10-10-2014, 02:09 PM
The dynamic response of reinforced concrete structures (beams) is studied taking
account of initiation and closing and reopening of cracks. The computational
procedure is based on nonlinear finite-element method and is at present
restricted to two-dimensional situations. 8-noded isoperimetric elements are
used for steel as well as concrete. Perfect bond between steel and concrete is
assumed. The validity of this assumption may be questioned but the nature of
distribution of bond stresses near the contact surface between steel and concrete
has not yet been exactly established. Von - mises yield criterion is used for both
steel and concrete. The nonlinearity comes due to elastic-plastic behaviour of
steel and concrete and cracking of concrete. The cracks are simulated by
smeared cracking modelling in which cracks are assumed to be uniformly
distributed in the direction perpendicular to maximum principal tensile stress.
Tensile- strength criterion is used for the initiation of crack. After cracking has
occurred, the cracked concrete is assumed to behave as an orthotropic material
and elasticity matrix (D matrix) is modified. This modified elasticity matrix
contains positive shear modulus to account for aggregate - interlocking. The
equations of motion are integrated numerically using an explicit formulation
with central difference scheme. The procedures outlined are demonstrated on a
reinforced concrete beam subjected to different kinds of dynamic loading e.g.,
sinusoidal loading, step loading and initial velocity. The effect of various
parameters such as area of longitudinal steel (As), area of web steel (Aw), grade
of concrete, grade of steel, aggregate interlocking after cracking, cracking
opening and closing, energy absorbed due to cracking opening and closing in
performing hysterisis loops on the dynamic response of reinforced concrete
beam is studied.