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A symmetrical three-hinged parabolic arch of span L and rise h is hinged at springing and crown. It is subjected to a UDLw throughout the span. What is the bending moment at a section L/4 from the left support?
- a)wL2/8
- b)wL2/16
- c)wL3/8h
- d)Zero
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A symmetrical three-hinged parabolic arch of span L and rise h is hing...
Solution:
Given, span of the arch = L, and rise of the arch = h
The arch is symmetrical and three-hinged.
The arch is subjected to a uniformly distributed load (UDL) of w throughout the span.
We need to find the bending moment at a section located L/4 distance from the left support.
Let the left support be A, the right support be C and the crown be B.
The UDL w will be resolved into vertical and horizontal components.
The vertical component of the UDL will be resisted by the arch as compression.
The horizontal component of the UDL will be resisted by the horizontal thrust developed at the supports.
The shape of the arch is parabolic, which means that the bending moment is zero at the crown (point B) and increases as we move towards the supports.
At the left support A, the bending moment is zero because there is no load on the left of A.
At the right support C, the bending moment is zero because the horizontal thrust balances the bending moment due to the UDL.
At the section located L/4 distance from the left support, the bending moment will be zero because of the symmetry of the arch.
Therefore, the correct option is D) Zero.
Given, span of the arch = L, and rise of the arch = h
The arch is symmetrical and three-hinged.
The arch is subjected to a uniformly distributed load (UDL) of w throughout the span.
We need to find the bending moment at a section located L/4 distance from the left support.
Let the left support be A, the right support be C and the crown be B.
The UDL w will be resolved into vertical and horizontal components.
The vertical component of the UDL will be resisted by the arch as compression.
The horizontal component of the UDL will be resisted by the horizontal thrust developed at the supports.
The shape of the arch is parabolic, which means that the bending moment is zero at the crown (point B) and increases as we move towards the supports.
At the left support A, the bending moment is zero because there is no load on the left of A.
At the right support C, the bending moment is zero because the horizontal thrust balances the bending moment due to the UDL.
At the section located L/4 distance from the left support, the bending moment will be zero because of the symmetry of the arch.
Therefore, the correct option is D) Zero.
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A symmetrical three-hinged parabolic arch of span L and rise h is hing...
For 3 hing arches and 2 hinge arches when the arches are loaded with udl throught the span bending moment and shear force is zero
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