 21 31.25 34 0.78 Shear-Compression

B-4 40 17 20 43 0.50 Shear-Compression

*Vu =Pu/2

As shown in Table (4-1), the ultimate shear strength decreased when the depth

of tested beams decreased (in shear span) and when we moved toward of and

closes up to the support.

4-5- Deflection

Load-deflection curves of the tested beams at mid-span at all stages of

loading up to failure are constructed and shown in Figures (4-2).

As shown in Figure (4-2), at the beginning, all curves are identical and

the tested beams exhibited linear behavior and the initial change of slope of the


21

load-deflection curves occurred between (10 kN to 30kN), which may be

indicated the first crack loads. Beyond the first crack loading, each beam

behaved in a certain manner. Behavior of reference Beam (B-1) exhibited

greater loads and deflections in comparison with the other beams. This beam

had the greatest stiffness due to uniform section.

Load-deflection curves for the tested beams (B-2, B-3 and B-4) exhibits smooth

increase in both applied loads and deflections. Gradual reduction in depth

caused decreasing in the load carrying capacity beyond the first cracking, this

associated with reduction in beams stiffness and this is reflected on the

corresponding deflections (excessive deflection).

Figure (4-2) Load-Deflection Relationship of Tested Beams

4-6- Comparison between Experimental Results and ACI-318

The ACI-318 empirical equation can be used directly to calculate shear

strength of solid sections, see (chapter three). Comparison between experimental

results and ACI-318 are reported and presented in Table (4-2). The analytical

0

10

20

30

40

50

60

70

80

90

0 0.5 1 1.5 2 2.5 3

B-1

B-2

B-3

B-4

Deflection (mm)

Load

(k

N)


22

results indicated that the calculated values are underestimated in comparison

with the experimental results.

Table (4-2) Experimental and Calculated Shear Strength

Beam Designation Vu (kN) (Vu)Exp./ (Vu)ACI

(%) Exp. * ACI-318**

B-1 40 27.4 1.46

B-2 37.5 26.35 1.42

B-3 31.25 21.08 1.48

B-4 20 17.92 1.12

*Table (4-1) **Chapter three

Chapter five Conclusions and Recommendations

23

Chapter five

Conclusions and Recommendations

Chapter five Conclusions and Recommendations

24

Chapter five

Conclusions and Recommendations

5-1-Conclusions

Based on the results obtained from the experimental and theoretical work, the

following conclusions are obtained:-

1- Since the beam specimens are poured without shear reinforcement, all beams were

failed by shear.

2- The ultimate shear strength decreased for about (6-50%), when the depth of tested

beams decreased and when we moved toward of and closes up to the smallest depth

near support.

3- The cracking load are varied between (34-43%) from the ultimate load.

4- The ACI-318 empirical equations can be used directly to determine shear strength

based on concrete section only (taking into account absent of web reinforcement).

The analytical results indicated that the calculated values are underestimated in

comparison with the experimental results.

5-2- Recommendations

1-Same experimental program can be adopted by using other types of concrete, such

as high strength concrete or steel fiber reinforced concrete.

2- Same experimental program can be adopted by using two point loads.

3- Same experimental program can be adopted by using repeated load

References

23

References

[1]-Ruaa Y. Hassan, "Shear Behavior of RC Deep Box Beams Strengthened

Internally by Transverse Ribs", M.Sc. Thesis, College of Engineering, Civil

Engineering Department, Al-Mustansiria University, Baghdad, Iraq, 2015.

[2]- Vanissorn V. et al, "Reinforced Concrete Beams with Lightweight Concrete

Infill", Scientific Research and Essays Vol. 7(27), pp. 2370-2379, 19 July, 2012.

[3]- Iraqi Specifications No. (5), “Portland Cement”, the Iraqi Central Organization

for Standardization and Quality Control, Baghdad-Iraq, 1984.

[4]- Iraqi Specifications No. (45), “Aggregates from Natural Sources for Concrete

and Building Construction”, the Iraqi Central Organization for Standardization

and Quality Control, Baghdad-Iraq, 1984.

[5]- ACI Committee 318,2008, "Building Code Requirements for Structural

Concrete (ACI 318-08 M) and commentary (318R-08)", American Concrete

Institute, Farmington Hills, MI, USA, 430pp.

[6]- ASTM C 1386-07. "Standard Specification for Precast Autoclaved Aerated

Concrete (AAC) Wall Construction Units", ASTM International, PA.

[7]-ACI Committee 530, 2008, "Building Code Requirements and Specification for

Masonry Structures (AC1-530-08)", American Concrete Institute, Farmington

Hills, MI, USA.

[8]- BS1881-116, "Method for Determination of Compressive Strength of Concrete

Cubes", British Standards Institute, London, 1983.

جمهورية العراق وزارة التعليم العالي والبحث العلمي

الجامعة المستنصرية ةــلية الهندســك

ا عت ص ل و ال رساني س تغير ال ق ال ا الع ح س ال

) ري ت راس م (

ع الم مشر

س ن نيـــقسم ال سـ ال ن ي ال ء من مـــ في ك ستنصري كج ا /الجامعـــ ال ا نيل ش تط

وريو ك نيـــال ســــ ال ن في ال

راسي ) (2016-2015العا ال

ل الط من ق

مح حسين ع الله عائش اركا مح

باشراف

. . يــــأ. يـــــــ عـ ـــــي ح عـ

هجر 1437 ميلا 2016

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Shear Behavior of Reinforced Concrete Varying Depth Beams