Question 1 (10 marks). Assembly A model consists of two 1D trusses with dimensions as given in Figure 1. Element 1 runs parallel to the x-axis, connecting node 1 and 2. Element 2 is running at an angle, connecting node 1 and 3. Node 1 has an applied force in the negative y-direction. Node 1 can only move in y-direction, while nodes 2 and 3 are fixed in both x and y-direction. 2 Element 1 50 N 1000 mm/2 E = 200 GPa 500 mm y 1250 mm^2 Element 2 ட். 750 mm Figure 1: 2D truss structure with boundary conditions a) Calculate the stiffness matrices K₁ and K₂ for truss 1 and 2 in the global coordinate system using the following expression: cos² a K=TKT = k cosa sin a - cos² a - cosa sin a cos α sin a sin² a - cosa sin a cos² a - cos² a - cos α sin a - cosa sin a - sin² a cos α sin a EA with k L - sin² a cos α sin a sin² a b) Demonstrate the assembly process for obtaining the global stiffness matrix of the whole system (no boundary conditions or truss parameters to be used at this point). c) Derive the reduced system of equations using the given boundary conditions for displacements and force. Note: this can be done without solving b) d) Solve the matrix system for the unknown vertical displacement at node 1 for the given force and truss dimensions.