Date post: | 04-Apr-2018 |
Category: |
Documents |
Upload: | sanjaymits2 |
View: | 222 times |
Download: | 0 times |
of 37
7/29/2019 seminar on shear connectors
1/37
CHAPTER 1
INTRODUCTION
1.1General:-
The design of structures for bridges is mainly concerned with provision and support of
horizontal load bearing surfaces. Except in long span bridges, these floors or decks are
made up of reinforced concrete, since no other material have better combination of low
cost, high strength and resistance to corrosion, abrasion and fire.
In conventional composite construction these concrete slabs rest over steel beams or box
girders and supported by them. Under load these two components act independently and a
relative slip occurs at the interface if there is no connection between them.
At spans of more than about 10 m, and particularly where the susceptibility of steel to
damage by fire is not a problem, as for example in bridges and multi-story car parks, steel
beams become cheaper than concrete beams.
It used to be customary in design the steel work to carry whole weight of concrete slab
and loading on it; but by about 1950 the development of shear connectors had made it
practicable to connect the slab to the beam, and so as to obtain the T-Beam action.
Concrete is stronger in compression than in tension and steel in susceptible to buckling in
compression. By composite action between the two, we can utilize their respective
advantages to the fullest extent.
In composite members, the structural steel component is usually built first, so a
distinction must be made between load resisted by steel component only, and load
applied to the member after concrete has developed sufficient strength for composite
action to be effective. The division of dead load between these two categories depends
upon method of construction. Composite beams and slabs are classified as propped or
unpropped. In propped construction, the steel member is supported at intervals along its
length until the concrete has reached a certain proportion, usually three-quarters, of its
1
7/29/2019 seminar on shear connectors
2/37
design strength. The whole of the dead load is then assumed to be resisted by composite
member. Where no props are used, it is assumed in elastic analysis that the steel member
alone resists its own weight and that of the formwork and the concrete slab.
1.2 Advantages associated with composite construction:-
The most effective utilization of steel and concrete is achieved.
Keeping the span and loading unaltered; a more economical steel section (in
terms of depth and weight) is adequate in composite construction compared
with conventional non-composite construction.
As the depth of beam reduces, the construction depth reduces, resulting in
enhanced headroom.
Because of its larger stiffness, composite beams have less deflection than steel
beams.
Composite construction provides efficient arrangement to cover large column
free space.
Composite construction is amenable to fast track construction because of
using rolled steel and pre-fabricated components, rather than cast-in-situ
concrete. Encased steel beam sections have improved fire resistance and corrosion.
1.3 Shear connection:-
The established design methods for reinforced concrete and for structural steel give no
help with respect to basic problem of connecting steel to the concrete. The force applied
to this connection is mainly but not entirely the longitudinal shear. Since these
connections are region of severe and complex stresses defies accurate analysis and somethods of connection are developed empirically and verified by tests.
1.4 Types of shear connector:-
2
7/29/2019 seminar on shear connectors
3/37
There are three main types of shear connector, viz., Rigid Shear Connector, Flexible
Shear Connector and Anchorage Shear Connector.
1.4.1 Rigid shear connector:-
As the name implies, these connectors are very stiff and they sustain only a small
deformation while resisting the shear force. They derive their resistance from bearing
pressure on concrete, and fail due to crushing of concrete. Rigid shear connector consists
of short length bars, stiffened angels, channels or tees welded to the flange of the steel
girders (some of this type are as shown). Such connector should be provided with
anchorage devices.
Fig. 1.1 Rigid Shear Connector
1.4.2 Flexible shear connector:-
3
7/29/2019 seminar on shear connectors
4/37
Flexible shear connector consists of studs, angels or tees welded to steel girders and
derive resistance to horizontal shear through bending of the connector (some of these
types are shown in fig.). Where necessary, such shear connector shall be provided with
anchorage device.
Fig. 1.2 Flexible Shear Connectors
1.4.3 Anchorage shear connector:-
4
7/29/2019 seminar on shear connectors
5/37
This connector is used to resist horizontal shear and to prevent separation of the girder
from the concrete slab at the interface through bond.
Fig. 1.3 Anchorage Shear Connectors
CHAPTER2
5
7/29/2019 seminar on shear connectors
6/37
STATE OF ART
2.1 Effect of stiffness of shear connector on Elastic Behavior of
composite Beam:-
Fig. 2.1 Bending and Shear Stress Distribution in Composite beam
2.1.1. Connector with zero stiffness
6
7/29/2019 seminar on shear connectors
7/37
(No interaction case):-
In this case upper beam cannot deflect more than lower one, so each beam carries a load
W/2 per unit length.
