Study of an Optimum Design Method for Links

Under severe earthquakes, eccentrically braced frames might experience large inelastic deformations, and the inelastic action is restricted primarily to the ductile links. In order to study the reasonable design method for links, seventy analyses of links are conducted to investigate the effect of different flange width-thickness ratio and length, fifty links are also designed to study the influence of stiffeners spacing, stiffeners thickness and placing on side(s), and thirty-six links are designed to consider the effect of axial loads, which are all based on the material properties of Q235 steel. The accuracy of finite element models is verified using the experimental data during cyclic loading. Numerical analysis results show that the flange width-thickness ratio of short and long links can be relaxed to 10 235/fy , and stiffeners can only be placed on one side. However, the flange width-thickness ratio of intermediate links is limited to 8 235/fy , and stiffeners should be placed on both sides due to the unstable behavior. Stiffener thickness has no significant influence on the performance of links with varying length. Unlike short links, intermediate and long links are susceptible to the axial forces. Then an optimum design method is proposed by analyzing the main influencing factors, so links can have good ductility and stiffness at high load levels.


INTRODUCTION
Eccentrically braced frames (EBFs), which combined the advantages of moment resisting frames (MRFs) and concentrically braced frames (CBFs), can exhibit both adequate ductility and lateral stiffness during rare earthquake.The inelastic deformations were only limited to links while the other members, including columns, beam segment outside of links and columns, were designed to remain essentially elastic, so damage on the EBFs can be controlled.Moreover, the ductility mainly depended on links, which was determined by the inelastic rotational capacity and energy dissipation [1][2][3][4][5].Therefore, links were the most important members in EBFs, and the seismic performance of EBFs can be improved by reasonable design of the links.
Link length has a great influence on the inelastic rotation γ p .The length ratio ρ is equal to eV p / M p , where e is the link length, M p and V p are the nominal plastic flexural and shear strength, respectively.According to AISC [6], Links with ρ less than 1.6, called short(shear) links, form plastic hinges at either end and γ p can be designed for 0.08 rad.Links with ρ more than 2.6, called long (flexural) links, yield primarily in flexural and γ p can be designed for 0.02 rad.Links with ρ between 1.6 and 2.6, called intermediate (shear-flexural) links, yield combined of shear and flexural, and γ p can be designed by linear interpolation between 0.08 and 0.02 *Address correspondence to this author at the School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China; Tel:(+86)15579183858; Fax: (+86)15579183421 , (+83)2087113421; E-mail:husj.1229@163.comdepending on the length ratio ρ.Many designers preferred to use links yielded in shear because they showed better stiffness, strength and ductility.However, architectural consideration restricted the application of short links in some situations, so intermediate and long links were also important and inevitable to be used.
As the high significance of the links in the overall performance of the EBFs, many researchers had been dedicated to study the seismic behaviour of links, including the effect of flange with-thickness ratio [7], loading protocol [8], stiffeners [9], overstrength factor [10], tubular links [11] and the performance of intermediate and long links [12].However, more investigations were concentrating on the independence parameters or part of links.In addition, previous studies mainly focused on the A36 [1] , A992 [9] and European steel [13], and the performance of links with different steel is quite different.So it is not known whether the parameters and design method of links given by the AISC can be used for the links with Q235 or Q345 steel.Based on the Q235 steel, a comprehensive analysis of all the links with varying length ratio should be studied, and the maximum inelastic rotation and energy dissipation can be obtained.The influencing factors of links mainly include flange width-thickness ratio, stiffener thickness and placing on side(s), stiffener spacing and axial forces.Moreover, the current flange width-thickness requirement for all the links was derived from Code for seismic design of buildings [14], it may be conservatively for some links, so many rolled steel cross-sections cannot be used as links, and it is also necessary to In this st consider the element mod data, so num short links to ratio is reev reasonable a thickness an analyzing fif forces is con to the analy types of link it can provi better and sa

FINITE E
The accu investigated, of specimen curves, failu compared.F loading pro properties by

Modelin
Many sol in ANSYS, a [15].This el node having nonlinear la stiffening, la in this eleme low cycle fa can be mesh high stress re thickness of

PARAME
The influ width-thickn side(s), stiff forces for lin So many typ which are all

Materia
For mode kinematic ha von mises yi placed on one side because the section depth is less than 640mm.The stiffener thickness, stiffener spacing and web slenderness ratio can all satisfy the requirements of current specification [14].
The maximum inelastic rotation γ max that a link achieves prior to strength degradation is determined from a backbone curve by extracting the points at the maximum displacement of each analysis step in the hysteresis curve.If strength degradation is not happened in the backbone curve, the maximum applied inelastic rotation is chosen as the plastic rotation capacity [12].

