Modified Model
Fig. 10.3.1 Failure Mechanism of the Top Angle of North Connection
The virtual work equation for the top angle at the failure state is
(10.3.1)
Where,
Mpt1 = plastic moment of hinge 1 with coupling of the shear force
Mpt2 = plastic moment of hinge 2 with coupling of the shear force
g2 = distance between two plastic hinges
Vpt = tensile force in the horizontal leg
c = crushing strength of the concrete
k = distance from the heel to the teo of fillet of the angle
tt = thickness of the angle
ltv = width of the angle
As stated in Kim and Chen’s work, the bending moment-shear interaction formula for the yielding state proposed by Drucker (1956) is used to include the effect of the shear force on the moment capacity. That is
(10.3.2)
(10.3.3)
where,
Vpt1 = plastic shear force in the location of hinge 1 with coupling of moment
Npt2 = plastic axial force in the location of hinge 2 with coupling of moment
Mpt,i = plastic shear force in the location of hinge i with coupling of moment
M0, V0 and N0 are the plastic bending moment without coupling, the plastic shear force without coupling and the plastic axial force without coupling, respectively, and they are
(10.3.4)
(10.3.5)
(10.3.6)
where,
Fy= yielding strength of the angle
Vpt1 and Npt2 can be related to Vpt as follows:
(10.3.7)
(10.3.8)
From Equations 5.4.1 to 5.4.7, Vpt can be simplified as
(10.3.7)
where,
Vpt can be determined by using iterative procedure in Eq. 10.3.7. For the L535/165 angle used in the PR connection of the specimen, the dimensions used in Eq. 5.4.8 are given in Appendix A. As for the effective crushing strength of the concrete, MacGregor (1997) recommended it to be 0.85fc’ in the node region bounded by compressive strut and bearing areas. The average compressive strength fc’ of the concrete in the specimen was approximately 3.75 ksi. Using the actual yielding strength in the angle in Eq. 10.3.4 gives V0= 41.2 kips. As a result, the tensile force Vpt in the horizontal leg at the failure state is equal to 39.9 kips, 35% greater than that in the PR connection of a bare steel frame.
Figure 10.3.2 shows the free body diagram of the PR connection in the infilled steel frame at the failure state and the PR is subjected to the pure bending. It can be seen that the moment capacity of this PR connection is the combination of the moment capacities provided by the top angle, the seat angel angle and the double web angles,
(10.3.8)
where,
Mut = the moment capacity contributed by the top angle
Mus = the moment capacity contributed by the seat angle
Muw = the moment capacity contributed by the double web angles
Figure 10.3.2 Free-Body Diagram of the PR Connection at Failure State
When Subjected to Pure Bending
Due to the effect of the concrete, the moment capacity of the top angle is given by
(10.3.9)
where,
Equation 10.3.5 gives Vpt1 = 26.8 kips and Eq. 10.3.2 gives Mpt1 = 5.3 kip-inches. According to Eq. 10.3.9, the contribution of the top angle to the moment capacity is 244.0 kips-inches. Since the web angle and the seat angle is not affected by the concrete in the infill wall, the moment capacities contributed by these two can still be calculated based on the pre procedures proposed by Kim and Chen (1998). The contributions of the double web angles and the seat angle to the moment capacity are 182.7 kip-inches and 6.4 kip-inches, respectively. Therefore, including the restraining effect of the concrete, the total moment capacity of the PR connection is 433.0 kip-inches, 5% less than that of the PR connection in the bare steel frame.
When the PR connection in the infilled steel frame reaches its tensile capacity under pure tensile force, the top and seat angles have the same failure mechanisms as shown in Figure 10.3.1. Therefore, the tensile forces in the horizontal legs of both the top and seat angles are equal to 39.9 kips. The failure mechanism of the double web angles are the same as those in the PR connections in a bare steel frame since no concrete surrounds the double web angles. The tensile force provided by the double wen angles can be calculated according to the procedure in Appendix A.1.4 and the result is 29.4 kips. Therefore, including the restraining effect from the concrete, the total tensile capacity of the PR connection is 138.6 kips.
The test date can be used to calibrate the moment-tensile interaction equation of the PR connection in the infilled steel frame. It is assumed that the interaction equation is
(10.3.10)
Averaging the test data of both PR connections in the middle beams gives the moment MPR = 190 kip-inches and the tensile force TPR = 107.5 kips when the specimen reached their maximum strength. Substituting them with Mu,PR = 433.0 kip-inches and Tu,PR = 138.6 kips into Eq. 10.3.10 give = 2.28. Taking = 2, the interaction equation for estimating the maximum strength capacity of the PR connection in the infilled steel frame can be conservatively written as in
(10.3.11)
The interaction equation is shown in Figure 10.3.3, with plots of the test results of the two PR connections of the middle beam. One pair of test data is right on of elliptical curve denoting the interactive equation and the other is outside the elliptical curve. More experimental data are needed to verify this interaction equation for estimating the maximum strength capacity of the PR connection in the RC infilled steel frame. Presently, it is recommend using this equation to estimate the moment capacity of the PR connection with coupling of the axial force when is needed.
Figure 10.3.3 Moment and Axial Force Interaction Equation of the PR Connection