5003 Lectures - Faculty of Engineering and Applied Science

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E5003 - Ship Structures I 154 © C.G. Daley Beam 3 has a local [k] that is the same as beam 1. The global [k] also looks similar to the global [k], of beam 1 because a rotation of +90 produces a similar effect to -90. The only change is that the numbering is shifted.
E5003 - Ship Structures I 155 © C.G. Daley The structural stiffness matrix is just the sum of the global versions of the member stiffness matrices. Where two terms share a dof, the two values are added. This is again reflecting the simple idea of superposition in linear systems that Hooke first saw. Stiffness matrices are symmetrical. This is a curious property, especially when you think about the off-diagonal terms. Some of the terms refer to forces per unit rotation and moments per unit translation. With the whole stiffness matrix assembled, we have a single equation that relates all actions (forces and moments) with all movements (translation and rotations):
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5003 Lectures - Faculty of Engineering and Applied Science

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