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INTERMEDIATE THESIS REPORT

ON

EXPERIMENTAL AND ANALYTICAL INVESTIGATION ON

BEHAVIOUR OF DEEP BEAMS

GUIDED BY: SUBMITTED BY:

Prof. THOMAS PAUL PRASANTH NAIRC

ASSOCIATE PROFESSOR IN CIVIL ENGINEERING S4 M TECH (CASE)

M A C E M A C E

INTRODUCTION


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Deep beam is a beam having Span/ depth ratio such as less than 2 for simply

supported beams and less than 2.5 for continuous beams. Because the geometry of deep beams,

they behavior is different with slender beam or intermediate beam.Concrete structural members

having depth comparable to the span are generally termed as deep beams. In these members, the

distribution of strain across the depth of the cross section is nonlinear and a significant amount of

load is carried to the supports by a compression strut joining the load and the reaction.

Structural members can be broadly divided into two regions, namely, B (or

Bernoulli) regions where the strain distributions are linear, and D (or Disturbed) regions where the

strain distributions are non linear. While well defined theories are available for designing B

regions, thumb rule or empirical equations are still being used to design D regions, though B and D

regions are equally important. The design procedure for deep beams recommended by IS456:2000 is empirical in nature and based on the experimental investigations conducted by

Leonhardt and Walter at University of Stuttgart. It has been recently understood that the Strut

Tie- Method (STM) is an effective tool for the design of both B and D regions. Also, the STM

provides design engineers with a more flexible and intuitive option for designing structural

elements. The main objective of this study is to highlight the STM concept as a powerful design

concept for the analysis and design of concrete deep beams.

BEHAVIOUR OF DEEP BEAM

The followings are the major difference of deep beams compared with ordinary beam based on the

design assumption, as follows:

1. Plane Section do not remain plane, the assumption of plane section remain plane cannot be

used in the deep beam design.

2. The strain distribution is not longer linear. Shear Deformation, the shear deformation

cannot be neglectedas in the ordinary beam.

3. The stress distribution is not linear even in the elastic stage.

OBJECTIVES OF STUDY


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The objective of study is to investigate the behavior of RC deep beams by means of Strut- Tie-

Method along with analytical simulation. The reinforced concrete deep beams have become an

important structural elements having small span-to-depth ratio. The investigation of their behavior

is a subject of considerable interest in RC structural researches. Several different failure modes

have been identified from experimental studies, due to variability in failure, the determination of

their strength and identification of failure mechanism are very complicated.

It has been recently understood that the Strut Tie- Method (STM) is an effective tool for the

design of deep beams.

The objectives of investigations are,

To Study and suggest for the strength and efficiency factor of Struts in the Strut-Tie Model

for structural concrete.

To study the strength and deformations of struts when micro fiber reinforced concrete is

used which has improved dispersion characteristics.

To study the different characteristics of both RC and FRC deep beams analytically.

SCOPE OF STUDY


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Regions of reinforced concrete elements can be divided into two regions, namely, B or Bernoulli

regions, where the strain distributions are linear and D or disturbed regions, where the strain

distributions are nonlinear. Deep beam belongs to D regions. It has been recently understood that

the strut and tie model (STM) is an effective tool for the design of both B and D regions. The

present codal recommendations are inadequate for the design of deep beams. The STM approach

is not described in detail in the current IS 456:2000 code of practice for plain and reinforced

concrete. The concrete members with fiber reinforced concrete have improved dispersion property which

will control the bulging of concrete. But we had no codal recommendations for the same. So

The scopes of study are,

1. To recommend Strut- and -Tie Merhod of design of RC deep beams.

2. To highlight the concept of micro FRP concrete deep beams.

LITERATURE REVIEW

Concrete structural members having depth comparable to span are generally termed as deep beams.

In these members, the distribution of strains across depth will be non linear and thus these

structural elements belong to D regions, which have traditionally been designed using empirical

formulae or using past experience. Strut-Tie Model offers an alternative to such empirical methods.

Strut- Tie Method (STM)

In the Strut and Tie Method, a reinforced concrete member is replaced by a system of truss

members that can resist the applied loads. For analytical purposes, the strut and tie models

condense all stresses in compression and tension members and join them by nodes. These models

are generally used for the analysis, design and detailing of D regions, such as vicinities of point

loads, frame corners, corbels and also where sudden changes in cross section occurs.


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The STM is based on the lower bound theory of plasticity. Therefore, the actual capacity of the

structure is considered to be equal to or greater than that of idealized truss. Hence designs done

using this method will always be on the safer side.

