Divergence Theorem

Step 1: Apply Divergence Theorem.
The divergence theorem states:

Step 2: Compute divergence.

Step 3: Set up the volume integral.
The region is bounded by , , , . In cylindrical coordinates ( ), with : Jacobian = .

Step 4: Evaluate integral.
After simplification and performing integration, the value comes out to be:

Step 5: Conclusion.
Thus, the required flux is .

Concept: Structural elements are designed to carry different types of loads such as axial forces, bending moments, and shear forces.
Step 1: Understanding axial force.
Axial force acts along the length of a member, either in tension or compression.
Step 2: Behavior of truss members.
In an ideal truss, members are connected by pin joints and carry only axial forces (tension or compression), with no bending moment.
Step 3: Evaluating the options.

• Beam Carries bending and shear (incorrect)
• Column Mainly compression but may have bending (incorrect)
• Truss member Carries only axial force (correct)
• Slab Carries bending (incorrect)

Step 4: Conclusion.
Thus, a truss member ideally carries only axial forces.