reinforced concrete beams v2.ppt - Memphis

1 reinforced concrete BeamsMathematical modeling of reinforced concrete is essential to civil engineeringConcrete as a materialConcrete in a structureMathematical modeling of reinforced concrete is essential to civil engineeringReinforced concrete BeamsStress distribution in a reinforced concrete beamReinforced concrete BeamsMathematical modeling of reinforced concrete is essential to civil engineeringGeometric model a reinforced concrete bridgeReinforced concrete BeamsMathematical modeling of reinforced concrete is essential to civil engineeringBlast failure of a reinforced concrete wallReinforced concrete BeamsMathematical modeling of reinforced concrete is essential to civil engineeringBlast failure of a reinforced concrete wallReinforced concrete BeamsMathematical model for failure in an unreinforced concrete beamCIVL 1112 Strength of reinforced concrete Beams1/11 reinforced concrete BeamsMathematical model for failure in an reinforced concrete beamReinforced concrete BeamsPIn the reinforced concrete beam project, there are three different failure mode we need to investigate reinforced concrete BeamsPP/2P/2 First.

2 Lets consider the loading of the beamReinforced concrete BeamsPP/2P/2 The purpose of RC is the reinforcement of areas in concrete that are weak in tensionReinforced concrete BeamsPP/2P/2 Let s look at the internal forces acting on the beam and locate the tension zones2 PFV V is the shear force 2PV VReinforced concrete BeamsP/2 The shear between the applied load and the support is constant V = P/2P/222 PPFV V CIVL 1112 Strength of reinforced concrete Beams2/11 reinforced concrete BeamsP/2 The shear between the applied load and the support is constant V = P/2P/2 reinforced concrete BeamsP/2 The shear between the applied load and the support is constant V = P/2P/2 The shear force V = P/2is constant between the applied load and the supportReinforced concrete BeamsPP/2P/2 Let s look at the internal moment at section between the supports and applied loadP/2 Mis the bending moment2 PMx xX max= 8 in.

3 ( )4 MPReinforced concrete beams Let s look at the internal moment at section between the supports and applied load The bending moment is the internal reaction to forces which cause a beam to bend. Bending moment can also be referred to as torqueM2 PReinforced concrete BeamsThe top of the beam is in compression and the bottom of thebeam is in tensionBending moment distributed on the cut surfaceCTCompression force on the upper part of the concrete beamTension force on the lower part of the concrete beamReinforced concrete BeamsTo model the behavior of a reinforced concrete beam we will need to understand three distinct regions in the are illustrated below; the third is called moment distributed on the cut surfaceCompressionTensionCTCIVL 1112 Strength of reinforced concrete Beams3/11 reinforced concrete BeamsPTensionWe need models to help us with compression, tension, and shear failures in concrete reinforced concrete BeamsPCompressionWe need models to help us with compression, tension, and shear failures in concrete reinforced concrete BeamsPShearShearWe need models to help us with compression, tension, and shear failures in concrete PTensionCompressionShearShearWe need models to help us with compression, tension.

4 And shear failures in concrete reinforced concrete BeamsReinforced concrete BeamsCompression and tension failures in a reinforced concrete beam Compression and tension failures in a reinforced concrete beam reinforced concrete BeamsCIVL 1112 Strength of reinforced concrete Beams4/11 reinforced concrete BeamsShear failure in a reinforced concrete beamShear failure in a reinforced concrete beamReinforced concrete BeamsReinforced concrete BeamsPTensionLet s focus on how to model the ultimate tensile load in a reinforced concrete beamTypical rebar configuration to handle tension and shear loadsReinforced concrete BeamsTypical rebar configuration to handle tension and shear loadsReinforced concrete BeamsTypical rebar configuration to handle tension and shear loadsReinforced concrete BeamsCIVL 1112 Strength of reinforced concrete Beams5/11 Whitney Rectangular Stress DistributionIn the 1930s, Whitney proposed the use of a rectangular compressive stress distribution Whitney Rectangular Stress DistributionIn the 1930s.

5 Whitney proposed the use of a rectangular compressive stress distribution ck2xWhitney Rectangular Stress DistributionAssume that the concrete contributes nothing to the tensile strength of the beambhdAsTCck3f Rectangular Stress DistributionAssume that the complex distribution of compressive stress in the concrete can be approximated by a ck2xWhitney Rectangular Stress DistributionThe height of the stress box, a, is defined as a percentage of the depth to the neural Whitney Rectangular Stress DistributionThe height of the stress box, a, is defined as a percentage of the depth to the neural axis1' '4000cfpsi 1' 1112 Strength of reinforced concrete Beams6/11 Whitney Rectangular Stress DistributionThe values of the tension and compression forces 'cCfba syTAf 'sycAfafb 0 FTC Rectangular Stress DistributionIf the tension force capacity of the steel is too high, than the value of ais 'sycAfafb If a> d, then you have too much Rectangular Stress DistributionIf the tension force capacity of the steel is too high.

