Homogenized rigid body and spring-mass (HRBSM) model for the pushover analysis of out-of-plane loaded unreinforced and FRP reinforced walls

2017 ◽  
Author(s):  
Elisa Bertolesi ◽  
Gabriele Milani
Keyword(s):  
Rigid Body ◽  
Pushover Analysis ◽  
Reinforced Walls ◽  
Out Of Plane

Conditions for the planes of symmetry of an elastically supported rigid body

2009 ◽  
Vol 223 (8) ◽  
pp. 1755-1766 ◽  
Author(s):  
S J Jang ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Eigenvalue Problems ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Mass Matrices ◽  
Out Of Plane ◽  
Modes Of Vibration ◽  
Compliance Matrices ◽  
Special Points ◽  
Elastically Supported

Introducing the planes of symmetry into an oscillating rigid body suspended by springs simplifies the complexity of the equations of motion and decouples the modes of vibration into in-plane and out-of-plane modes. There have been some research results from the investigation into the conditions for planes of symmetry in which prior conditions for the simplification of the equations of motion are required. In this article, the conditions for the planes of symmetry that do not need prior conditions for simplification are presented. The conditions are derived from direct expansions of eigenvalue problems for stiffness and mass matrices that are expressed in terms of in-plane and out-of-plane modes and the orthogonality condition with respect to the mass matrix. Two special points, the planar couple point and the perpendicular translation point are identified, where the expressions for stiffness and compliance matrices can be greatly simplified. The simplified expressions are utilized to obtain the analytical expressions for the axes of vibration of a vibration system with planes of symmetry.

Assessment of ASCE 41 Height-to-Thickness Ratio Limits for URM Walls

2007 ◽  
Vol 23 (4) ◽  
pp. 893-908 ◽  
Author(s):  
Iman Sharif ◽  
Christopher S. Meisl ◽  
Kenneth J. Elwood
Keyword(s):  
Numerical Model ◽  
Rigid Body ◽  
Ground Motions ◽  
Shake Table ◽  
Shake Table Tests ◽  
Site Class ◽  
Seismic Rehabilitation ◽  
Crack Location ◽  
Out Of Plane ◽  
Low Probability

Unreinforced masonry (URM) walls with sufficient anchorage to the diaphragms will crack above mid-height when subjected to out-of-plane ground motions. This study investigates the sensitivity of the out-of-plane response to varying height-to-thickness ( h/ t) ratios for URM walls connected to rigid diaphragms. ASCE 41, Seismic Rehabilitation Standard, provides guidelines for permissible h/ t ratios for out-of-plane URM walls. To assess these limits, a rigid-body numerical model, calibrated to full-scale shake table tests, was used. The focus of the analysis was to identify the minimum h/ t ratio that would cause collapse of the wall when subjected to seismic shaking. The analysis was performed for 80 input motions and accounted for variability in the crack location. The results of the study suggest that the probability of collapse is dependent on the site class and that walls with limited overburden and satisfying the h/ t limits in ASCE 41 have a very low probability of collapse.

Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

2011 ◽  
Vol 226 (5) ◽  
pp. 1254-1262 ◽  
Author(s):  
S-J Jang ◽  
J W Kim ◽  
Y J Choi
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Geometrical Properties ◽  
Plane Vibration ◽  
Numerical Example ◽  
Mass Centre ◽  
Out Of Plane ◽  
Triangular Relationship ◽  
Elastically Supported

The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

Analysis of large deflections for pressure loaded plates with rigid inclusions

1998 ◽  
Vol 33 (3) ◽  
pp. 217-222 ◽  
Author(s):  
K Kimura ◽  
M Okamoto
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Static Load ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Rectangular Plates ◽  
Matching Method ◽  
Point Matching ◽  
Isotropic Plates ◽  
Out Of Plane

In the present paper, the non-linear Berger equation for large deflection problems of isotropic plates and the point-matching method are utilized to obtain solutions for out-of-plane deformations in rectangular isotropic plates with a circular rigid body at the centre. Numerical solutions are presented in order to illustrate the influence of the rigid body size on the deflection distribution in rectangular plates subjected to uniform static load. The numerical procedure is easier than other procedures based on the von Kármán theory, and reasonable results are obtained.

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