Higher mode effects in hinged wall with BRBsin base-frame structures using distributed parameter models

To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame structure and the HWBB-MRF(moment resisting frame)structure are built.The hinged wall is simplified as a flexural beam.BRBs(bucking-restrained braces)are simplified to a rotational spring.MRF is simplified to a shear beam.Vibration equations of distributed parameter models are derived.Natural periods,natural modes of vibration,inner forces and displacements of the distributed parameter models are derived based on the vibration equations using numerical methods.The effect of the relative stiffness ratio and the rotational stiffness ratio on the higher mode effects is investigated.For elastic structures,the global displacement and shear in MRF are predominantly controlled by the first mode,while the shear and bending moment in the wall are significantly affected by higher mode effects.The effect of the yielding of BRB on the inner forces distribution in the HWBB-hinged frame is investigated.The results indicate that the first mode will no longer contribute to the inner forces and the contribution from higher modes to inner forces increases after the BRBs yield.Displacement is not sensitive to higher mode effects and it is controlled by the first mode after the BRBs yield.Parameter analysis demonstrates that the displacement amplitudes are reduced with the increase in the flexural stiffness of the wall before the flexural stiffness reaches a certain value.The first three periods decrease with the increase in the rotational stiffness.With the increase in the rotational stiffness ratio,the contribution from the first mode decreases while contributions from both the second mode and third mode increase.