Fig 2.2 Deflection, slip and slip strain
7
7/29/2019 seminar on shear connectors
8/37
Fig 2.3 Stress and Strain in a beam without composite action
Bending stress:-
max = I
M
* ymax =
16
** llw* *
**
12
hhbh 2
h=
hbh
lwl
*8
*3
Shear stress:-
max = *2
3
A
V=
bh
wl
8
3
Moment:-
Mx = w[l2-4x2]/16
Strain:-
=hEbh
wEIyM
*83max* = [l2-4x2]
There is equal and opposite strain of each beam at interface.
s = 2* x
Where, s is slip strain
dx
ds= s = 2x=
hEBh
w
*4
3(l2-4x2)
S =hEbh
w
*4(3l2x-4x3)
These equations show that slip strain is maximum and slip is zero at centre of span while
slip strain is zero and slip is maximum at end of the beam.
8
7/29/2019 seminar on shear connectors
9/37
2.1.2. Connection with infinite stiffness
(Full interaction case):-
Fig 2.4 Stress and Strain in beam with full interaction
It is now assumed that two halves of beam shown are joined together by an infinite stiff
shear connector. The two members then behave as one. Slip and slip strain is zero
everywhere and it can be assumed that plane sections remains plane.
max=I
Mymax=
hbh
lwl
*16
*3
This bending stress is half in magnitude of no interaction case
max = bhwl
8
3
This longitudinal shear is same as previous in magnitude.
2.1.3. Connector with finite stiffness
(Partial interaction case):-
Current composite steel and concrete bridges are designed using full interaction theory
assuming there is no any relative displacement or slip at interface of concrete and steel.
But results obtained from small scale and full scale tests shown that slip occurs even
under very small loads. Slip occurs because mechanical shear connector has finite
stiffness. Hence the connector must deform before they carry any load and this is the case
of partial interaction.
9
7/29/2019 seminar on shear connectors
10/37
Fig. 2.5 Stress and strain in Beam with Partial Interaction
Current full interaction design procedures are safe and simple. However in fatigue
assessment of existing structures, more accurate assessment techniques are required in
order to extend the life of structure as possible.
R. Seracino, D.J. Oehlers, M.F.Yeo develops a new concept [July 2000] of a partial
interaction focal point and extends the classic linear-elastic partial interaction theory.
Fig. 2.6 Strain Distribution
10
7/29/2019 seminar on shear connectors
11/37
The linear elastic strain distribution at any point along a beam can be defined by
determining the curvature and location of neutral axis. The curvature can be found using
well known relationship.
=M/EI
Where,
M= Bending moment
EI= Flexural rigidity
As we are dealing with composite section
For full interaction:-
EI(f) = Ec * Inc
For no interaction:-
EI(n) = EcIc + EsIs
Where,
Ec= Modulus of Elasticity of concrete
Inc= Second moment of transformed concrete area.
Es= Modulus of Elasticity of steel
Ic & Is = Second moment of concrete and steel areas respectively.
Having determined curvature we can find strain distribution. The full interaction strain
distribution passes through the centroid of transformed section. While no interaction
strain distribution passes through centroids of concrete and steel areas respectively.
The two points where the boundary strain distribution intersect are of special interest as it
can be theoretically shown that every strain distribution passes through these two points
irrespective of stiffness of shear connector for a given section and moment.
It is evident from partial interaction strain distribution that flexural stresses are greater
than full interaction stresses currently being used. This can potentially induce tensile
stresses in concrete slab that can lead to premature failure (cracking) and / or reduce the
fatigue life of steel section. It is suggested that partial interaction flexural stresses should
be considered particularly when assuming the remaining life of existing structures as
realistic assessment techniques are required.
11
7/29/2019 seminar on shear connectors
12/37
2.1.3.1 Calculation of slip:-
This is best illustrated by an analysis based on elastic theory. It leads to a differential
equation that has to be solved afresh for each type of loading, and is therefore too
complex for use in design offices. Even so, partial-interaction theory is useful, for it
provides a starting point for the development of simpler methods for predicting the
behaviour of beams at working load, and finds application in the calculation of interface
shear forces due to shrinkage and differential thermal expansion.
