To solve this problem, we need to follow a series of steps. Let's break it down into manageable parts:

### (a) Build the element equilibrium equations [𝑘] 𝑖 {𝑢} 𝑖 = {𝑆} 𝑖 for Elements 1, 2, and 3
For each element 𝑖 = 1, 2, 3, we have:
- Element 1: 
  - Equilibrium equation: [𝑘]₁{𝑢}₁ = {𝑆}₁
  - Cross-sectional area: 𝐴₁
  - Length: 𝐿₁
  - Young's modulus: 𝐸₁
  - Displacement vector: {𝑢}₁
  - Internal force vector: {𝑆}₁

- Element 2: 
  - Equilibrium equation: [𝑘]₂{𝑢}₂ = {𝑆}₂
  - Cross-sectional area: 𝐴₂
  - Length: 𝐿₂
  - Young's modulus: 𝐸₂
  - Displacement vector: {𝑢}₂
  - Internal force vector: {𝑆}₂

- Element 3: 
  - Equilibrium equation: [𝑘]₃{𝑢}₃ = {𝑆}₃
  - Cross-sectional area: 𝐴₃
  - Length: 𝐿₃
  - Young's modulus: 𝐸₃
  - Displacement vector: {𝑢}₃
  - Internal force vector: {𝑆}₃

### (b) Build the global equilibrium equations [𝐾]{𝑞} = {𝑆} with respect to the global coordinate system
- Global stiffness matrix: [𝐾]
- Nodal displacement vector: {𝑞}
- External force vector: {𝑆}

### (c) Apply the boundary conditions to {𝑞} and {𝑆}
- Known individual components should have numerical values with units, while the unknown components should keep the symbols.

### (d) Build two sets of the partitioned global equilibrium equations
- Set 1: Partitioned equations for the unknown displacements and known external forces, [𝐾]𝑘𝑢{𝑞}𝑢 = {𝑆}𝑘
- Set 2: Partitioned equations for the unknown displacements and unknown reaction forces, [𝐾]𝑢𝑢{𝑞}𝑢 = {𝑆}𝑢

### (e) Solve the partitioned equations to obtain {𝑞}𝑢 and {𝑆}𝑢 in numerical values with units
- Use the formula: {𝑞}𝑢 = [𝐾]𝑘𝑢^(-1){𝑆}𝑘
- Find {𝑆}𝑢 = [𝐾]𝑢𝑢{𝑞}𝑢

### (f) For Elements 1, 2, and 3
- Find the element nodal displacements {𝑢̅} 𝑖 with respect to the local coordinate systems using transformation matrices [𝑇] 𝑖
- Find the reaction forces {𝑆̅} 𝑖 with respect to the local coordinate systems using the element equilibrium equations [𝑘̅] 𝑖 {𝑢̅} 𝑖 = {𝑆̅} 𝑖
- Find the strains 𝜖𝑥̅̅̅𝑥̅ 𝑖 and stresses 𝜎𝑥̅̅̅𝑥̅ 𝑖 with respect to the local coordinate systems.

Please let me know if you need further explanation or assistance with any specific part of this problem.