Prob. 3.5-10. A three-segment rod is attached to rigid sup- ports at ends A and D and is subjected to equal and opposite external loads P at nodes (joints) B and C, as shown in Fig. P3.5-10. The rod is homogeneous and linearly elastic, with modulus of elasticity E. Let A = A₂ = A, and A₂ = 2A; let L₁ = 2L and L₂ = L = L. (a) Determine the axial stresses ₁, ₂, and o, in the elements, and (b) determine expressions for the horizontal displacements, and uc at nodes B and C, respectively. (1) L₁ P B (2) P3.5-10 and P3.9-2 (3) D P

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Finite element procedure and modelling

Finite element method (FEM) is a mathematical technique that primarily implements the numerical approach and finds approximate solutions to the engineering problems. The finite element method is widely used in many civil engineering applications, especially in the domain of structural mechanics to find solutions to partial differential equations (PDEs), which governs the motion of structures under external influences like loads.