Fig. 2.7 Composite Beam
The above fig. shows in elevation a short element of the beam, of length dx, distance x
from mid-span cross-section. For clarity, the two components are shown separated, and
displacements are much exaggerated. The slip is s at cross-section x, and increases over
the length of the element to s + (ds/dx)dx, which is written as s+. This notation is used in
above fig. for increments in other variables, Mc, Ma, F, Vc and Va, which are respectively
the bending moments, axial force, and vertical shears acting on the two components of
the beam, the suffixes c and a indicating concrete and steel. It follows from longitudinal
equilibrium that the forces F in steel and in concrete are equal. The interface vertical
force v per unit length is unknown, so it cannot be assumed that Va equals to Vc.
12
7/29/2019 seminar on shear connectors
13/37
If the interface longitudinal shear is v per unit length, the force F on each component is
Vdx. It must be in the direction shown, to be consistent with sign of slip, s. The load slip
relationship is
pv = ks (A.1)
since the load per connector is pv.
We first obtain equations deducted from equilibrium, elasticity and compatibility, then
eliminate M, F, V and v from them to obtain a differential equation relating s to x, and
finally solve this equation and insert boundary conditions. These are as follows.
1. Zero slip at mid-span, from symmetry, so s=0 when x=0.
(A.2)
2. At supports, M and F are zero, so the difference between the longitudinal strains
at the interface is the differential strain, c, and therefore,
c
dx
ds= when x =
2
L (A.3)
Equilibrium
Resolve longitudinally for one component:
vdx
dF= (A.4)
Take moments:
ccc
vhVdx
dM
2
1=+ , sa
avhV
dx
dM
2
1=+ (A.5)
The vertical shear at section x is wx, so
Vc + Va = wx. (A.6)
Now (hc + hs) = dc, so from (A.5) and (A.6)
cac
vdwxdx
dM
dx
dM=++ (A.7)
Elasticity:
In beams with adequate shear connection, the effects of uplift are negligible in the elastic
range. If there is no gap between the two components, they must have the same curvature,
, and simple beam theory gives the moment-curvature relations.
13
7/29/2019 seminar on shear connectors
14/37
kcEaIc
nMc
EsIa
Ma== (A.8)
The longitudinal strains in concrete along AB and in steel along CD are:
c
cac
cAB
AEk
nFh
= 2
1
(A.9)
aa
sCD
AE
Fh +=
2
1(A.10)
Compatibility
The difference between AB and CD is the slip strain, so from (A.9) and (A.10) and putting
(hc + hs) = dc
cAakcAc
n
Ea
Fd
dx
dsc
+=
1(A.11)
It is now possible to derive the differential equation for s. Eliminating Mc and Ma from
(A.7) and (A.8),
cvdwxdx
dIa
n
kcIcEa =+
+
(A.12)
0
/
EaI
wxpskd
dx
d c =
(A.13)
Differentiating and eliminating from (A.13), F from (A.4), and v from (A.1):
0000
2
22
2 /
IE
xwd
A
IdIE
ks
pAE
ks
IE
xwdpskd
dx
sda
c
o
oc
aaa
cc
+=+=
This equation leads to equation in standard form,
wxssdx
sd 22
2
2
= (A.14)
Solution for s,
s = K1 sinh x + K2 cosh c + wx
Where,
acc AAk
n
A
11
0
+=
14
7/29/2019 seminar on shear connectors
15/37
0
02
'
1
A
Id
Ac +=
a
ccI
n
IkI +=0
'
2
AIpE
k
oa
=
k
pdA c'=
The boundary conditions (A.2) and (A.3) give
K2 = 0, c = -K1 cosh(L/2)-w
Substitution in (A.14) gives s in terms of x:-
xL
hw
wxs c
sinh
2sec
+=
2.1.3.2 Modeling of stud connectors:-
1. Dennis Lam and Ehab EI-Lobody (2005) Behaviour of Headed Stud Shear
Connectors in Composite Beam January ASCE 12, 96-107:-
For a successful model of shear connector, all different components associated with
the connection must be properly presented. ABAQUS, which is general purpose finite
element modeling package, was selected for this purpose.