Fig.1. STRUT TIE MODEL OF DEEP BEAM

Struts

Struts are compression members in the STM. These represent concrete stress fields whose

principal compressive stresses predominantly acting along the centerline of the strut. Struts are

often idealized as prismatic or as bottle shaped elements.

Fig.2. Different types of Struts

Ties

Ties are tension members and represent the reinforcing steel.


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Node

Nodes in STM are the intersection points of three or more straight struts and ties. These are

analogous to joints in real truss. Depending on the nature of forces, nodes can be classified as

CCC, CCT, CTT, TTT nodes. C is the compression force and t is used to denote the tension force.

Fig.3. Different types of nodes

The design procedure using STM involves five major steps as

Identify the D region.

Sketch the truss and determine the equivalent boundary loads and analyse the truss to get

the member forces.

Evaluate the dimensions of the struts and nodes, such that, the capacities of the struts and

nodes are sufficient to carry the member forces.

Provide sufficient steel reinforcement for the required tie capacity and ensure that this

reinforcement is properly anchored.

Provide distributed reinforcement to ensure ductile behaviour of the D region.


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THE ANALYSIS MODEL


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D =2000mm

L= 3000mm

L/D = 3000/2000= 1.5


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By intuitively considering the mode of load transfer to the supports in the case of a continuous

deep beam, a truss model consisting of a network of struts and ties intersecting at nodes, can be

built up. The deep beam under consideration can be assumed to be made up of a primary negative

moment truss and a primary positive moment truss as presented in Figure.


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Both these trusses superimposed upon each other give a strut-and-tie model for the continuous

deep beam,

2. LOADS AND MATERIAL PROPERTIES

The loads, spans and dimensions of the deep beam selected for analysis are presented in Figure.

Design vertical load = 1500 kN and 2000 kN at mid-spans of both spans,

Characteristic cube compressive strength of concrete (assumed) =fck= 30 MPa

Take cylinder compressive strength =fc = 0.80fck= 24 MPa

Yield strength (0.2% proof stress) of reinforcement bars (assumed) =fy = 415 Mpa

The strut and tie model is analyzed in software CAST. The analysis of the strut tie model will

give the support reaction and the member forces. Using these forces, we can design the deep beam

with strut - tie method.


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3. DETERMINATION OF TRUSS FORCES

The analysis model in CAST is,

After analysis the forces are,


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4. DESIGN OF BEARING PLATES

The bearing plates are to be provided at the loading points and at the supports. The reactions are

determined as 625 and 875kN at the exterior supports and 2000kN at the interior support.

The sizes of the bearing plates are to be determined next. The bearing plates at the points of

application of the loads will be resting above the underlying C-C-T (Compression-Compression-

Tension) nodes of the strut-and-tie model. The bearing stresses exerted by the bearing plates on the

faces of the underlying nodes should be less than the permissible bearing stresses for these nodes.

Similarly, the bearing plates at the support locations are below the overlying C-C-T nodes of the

strut-and-tie model and the bearing stresses at the faces of these nodes should be less than the

permissible bearing stresses for these nodes. Assume the size of all the bearing plates as 600 x 500

mm each. Since the interior support carries the maximum reaction, the adequacy of the assumed

size of the bearing plates is checked for this support and if found safe, the same size of the bearing

plates is provided at the two exterior supports.

Hence, the bearing stress at the interior support is = 2000x103/600x500 =6.67 MPa

As per Clause A.5.2 eq. (A-8) ACI318-02, the effective compressive strength of a C-C-T node


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fcu = 0.85nfc . As per Clause A.5.2.3 of [3] for a C-C-T node anchoring two or more ties

(T), n = 0.60.

Hence,fcu = 0.85 0.60 24 = 12.24 MPa

The allowable bearing stress = fcu , where is the strength reduction factor, which for

strut-and-tie models, as per Clause 9.3.2.6 of ACI318-02 = 0.75

Hence, the allowable bearing stress = fcu = 0.75 12.24 = 9.18 > 6.67 MPa, ok.

Hence, the selected size of the bearing plates is adequate.

Provide bearing plates of size 600500 mm at all the supports and at the loading points.

5. DESIGN OF TIES

The tie capacity is furnished by steel reinforcement and concrete is not assumed to carry any

tensile loads.

The area of reinforcement required for a typical tie is equal to Ast = Ft/ y where Ft is the tensile

force in the tie and y is the permissible tensile stress in the steel reinforcement and is equal to fy.

