2.4 Strength of SCS sandwich composite beam and plate structure
2.4.1 Shear strength of the mechanical shear connectors
As aforementioned, there were many types of shear connectors proposed and used in the SCS sandwich structures. Among them, headed shear studs were the most widely used connectors due to their easy fabrication and installation.
Studies on shear strength of the Nelson stud or headed shear stud can be traced back to 1950s. Viest et al. (1956) proposed formulae to calculate the shear strength of the headed
‐ 27 - shear stud based on his experimental works. The proposed formulae are
2 4000 4000
5.25 1in; 5 1in
u ck ck
ck ck
P d f for d df for d
f f
(2.1)
where,Pu = critical load, lb; d = stud diameter, in; H = headed stud height, in; fck
=concrete strength, psi.
Slutter and Driscoll proposed design formulae on calculating shear strength for both headed shear stud connectors and C-channel connectors (Slutter and Driscoll, 1965). The formulae are
930 2
550 0.5
ck u
ck
d f for headed shear stud P h t w f for channelconnector
(2.2)
where, d=stud diameter, mm; w = length of a channel shear connectors, in; t =thickness of the concrete slab, in; h= height of the connector, in. However, the concrete compressive strength for Eqn. (2.2) was limited to 4000 psi (28 MPa).
Goble carried out 72 push-out tests on shear stud connectors welded to thin flange composite structures (Goble, 1968). He proposed a model on calculating shear bearing capacity of the connectors. As specified in Eqn. (2.3), the concrete compressive strength herein was limited to 4000 psi (28 MPa). The proposed model is as below
882 2
u ck
P d f (2.3)
Eqn. (2.3) is similar to Eqn. (2.2) except the constant coefficient.
Important design formulae were proposed to calculate the shear strength of the shear stud connectors embedded in both normal weight and lightweight concrete by Ollagarrd et al.
(1971) at Lehigh University. Based on their 48 push-out test results, the regression analysis was carried out. Finally, the function describing the test results including cases
‐ 28 - with both NWC and LWC is described as following:
0.3 0.44
1.106
u s ck c
P A f E (2.4a)
For design purpose, the formula is proposed as below:
u 0.5 s ck c
P A f E (2.4b)
where, As=cross section area of the headed shear stud, mm2; fck=concrete strength, MPa;
Ec=elastic modulus of concrete, MPa.
The predictions by Eqn. (2.4a) agreed well with the test ones. Eqn. (2.4b) is finally adopted in ANSI/AISC 360-05.
Oehlers and Johnson (1987) proposed another formula to calculate the shear strength of the headed shear stud connector that considered the relative stiffness between the steel stud and the concrete where they were embedded. The characteristic strength of the shear stud connectors in the SCS sandwich beams is specified by
0.4 0.35
c cu
u s
s ul
E f
P KA
E f
(2.5)
where, Ecin N/mm2; Esin N/mm2; As=cross sectional area of the stud connector, mm2; fcu=cubic compressive strength, N/mm2; ful = ultimate strength of stud connector, N/mm2; K4.1n1/2, n=number of the shear stud in the shear span.
Hiragi et al. (1989) proposed another formula to calculate the shear strength of the stud shear connector, which is
31 / 10,000
u s ck
P A H d f (2.6)
where, the units in N, mm; H= height of the shear connector, mm; As=cross sectional area of the stud connector, mm2;fck =concrete compressive strength, N/ mm2.
In Eurocode 4 (1992), the shear strength of the connectors was governed by the lesser of
‐ 29 - the shear strength of the steel shank and concrete bearing capacity. Shear strength of the headed shear stud connectors is specified as
2
0.8 / 4 /
u u v
P f d for shank shear (2.7a)
0.29 2 /
u ck c v
P d f E for concrete bearing (2.7b) where, fu=ultimate strength of connector, N/ mm2; d=stud diameter, mm; fck=concrete compressive strength, N/ mm2;Ec=concrete modulus, N/mm2; v = partial safety factor (=1.25); =0.2(H/d+1) for 3≤ H/d ≤ 4, =1 for H/d >1;H=stud height, mm.
In ANSI/AISC 360-05 (ANSI/AISC, 2005), the shear strength of the headed shear stud connector used in the sandwich structure is governed by the following equation:
u 0.5 s ck c g p s u
P A f E R R A f (2.8)
where, fck in N/mm2; Ec in N/mm2; As in mm2; fu in N/mm2; Rg and Rp are the coefficients considering the influences of the decking shapes and the locations of the connectors that can be referred to ANSI/AISC 360-05.
Similar design formula was adopted in AASHTO LRFD (2004) as in ANSI. The formula is the same but with a more conservative safety factor. The formula is specified as following:
u 0.5 s ck c s u
P A f E A f (2.9)
where, = 0.85 (resistance factor of shear connector).
More recently, Xue et al. (2008) had carried out push-out tests on 36 specimens to investigate the shear strength of headed shear stud connectors. The investigated parameters were stud diameter and height, concrete strength, stud welding technique, transverse reinforcement, and steel beam type where the studs were welded to. Based on
‐ 30 - the test results, a design formula was proposed based on the regression analysis of the push-out test results. The design formula is
0.4 0.2
3 c cu
u s u
s u
E f
P A f
E f
(2.10)
where, =coefficient of influence of stud height-to-diameter ratio and specified as follows:
6 / 1.05 / 5
1 5 / 7
/ 6 / 7
H d for H d
for H d
H d for H d
From the above review on the shear strength of the connectors, several observations are summarized as below:
1) All these proposed formulae were based on the regression analysis on the push-out test results; 2) The tested specimens were designed with either NWC or LWC; 3) All the proposed formulae were mainly developed for the headed shear stud connectors.