Theoretical And Experimental Study On Design Methods For Pre-tensioned Cable Stayed Buckling-restrained Braces

A pre-tensioned cable stayed buckling-restrained brace(PCS-BRB)is a new type of buckling-restrained brace(BRB).It is formed through introducing an additional structural system of pre-tensioned cables and a number of cross-arms to the outside of a common BRB.This new system significantly improves the BRB's overall external restraining stiffness,hence increasing the load-carrying efficiency in its structural design.Due to its aesthetically appealing structure,it can be utilised in stadiums and so forth as a laterally resistant brace.This paper particularly explores and analyses the single cross-arm with 4-stay PCS-BRB in details.The elastic buckling performance of the single cross-arm PCS-BRB is investigated at first,and equilibrium method is utilized to deduce formulas of elastic buckling load of pin-ended single cross-arm PCS-BRB.The findings indicate that two different types of buckling modes may occur in this PCS-BRB,namely single-wave symmetric and double-wave antisymmetric buckling modes.It was found from theoretical and numerical analyses that a negative linear correlation exists between elastic buckling load and initial pre-tensioning force of the cables if the geometric parameters of the cable stayed system are defined.Under the actions of axial loads,the first design method of the lower limit of restraining ratio of the single cross-arm PCS-BRB considering single-wave symmetric initial imperfections where the first order buckling mode is of single-wave type is established based on the principle that cross-sectional bending capacity of the external tube shall be no less than its maximum bending moment considering the secondary effect.In addition,the second design method of the lower limit of restraining ratio of the single cross-arm PCS-BRB considering double-wave antisymmetric initial imperfections where the first order buckling mode is of double-wave type is established based on the principle that the external tube shall not lose its overall stability when it is subjected to a combination of axial compression and bending moment.The worst case of initial imperfection mode is determined through the analysis of the effect of the initial imperfection on the axial compressive load-carrying capacity of the PCS-BRB.Thus the overall instability of the PCS-BRB would not occur before the core reaching its full cross-sectional yield capacity under static axial compression based on the two design methods of the lower limit of restraining ratio mentioned previously.By ignoring the contribution of the lateral translational stiffness from the core to the overall PCS-BRB,and according to the consideration that the extreme fiber of the external restraining tube would yield when the core is under strain hardening,the design methods of the lower limit of restraining ratio are established based on appropriate hysteretic loading protocol,which fulfils the energy dissipating requirement.The initial pre-tensioning force of the cables possesses remarkable effect on the load-carrying capacity of the PCS-BRB.The design method of the lower limit of initial pre-tensioning force of the single cross-arm PCS-BRB that overall instability of the PCS-BRB would not occur before the core reaching its full cross-sectional yield capacity under static axial compression is established by considering the effect of the core being fully sectional yielded on the overall reduction of the bending stiffness of the PCS-BRB and the initial pre-tensioning force of the cables.The optimal initial pre-tensioning force of the cables is established according to a critical condition where the external tube is yielded at the edge while one side of the cables become loose.This optimal value can be used as the maximum initial pre-tensioning force to ensure that overall instability of PCS-BRB would not occur in advance due to excessive initial pre-tensioning force of the cables.Ultimately,experimental investigation were conducted on single and double cross-arm PCS-BRBs to investigate their hysteretic performance,thus validating the theoretical derivations and the rationality of the FE analyses.In addition,the feasibility different end structural forms of the core are compared.This paper also provides several issues that may arise in the design and manufacture of the PCS-BRB according to the failure modes and variations of the cable force observed from the experimental tests.This provides useful reference for engineering applications.