TY - GEN

T1 - Probability distribution of torsional response induced by lateral displacement and inertial force

AU - Yokoyama, Hiroki

AU - Kohiyama, Masayuki

N1 - Funding Information:
This work was financially supported by JSPS KAKENHI Grant Number 16H04455.

PY - 2020

Y1 - 2020

N2 - In previous studies of torsional response, researchers considered torsional vibration of a building to be caused by an eccentric distribution of stiffness, damping, and the structure's mass, as well as spatially non-uniform ground motion input into a long or large base mat of a structure. However, we have discovered that the torque generated by horizontal displacement and the perpendicular inertial force, which we call the Q-? effect, can cause torsional vibration. To investigate this effect, we considered a single finite-size mass-linear elastic shear and torsion spring model and derived the resonance condition with respect to a torsional response from the equation of motion. In this study, we discuss the probability distribution of the induced torque and torsional-displacement response to the input ground acceleration of the uncorrelated Gaussian white-noise in two translational directions. In the frequency domain, the power spectral density function of the torque induced by the Q-? effect is proportional to a convolution of two frequency-response functions in two translational directions. In the time domain, the probability density function of the induced torque is a modified Bessel function of the second kind. Time-history response analysis was conducted to verify these theoretical results and to investigate the distribution of torsional response to Gaussian white-noise input ground acceleration.

AB - In previous studies of torsional response, researchers considered torsional vibration of a building to be caused by an eccentric distribution of stiffness, damping, and the structure's mass, as well as spatially non-uniform ground motion input into a long or large base mat of a structure. However, we have discovered that the torque generated by horizontal displacement and the perpendicular inertial force, which we call the Q-? effect, can cause torsional vibration. To investigate this effect, we considered a single finite-size mass-linear elastic shear and torsion spring model and derived the resonance condition with respect to a torsional response from the equation of motion. In this study, we discuss the probability distribution of the induced torque and torsional-displacement response to the input ground acceleration of the uncorrelated Gaussian white-noise in two translational directions. In the frequency domain, the power spectral density function of the torque induced by the Q-? effect is proportional to a convolution of two frequency-response functions in two translational directions. In the time domain, the probability density function of the induced torque is a modified Bessel function of the second kind. Time-history response analysis was conducted to verify these theoretical results and to investigate the distribution of torsional response to Gaussian white-noise input ground acceleration.

KW - Geometric nonlinearity

KW - High-rise building

KW - Large displacement

KW - Lateral force

KW - Probability distribution of response

KW - Q-? effect

KW - Torsional response

UR - http://www.scopus.com/inward/record.url?scp=85089197224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089197224&partnerID=8YFLogxK

U2 - 10.3850/978-981-11-2724-3_0419-cd

DO - 10.3850/978-981-11-2724-3_0419-cd

M3 - Conference contribution

AN - SCOPUS:85089197224

T3 - Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019

SP - 3224

EP - 3231

BT - Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019

A2 - Beer, Michael

A2 - Zio, Enrico

PB - Research Publishing Services

T2 - 29th European Safety and Reliability Conference, ESREL 2019

Y2 - 22 September 2019 through 26 September 2019

ER -