By Saouma V.E.
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Extra info for Lecture Notes in Structural Engineering: Analysis and Desig
6: Semi-Circular three hinged arch Solution: I Reactions The reactions can be determined by integrating the load over the entire structure 1. 6-b) 2. e. limit deflections under service loads to acceptable values (such as ∆ L ≤ 360). 1 2 Later on, we will see that deflection calculations play an important role in the analysis of statically indeterminate structures. 3 We shall focus on flexural deformation, however the end of this chapter will review axial and torsional deformations as well. 4 Most of this chapter will be a review of subjects covered in Strength of Materials.
Like cables, arches can be used to reduce the bending moment in long span structures. Essentially, an arch can be considered as an inverted cable, and is transmits the load primarily through axial compression, but can also resist flexure through its flexural rigidity. 3 4 A parabolic arch uniformly loaded will be loaded in compression only. A semi-circular arch unifirmly loaded will have some flexural stresses in addition to the compressive ones. 1 Arches 6 In order to optimize dead-load efficiency, long span structures should have their shapes approximate the coresponding moment diagram, hence an arch, suspended cable, or tendon configuration in a prestressed concrete beam all are nearly parabolic, Fig.
4 Assume girders to be numbered from left to right. 5 In all free body diagrams assume positivee forces/moments, and take algeebraic sums. 6 The key to the approximate analysis method is our ability to sketch the deflected shape of a structure and identify inflection points. We begin by considering a uniformly loaded beam and frame. In each case we consider an extreme end of the restraint: a) free or b) restrained. For the frame a relativly flexible or stiff column would be analogous to a free or fixed restrain on the beam, Fig.
Lecture Notes in Structural Engineering: Analysis and Desig by Saouma V.E.