Sommario
Viene qui tentata la definizione del modello reologico del calcestruzzo, o cemento armato non parzializzato, in campo di sforzi dinamici sufficientemente lontani dalla rottura; fine al quale avevamo di recente già indirizzato una serie di indagini, volte a chiarire i diversi aspetti del comportamento sperimentale.
Pur con lacune di dettaglio, il modello trovato sembra correttamente interpretare ilmeccanismo dissipativo del nostro materiale, ed è — contrariamente a correnti schematizzazioni viscose — a caratteristica prevalentemente elastoplastica, con smorzatori di tiposolid-friction.
Il lavoro si conclude trattando della determinazione sperimentale dei parametri del modello e di particolari soluzioni approssimate del moto.
Summary
The definition of the rheological model of concrete, or uncracked reinforced concrete, in the field of dynamic stresses sufficiently far from breaking, is here attempted; an aim towards which we had already recently directed a series of investigations to clarify the different aspects of experimental behaviour.
Even with gaps in detail, the model found seems to correctely interpret the dissipativemechanism of our material, and it is — contrary to current viscous schematizations — of a prevalently plasto-elastic characteristic, with dampers of asolid-friction type.
This work concludes dealing with the experimental determination of the parameters of the model and with particular approximate solutions of motion.
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Abbreviations
- d log :
-
logarithmic decrement
- X :
-
amplitude of vibration
- u, w :
-
displacements
- x :
-
abscissa
- z :
-
ordinate
- L :
-
length (of a bar, or beam)
- S :
-
cross-sectional area
- M :
-
mass, bending moment
- \(\bar m\) :
-
specific mass
- K :
-
elastic modulus (force/length)
- E :
-
Young's modulus
- E d :
-
dynamic Young's modulus
- J :
-
moment of inertia of area
- N, P :
-
forces
- p(x):
-
distributed longitudinal load
- q(x):
-
distributed transversal load
- t :
-
time
- T :
-
period of vibration
- ω :
-
circular frequency
- ω 0 :
-
undamped fundamental c.f.
- ω*:
-
damped natural c.f. in a viscous system
- \(\bar \omega \) :
-
2π/T= damped natural c.f. in a system based on the proposed model
- ω i :
-
c.f. relating toith range
- σ :
-
normal stress
- ɛ :
-
normal strain
- r :
-
Newtonian damping constant
- μ :
-
damping constant of the proposed model
- δ :
-
viscous damping coefficient
- γ :
-
solid damping coefficient
- sign (x):
-
x/|x|, respectively 1, 0, − 1 forx: +, 0, −
- exp (x):
-
e x
- i, j :
-
indexes
- n :
-
index, referred to mode of vibration
- \(\dot x, \ddot x\) :
-
∂x/∂t,∂ 2 x/∂t 2
- a, a(u), a(w) :
-
constants
- ξ :
-
cos (πx/L)
- Φ(t):
-
time-function
- ψ(x):
-
shape-function
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Pozzo, E. Rheological model of concrete in the dynamic field. Meccanica 5, 143–158 (1970). https://doi.org/10.1007/BF02134218
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DOI: https://doi.org/10.1007/BF02134218