Question

A rectangular barge is freely floating in a drydock as shown in the following figure. For longitudinal strength analysis which of the following are TRUE? 

 

• A. The barge is considered as a free-free beam
• B. At aft and forward ends: shear force = 0, bending moment = 0
• C. The barge is considered as a fixed-fixed beam
• D. At aft and forward ends: shear force \(\neq\) 0, bending moment \(\neq\) 0

Hint:

Remember that a ship's hull is modeled as a "free-free" beam. The word "free" in this context implies that the boundary conditions are zero force (shear) and zero moment. This is a fundamental concept in longitudinal strength calculations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Longitudinal strength analysis of a ship or barge involves modeling the hull as a beam. The beam is subjected to distributed loads from its own weight and the buoyant force of the water. The question asks for the correct beam model and boundary conditions for a freely floating vessel.
Step 2: Detailed Analysis:
- Beam Model (A vs C):
A "freely floating" vessel is not held or supported by any external rigid constraints at its ends. It is free to move and rotate in space, supported only by the fluid pressure along its length. This condition is best modeled as a free-free beam. A free-free beam is a beam that is not supported by pins, rollers, or fixed supports. A fixed-fixed beam would imply that the ends of the barge are rigidly clamped, preventing both translation and rotation, which is clearly not the case for a floating object. Therefore, statement (A) is TRUE and (C) is FALSE.
- Boundary Conditions (B vs D):
For a free-free beam, there are no external forces or moments applied at the ends.
- The shear force at any cross-section of a beam is the integral of the net load (weight minus buoyancy) up to that section. Since there is no concentrated force at the very end of the beam, the shear force must be zero at both the aft and forward perpendiculars.
- The bending moment at any cross-section is the integral of the shear force. Since there is no concentrated moment applied at the very end of the beam, the bending moment must also be zero at both ends.
These boundary conditions (zero shear and zero moment at both ends) are the defining mathematical characteristics of a free-free beam. Therefore, statement (B) is TRUE and (D) is FALSE.
Step 3: Why This is Correct:
The physical situation of a ship floating in water is the classic real-world example of a free-free beam. It is unsupported at its ends, leading to the boundary conditions of zero shear force and zero bending moment at those ends. Statements (A) and (B) correctly describe this model and its consequences.