In the above equation, s is the length of the centerline of the arch, I is the moment of inertia of the arch cross section, E is the Youngs modulus of the arch material. However, in this case, the integration needs to be evaluated along the curved arch length. The above expression is similar to the one used in the case of straight beams. The strain energy due to bending U b is calculated from the following expression. Typically, any section of the arch (vide Fig 33.1b) is subjected to shear force V, bending moment M and the axial compression N. Hence to obtain, horizontal reaction, one must develop an expression for strain energy. In general the horizontal reaction in the two hinged arch is evaluated by straightforward application of the theorem of least work (see module 1, lesson 4), which states that the partial derivative of the strain energy of a statically indeterminate structure with respect to statically indeterminate action should vanish. The unknown redundant reaction H b is calculated by noting that the horizontal displacement of hinge B is zero. The fourth equation is written considering deformation of the arch. Hence, the degree of statical indeterminacy is one for twohinged arch. In the case of two-hinged arch, we have four unknown reactions, but there are only three equations of equilibrium available. In this lesson, the analysis of two-hinged arches is discussed and few problems are solved to illustrate the procedure for calculating the internal forces.ģ3.2 Analysis of two-hinged archA typical two-hinged arch is shown in Fig. Usually, the horizontal reaction is treated as the redundant and is evaluated by the method of least work. Two-hinged arch is the statically indeterminate structure to degree one. However, with the development in structural analysis, for long span structures starting from late nineteenth century engineers adopted two-hinged and hingeless arches.
In the early part of the nineteenth century, three-hinged arches were commonly used for the long span structures as the analysis of such arches could be done with confidence.
Compute reactions developed in two hinged arch due to temperature loading.ģ3.1 IntroductionMainly three types of arches are used in practice: three-hinged, two-hinged and hingeless arches. Analyse two-hinged arch for external loading.
Write strain energy stored in two-hinged arch during deformation. Compute horizontal reaction in two-hinged arch by the method of least work. Instructional Objectives:After reading this chapter the student will be able to 1. Lesson 33Two-Hinged ArchVersion 2 CE IIT, Kharagpur Module 5Cables and ArchesVersion 2 CE IIT, Kharagpur
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