The elements used:-
Fig. 2.8 Three-dimensional solid elements
15
7/29/2019 seminar on shear connectors
16/37
Combinations of three-dimensional solid elements, which are available in the ABAQUS
element library, are used to model the push-off test specimen. These are a three-
dimensional eight-node element (C3D8), a three-dimensional fifteen-node element
(C3D15), and a three-dimensional twenty-node element (C3D20) as shown in Fig. 2. In
the modeling of the concrete slab around the stud, C3D15 elements are used and C3D8
elements are used elsewhere. The shank of the stud consists of C3D15 elements and the
stud head consists of both C3D15 and C3D20 elements. The width of the head is 1.5
times the stud diameter and its thickness is 0.5 times the diameter.
2. Kuan-Chen Fu and Feng Lu (2003) Nonlinear Finite-Element Analysis for
Highway Bridge Superstructures May ASCE, 7, 173-179:-
The shear stud is modeled by a bar element, which can be seen as two independent linear
springs with a stiffness knparallel to the longitudinal axis of the bar and kt perpendicular
to the axis. Note that
kn =s
ss
h
AE
where Es = elastic modulus; As = area of cross section; and hs = height of stud.
Along the tangent surface, the constitutive behaviour is defined by a typical load-slip
function proposed by Yam and Chapman (1972), which is
P = a(1-e-by)
Where P = load; a and b = constants; and y = interface slip.
By choosing two points on the function such that the relationship y2=2y1 is maintained,
the constants a and b can be determined as
a =122
*
PP
PP
b =
121
1
log1PP
Py
Therefore, the stiffness in the tangential direction is
kt =dy
dP= a b e-by
16
7/29/2019 seminar on shear connectors
17/37
Each bar element provides a dimensionless link between the concrete deck element and
neighboring top flange element of the girder.
2.2 Headed stud as shear connector:-
The most widely used type of connector is the headed shear stud. These range in diameter
(d) from 13 to 25 mm, and in length (h) from 65 to 100 mm though longer studs may also
be sometimes used.
The advantages associated with stud connectors are, welding process is rapid, provide
little obstruction to reinforcement in the concrete slab and they are equally strong and
stiff in shear in all direction normal to the axis of stud.
There are two factors that influence the diameter of studs. One is welding process, which
becomes increasingly difficult and expensive at diameters greater than 20 mm and other
is thickness should be welded.
Fig 2.9 Headed Shear Stud
The ratio d/t should be less than 2.5 to achieve maximum static strength of stud. The
maximum shear force that can be resisted by a stud is relatively low about 150 KN.
17
7/29/2019 seminar on shear connectors
18/37
2.3 Use of larger stud as shear connector:-
Shear studs used in composite steel bridge construction are typically 19.1 mm or 22.2
mm in diameter. This paper presents the development and implementation of the 31.8
mm stud diameter. Because the 31.8 mm stud has about twice the strength and a higher
fatigue capacity than the 22.2 mm stud, fewer studs are required along the length of the
steel girder. This would increase bridge construction speed and future deck replacement,
and reduce the possibility of damage to the studs and girder top flange during deck
removal. Studs also can be placed in one row only, over the web centerline, freeing up
most of the top flange width and improving safety conditions for field workers. This
paper provides information on the development, welding, quality control, and testing of
the 31.8 mm stud. Information on the first bridge built in the state of Nebraska with the
31.8 mm studs is provided.
2.4 Characteristics of shear connector:-
Though in the discussion of full interaction it was assumed that slip was zero everywhere,
results of tests have proved that even at the smallest load, slip occurs. This load-slip
characteristic of shear connector affects the design considerably. To obtain the load-slip
curve push-out tests are performed. Arrangement for these tests as per Eurocode 4 and
IS: 11384-1985 are as shown in Fig. respectively.
To perform the test, IS: 11384-1985 suggests that,
At the time of testing, the characteristic strength of concrete used should not
exceed the characteristic strength of concrete in beams for which the test is
designed.
18
7/29/2019 seminar on shear connectors
19/37
A minimum of three tests should be made and the design values should be taken
as 67% of the lowest ultimate capacity.
2.4.1 Push out test:-
The property of shear connector most relevant to design is the relationship between shear
force transmitted, P and the slip @ interface, S. The load slip curve should ideally be
found from tests on composite beams, but in practice a simpler specimen is necessary.
Most of the data on connectors have been obtained from various types of push out tests.
2.4.1.1 Experimental Details:-The flanges of a short length of I section are connected to two small concrete slabs. The
slabs are bedded on to lower platen of a compression testing machine or frame and load is
applied to upper end of steel section. The slip between steel member and two slabs is
measured at several points and the average slip is plotted against the load per connector.
