The Effect of tapering on the total amount of tension reinforcing bars in a three span reinforced concrete prismatic beams

The limited amount of natural resowrces have been eontiniously consumed by the human beings over the centuries. If economy is not considered in such consumption, not onJy wasteful expenditure can be prcvended nor there could be a chance of leaving rich natural heritage to the coming generations, which is a social obligation of the mankind. It is obvious that in an any reinforced concrete engineering structure, the amount of reiıtforeiııg material should be selected in tiie most economic and appropriate amount. Emerging from the thought that ; also in the bridge beams tapering would effect the total amount of reutforciment, this research is done to intend to take the attention of designers and constructors to this fact. 11 lis research concentrates on " The Effect of Tapering on the total amount of tension Reinforcing Bars in a Three Span Reinforced Concrete Prismatic Beams." In this contex, the amount of reinforcement in the continious beams without tapering and with tapering is calculated by the method of Bending Moments Influence Lines (BMIL). First, BMIL for the prismatic concrete beams without tapering is calculated, then BMIL for the prismatic concrete beams with tapering is calculated. Hie model taken is a three span continious reinforced concrete prismatic beam and the mid-span nodes in the first and second spans and at the intermediate supports, then using these BMIL 's Dead Loads ( g ) and Live Loads ( q ) are loaded to the beams and for the rectangular cross sections at the chosen nodes, the Ultimate Bending Moments ( UBM ) are calculated. These Calculations are presented in three main sections. hi the Introduction Section, the objective, the contents and the Methods used is explained. In the Second Section ; first the ordinates of the BMIL far the Continious Beam without tapering is calculated with the known methods in the literature. Then th© ordinates of the BMIL 's for the tapered beam is calculated with Kinematic and Moving Unit Load Method, taking in to the account, the ( %, ) ratio of the tapering length arid the ( h^Q ) parameter which gives the rate of chance of BMIL 's are calculeted for the specified nodes and for the sake of generality, they are given in intenns of span length (Lj).In the Third Section ; again first for the continious beam without tapering, for a specified span length, Dead Loads ( g ) and Live Loads ( q ) are loaded in such a way to give the most unsuitable loading position and the Ultimate Bending Moments arc calculated. Then theese moments are used to calculate the raiirfbrcement at the specified nodes along the beam and the rate of change of reinforcement in the beam is observed. Then calculations are carried out for the continious beam with tapering, for the specified ( X ) and (h^/h^) parameters of the tapering in such a way that the Dead ]/oads ( g ) and the live loads ( q ) are loaded again to Hie BMTL's in the most unsuitable loading position to obtain the ultimate Bending Moment. Using these moments, consecutively, for X =0.50, 0.40, 0.30, 0.20 and for h^,^ =2.00, 1.75, 1.50, 1.25 the total A^ value of reinforcing bars are calculated at the mid points of the first and second span and at ih& intermediate support. The rate of change of reinforcement in the continious beam is observed over this A^ value. In the final section ; first, concentration is given to the fact that ; as known from the theory of reinforced concrete ; the area of reinforcement in as section increases proportional to the increase in the Bending Moment up to a curtain area of the concrete cross section. Then after, trie increase in Ûvt area of reinforcement increases in a decreasing manner as the cross section of the concrete increases. Finaly, as the objective of this research, concentration is given to the comparision of this well known fact with the effect of tapering. As a result, it is found that, for a continious three span tapered beam, if the spans are taken equal length, for X =0.20 and h^/ho =1.75, the total area of reinforcement Agj is optimum (^minimum). For the Live Loads, it is found that the decrease in the loads leads to decrease in the ultimate Moments and Agt total area of reinforcement is minimum for X =0.20 and hjho=1.50.