STUDIES ON BRICK AND RCC COMPOSITE BEAMS BY
USING METHOD OF INITIAL FUNCTION
Piyush Kumar1
1
P.G. scholar, Department of Civil Engineering, M.M.M.U.T. Gorakhpur-273010
Email Id: Piyushkumar199126@gmail.com
Arvind Kumar2
2
Lecturer, Department of Mechanical Engineering U.N.S.I.E.T.
V.B.S.Purvanchal University, Jaunpur-222011
Email Id: arvind28309@gmail.com
ABSTRACT
This paper present carried out on composite beams of RCC and Brick. In reinforced
concrete beams, near the neutral axis less stressed concrete replaced by bricks. The
concrete just above the neutral axis is less stressed and below the neutral axis concrete
work as a shear transmitting media. In this study partially utilized concrete of RCC beam
has been replaced by bricks in order to reduce the weight of structure and also achieve the
economy, and by reducing concrete we have to save cement and by saving cement reduced
the greenhouse gases emissions. So it is environment friendly. RCC and brick beams act
like a composite beams.
The brick replacement zone in composite beams is found out with the help of stress-strain
block diagram, given in IS456:2000 used for limit state design of RC beams. We have
method of initial function for analysis of brick and RCC composite beams.
KEY WORDS: Brick filled, RC beams, method of initial function, composite beams
I.
INTRODUCTION
Beams which are built of more than single material are called composite beams. Examples
are sandwich beams, reinforced concrete beams and bimetallic beams, which consist of two
different metals bonded together. Brick and RCC composite beams an attempt is being made to
reduce the weight and cost of reinforced concrete beams, replacing concrete by lightweight
materials like brick near the neutral axis. The behaviour of brick and RCC composite beams is
same to that of reinforced concrete beams. Looking to the limitation of this types of structure is
that bond in between brick zone and concrete layer at the brick concrete interface should be good
and ensured having no slip occurs in between layers. In brick and reinforced concrete composite
types of structure large depth of section obstructs the head room requirements. In such condition
RCC beam is one of the alternatives, however, in RCC beams strength of concrete lying near the
neutral axis is not fully utilized so partially utilized concrete in reinforced concrete beam and
concrete has been replaced by bricks near the zone of neutral axis.
Experimental work is conducted on the brick and reinforced concrete composite beam and shows
the stresses in beams are maximum at bottom and top and zero at the neutral axis zone. So a
cheap material like brick can be used near the neutral axis zone. Behaviour of this types of beam
under the cyclic loading is determined and examine to find out similarity with conventional
reinforced concrete beams. The experimental work was perform to obtained a stress-strain curve
for masonry and found the Poisson’s ratio of the masonry and splitting tensile strength of bricks.
The examine work was conducted on beams with light weight brick core with Ferro cement form
and observed that beam to accomplish higher ultimate load when welded wire mesh is used in
Ferro cement forms(Ezzat et al.2005).
Method of initial function is used to analysis of reinforced concrete and brick composite beams
and also free vibration of rectangular beams of arbitrary depth. This method is also used for study
the composite beams under uniform and symmetric central loading and study behaviour of
concrete beams.
II.
BRICK REPLACEMENT ZONE
The replacement zone of brick in composite beam can be calculated by help of stress block
diagram, given in IS456:2000 used for limit state design of RC beam. The replacement zone in
RC beam, is near the neutral axis which is less stressed zone.
Brick Replacement Zone in reinforced concrete Beams
By equating total tension to total compression,
Xu = (0.87 fy. Ast)/ (0.36fck.b)
Xu = depth of neutral axis
Ast= Area of tension steel
…………………
(1)
Depth of parabolic portion of stress block=
[ 0.0020/0.0035].xu= 4/7xu
depth of rectangular portion of stress block=
[0.0035-0.0020/0.0035]xu= 3/7xu
d = (2 x cover + diameter of bar)
(2)
d’ is the thickness of concrete layer available to maintain bond between steel and concrete. It is
assumed the provision of thickness of concrete not less than the cover provided on each side of
the tension reinforcement will satisfy the bond requirement.
Xb =(4Xu/7)√ {1- (fbk/fck)}
(3)
dmin = 3Xu/7+Xb
(4)
dmax = D-d’
Brick replacement zone = dmax-dmin
III.
(5)
ANALYSIS OF COMPOSITE BEAM USING MIF
The reinforced concrete and brick composite beams are examine by using method of initial
function and it is an analytical method of elasticity theory. This method makes it possible to
found exact solution of different types of doubts without taking any assumption about the
character of stress and strain. The order of governing equation depends upon the stage at which
the series representing the stress and displacement are truncated. According to MIF, the basic
desired functions are the displacement and stress, the system of differential equation which is
found from equation of Hooke’s law and equilibrium equations by replacing stresses by the
displacements by using elasticity relations.
