Chapter 5 Shear Connection组合梁的抗剪连接

By Professor Shiming Chen

Lecture Notes for Presentation

2015

5.1 IntroductionShear connection is an important feature in steel-concrete composite construction 。•If slip at the interface is free to occur, each component (steel beam/concrete slab) will act independently.•If slip at the interface is eliminated, the slab and steel beam will act together as a composite unit. The resulting increase in strength and stiffness depends on the extent to which slip is prevented. •The use of mechanical shear connectors is essential for the satisfactory performance of composite beams.

Composite steel beam and concrete slab interaction

The Shear Transfer Mechanisms-General

• adhesion and chemical bond• interface friction• mechanical interlock• dowel action

Test on shear connectors. (a) Push-out specimen. (b) Non dimensional load-slip

relationship

• PBS (Perfobond Strip)

5.2 Classification of shear connectors• ductility -the most important material property• ductile connectors - those having sufficient

deformation capacity, in slip, to justify the assumption of perfectly plastic behaviour for the shear connection.

• For slip capacity su, EC 4 estimates that a value greater than 6 mm allows shear connectors to be considered as ductile.

• rigid shear connectors, i.e. non-ductile- as those which fracture when the ultimate load PR of the connector is reached without any significant slip; in this case, the subsequent shear resistance falls suddenly to zero.

Ductile and non-ductile shear connectors

Ductile and non-ductile connectors• Slip capacity of headed stud connectors increases with

the diameter of the shank;• Slip enables longitudinal shear to be redistributed

between the connectors in a critical length, before any of them fail;

• The definitions of ‘ductile’ connectors is interpreted that the connector has sufficient slip capacity to enable the shear force redistribution at the ultimate state;

• Ductile connectors may be spaced uniformly along the critical length, whereas, for non-ductile connectors, the spacing must be based on elastic analysis for longitudinal shear.

5.3 Behaviour of shear connectors• Standard Push-out tests• relationship between the

shear force transmitted and slip at the interface.

Push-out tests and load slip

curves

Stud connectors

• The most widely used type of connector is the headed stud, ranging in diameter from 13 to 25mm, and from 65 to 100 mm or more in length.

• Speed of welding process. This is carried out using a portable hand-tool, connected via a control unit to mains or generator. Headed stud shear connector

• The push-out test enable the behaviour of different types and sizes of connector to be compared, the test must be standardized.

Load-slip curve

Bearing stress distribution on the

shank of stud

• At the ultimate load, the concrete at the base maybe subjected to a local pressure, leading highstresses in connectors and the surrounding concrete.Possible modes of failure are crushing/splitting ofthe concrete, and shearing of the stud.

• For studs embedded in strong concrete, it is foundthat their strength depends on the ultimate tensilestrength of the stud material, rater than the yieldstress.

Table 5.1 Nominal static strength of shear connectors

Headed studs Nominal static strength in kN for concrete strengths fcu in N/mm2

Diameter (mm)

Height (mm) 20 30 40 50

25 100 139 154 168 183 19 100 90 100 109 119 13 65 42 47 52 57

Stud connector shear resistance–concrete resistance relationship

Stud Connectors Used with Profiled Steel Decking

Different locations of the stud in the rib

Behaviour of shear connectors in beams:There are four situations in which a connectorstrength found from a push-out test may be toohigh for use in design

When the beam is subjected to repeated loadingWhen the lateral restraint to the concrete in contact

with the connector is less than that provided in a push-out test, as may be the case when the slab is hunched

When lightweight concrete is to be used When the slab is in tension

5.4 Shear connection: full/partial• Full-interaction design：—with sufficient shear

connectors for the beam to enable the composite section plastic strength（Nf）

• Partial-interaction: the degree of interaction between the slab and the steel member just sufficient to provide the required flexural strength（N< Nf）

• Partial-interaction design may only be applied to beams not exceeding 20 m in span and subject to predominantly static loading

• Slip occurs even in the full shear connection composite beam, but is substantial if the shear connection decreases

• Effect of slip on stresses and deflectionsFull- interaction model, using transformed section method.Partial-interaction modelconsidering effect of interface slip: A transformed section

Longitudinal strain at mid-span

A linear approximation of deflection for partial connection beam

A linear approximation of design moment for partial

connection beam

5.5 Design of shear connection DESIGN with Non-ductile Connectors

• Longitudinal shear per unit length of interface by :τ(x) =V(x) S/I

V(x) : the shear at cross-section x; S is the first moment of area taken at the steel-concrete interface; I is the second moment of area of the whole cross-section. S and I are calculated by replacing the concrete area Ac, by an equivalent steel area equal to Ac /n, （n = Ea/Ec ）

The total longitudinal shear force should not exceed the product of the number N of connectors and the design resistance per connector.

Design of Simply Supported Beams with Ductile Connectors

• "critical cross-section" of the beam is the cross-section of maximum bending moment.

