## T Fu 1 214

the condition for adequate ductility expressed in Equation 14.1 is automatically satisfied if the member is designed according to code provisions.

Tests on full-sized girders made of HPS have also been performed (Dexter et al. 2002; Yakel et al. 2002). One objective of these tests was to determine the rotation ductility R of these girders under flexure. R is defined by the equation

Moment

Moment

FIGURE 14.1 Moment rotation curve.

where, in reference to Figure 14.1, 0p1 = Mp/El, and 0p2 is the maximum value of beam end rotation when a simply supported beam is sustaining Mp. Mp is the plastic moment capacity of the cross-section and El is the flexure rigidity. To allow for moment redistribution, AASHTO implies an R value of 3. While the test of a simply supported hybrid girder (Dexter et al. 2002) with tension flange and web made of HPS70W (HPS345W) steel and compression flange made of A572 Grade 50 under a three-point bending test has indicated that an R value exceeding 3 was achieved, an R value less than 3 was reported for tests of compact and (web) noncompact girders (Yakel et al. 2002) made entirely of HPS70W (HPS345W) steel. In addition, numerical studies on HPS girders under negative moment (Barth et al. 2000) have shown that while HPS girders are able to develop their plastic moment capacity, they are not able to provide the necessary rotation ductility for moment redistribution. As a result, the 10% reduction in negative moments that is allowed for continuous girders to account for moment redistribution should not be applied to HPS girders.

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