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.