Question

plot the diagram of the axial force of the rod
6kn a i b ii c iii d
10kn 8kn 4kn

Explanation:

Step1: Analyze Segment I (A - B)

Take a section in segment I, consider the left part. The axial force \( F_{N1} \) is equal to the force at A, so \( F_{N1}=- 6\,\text{kN} \) (compression, negative for compression, positive for tension).

Step2: Analyze Segment II (B - C)

Take a section in segment II, consider the left part. Forces: \( 6\,\text{kN} \) left and \( 10\,\text{kN} \) left. So \( F_{N2}=-(6 + 10)=-16\,\text{kN} \) (compression).

Step3: Analyze Segment III (C - D)

Take a section in segment III, consider the right part (easier). Force \( 4\,\text{kN} \) right. So \( F_{N3}=4\,\text{kN} \) (tension, positive as it's tension).

Step4: Plot the Axial Force Diagram

• For segment I (A - B): axial force is \(-6\,\text{kN}\) (constant, horizontal line at \( y = - 6\)).
• For segment II (B - C): axial force is \(-16\,\text{kN}\) (constant, horizontal line at \( y=-16\)).
• For segment III (C - D): axial force is \(4\,\text{kN}\) (constant, horizontal line at \( y = 4\)).

Answer:

The axial force diagram has three horizontal segments: \( F_{N}=-6\,\text{kN} \) (A - B), \( F_{N}=-16\,\text{kN} \) (B - C), \( F_{N}=4\,\text{kN} \) (C - D).