8/13/2019 Shear Strength Prediction of Crushed Stone Reinforced Concrete Deep Beams Without Stirrups

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36thConferences Our World in Concrete & StructuresSingapore, August 14- 16, 2011

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Shear Strength Prediction of Crushed Stone Reinforced ConcreteDeep Beams without Stirrups

Omar Qarani Aziz Ramzi B. Abdul-AhadPhD, Assist. Professor PhD, Assist. Professor

Civil Engineering Department Building & Construction Department,College of Engineering University of Technology, IraqUniversity of Salahaddin, IraqDr_omer_qarani2yahoo.com

Abstract

Reinforced concrete deep beams appear as common structural elements in many structures fromtall buildings to offshore gravity structures. They are used as panel beams, founded on beams and,more recently, as deep grid walls in offshore gravity-type concrete structures. The term deep beamsapplies to any beam which has a depth to span ratio great enough to cause non-linearity in the elasticflexural stresses over the beam depth and the distribution of shear stress to be non-parabolic. Thecombination of stresses (bending and shear) in the shear span results in inclined cracks whichtransform the beam into a tied-arch. The strength of deep beams is usually controlled by shear, ratherthan flexure, provided that normal amounts of longitudinal reinforcement are used. On the other hand,shear strength of deep beams is significantly greater than that predicted using expressions developedfor slender beams, because of their special capacity to redistribute internal forces before failure anddevelop mechanisms of force transfer quite different from beams of normal proportions.

Effect of crushed stones and their contribution to the shear strength of reinforced concrete deep

beams without shear reinforcement was taken into account different parameters, such as l/d, a/d,fc,...etc. For this purpose eleven reinforced concrete deep beams were cast and tested.

All the tested beams were rectangular in cross-section having the dimensions ( b=120 , l=1000 )mm . The overall depth varied from 150 to 450 mm to get the required l/d and a/d ratios. OrdinaryPortland cement , 10- mm maximum size crushed stone , and sand of 2.85 fineness modulus ( mixproportion 1 : 1.40 : 2.80 ), ( cement: sand: crushed stone), were used throughout . Verticaldeflections were measured at the mid-span of the tested beams. Electrical resistance strain gages (10mm in length) were used for measuring strain of concrete and main reinforcement.

Ultimate shear stress of crushed stone concrete deep beams without shear reinforcementdecreases by increasing the span to depth ratio. When, the span to depth ratio is increased from 2.53to 7.41, the ultimate shear stress decreases by about 37%. This reduction is attributed to the differenttypes of shear transfer mechanisms.

By increasing the shear span to depth ratio from 1.05 to 2.22 (for d/b between 1.14-3.29), the

ultimate shear stress decreases by about 37%, while the ultimate shear stress decreased by about27.5% where the ratio d/b is constant (d/b = 1.82). The reduction in the ultimate shear stress isattributed to the different types of shear transfer mechanisms which are strongly dependent on theshear span to depth ratio.

The ultimate shear stress increased by about 33.8% and 34% when the compressive strength wasincreased from 30 MPa to 43 MPa for shear span to depth ratios of 1.5 and 1.25 respectively.

The ultimate shear stress increases by about 37% when the depth to width ratio is increased from1.14 to 3.29. This increase is not only due to the increasing of depth to width ratio, but also dependson the span to depth ratio. Increasing maximum size of course aggregate from 9.5 mm to 19 mmleads to a decrease in the ultimate shear stress of about 3.9% , the difference between the crackingand ultimate shear stress decreases with an increase in l/d ratio, a/d ratio and maximum size of coarseaggregate. It has been noticed that for a given shear stress, the deflection decreased with increasingl/d, a/d, compressive strength of concrete and a maximum size of aggregate. By increasing l/d from

2.53 to 7.47, a/d from 1.0 to 2.29 and a maximum size of coarse aggregate from 9.5 mm to 19 mm,the deflection at ultimate shear stress decreased by about 47.3%, 24.9% and 29.1% respectively,

8/13/2019 Shear Strength Prediction of Crushed Stone Reinforced Concrete Deep Beams Without Stirrups

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Omar Qarani Aziz and Ramzi B. Abdul-Ahad

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while the deflection increased by about 15%, when the compressive strength was increased from 30MPa to 43.5 MPa.

Cracks in the concrete beams are formed generally in regions where tensile stresses exist andexceed the specified tensile strength of concrete. Two types of cracks were observed in the testedbeams: the flexural cracks which result from flexural tensile stresses in the region of the beam cross-section below the natural axis and shear cracks which are formed as a result of the inclined or

principal tensile stresses acting on the web of the beam in the region of combined bending andshear.

In addition to the present work (11 beams), results of (196) reinforced concrete deep beams (fromliterature) failing in shear are also included

[3,4,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] in the

analysis. Nonlinear multiple stepwise regression was adopted to relate the ultimate shear stress interms of the affecting parameters

The strut - and - tie model was used here to develop an equation based on stresses in concreteand steel for predicting the shear strength of deep beams without shear reinforcement . To do this firstthe load - path of transfer stresses is assumed and then the more details of struts are assumed.The equations which were proposed were tested and compared with other proposed equations givenby codes of practice and researchers). Theses equations were applied to 206 reinforced concretedeep beams without shear reinforcement failing in shear to investigate the reasons behind the weakrepresentation of code design equations for the shear strength when compared with the proposed

equations. The relative shear strength values (vu exp./ vu cal.) were found using these equations, thenthe value of SD, SE, COV., and r were also calculated for each equation.

The relations show that the code design equations underestimate the shear stress of reinforcedconcrete beams with shear span to depth ratio ranging from 1.0 to 2.5. This is because of the fact thatthese equations neglect the effect of arch action on the shear strength and consider the inclinedcracking load as ultimate shear strength. Siao and proposed equations had lower values of COVwhen compared with the other equations.