Nonlinear analysis of reinforced concrete portal frames

There are considerable difficulties in describing the properties of reinforced concrete
materials and their interaction. It is therefore necessary to calibrate the mathematical
model by accurate testing of laboratory specimens. It can be shown that momentcurvature
relationship varies along the length of a member and at beam-column joints.
This behaviour depends critically on the geometry of the joint, reinforcement details and
the stress-strain characteristics of concrete and steel.
Tests have been carried out on model reinforced concrete portal frames and independent
specimens making up the frame to predict their non-linear behaviour. The stiffness of
the joint plays an important role in the response of the complete frame structure. The
behaviour of the corner joints is of particular interest because both the strength and
ductility differs for opening and closing joints. The loss of stiffness at joints has a
significant effect on the inelastic deformations. The non-linear finite element (FE)
program developed takes into account the loss of stiffness at joints and the falling
branch behaviour of the material stress-strain relationships. Constant, linear, and
parabolic variation in flexural rigidity (EI) and axial rigidity (EA) are taken into
consideration along the element length. The combined effect of material and geometric
non-linearity is considered. The FE program may use either calculated momentcurvature
relationship of different elements or the experimental data obtained from tests.
The results show good agreement between the theoretical and experimental beam
moment-curvature relationships. Horizontally loaded frame analysis, which involves
opening and closing joints, shows that ignoring the joint effect over-estimates the
strength. In the case of vertically loaded frames, which involves two closing joints,
ignoring the joint effects had little or no influence. The results show good agreement
between the theoretical and experimental frame force-displacement relationships
throughout the loading range providing the change of stiffness at joints is taken into
account for horizontally loaded frames.

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