19
7/29/2019 seminar on shear connectors
20/37
Fig. 2.10 Push-Out test
2.4.1.2 Load-slip relationship:-
This load slip relationship is influenced by many variables including:-
1. Number of connectors in test specimen,
2. Mean longitudinal stress in concrete slab surrounding connectors,
3. Size, arrangement and strength of slab reinforcement in the vicinity of the
connector,
4. Thickness of concrete surrounding the connectors,
5. Freedom of the base of each slab to move laterally and so to impose uplift
forces on the connectors,
6. Bond at steel concrete interface,
7. Strength of concrete slab and
8. Degree of compaction of concrete surrounding the base of each connector.
20
7/29/2019 seminar on shear connectors
21/37
Fig. 2.11 Typical Load-Slip curve for 19 mm stud connectors in composite slab
21
7/29/2019 seminar on shear connectors
22/37
Fig. 2.12 Standard Test for shear connectors (according to IS: 11384-1985)
22
7/29/2019 seminar on shear connectors
23/37
2.5 Load bearing and failure mechanism of shear connector:-
In a composite beam where the interaction is achieved by means of stud shear connectors,
the forces acting on the stud are sketched in Figure 2-13. This is a simplified model taken
from Oehlers & Bradford (1995). The shank and weld collar of a shear stud is designed toresist longitudinal shear force, and the head is designed to resist tensile forces normal to
the steel/concrete interface due to separation of concrete and steel. In order for the stud
shear connectors to start transmitting shear forces, certain slip has to be introduced. This
slip forces the shank of the stud to bear on to the concrete.
Fig. 2.13 Transfer of force at a shear connector
(from Oehlers & Bradford 1995)
In course of resisting the shear load, the connectors deform and transfer the load to
concrete through bearing. This is illustrated as in fig.2.13. The dispersion of load can
cause tensile cracks in concrete by ripping, shear and splitting action. However the steel
dowel may also fail before concrete fails.
Since the bearing zone of concrete has a certain height, the force on the shank of the stud
acts with eccentricity, and moment is introduced in the stud shear connector (F multiplied
by e). This bending moment (F*e) has to be resisted by flange stud interface. The
resistance of the stud shear connector is called dowel action.
23
7/29/2019 seminar on shear connectors
24/37
Fig. 2.14
It has been found by research that the bearing stress on a shank is concentrated near the
base in shown in fig.2.14. Assuming that the force is distributed over a length of 2d
where d is shank diameter; it can be shown that concrete has to withstand a bearing stress
of about seven times its cube strength. This high strength is possible, because concrete
bearing on connector is confined laterally by the steel element, reinforcement and
surrounding concrete.
Fig. 2.15 a) Transfer of longitudinal shear by dowel action
b) Schematic visualizations of contributions to shear resistance.
24
7/29/2019 seminar on shear connectors
25/37
Figure 2.15 a) shows a stud moving to the right. Figure 2.15 b) schematically show the
active forces. PA is the force acting on the weld collar; it is biggest in the beginning of
the dowel action. When the concrete in front of the weld collar crushes the force resultant
moves up and the value of PA decreases. The force resultant acting on the stud shank, PB
give rise to an increasing bending moment, PBe. Pc is the tensile force acting in the stud,
as the bending moment increases so does the tensile forces. Compressive forces in the
concrete lead to additional frictional forces in the interface between the concrete slab and
steel flange, denoted as PD.
The size of the bearing zone of the concrete is dependent of the ratio Ec/Es. Keeping Ec
constant and decreasing Es, (as is the case when the stud is cracking) means that the stud
is more prone to bending, and so the height of the bearing zone is decreased as Es
decrease. If Ec is decreased (the case when the concrete cracks), the stud is less prone to
bending, and so the height of the bearing zone is increased. High compressive forces in
the concrete bearing zone cause the concrete to crush. The horizontal forces introduce
shear forces, and the bending moment give rise to high tensile stresses in the weld-
collar/shank interface where the steel failure zone is. Increasing the eccentricity e means
introducing higher tensile stresses in the steel failure zone, and thus, decreasing the ration
Ec/Es, decreases the strength of the dowel.
25
7/29/2019 seminar on shear connectors
26/37
2.5.1 Static failure
During static loading three different modes of failure occur in a stud shear connector. All
three types illustrate the strong interaction between the steel and concrete elements on the
dowel action.
1. Concrete failure steel failure
Assume that Es and Ec are constants. A force F is applied to the composite member.