In brick and rcc composite beam loaded at the top surface, the state of stresses and displacement
at free bottom surface of the beam is given by;
(6)
(7)
Let
where, uT , vT ,YT and XT are the values of stresses and displacements at the top surface of the
composite beam.
Relating the stresses and displacements at the top surface of the layer to those at the bottom
surface by successive application of the transfer matrix [Li] across each layer, one obtains
where, The terms of the matrix [B] are evaluated after expending the exponential in the form of
series
The terms of matrix [B] are determined after expending the exponential in the form of series. The
equation (8) relates the boundary conditions at the bottom surface and it is useful for deriving
governing differential equations for a layered beem having a particular number of layer.
The method adopted for analyzing layered beams involves the determination of initial
functions at the bottom surface of the beam by relating them through the matrix [A] to the
stresses at the top surface.
The matrix has a form
(10)
Application of MIF
Reinforced concrete and brick composite beam consists of the three layers. Top and
bottom layers are of concrete and middle one is of brick. The area of reinforcement below the
brick replacement zone is also changed into the equivalent area of concrete using modular ratio .
Therefore the matrix [B] becomes
(11)
Where h1, h2 and h3 are the thickness of three layers.
h1 and h3 are the thickness of concrete layers, and h2 is the thickness of brick layer. The
conditions at top are given by:
(12)
Substituting the expressions (6) and (10) in the equations (8) we get:
(13)
(14)
These equations are exactly satisfied by,
(15)
(16)
(16)
Where ∅ is an unknown auxiliary function substituting the value of u1 and v1 from the
equations (15) and (16) in the equation (9), the differential equation governing the problem of
Brick and reinforced concrete composite beam is obtained:
(17)
The order of the governing differential equation (12) depends on the order of the terms in the
matrix [B].
The auxiliary function is chosen such that it satisfies the governing differential equation
as well as the boundary conditions at the edges of the beam. Initial functions are
found from equations (15) and (16). By operating on the initial functions by the transfer
matrix [Li] successively across every layer, we can obtained the stresses and displacements,
within the entire beam.
Analysis of brick and rcc composite beam
Consider a brick and rcc composite beam having three layers of thickness, h1and h3 are the
concrete layers and h2 of brick layer.
Geometry of beam section
The following values of beam dimensions are chosen for the particular problem.
h = 500mm, b =250mm,
l=5000mm, h1 =70mm,
h2 =260mm, h3=170mm
The following material properties
are taken:
For concrete layers,
E = 22000 N/mm2
μ = 0.20
G = 9200N/mm2
For brick layer
E = 5000 N/mm2
μ = 0.17, G = 2200 N/mm2
where,
E - Young’s modulus of Elasticity
G - Shear modulus of Elasticity
μ - Poisson’s ratio
Loading and boundary condition
The following condition of the simply supported edges are;
X = Y = v = 0, at x = 0 and x = l
The boundary conditions are exactly satisfied by the auxiliary function.
A1sin (
)
IV.
RESULT AND DISCUSSION
A sinusoidal normal loading is assumed, on the top surface of the beam:
P(x) = -P0 sin ( )
Taking P0 = 100N/mm and x = l/2
The value of auxiliary function is obtained from equation (17), using this value of auxiliary
function the values of initial functions u1 and v1 are obtained from equation. (15) and (16).
These values of u1 and v1 are substituted in expression (8) for obtaining the values of
stresses and displacements.
Y = -100.0 N/mm2 X = 0
V.
CONCLUSION
By saving concrete it saves cement and reduces the greenhouse gases and makes the environment
green. Presence of bricks in less stressed zone has not a significant reduction in strength of
reinforced concrete and beams.
Concrete is replaced by brick in beam. By this replacement reduction in weight is achieved.
Saving of cost is directly proportional to the percentage replacement of concrete.
It has been examine that the replacement of concrete by bricks in reinforced concrete beams does
not require any extra labour and time.
VI.
REFERENCE
[1] Gupta, M. and Pandey, A.K., 2012. Experimental studies on brick masonry in
compression , Indian Concrete Journal, Vol.86 (1), p. 43-50.
[2] Iyengar, KTS, Chandrashekhara K and Sebastian V.K., 1974.Thick Rectangular Beams,
Journal of the Engineering Mechanics Division, Vol.100 (6), p.1277-1282.
[3]
Iyengar, KTS and Pandya, S.K. (1986), Application of the method of initial functions for
the analysis of composite laminated plates. In: Archive of Applied Mechanics, Vol.56 No.6,
and pp. 407- 416.
4] Arulselvan S, K Subramanian, Pillai P E B , Santhakumar A R(2007) RC Infilled frame- RC
plane frame interactions for seismic resistance, J Applied sciences,7(7): 942-959.
[5] Gupta M and Pandey AK (2012) Experimental studies on brick masonry in compression,
Indian Concrete Journal, 86(1): 43-50.
[6] Iyengar KTS, Chandrashekhara K, Sebastian VK (1974) Thick Rectangular Beams, J
Engineering Mechanics Division, 100(6):1277-128