Civil Engineering - UPSC Civil Service Exam Questions - Discussion


In the case of a three-pinned parabolic arch carrying a uniformly distributed load on the entire span, then bending moment will be

[A]. equal to that of a simply supported beam loaded in the same manner
[B]. maximum at quarter span
[C]. zero only at the centre
[D]. zero throughout the span

Answer: Option D


No answer description available for this question.

Ankit Poriya said: (Aug 4, 2015)  
Please give me full detail of this question.

Amit Kumar said: (Aug 19, 2016)  
It should be zero only at hinge point. In this case only 3 point have 0 bm. However other point might go some bm. How it will be zero throughout the span?

Vithal said: (Jan 14, 2018)  
It is because the structure is funicular with respect to the loading.

If shape of the bending moment as well as the structures geometry is similar in proportion, then the bending moment will be zero. The same happens with a triangular structure which has point load at the top of the vertex.

All those structures are funicular with respect to their loading. Similar concept is used in prestressed concrete cable profile (parabolic/linear variation along span).

The implication I get out of this is that, a flexible structure such as cable will experience negligible bending moments because the it can change its shape to become funicular with load.

However caution must be exercised, as a rigid structure such as concrete and steel will not be able to adapt its geometry to the loading. If designed for zero bending moment for a given loading (say for uniform Dead load and live load) the members or the structure as whole will experience moment under different loading condition say due to a point load or a lateral force due to wind or seismic actions.

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