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Truss elements are oftenly defined as a twonode members which can allow the arbitrary orientation in the coordinate system XYZ. The truss transmits only axial force. In general it is a three degreeoffreedom (DOF) element, such that three global translation components at each end of the member. Trusses are used to model a structures such as bridges, towers and buildings.
Truss element with threedimensional (3D) crosssection, is assumed to have a constant crosssectional area and can be used in linear elastic analysis of a structure. The linear elastic material behavior of the structure is defined only by the modulus of elasticity (E) which is ratio of the stress to the strain. Linear trusses can also be used to simulate transnational and displacement boundary elements.
By its definition, trusses cannot have a rotational degrees of freedoms (DOFs), and even if you released these degrees of freedoms when you applied the boundary conditions to the structure. You can apply translational DOFs as needed, and below figure 1 shows the formulation of a truss element.
Spring element is also in many cases used to represents the flexible nature of supports for more complicated systems in automobile and aerospace industry. In a more general application, yet similar characteristics, element is an elastic bar subjected to axial forces. This element, oftently which we simply call a bar (or) truss element, particularly useful in the analysis of both the 2dimensional and 3dimensional frame or truss structures.
The formulation of the finite element features of an elastic bar element is completely based on the following assumptions:
First of all, we can acquire an expression for the stiffness matrix “K” for the bar element. As we recollect from elementary strength of materials that the change in length (deflection “δ“) of an elastic bar of length L and the uniform crosssectional area A when it is subjected to the axial load P, the relation is as follows:
δ = PL/AE
In the above expression, E defines the materials modulus of elasticity. Then the equivalent spring constant “k” defined as
k = P/δ
k = AE/L
Therefore, the stiffness matrix for single element is:
And the equation of equilibrium in matrix form is:
[ke] { u } = { f }
Substitute the stiffness matrix [ke] in this equation, and we get resultant equilibrium equation in matrix form.
Hence, the above derived expression is Truss Element and its Stiffness Matrix.
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