Abstract
The most known continuum damage theories for brittle structures are suitable to model the degradation of the material due to the deformation process and the consequent initiation of a macro-crack Nevertheless; they are not able to describe the propagation of the crack that leads, eventually, to the breakage of the structure into parts that undergo rigid body motion. This paper presents a theory, formulated from formal arguments of Continuum Mechanics, that may describe not only the degradation but also the fracture of elastic structures. The modeling of such a discontinuous phenomenon through a continuous theory is possible by taking a cohesion variable, related with the Links between material points, as an additional degree of kinematical freedom. The possibilities of the proposed theory are discussed through examples.
Address
Heraldo S. Costa Mattos: Department of Mechanical Engineering, Universidade Federal Fluminense, 24210-240 Niteroi-RJ-Brazil;
Rubens Sampiao:
Department of Mechanical Engineering, Pontificia Universidade Catolica do Rio de Janeiro, 22453-900 Rio de Janeiro-RJ-Brazil.
Abstract
The deformational response of plastic board drains installed to accelerate consolidation of soft soils, is examined as a problem of downdrag. The drain is modelled as a beam-column in which the axial load increases nonlinearly with depth. The soil response is represented by the Winkler medium whose coefficient of subgrade modulus increases linearly with depth. The governing equations for the drain-soil system are derived and solved as an eigenvalue problem. The critical buckling loads and the shape of the drain are obtained as functions of the normalized subgrade modulus of the soil at the top, the parameters signifying the variation of axial load along the length of the drain and the increase of subgrade modulus with depth. The derived deformed shapes of the drain are consistent with the observed ones.
Key Words
BUCKLING, CONSOLIDATION, DOWNDRAG, FLEXURAL STIFFNESS, KINKING, MECHANICS, MODULUS OF SUBGRADE REACTION, PLASTIC BOARD DRAINS
Abstract
Previous studies of a stepped cantilever with two straight segments under a suddenly applied constant force (a step load) applied at its tip have shown that the validity of deformation mechanisms is governed by certain geometrical restrictions. Single and double-hinge mechanisms have been proposed and it is shown in this paper that for a stepped cantilever with a stronger tip segment, i.e. M(0.1) > M(0.2), where M(0.1) and M(0.2) are the dynamic fully plastic bending moments of the tip and root segments, respectively, the family of possible yield mechanisms is expanded by introducing new double and triple-hinge mechanisms. With the aid of these mechanisms, it is shown that all initial deformations can be derived for a stepped cantilever regardless of its geometry and the magnitude of the dynamic force applied.
Abstract
When a tubular cantilever beam is loaded by a dynamic force applied transversely at its tip, the strain hardening of the material tends to increase the load carrying capacity and local buckling and cross-sectional overlization occurring in the tube section tends to reduce the moment carrying capacity and results in structural softening. A theoretical model is presented in this paper to analyze the deformation of a tubular beam in a dynamic response mode. Based on a large deflection analysis, the hardening/softening M-kappa relationship is introduced. The main interest is on the curvature development history and the deformed configuration of the beam.
Key Words
ELASTOPLASTIC DEFORMATION, DYNAMIC PLASTICITY, LARGE DEFLECTION, HARDENING SOFTENING MOMENT CURVATURE RELATIONSHIP, IMPACT, PIPE WHIP
Abstract
In the past, physical models have been proposed, in compliance with the concept of the compressive-force path, for the realistic design of various statically determinate structural concrete members. The present work extends these models so as to encompass indeterminate RC structural forms. Pilot tests conducted on continuous beams and fixed-ended portal frames have revealed that designing such members to present-day concepts may lead to brittle types of failure. On the other hand similar members designed on the basis of the proposed physical models attained very ductile failures. It appears that, unlike current design approaches, the compressive-force path concept is capable of identifying those areas where failure is most Likely to be triggered, and ensures better load redistribution, thus improving ductility. The beneficial effect of proper detailing at the point of contraflexure in an indeterminate RC member is to be noted.
Abstract
Effectiveness of multiple tuned mass dampers (MTMD) in suppressing the dynamic response of base excited structure for first mode vibration is investigated. The effectiveness of the MTMD is expressed by the ratio of the root mean square (RMS) displacement of the structure with MTMD to corresponding displacement without MTMD. The frequency content of base excitation is modelled as a broad-band stationary random process. The MTMD\'s with uniformly distributed natural frequencies are considered for this purpose. A parametric study is conducted to investigate the fundamental characteristics of the MTMD\'s and the effect of important parameters on the effectiveness of the MTMD\'s. The parameters include: the fundamental characteristics of the MTMD system such as damping, mass ratio, total number of MTMD, tuning frequency ratio, frequency spacing of the dampers and frequency content of the base excitation. It has been shown that MTMD can be more effective and more robust than a single TMD with equal mass and damping ratio.
Key Words
EFFECTIVENESS, MTMD, VIBRATION CONTROL, STOCHASTIC RESPONSE AND SYSTEM PARAMETERS
Address
JANGID RS, INDIAN INST TECHNOL,DEPT CIVIL ENGN,BOMBAY 400076,MAHARASHTRA,INDIA
Abstract
The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.
