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Numerical Methods for Nonlinear Analysis

Load Incremental Schemes

It describes the solution method for control of load increment size. There are five methods to be selected.

Newton-Raphson (Constant Load) Method

Single Displacement Control Method

Minimum Residual Displacement Method

Arc Length Method

Constant Work Method

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Plastic Hinge Method

In the process of time history analysis by NIDA, a simple, accurate and efficient method for determining the plastic hinge(s) is used to capture the progressive strength and stiffness degradation of the structure under an earthquake attack.

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Theory of Second-Order Analysis

Background of Second-Order Analysis

Nida checks the section capacity along the length of every initially curved member for P-δ effect, which is required by design code for member imperfection and member second-order effect. Other software only check the P-Δ effect at element ends which is inadequate for full second-order analysis. As the P-Δ and the P-δ effects have been considered in Nida, no effective length or λcr factor is required to be determined.

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Semi-Rigid Connection

A semi-rigid connection must have the required strength, stiffness and ductility. Some typical moment versus rotation (M-θ) curves and various analytical and mathematical models representing the M-θ relationships can be found in previous chapters. Conveniently, a joint can be considered in an analysis as dimensionless with location at the intersection of the element centre lines. Further, a rotational spring element satisfying the M-θ relationship is inserted into each end of beam element to model the connection behaviour. The joint equilibrium condition can be expressed as,

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