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Apply a free-body analysis to the bar BDE to find the forces exerted by links AB and DC. Evaluate the deformation of links AB and DC or the displacements of B and D. Work out the geometry to find the deflection at E given the deflections at B and D. Example 5 (cont’d) SOLUTION: Free body: Bar BDE. ∑ MB = 0.
Displacement diagram (to Scale) Horizontal Displacement = PL AE to the left vertical displacement = 12.9 PL AE
Displacement diagrams are effectively plotting the displacement vectors of the joints as defined by the end of the bars. The displacement vector for the end of a bar is made up of two components: (1) an extension, of a magnitude defined by the bar force and the constitutive behavior of the bar which is parallel to the direction of the bar and (2) a
– Difficult to find approx solution that satisfies displacement BC • Finite element approximates solution in an element – Make it easy to satisfy dis placement BC using interpolation technique • Beam element – Divide the beam using a set of elements – Elements are connected to other elements at nodes
Consider the beam of Fig. 1.14 axially loaded along the x axis in com-pression. If a small load or displacement is applied laterally at the location of the axial load, the beam bends slightly. If the lateral load is removed, the beam returns to its straight position.
• Determine the relative displacement of the free end at A with respect to the fixed end at D. The modulus of elasticity for aluminum is 10 x 10 6 psi • Solve the problem using the ( a)discrete element method, and (b) the superposition method.
You're trying to find the displacement of the bar with the load distributed longitudinally at a point A. You use the formula displacement = PL/AE where P=load, L=length of member, A=cross-sectional area tangent to the load, and E=Young's modulus.
