# Initial Stress Stiffness for Second Order Aanalysis of Frames

Project: Research

## Researcher(s)

- Yee Tak Andrew LEUNG (Principal Investigator / Project Coordinator)Department of Architecture and Civil Engineering

## Description

The project aims to investigate the various forms of a torque applying at the free end of a straight or curved column and their effects on the second order initial stress stiffness which is essential during Newton iteration in a nonlinear structural analysis. Classically, there are two ways to apply the torque. One is quasi-tangential when a fictitious rigid rod about the neutral axis z is welded along the x- or y- axis of the free end of a column and a pair of equal and opposite forces is applied at the two ends of the rod to produce the resultant torque. The other is semi-tangential (Ziegler 1977 and Argyris 1979) when two fictitious rigid rods are welded orthogonally along the x- and y- axes and two pairs of equal and opposite forces are applied at the four ends of the rods to produce the resultant torque. That becomes four ways when follower is considered. In real life, it is difficult to determine how much the torque is applied in which direction. Also, it is not possible to define the induced shear stress in an oblique direction in both cases. Since these torques are self equilibrating, the stress distribution far away from the end is not affected according to the Saint Venant principle. The errors are acceptable when there is no free end. The PI shows that the buckling torque for a cantilever column can differ by 100% depending on the ways of torque application at the free end. The errors can propagate rapidly in a nonlinear analysis when each iterative step is treated as linear. The formulation will be extended to spatially curved beams when a straight beam becomes curved after loading during the iteration. The success of the project will help to assess the accuracy of commercial packages in a structural analysis for structures having free ends, typified by many falling canopy structures in Hong Kong.## Detail(s)

Project number | 9041358 |
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Grant type | GRF |

Status | Finished |

Effective start/end date | 1/01/09 → 31/03/11 |