The strength reduction factor, , for the reinforcement yield stress fy, is taken as 0.75 as per

recommendations of Clause 9.3.2.6.

Therefore, the area of reinforcement required for tie BC = FBC/y = 202.6x103/0.75x415

= 650 mm2

Provide 4 nos. of 16 mm diameter bars for the tie BC. Area of steel provided = 804mm2>650 mm2,

ok.

The area of reinforcement required for tie AE = FAE/y = 506.8x103/0.75x415 = 1628 mm2

Provide 9 nos. of 16 mm diameter bars for the tie AE. Area of steel provided

1809 mm2> 1607.71 mm2,ok.


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The area of reinforcement required for tie DE = FDE/y = 709.5x103/0.75x415 = 2280mm2

Provide 12 nos. of 16 mm diameter bars for the tie DE. Area of steel provided = 2412 mm 2 > 2280

mm2, ok.

To ensure continuity of reinforcement in the bottom tie at the node E, the reinforcement in the tie

AE is changed to 12 nos. of 16 mm diameter bars.

As per Clause 11.9.5 [3], the minimum required area of tensile reinforcement in any tie =

=.04(fc/fy)bd=0.04(24/415)x500x1925=2226.5mm2

The minimum amount of reinforcement is required to prevent the possibility of sudden failure

under the action of flexural moment. The area of reinforcement provided in the ties BC (804 mm 2)

and AE (1809 mm2) is less than the minimum. Hence, provide 12 nos. of 16 mm diameter bars in

each of the ties BC and AE. Area of steel provided = 2412 mm2 > 2226.50 mm2.ok.

7. CHECK ON STRUTS

The check on struts involves determination of strut widths required to shoulder the computed strut

forces and to determine whether the required strut widths fit within the geometry of the structure.

The effective compressive strength of the concrete in all the struts is limited to fcu wheref'cu =

0.85s f'c; the parameters being taken equal to 0.75 as per Clause A.3.2.2 of ACI318-02. For this

value ofs, it will be necessary to provide reinforcement suitably proportioned to resist the

transverse tensile force resulting from the spreading of the compression force in the concrete struts.

Therefore, fcu = 0.75 0.85 0.75 24 = 11.47 MPa.

Hence, the required width for strut AB = FAE/ fcub = 804.7x103/11.47x500 = 140.31mm. Choose a

width of 150 mm for strut AB.

Hence, the required width for strut BE = FBE/ fcub = 1126.4x10

3

/11.47x500 = 196.40 mm. Choosea width of 200 mm for strut BE = CD

Hence, the required width for strut CE = FCE/ fcub = 1448.3x103/11.47x500 = 252.31mm. Choose

a width of 260 mm for strut AB.

As can be seen in Figure 10, all the strut widths fit within the geometry of the beam and thus the

proposed strut-and-tie model is acceptable.


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VALIDATION OF STRUT AND TIE MODEL DESIGN USING SOFTWARE CAST

The deep beam is designed using the strut tie method. This design is validated with the software

CAST. CAST is good software for the design of D regions using strut- tie model method.

Details

Strut width As per the design

Strut type ACI Prismatic

Tie reinforcement- As per the design, 12 no.s of 16mm dia bars.

Tie reinforcement type non pre stressed reinforcement

Bearing plate- 600mmx500mmx220mm

The stress ratio, (stress produced/permissible stress)


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When ACI bottle shaped with steel, struts used,

The stress ratio, (stress produced/permissible stress),


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REFERENCES

1. Abolfazl Arabzadeh, Reza Aghayari, Ali Reza Rahai Investigation of

experimental and analytical shear strength of reinforced concrete deep beams,

International Journal of Civil Engineering.

2. Mohammad Reza Salamy, Hiroshi Kobayashi and Shigekiunjoh Experimental

study on RC deep beams.

3. Y K Sabapathy, Dr. K Nagamani Experimental and analytical study on GFRP

deep beams.

4. P Nagarajan, Dr T M M Pillai, Dr N Ganesan Design of Simply Supported Deep

Beams using IS456: 2000 and Strut and Tie Method.

5. P Nagarajan, Dr T M M Pillai Strut and Tie Model for Continuous Deep Beam:

Analytical and Experimental Studies.

6. D K Sahoo, R K Gautam, B Singh, P Bhargava Strength and Deformation

Characteristics of bottle Shaped Struts.magazine of Concrete Research, IIT

Rourkee

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