seminar on shear connectors

7/29/2019 seminar on shear connectors

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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

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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:-

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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:-

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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:-

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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

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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

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(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

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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.

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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.

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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

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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.

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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.

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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.

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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

+=

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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

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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

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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.

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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.

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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.

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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.

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Fig. 2.11 Typical Load-Slip curve for 19 mm stud connectors in composite slab

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Fig. 2.12 Standard Test for shear connectors (according to IS: 11384-1985)

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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.

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(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

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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

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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)

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(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.

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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

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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.

seminar on shear connectors

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