• "critical length (m) " of the beam is the length between two adjacent critical cross-sections.

Strength of shear connection• Assumption: each connector possesses sufficient

plasticity to redistributed load between studs until all those in a shear span fail as a group strength

• The shear resistance of an individual stud be calculated as (or Table 5. 1)

• k — strength coefficient, influence by height to diameter ratio (h d /d d) of stud, k = 0.43 when the ratio > 4.0

dudccdd fAfEkAP 7.0≤=

• For composite slab with profiled steel sheeting resistance of the connection will be reduced.

• If the ribs of the steel deck are parallel to the beam axis ,the shear resistance of stud be multiplied by a reduced factor :

• If the ribs of the steel deck are perpendicular to thebeam axis, the reduced factor is:

0.16.0 0 ≤

−=

s

sd

sl h

hhhbη

0.185.0 0 ≤

−=

s

sd

sdt h

hhhb

nη

b0 is the effective width of steel rib, hd is height of stud, h d = h s + 75 mm when h d > h s + 75 mm. n d is the numbers of studs within one rib trough.

Design method for partial shear connection• For the purpose of

design (ductile connectors), it will be sufficient to introduce the concept of a reduced ultimate moment curve.

• Reduced ultimate moment curve

A simple linear interaction method• Mu(r) = Mu, steel, + (N/Nf)(Mu – M u,steel)

in the range of N/Nf = 0.5 to 0.7.• Requirement of minimum degree of shear connection

for steel sections with equal flanges:• (N/Nf)B = 0.4 where L ≤ 5 m• (N/Nf)B = 0.25 + 0.03 L ≤ 1 where L > 5 m

for steel sections having a bottom flange with an area not exceeding 3 times the area of the upper flange:• (N/Nf)B = 0.4 + 0,03 L ≤ 1• In the case of slabs cast on profiled steel sheeting:• 0.4 (N/Nf)B = 0.04 L ≤ 1

Numbers and spacing of shear connectors• In buildings, the number of shear connectors

required in beams under static loading isdetermined by two criteria:

There must be sufficient connectors for the beamto fail in flexure, not in shear

There must be sufficient connectors for theresistance of the beam in bending to be not lessthan the calculated value. For a beam in positivebending designed for full interaction, theresistance is calculated using plastic analysis ofthe cross-section

As failure of some connectors, such as large studs, occurs mainly in the surrounding concrete, whilst small diameter studs may shear off, γ m (say 1.1) should lie between the values for concrete and structural steel. The design load per stud (Pd) is then expressed as the follow:

In buildings not subjected to heavy point loads, connectors can be spaced uniformly between supports and sections of maximum positive bending moment.

1.18.0 u

dPP =

The number of shear connectors may also be influenced by empirical limits of the maximum spacing of connectors. The limits aim to control uplift between connectors and to avoid excessive stress concentrations in the slab.

If redistribution of load is to occur between connectors, some longitudinal slip must occur. In beams in buildings at ultimate load this will be of the order of 1 to 2 mm.

5.6 Longitudinal shear resistance and transverse reinforcement

• In order to achieve the composite action, force must be transferred from the shear connection to the full effective width of the slab, so that shear failure of concrete surrounding the connectors must be prevented.

• When sufficient connectors are provided, the critical planes for shear failure pass round the connectors or through the slab.

• Transverse reinforcement should be provided to enhance the resistance to the longitudinal shear of the vertical section of a concrete slab.

• The situation is complicated due to transversebending of the slab in the vicinity of the steel section.

• The design recommendations used to check theresistance of the slab to longitudinal shear are basedon research into the behaviour of reinforced concreteslabs.

• On the shear plane 2—3—3—2(shown in Figure )

5.7 Detailing rules• The minimum dimensions for the head of a stud:

h .GE.3d; the minimum projection above bottom reinforcement 30 mm (no haunch, shown in Figure).

• d.LE.2.5 tf ; and .LE. 1.5 tf (repeated loading).

Shear connector detailing

• The minimum centre-to-centre spacing of studs is 5d in the longitudinal direction and 2.5 d across the width of a steel flange in solid slab; and 4d in composite slabs.

• The maximum longitudinal spacing is limited to the lesser of 800mm and six times the total slab thickness (in buildings).

• The 50 mm side cover to the concrete edge and 20 mm to the flange tip.

5.8 Conclusions In composite beams, the use of mechanical shear

connectors is essential (headed stud).The values are mainly dependent on the ultimate

tensile strength of the stud material and the grade ofthe concrete.

In buildings, individual connectors possess sufficientductility to redistribute load until all those in a shearspan fail as a group.

Connectors can be spaced uniformly between supports/sections of the maximum positive bending moment, in the absence of heavy point loads.

Transverse reinforcement must be provided to enable force to be transferred from the shear connection to the full effective width of the slab.

In negative moment regions of continuous composite girders, crack width may need to be controlled (for details, see shear connectors for continuous composite beams)