2. Concrete failure no steel failure bending
In this case, a large volume of concrete crushes, but the steel is strong enough to
withstand the increase in tension by F e and is bent over.
3. Steel failure concrete failure
The same mechanism as in (1) but the steel starts to fail before the concrete, decreasing
Es and increasing e, which lead to increased bearing pressure in the concrete and
eventually cracking of the concrete and so on.
26
7/29/2019 seminar on shear connectors
27/37
2.5.2 Fatigue failure:-
In real structures the load often varies and the assumption that the load has constant range
and a constant peak is not accurate. The best way to get a good estimation of real problem
is to know how the loading has been or will be, then count the numbers of cycles with a
specific range and peak load and do test according to this data. To do this kind of test a
big part is to determine the loading condition. Many tests carried out around the world are
made with constant range. These types of testing is accepted for fatigue testing due to the
problems with collecting data for more exact testing and it have been seen that this type
of testing gives good results.
Fatigue failure occurs in structural member subjected to cyclic, vibratory or frequently
repeated loads. A fatigue failure occurs at stress much lower than permissible static
stress.
Fig. 2.16 Different propagation of failure mode(from Hallam 1976)
During fatigue loading there are four different modes of failure in a stud shear connector.
1. The first failure mode and also the most common is when a crack starts in the weld
collar/shank interface (point B in Figure 2.13) and propagates in one of three different
ways according to Figure 2.16. This failure mode is introduced because of discontinuities
in the connection between weld and shear stud.
27
7/29/2019 seminar on shear connectors
28/37
2. The second failure mode is when a crack starts in the weld collar/flange interface
(point A in Figure 2.13) and propagates across the flange of the beam during fatigue
loading. This failure mode has the same background as failure mode one.
3. The third failure mode is a crack starting in the middle of the shank (point C) due
to tension in the shear stud. This tension comes from the fact that the stud is bending but
the head of the stud is constraint from bending in all directions because of the embedment
in concrete.
4. The fourth failure mode is a combination of failure mode one or two and failure
mode three. This failure mode allows the shank between A and C (in Figure 2.13) to
rotate to a more horizontal position.
-N curves may be developed for determination of e, the endurance limit stress, for
different combination of min and max. Alternatively max is given as a function of stress
ratio, max / min and the permissible number of stress cycles, usually in range of 10e5 to
10e8 cycles. The endurance limit is that level of stress at which the material can take any
number of load repetitions.
The paper (Thorsten Faust, Andreas Leffer, Martin Mensinger) presents push-out tests
performed with headed studs embedded in lightweight aggregate concrete (LWAC) underdynamic loads. Based on the test results in solid slabs, a somewhat more inclined S-N-
curve could be observed in comparison to normal weight concrete (NWC). The
endurance of headed studs subjected to high stress ranges is governed more by the peak
load applied and the shank diameter than by the kind of concrete, while for low stress
ranges the influence of the concrete dominates the fatigue. Particularly for high stress
ranges further investigations concerning the real effects of action for the studs in the
structure are desirable.
28
7/29/2019 seminar on shear connectors
29/37
Fig. 2.17 Example of Unidirectional and Reverse Loading
2.6 Effective cross-section:-
Longitudinal shear in the slab causes shear strain in its plane, with the result that vertical
cross-section through the composite T-Beam do not remain plane, when it is loaded. At a
cross-section, the mean longitudinal bending stress through the thickness of the slab
varies as sketched in fig below.
Fig. 2.18 Use of Effective width to allow for shear lag
Simple bending theory can still give the correct value of the maximum stress (at point D)
if the true flange width B is replaced by an effective breadth, b, such that the area GHJK
equals the area ACDEF. Research based on elastic theory has shown that the ratio b/B
depends in a complex way on the ratio of B to the span L, the type of loading, the
boundary conditions at the supports, and other variables.
29
7/29/2019 seminar on shear connectors
30/37
2.7 Strength of connectors (According to Euro code 4):-
From the discussion, it can be inferred that dowel strength is a function of the following
parameters.
PRD = f(Ad, fu, fckcy, Ec/Es)Where,
Ad = cross section of dowel
fu = tensile strength of steel
fckcy = characteristic compressive (cylinder) strength of concrete
Ec/Es = ratio of modulus of elasticity of concrete to that of steel.
Tests have to done for a range of concrete strengths, because the strength of concrete
influences the mode of failure as well as the failure load.
