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This form reveals how to generalize the element stiffness to 3-D space trusses by simply extending the pattern that is evident in this formulation. After developing the element stiffness matrix in the global coordinate system, they must be merged into a single “master” or “global” stiffness matrix.
The full stiffness matrix A is the sum of the element stiffness matrices. In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. For many standard choices of basis functions, i.e. piecewise linear basis functions on triangles, there are simple formulas for the element stiffness matrices.
This type of element is suitable for modeling cables, braces, trusses, beams, stiffeners, grids and frames. Straight elements usually have two nodes, one at each end, while curved elements will need at least three nodes including the end-nodes. The elements are positioned at the centroidal axis of the actual members.
It is a function of the Young's modulus, the second moment of area of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force.
The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. The method is carried out, using either a stiffness matrix or a flexibility matrix.
Elastic constants are specific parameters that quantify the stiffness of a material in response to applied stresses and are fundamental in defining the elastic properties of materials. These constants form the elements of the stiffness matrix in tensor notation, which relates stress to strain through linear equations in anisotropic materials.
The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law .
The stiffness matrix _ _ satisfies a given symmetry condition if it does not change when subjected to the corresponding orthogonal transformation. The orthogonal transformation may represent symmetry with respect to a point , an axis , or a plane .