Stiffener Spacing and Placing
In order to investigate the influences of stiffener spacing and placing, links with varying length from short links to long links are designed based on H400x250x10x15, and the section properties, stiffener spacing and stiffener spacing are all shown in Table 1.

Axial Fo
The effec K-type EBF are large eno V-type EBF sensitive to t is necessary Thirty-six H400x250x1 axial forces properties, le Table 3  rotations.The ons by the pro dicates the desig men 2; the lines 0.055 for spec is 0.02 for spe have no signi s while N is le ailure modes w ease and excee links and the l hanged from 0 rotations for sp en 2 has a min 0 fA, the inela ign rotation, b alue.Axial forc tic rotations a ses stresses (u    are suggested to use short links and decrease the link length as far as possible, so the maximum inelastic rotation and stable energy dissipation can be obtained.

OPTIMUM DESIGN METHOD FOR LINKS
By means of studying the main influencing factors for links with varying length ratio, an optimum design method for links is developed according to the following steps: (1) Selection of link sections.The first members to be sized in EBFs are links, and the link shear force in each story can be derived by the accumulated story shear force, so the web depth and thickness of link can be determined by the shear forces and web slenderness.The flange width and thickness can be obtained by considering the effect of flange width-thickness ratio, which can be relaxed to 10 235/fy for short and long links and be limited to 8 235/fy for intermediate links.Then the link sections can be selected.
(2) Stiffeners spacing.Stiffeners spacing of all types of links should only satisfy the provision.
(3) Stiffeners place on side(s).Stiffeners of short and long links can only place on one side, but stiffeners of intermediate links are advisable to place on two sides.
(4) Stiffeners thickness.The stiffeners thicknesses of all types of links are only required to satisfy the provision, more than 0.75t w and 10mm.
Moreover, short links will be the most proper links when the axial force should be considered, and the length ratio from 1.3 to 1.5 would be the best choice.

CONCLUSION
Effective finite element investigation of 156 links is conducted to comprehensively study the main influencing factors and global behavior of all types of links with Ishaped cross-section during cyclic loading.The conclusions are as follows: (1) The flange width-thickness ratio can be relaxed to 10 235/fy for short and long links, and the flange width-thickness ratio of intermediate links is always limited to 8 235/fy .
(2) Analysis results indicate that stiffeners spacing of links with varying length ratio have no significant effect on the inelastic rotations, so it is suggested to satisfy the design spacing.Stiffeners of short and long links can only be placed on one side, but stiffeners of intermediate links are advisable to be placed on two sides due to the unstable behavior.
(3) Different stiffeners thicknesses do not affect the failure modes and inelastic rotations significantly.Therefore, more than 0.75t w and 10mm that is considered the structural factor by the provision is suggested.
(4) The effect of axial force of short links should only be considered when the axial force is more than 0.15fA, but the behaviors of intermediate and long links are unstable and susceptible to the axial forces, so it cannot be neglected under any condition.Furthermore, the ductility and strength of short links are better than the other links, it is suggested to use short links and decrease the link length when axial force should be considered, then the maximum inelastic rotation and stable energy dissipation can be obtained.
(5) An optimum design method is proposed by analyzing the main influencing factors for all types of links.

Fig. ( 5
Fig. (5) shows the maximum inelastic rotation γ max versus length ratio ρ, and Fig. (6) shows the normalized inelastic rotation (maximum inelastic rotation/design rotation) versus length ratio for all of seventy links.Short links, intermediate links and long links are indicated by squares, triangles and rhomboids.All of the filled icons indicate links satisfy the requirement of flange width-flange ratio (b f /t f <8 235/f y ), and the empty icons are those that exceed the value.A solid line indicates the allowable maximum design rotation.From Fig.(5) and Fig. (6), all of the short links that include filled and empty icons can reach the maximum design rotation, the intermediate links with filled rhomboids can also satisfy the requirement, but some intermediate links with empty rhomboids cannot reach the design rotation because of the premature failure of flange and web.

Fig.( 7 )
Fig.(7) shows the normalized inelastic rotation versus flange width-thickness ratio for all of the link models.In Fig. (6), all of links satisfy the current flange width-thickness ratio 8 235/f y can reach the design rotation.As the flange width-thickness ratio is relaxed to 10 235/f y , all of the short and long links can reach the requirement of design rotation, but some intermediate cannot reach the design rotation due to the premature failure.These results indicate that the relaxation of flange width-thickness ratio to 10 235/f y can be justified for short and long links, and the value of intermediate links is also limited to 8 235/fy .