Shear connection at steel-concrete interface

6.7.1 RESISTANCE OF HEADED STUDS

The design shear resistance of a headed stud (Fig. 6.22) (PRd) automatically welded in accordance with EN-14555 is defined in EN-1994-2, 6.6.3:

=min( ⁽¹⁾ ; ^{( 2 )} )

Rd Rd Rd

P P P

P⁽¹⁾Rd is the design resistance when the failure is due to the shear of the steel shank toe of the stud:

π

P⁽²⁾Rd is the design resistance when the failure is due to the concrete crushing around the shank of the stud:

d is the diameter of the shank of the headed stud (16≤d≤25mm).

f_u is the specified ultimate tensile strength of the material of the stud (f_u≤500MPa).

fck is the characteristic cylinder compressive strength of the concrete. In our case fck=35 MPa.

E_cm is the secant modulus of elasticity of concrete (EN-1992-1-1, 3.1.2 table 3.1). In our case Ecm=22000(fcm/10)^0.3=34077.14 MPa. (fcm=fck+8 MPa)

h_sc is the overall nominal height of the stud.

In our case, if we consider headed studs of steel S-235-J2G3 of diameter d=22 mm, height hsc=200 For Serviceability State Limit, EN-1994, 7.2.2 (6) refers to 6.8.1 (3). Under the characteristic combination of actions the maximum longitudinal shear force per connector should not exceed ks·PRd

(the recommended value for ks=0.75).

Then: k_s ⋅P_Rd =0.75 0.1095 MN=0.0766 MN× . Each row of 4 headed studs (Fig. 6.21) resist at SLS:

⋅ ⋅ =

4 k_s P_Rd 0.3064 MN

Fig. 6.21 Detail of headed studs connection

6.7.2 DETAILING OF SHEAR CONNECTION

The following construction detailing applies for in-situ poured concrete slabs (EN-1994-2, 6.6.5).

When the slab is precast, these provisions may be reviewed paying particular attention to the various instability problems (buckling in the composite upper flange between two groups of shear connectors, for example) and to the lack of uniformity of the longitudinal shear flow at the steel-concrete interface (EN-1994-2, 6.6.5.5 (4))

Maximum longitudinal spacing between rows of connectors

According to EN-1994-2, 6.6.5.5 (3), to ensure a composite behaviour of the main girder, the maximum longitudinal center to center spacing (s) between two successive rows of connectors is limited to: smax ≤ min (800 mm ; 4 hc), with hc the concrete slab thickness.

When verifying the mid-span P1/P2 cross-section (see paragraph 6.1.2), it was considered that the upper structural steel flange in compression was a Class 1 element as it was connected to the concrete slab.

However if we consider the upper flange non-connected to the upper concrete slab, according to EN-1993-1-1 table 5.2 sheet 2 of 3, c/tf = ((1000-18)/2)/40=12.275 and that would result a Class 4 flange as c/t =12.275>14· =14_f × 235 345=11.55

In order to classify a compressed upper flange connected to the slab as a Class 1 or 2 because of the restraint from shear connectors, the headed studs rows should be sufficiently close to each other to prevent buckling between two successive rows (EN-1994-2, 6.6.5.5(2)). This gives an additional criterion in smax :

max ≤

s 22t_f 235 fy if the concrete slab is solid and there is contact over the full length.

max ≤

s 15t_f 235 fy if the concrete slab is not in contact over the full length (e.g. slab with transverse ribs). This is not our case.

Where tf is the thickness of the upper flange, and fy the yield strength of the steel flange.

Table 6.3 summarizes the results of applying both conditions to our case.

Table 6.3 Maximum longitudinal spacing for rows of studs Upper Steel flange

* Only applies for flanges in compression (not in tension)

This criterion is supplemented by EN-1994-2, 6.6.5.5(2) defining a maximum distance between the longitudinal row of shear connectors closest to the free edge of the upper flange in compression – to which they are welded – and the free edge itself (Fig. 6.22):

≤ ×9 235

D f

e t fy

Fig. 6.22 Detailing

Minimum distance between the edge of a connector and the edge of a plate

According to EN-1994-2, 6-6-5-6 (2), the distance eD between the edge of a headed stud and the edge of a steel plate must not be less than 25 mm, in order to ensure the correct stud welding.

In this example (Fig. 6.21), = − ⁰ − =1000−750−22= >

114 25

2 2 2 2

f D

b b d

e

Minimum dimensions of the headed studs

According to EN-1994-2 6.6.5.7 (1) and (2) the height of a stud should not be less than 3·d, where d is the diameter of the shank, and the head of the stud should have a diameter not less than 1.5·d, and a depth of at least 0.4·d (Fig. 6.23).

