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33 mm to the right; see Figure 3. Figure 3 Computed displacement With a2 , the support forces fb,1 and fb,3 can be computed as fb,1 = −3000 a2 = −40 (29) fb,2 = −4500 a2 = −60 (30) The support force at the left fixing is consequently equal to 40 N and directed leftwards and at the right fixing the support force is 60 N, this one directed leftwards as well; see Figure 4. 01333) = −40 (36) Element 2: Element 3: Element 1 is consequently exposed to a tensile force of 40 N and Elements 2 and 3 to compressive forces of 20 N and 40 N, respectively; see Figure 5.

The method is general and with some small modifications it will be used later for trusses and frames as well. It consists of two parts with a total of seven separate steps2 . Formulation of a computational model: • • • • define the computational model; formulate element matrices; establish compatibility conditions; assemble element matrices by establishing equilibria. Analysis of response for different influences on the computational model: • define boundary conditions and nodal forces; • solve the system of equations; • determine the internal forces.

26), can be simplified to the following steps: • A topology matrix is introduced. It describes in a compact way how a single element is related to the degrees of freedom for the global system. 27) • A matrix K is created and filled with zeros. The matrix K is given the dimensions n × n, where n is the number of degrees of freedom of the spring system. When the process of summation is completed, this matrix will be the global stiffness matrix. • An element stiffness matrix Ke is created for each of the single elements.

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