m5l32

# m5l32 - Module 5 Cables and Arches Version 2 CE IIT...

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Module 5 Cables and Arches Version 2 CE IIT, Kharagpur

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Lesson 32 Three Hinged Arch Version 2 CE IIT, Kharagpur
Instructional Objectives: After reading this chapter the student will be able to 1. Define an arch. 2. Identify three-hinged, two-hinged and hingeless arches. 3. State advantages of arch construction. 4. Analyse three-hinged arch. 5. Evaluate horizontal thrust in three-hinged arch. 32.1 Introduction In case of beams supporting uniformly distributed load, the maximum bending moment increases with the square of the span and hence they become uneconomical for long span structures. In such situations arches could be advantageously employed, as they would develop horizontal reactions, which in turn reduce the design bending moment. For example, in the case of a simply supported beam shown in Fig. 32.1, the bending moment below the load is 16 3 PL . Now consider a two hinged symmetrical arch of the same span and subjected to similar loading as that of simply supported beam. The vertical reaction could be calculated by equations of statics. The horizontal reaction is determined by the method of least work. Now Version 2 CE IIT, Kharagpur

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the bending moment below the load is Hy PL 16 3 . It is clear that the bending moment below the load is reduced in the case of an arch as compared to a simply supported beam. It is observed in the last lesson that, the cable takes the shape of the loading and this shape is termed as funicular shape. If an arch were constructed in an inverted funicular shape then it would be subjected to only compression for those loadings for which its shape is inverted funicular. Since in practice, the actual shape of the arch differs from the inverted funicular shape or the loading differs from the one for which the arch is an inverted funicular, arches are also subjected to bending moment in addition to compression. As arches are subjected to compression, it must be designed to resist buckling. Until the beginning of the 20 th century, arches and vaults were commonly used to span between walls, piers or other supports. Now, arches are mainly used in bridge construction and doorways. In earlier days arches were constructed using stones and bricks. In modern times they are being constructed of reinforced concrete and steel. Version 2 CE IIT, Kharagpur
A structure is classified as an arch not based on its shape but the way it supports the lateral load. Arches support load primarily in compression. For example in Fig 32.3b, no horizontal reaction is developed. Consequently bending moment is not reduced. It is important to appreciate the point that the definition of an arch is a

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m5l32 - Module 5 Cables and Arches Version 2 CE IIT...

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