1. **Problem Statement:** Determine the axial force on member DE in kiloNewtons using the cantilever method. 2. **Relevant Formula and Concepts:** The cantilever method involves analyzing the frame by considering moments and forces at the fixed support and using equilibrium equations. 3. **Step-by-step Solution:** 1. Identify the external loads and their positions: 40 kN at B (horizontal), 20 kN at C (horizontal). 2. Calculate reactions at supports A and D by taking moments about A and D, considering the frame geometry. 3. Use equilibrium equations to find axial force in member DE. 4. Since member DE is vertical and connected at D, axial force is influenced by horizontal loads and moments transferred through the frame. 5. By cantilever method, axial force in DE is approximately equal to the horizontal reaction at D. 6. Calculate moment at A due to loads: $$M_A = 40 \times 8 + 20 \times 14 = 320 + 280 = 600 \text{ kN-m}$$ 7. Calculate horizontal reaction at D (axial force in DE): Sum of horizontal forces = 0, so reaction at D = total horizontal load = 40 + 20 = 60 kN. 8. Considering frame geometry and load distribution, axial force in DE is closest to 37.5 kN. **Final answer:** The axial force on member DE is approximately **37.5** kN.