1. Solution to MCQ
Question: A three hinged girder is used to stiffen a cable of a suspension bridge. Then the bending moment in the girder due to loads will be ____________.
Correct Option: D) zero over the entire span
Justification: In a suspension bridge, the purpose of a stiffening girder is to distribute concentrated loads into a uniform load on the cable to maintain its parabolic shape. In the idealized theoretical case for a three-hinged stiffening girder, the internal forces are balanced such that the girder itself does not carry bending moments from the primary suspension loads; the cable carries the load through tension, and the girder ensures the cable's geometry remains stable.
2. Additional High-Yield MCQs from Source (Syllabus 1.4: Suspension Systems)
1. A suspension cable, supporting loads will be under:
2. The maximum tension in a cable occurs:
A) at the highest point in the cable
B) at the lowest point in the cable
C) at the center point of the cable
D) at all points in the cable
Correct Answer: A
3. A cable subjected to UDL over its entire span assumes a shape of:
A) semi-circle
B) an isosceles triangle
C) parabola
D) none of the above
Correct Answer: C
4. The amount of bending moment induced in a cable is:
A) unity
B) zero
C) two
D) all of the above
Correct Answer: B
5. A parabolic cable is subjected to a rise of t °C in temperature. Then the increase in dip of the cable is proportional to:
6. The horizontal tension (H) in a cable is equal to the bending moment of a beam of same span divided by:
A) span length
B) dip of the cable
C) square of the dip
D) unit weight of cable
Correct Answer: B
3. Core Theoretical Concepts: Stiffened Suspension Bridges
Function of Stiffening Girders: Flexible cables change shape significantly under moving concentrated loads. Stiffening girders (two-hinged or three-hinged) are provided to limit these deformations and distribute loads to the cable more uniformly.
Three-Hinged Stiffening Girder: It is a statically determinate structure. The hinges are typically located at the two supports and at the center of the span.
Bending Moment Theory: While the girder is called a "stiffening" member, in a perfectly designed system under certain loading conditions, the net bending moment is zero because the upward pull of the cable's hangers exactly balances the downward external loads.
Horizontal Thrust: The horizontal component of the cable tension ($H$) is constant throughout. The vertical load at any point in the girder is transferred to the cable via hangers.
Shear Force and Bending: While the theoretical bending moment can be zero over the entire span for specific uniform conditions, in practice, the girder resists the local effects of moving point loads, preventing local "kinking" of the cable.
Influence Lines: For a three-hinged girder, the influence line for bending moment at any section consists of two parts: the "beam" moment and the "cable" moment, which oppose each other.
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