5003 Lectures - Faculty of Engineering and Applied Science

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E5003 - Ship Structures I 152 © C.G. Daley Aside: There is a general way to find the global stiffnesses for a rotated bar. The rotation matrix can be used to find the stiffness terms for a rotated beam. In a rotated beam dof 1 is partly axial and partly shear, as is dof 2. But as superposition holds, any movement along dof 1 can be expresses as some axial and some shear, and the resulting axial and shear forces can be resolved back into the 1 and 2 directions. The matrix below and the matrix operation expresses the mix of effects in a concise way.
E5003 - Ship Structures I 153 © C.G. Daley (suggestion: derive the rotation matrix using vector algebra). In the case of a 90 degree rotation, the rotation matrix has the effect of doing row-column swaps. For other angles the effect is more complicated. Beam 2 has a local [k] that is similar to beam 1 except that area is 2A and modulus is 4I. The global [k] looks similar to the local [k], except that the numbering is shifted.
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5003 Lectures - Faculty of Engineering and Applied Science

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