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End-fixity factor, r

FIGURE 23.14 Lateral deflection increase due to second-order effects of 11-story frame.

End-fixity factor, r

FIGURE 23.14 Lateral deflection increase due to second-order effects of 11-story frame.

stiffness ratio RL/EI, and the connection stiffness. Figure 23.14 shows that as the end-fixity factor decreases, the lateral deflection due to second-order effects increases significantly, thus intensifying the second-order effects considerably.

Increasing the lateral deflection limit for serviceability, H/500, by a factor of 1.35 to account for factored loads gives a roof lateral deflection limit of 125 mm. As shown in Table 23.7, the lateral deflection obtained from the first-order rigid frame analysis (r = 1.0) is 125 mm, which satisfies the deflection limit. Also note from Table 23.7 that the lateral deflection of the frame is 145 mm for firstorder semirigid analysis with the value of end-fixity factor r = 0.9. This deflection is greater than the 140 mm obtained when second-order effects are considered for the rigid frame case (r = 1.0). Also note that the value of the stiffness ratio RL/EI = 27 for r = 0.9. According to the LRFD and Eurocode 3 connection classifications, connections are classified as rigid when the values of RL/EI are equal or greater than 20 (r = 0.87) or 25 (r = 0.89), respectively. Because the value of RL/EI is within the range for rigid connections used in typical building design, this demonstrates that the influence of the beam-to-column connection behavior on frame deflection may be more significant than the second-order effects. In turn, this perhaps suggests that a value of the end-fixity factor less than 1.0 should be used in mid- to high-rise rigid steel frame design where the beam-to-column connections are classified as rigid connections.

It is also observed from Figure 23.14 that for semirigid beams with an end-fixity factor value less than 0.75, an increase in the value of the end-fixity factor due to an increase in connection stiffness would result in appreciable decrease in the lateral deflection of the frame; such an effect can be substantial for flexible beam-to-column connections (r< 0.4 or RL/EI< 2, equivalently). However, for nearly rigid connections (r > 0.75), further increase in the end-fixity factor has a trivial effect on the deflection. A similar phenomenon is also observed for the strength of columns in the frame. Figure 23.15 illustrates

Beam end-fixity factor, r FIGURE 23.15 Interior column strength versus end-fixity factor.

the influence of beam end-fixity on the strength of the interior column (WWF400 x 274) between the third and fourth floors, in which the strength of the column is calculated based on LRFD with steel yield stress 350 MPa. Considering the relationship between the end-fixity factor and connection stiffness shown in Figure 23.9, it is concluded that it is important and economical to consider the semirigid behavior of connections in the design of unbraced steel frames having flexible beam-to-column connections.

This study also finds that the buckling load capacity of the frame increases considerably as the end-fixity factors increase from zero to 0.4 for beam-to-column connections. For an unbraced frame having flexible connections having a low value of connection stiffness, even a small increase in the stiffness would result in an appreciable increase in the end-fixity factor, which consequently causes a significant increase in the buckling load capacity. In practice, pinned connections always have some rotational stiffness, which considerably benefits the load capacity of the frame. Conversely, reducing the connection stiffness from rigid connection with full fixity (e.g., from r_ 1.0 to 0.75) will result in an insignificant decrease in the critical buckling loads. This is because large reductions in connection stiffness from rigid frames are shown to have little effect on the frame stability in that a large change to the stiffness of rigid connections will result in only a small change in the end-fixity factor, as shown in Figure 23.9. Consequently, potential savings in connection cost may be achieved from the replacement of rigid connections with semirigid connections. Therefore, considering the behavior of semirigid connections in frame stability can produce more appropriate and economical designs.

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