1. Stronger the concrete: - Stud will shear off. Since the failure load of
concrete is higher than yield stress of stud.
2. Lean concrete (comparatively):- Concrete surrounding fails in the region
near to stud in the form of a cone with apex towards steel section.
Since the value of shear resistance of studs depends upon strength of concrete the design
shear resistance should be taken lesser of two (according to Euro code 4) with h/d greater
than 4.
PRD =u
ddfu
)4/*(8.0
PRD =u
Ecmfckdd
5.0)*(*29.0
Where,
fu = ultimate tensile strength of steel.
fck and Ecm are the cylinder strength and mean secant modulus of
concrete.
u = partial safety factor 1.25
30
7/29/2019 seminar on shear connectors
31/37
2.8 Codal provisions for design of shear connector
(As per IRC: 22-1986):-
Shear connectors may be either of Mild Steel or High Tensile Steel according to the
material specification of steel girders.
2.8.1 High tensile shear connector from fatigue Strength consideration
Calculation of spacing of shear connectors:-
Based on the fatigue strength of connector and the range of horizontal shear per unit
length, the spacing of shear connector is given by:
P =Vr
Qr
Where,
P = Spacing of connectors
Qr = The allowable range of horizontal shear for each connector evaluated
from equations given before (Qr is the resistance of all connectors at one transverse
cross-section of the girder).
Vr = The range of horizontal shear per unit length of beam at the interface
and may be determined from equation given below.
Vr =I
yAcVR ..
Where,
VR= Range of vertical shear i.e. the difference between the maximum and
minimum shear envelope due to live load and impact.
Vr = Range of horizontal shear per unit length.
Ac = Area of transformed section on one side of interface.
y = The distance of centroid of the area under consideration from neutral axis of
composite section.
I = Moment of inertia of composite section.
To cater for effect of repeated loading, the shear connectors shall be designed for fatigue.
31
7/29/2019 seminar on shear connectors
32/37
(i) The fatigue strength of stud connector is given by the following expression:
Qr = A 10-3(for a ratio of h/d >= 4)
Where,
Qr = Allowable range of horizontal shear per stud connector (KN)
A = Area of stud (mm2)
d = Diameter of stud connector (mm)
h = Height of stud (mm)
= 55 MPA for 20 * 105 cycles
(ii) For channel angle or tee shear connector, the fatigue strength shall be calculated from
the following formula:
Qr = L. 10-2
Where,
L = Length of connector (mm), measured transverse to the beam axis
= 370 N/mm for 20 * 105 cycles
2.8.2 High tensile shear connector from the consideration of ultimate flexural strength of
the composite section:
Calculation of number of shear connectors:-
In addition to providing adequate fatigue strength, sufficient number of connectors should
be provided so that the flexural strength of composite member can be reached. Usually
the requirements will be satisfied in most composite beams because fatigue
considerations are usually critical except in cases of shored construction. The flexural
strength of composite members can be achieved if sufficient connectors are provided to
resist the maximum horizontal force in the slab and the connectors could be spaced
uniformly.
H1 = Ast . fy . .10-3
H2 = 0.85 fc bf hf 10-3
32
7/29/2019 seminar on shear connectors
33/37
Where,
H1 and H2 = Horizontal shear force (KN)
Ast = Area of tensile steel (mm2) in longitudinal direction
fy = Yield stress of steel (MPa)
fc = Cube (characteristic) strength of concrete (MPa)
bf = Effective width of flange of in-situ slab
hf = Thickness of in-situ slab
The ultimate flexural strength of any composite section will be governed by either of the
aforesaid equations depending upon whether the steel section or concrete section is large.
Therefore, the maximum possible compressive force in the slab would be the smaller of
H1 and H2 and sufficient connectors should be provided to resist the horizontal force H 1 or
H2 whichever is the lesser after calculating the ultimate strength of shear connectors.
