The Answer:

A suspension bridge with a two-hinged stiffening girder is classified as indeterminate of one degree (option B). This means that the internal forces and reactions within the bridge cannot be determined solely by applying the equations of static equilibrium.

Explanation:

To understand why this type of suspension bridge is indeterminate of one degree, let's break down the concept step by step.

1. Suspension Bridge:
A suspension bridge is a type of bridge that is supported by cables suspended from towers or piers. The main load-bearing element of a suspension bridge is the cables, which are anchored at both ends of the bridge and carry the weight of the bridge deck.

2. Stiffening Girder:
The stiffening girder is a horizontal beam that runs along the length of the bridge deck and provides additional support and rigidity to the structure. In a two-hinged suspension bridge, the stiffening girder is hinged at both ends, allowing it to rotate and move vertically.

3. Determinacy:
The determinacy of a structure refers to the ability to calculate the internal forces and reactions within the structure using the equations of static equilibrium. A statically determinant structure can be analyzed using these equations, while a statically indeterminate structure requires additional methods such as the flexibility method or the stiffness method to determine the internal forces.

4. Two-Hinged Stiffening Girder:
In a two-hinged suspension bridge, the stiffening girder is connected to the suspension cables at multiple points along its length. This introduces additional unknowns into the system, making it indeterminate of one degree.

5. Indeterminacy of One Degree:
Indeterminacy of one degree means that the structure has one additional unknown that cannot be determined solely by solving the equations of static equilibrium. In the case of a two-hinged suspension bridge with a stiffening girder, this additional unknown is typically the vertical displacement or rotation at one of the hinge points.

6. Solution Methods:
To determine the internal forces and reactions in an indeterminate structure, engineers use various methods such as the flexibility method, the stiffness method, or computer-based structural analysis software. These methods consider the behavior of the structure under different loading conditions and solve for the unknowns using iterative processes.

In conclusion, a suspension bridge with a two-hinged stiffening girder is classified as indeterminate of one degree because it introduces additional unknowns into the system that cannot be determined solely by applying the equations of static equilibrium.