Fig. 6.23 Minimum dimensions of a headed stud

As we have studs of d=22 mm, the head should have a diameter over 33 mm, and a depth of at least 8.8 mm. With a total height of the studs of 200 mm, we are far from the limit of 3·d=66 mm.

EN-1994-2 also establishes a condition between the diameter of the connector and the thickness of the steel plate (EN-1994-2, 6.6.5.7 (3)). For studs welded to steel plates in tension subjected to fatigue loading, the diameter of the stud should be:

≤1.5⋅ _f

d t

This is widely satisfied in the example, with tfmin=55mm in the tensile area, and d=22mm.

This limitation also applies to steel webs. This verification allows the use of the detail category ∆τc = 90 MPa.

Clause 6.6.5.7 (5) establishes that the limit for other elements than plates in tension or webs is d≤2.5·tf

Minimum spacing between rows of connectors

According to EN-1994-2 6.6.5.6 (4) the longitudinal spacing of studs in the direction of the shear force should be not less than 5d=110 mm in our case, while the spacing in the transverse direction to the shear force should be not less than 2.5d in solid slabs, or 4d in other cases. In our example 2.5d=55 mm. Both limits are widely fulfilled in the example, with strans=250 mm

Criteria related to the stud anchorage in the slab

Where a concrete haunch is used between the upper structural steel flange and the soffit of the concrete slab, the sides of the haunch should lie outside a line drawn 45º from the outside edge of the connector (Fig. 6.22) (EN-1994-2, 6.6.5.4 (1)).

Clause 6.6.5.4 (2) establishes that the nominal concrete lateral cover from the side of the haunch to the connector should not be less than 50 mm, and the clear distance between the lower face of the stud head and the lower reinforcement layer should be not less than 40 mm, according to clause

6.6.5.4 (2). This value could be reduced to 30 mm if no concrete haunch is used (EN-1994-2 6.6.5.1 (1)) (see Fig. 6.22).

Figs. 6.24 and 6.25 show a general view and a detail of the connection with headed studs of the upper flange of a composite bridge, and Fig. 6.26 shows the connection of the lower flange of the main steel girders in a double composite cross-section.

Figs. 6.24 & 6.25 View and detail of an upper flange connection

Fig. 6.26 View of the lower flange connection of a steel girder

6.7.3 CONNECTION DESIGN FOR THE CHARACTERISTIC SLS COMBINATION OF ACTIONS

When the structure behaviour remains elastic in a given cross-section, each load case from the global longitudinal bending analysis produces a longitudinal shear force per unit length νL,k at the interface between the concrete slab and the steel main girder. For a girder with uniform moment of area (S) subjected to a continuous bending moment, this shear force per unit length is easily deduced from the cross-section properties and the internal forces and moments the girder is subjected to:

ν_{L k,} =S V^{c k} I

Where:

νL,k is thelongitudinal shear force per unit length at the interface concrete-steel

Sc is the moment of area of the concrete slab with respect to the centre of gravity of the composite cross-section

I is the second moment of area of the composite cross-section

Vk is the shear force for the considered load case and coming from the elastic global cracked analysis

According to EN-1994-2, 6.6.2.1 (2), to calculate normal stresses, when the composite cross-section is ultimately (characteristic SLS combination of actions in this paragraph) subjected to a negative bending moment Mc,Ed, the concrete is taken as cracked and does not contribute to the cross-section strength. But to calculate the shear force per unit length at the interface, even if Mc,Ed is negative, the characteristic cross-section properties Sc and I are calculated by taking the concrete strength into account (uncracked composite behaviour of the cross-section).

The final shear force per unit length is obtained by adding algebraically the contributions of each single load case and considering the construction phases. As for the normal stresses calculated with an uncracked composite behaviour of the cross-section, the modular ratio used in Sc and I is the same as the one used to calculate the corresponding shear force contribution for each single load case.

For SLS combination of actions, the structure behaviour remains entirely elastic and the longitudinal global bending calculation is performed as an envelope. Thus the value of the shear force per unit length is determined in each cross-section at abscissa x by:

ν

( ) max x =   ν

( ) ; x ν

( ) x  

Fig. 6.27 shows the variations in this longitudinal shear force per unit length for the characteristic SLS combination of actions, for the case of the example.

In each cross-section of the deck there should be enough studs to resist all the shear force per unit length.

The following should be therefore verified at all abscissa x:

ν

( ) ≤

⋅ (

⋅ P )

i

x N k