The ultimate strength of shear connectors is given by the following:
(i) High Tensile Stud connectors
Qu = 0.5 A Ecfck* * 10-3
(ii) High Tensile Channel / Angle Tee flange (mm)
Qu = 45 (h + 0.5 h1) L 310* fck
Where,
Qr = Allowable range of horizontal shear per stud connector (KN)
A = Area of stud (mm2)
h = Average thickness of channel / Angle / Tee flange (mm)
h1 = Thickness of channel / Angle / Tee web (mm)
fck = Cube (characteristic) strength of concrete (Mpa)
Ec = Modulus of Elasticity of concrete (Mpa)
To ensure the development of the ultimate flexural strength of composite section, a larger
margin of safety against connector failure should be provided than is provided for
section. This margin should be achieved by providing a load reduction factor of = 0.85
to the ultimate shear strength of connectors. The number of connectors required from
fatigue consideration will usually exceed the requirements for flexural strength. The
33
7/29/2019 seminar on shear connectors
34/37
minimum number of shear connectors required between the points of maximum moment
and end supports shall be determined by:
n =Qu
H
Where,
n = Number of shear connectors between points of maximum moment and
end supports
= Load reduction factor = 0.85
Qu = Ultimate shear resisting capacity of one connector
H = smaller of H1 and H2 as given below.
If number of shear connector given by the above equation exceeds the number provided
by the spacing from formula additional connectors should be added to ensure that the
ultimate strength of the composite section is achieved.
2.8.3 Mild steel connector:-
For mild steel shear connectors, the safe shear for each shear connector shall be
calculated as below:
(i) For welded stud connector of steel with minimum ultimate strength of 460 MPa,
and yield point of 350 MPa and elongation of 20 percent.
(a) For a ratio of h/d less than 4.2
Q = 1.49 h d fck
(b) For a ratio of h/d equal to or greater than 4.2
Q = 6.08 d2 fck
Where,
Q = Allowable safe shear resistance in Newton of one shear connector (N)
d = Diameter of stud connector (mm)
h = Height of stud (mm)
34
7/29/2019 seminar on shear connectors
35/37
(ii) For channel / Angle / Tee connector made of mild steel with minimum ultimate
strength of 420 MPa to 500 MPa yield point of 230 MPa and elongation of 21
percent.
Q = 3.32 (h + 0.5t) L fck
Where,
Q = Allowable safe shear resistance in Newton of one shear connector (N)
L = Length of shear connector (mm)
h = The maximum thickness of flange measured at the face of the web in mm
t = Thickness of web of shear connector in mm
The spacing of shear connectors shall be determined from the formula
P =LV
Q
Where,
VL = The longitudinal shear per unit length as stated below
Q = Safe shear resistance of each shear connector as stated above
VL =I
yAV e..
Where,
V= Vertical shear due to dead load placed after composite section is effective and
working live load with impact.
Ae = Area of transformed section on one side of interface
y = Distance of the centroid of the area under consideration from the neutral axis
of the composite section.
M = Moment of inertia if the composite section.
35
7/29/2019 seminar on shear connectors
36/37
CHAPTER3
Conclusions
Even though mechanical shear connectors in composite steel and
concrete beams require slip to transmit shear, most composite bridge
beams are designed as full-interaction because of the complexities of
partial-interaction analysis techniques. However, in the assessment of
existing composite bridges this simplification may not be warranted as
it is often necessary to extract the greatest capacity and endurance
from the structure. This may only be achieved using partial-interaction
theory which truly reflects the behaviour of the structure.
Some test results from push-out tests of studs in normal and high strength concrete are
presented. It is found that the concrete compressive strength significantly affects the
strength of the stud connections. Increase of the transverse reinforcement in the concrete
slabs has a negligible effect when high strength concrete is used and some effect when
normal concrete is used. The present design code is not adequate to estimate the shear
strength of studs embedded in high strength concrete and it is suggested that a design
formula that takes account of the interaction between the studs and the surrounding
concrete should be used.
The concrete strength significantly affected the shear resistance of stud connectors. The
increase of the maximum shear load was about 34% when the cylinder compressive
strength of the concrete increased from 30 to 81 MPa. The test showed that the amount of
slip at the maximum load was on the same level for both NSC and HSC specimens.
However, ductile behaviour of the studs was observed for the NSC specimens after the
maximum load. The descending branch of the load-slip curves for the high strength
concrete was short and steep. The reinforcement in concrete slabs did not take very much
load, but confined the concrete surrounding the studs. The amount of reinforcement in the
concrete slab had a slight influence on the load capacity of the NSC specimens. The
increase was about 6%. No obvious influence of reinforcement on the capacity was
36
7/29/2019 seminar on shear connectors
37/37
observed in the HSC specimens. Evaluation of shear resistance of the studs according to
different formulas showed that the formula which combined contributions from both
concrete and studs could take variation of the concrete strength into account and give a
better estimation of the shear resistance of studs.