10-10-2014, 02:07 PM
The dynamic response of reinforced concrete beam-column joint is studied
taking account of initiation, closing and reopening of cracks with strain
softening effect. The computational procedure is based on two-dimensional non
linear finite element method (as is at present restricted to two-dimensional
situation). 8-noded iso-parametric elements are used for concrete as well as for
steel. 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-Mi3es yield criterion is used for both steel and concrete. The
non-linearity comes due to elastic-plastic behaviour of steel, concrete and
cracking of concrete. The cracks are simulated by smeared crack 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 differently in two perpendicular directions and elasticity
matrix (D-matrix) is suitable,, modified based on a modified stress-strain
diagram for concrete in tension, taking into account strain-softening effect. 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 column joint subjected to
dynamic (sinusoidal) loading.