6 Than the value of ais large2aMTd 2syaMAfd Rectangular Stress DistributionThe internal moment is the value of either the tension or compression force multiplied the distance between Substitute the value for 'sysycAfMAfdfb 4MP know that the moment in our reinforced concrete beans is 'sysycAfMAfdfb Whitney Rectangular Stress DistributionThe internal moment is the value of either the tension or compression force multiplied the distance between them4MP d-4f'b PShearShearLet s focus on how to model the ultimate shear load in a reinforced concrete beamReinforced concrete BeamsCIVL 1112 Strength of reinforced concrete Beams7/11ncsVVV reinforced concrete BeamsWe can approximate the shear failure in unreinforced concrete as:2'ccVfbd If we include some reinforcing for shear the total shear capacity of a reinforce concrete bean would be approximated as.

7 VysAf dVs 2nPV 22'vyshearcAf dPfbds reinforced concrete BeamsLets consider shear failure in reinforced concreteReinforced concrete BeamsPCompressionLet s focus on how to model the ultimate compression load in a reinforced concrete beamReinforced concrete BeamsPCompressionsAbd There is a balanced condition where the stress in the steel reinforcement and the stress in the concrete are both at their yield points The amount of steel required to reach the balanced strain condition is defined in terms of the reinforcement ratio:1' sAbd reinforced concrete BeamsThe limits of the reinforcement ratio are established as:Reinforcement ratio definition as function of c/dReinforced concrete BeamsThe limits of the reinforcement ratio are established Beam failure is controlled by compressionBeam failure is controlled by Transition between tension and compression controlCIVL 1112 Strength of reinforced concrete Beams8/1187,000steeldcfpsic 87,0002compressionsdcaMAd psic reinforced concrete BeamsLets consider compression failure in over reinforced , let define an equation that given the stress in the tensile steel when concrete reaches its ultimate fsteel< fythen or Lets consider compression failure in over reinforced concreteFirst.

8 Let define an equation that given the stress in the tensile steel when concrete reaches its ultimate strain87,00042scompressionAdcaPdpsic reinforced concrete Beams4MP only ifsyff reinforced concrete BeamsConsider the different types of failures in reinforced concrete : reinforced concrete Beam AnalysisLet s use the failure models to predict the ultimate strength-to-weight (SWR) of one of our reinforced concrete beams from labConsider a beam with the following characteristics: concrete strength f c= 5,000 psiSteel strength fy= 60,000 psiThe tension reinforcement will be 2 #3 rebarsThe shear reinforcement will be #3 rebars bent in a U-shape spaced at 4 the minimum width to accommodate the reinforcementReinforced concrete Beam AnalysisBa r #Dia me te r (in.)

9 As ( ) bars are denoted by the bar number. The diameter and area of standard rebars are shown on the choice of reinforcement we can compute an estimate of band d 2 #3 rebar diameterMinimum cover#3 rebar diameter2( )in 2( )in Space between bars #3 reinforced concrete Beam AnalysisCIVL 1112 Strength of reinforced concrete Beams9/11If we allow a minimum cover under the rebars were can estimate d6d Half of #3 bardiameterMinimum cover concrete Beam Analysis#3 rebar diameter b6 #3We now have values for b, d, and 'sysycAfMAfdfb reinforced concrete Beam Analysis 222( ) Asfor two #3 rebars is:b6 #3 Compute the moment 'sysycAfMAfdfb (60ksi) (60ksi) ( )ksi k in.

10 Kips4 MPReinforced concrete Beam Analysis 35, concrete Beam AnalysisLet s check the shear modelArea of two #3 rebars22'vyshearcAf dPfbds 22 ,000psi 5,000psi reinforcement spacingSince Ptension< Psheartherefore Ptensioncontrolsb6 #4sAbd reinforced concrete Beam AnalysisLet s check the reinforcement ratio1' To compute , first we need to estimate 1 Reinforcement ratio definition as function of c/dAn 1 estimate is given as:1' '4000cfpsi 1' reinforced concrete Beam Analysis15,000 4, ,000 CIVL 1112 Strength of reinforced concrete Beams10 ( )sAbdReinforced concrete Beam AnalysisCheck the reinforcement ratio for the maximum steel allowed for tension controlled behavior or c/d = ' ( ) The amount of steel in this beam is tension-controlled for tensioncontrolled behavior 333490lb.