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# Civil Engr Analysis CIVL 1112

University of Memphis

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This 17 page Class Notes was uploaded by Dana Yundt on Friday October 23, 2015. The Class Notes belongs to CIVL 1112 at University of Memphis taught by Charles Camp in Fall. Since its upload, it has received 31 views. For similar materials see /class/228415/civl-1112-university-of-memphis in Civil Engineering at University of Memphis.

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Date Created: 10/23/15

CIVL 1112 Introduction to Reinforced Concrete Beams 110 Reinforced Concrete Beams I Mathematical modeling of reinforced concrete is essential to civil engineering Concrete as a material Concrete in a structure Reinforced Concrete Beams I Mathematical modeling of reinforced concrete is essential to civil engineering Stress distribution n a re nforeed concrete beam Reinforced Concrete Beams I Mathematical modeling of reinforced concrete is essential to civil engineering Geometr c model a re nforced concrete bridge Reinforced Concrete Beams I Mathematical modeling of reinforced concrete is essential to civil engineering Blast failure of a re nforced concrete wall Reinforced Concrete Beams I Mathematical modeling of reinforced concrete is essential to civil engineering Blast failure of a reinforced concrete wall Reinforced Concrete Beams I Mathematical model for failure in an unreinforced e beam concret uM 7 V i CIVL 1112 Introduction to Reinforced Concrete Beams 210 Reinforced Concrete Beams I In the reinforced concrete beam project there are three different failure mode we need to investigate p Reinforced Concrete Beams I First lets consider the loading of the beam Reinforced Concrete Beams I The purpose of RC is the reinforcement of areas in concrete that are weak in tension p Reinforced Concrete Beams I Let39s look at the internal forces acting on the beam and locate the tension zones P P F et V Z 2 3 2 PZ Reinforced Concrete Beams I The shear between the applied load and the support is constant VIP2 Reinforced Concrete Beams I The shear between the applied load and the support is constant VIP2 CIVL1112 Introduction to Reinforced Concrete Beams 310 Reinforced Concrete Beams I The shear between the applied load and the support is constant VIP2 I The shear force VIP2 is constant between the applied load and the support Reinforced Concrete Beams I Let39s look at the internal moment at section between the supports and applied load 2 M E X X max 8 inches Reinforced Concrete Beams I Let39s 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 end I Bending moment can also be referred to as torque Reinforced Concrete Beams I The top of the beam is in compression and the bottom of the beam is in tension Compression force on the upper part of the concrete beam c 7 Tension force on the lower part of the concrete beam Reinforced Concrete Beams I To model the behavior of a reinforced concrete beam we will need to understand three distinct regions in the beam I Two are illustrated below the third is called shear Compression c T Tenston Reinforced Concrete Beams I We need models to help us with compression tension and shear failures in concrete p CIVL 1112 Introduction to Reinforced Concrete Beams 410 Reinforced Concrete Beams I We need models to nelp us w and snear failures in concret Reinforced Concrete Beams itn compression tension I We need models to help us with compression tension 2 and shear faliures in concre Reinforced Concrete Beams I We need models to help us with compression tension and shear failures in concrete concrete beam Reinforced Concrete Beams I Compression and tension failures in a reinforced Reinforced Concrete Beams I Compression and tension failures in a reinforced concrete beam Reinforced Concrete Beams I Shear failure in a reinforced concrete beam CIVL 1112 Introduction to Reinforced Concrete Beams 510 Reinforced Concrete Beams I Shear failure in a reinforced concrete beam Whitney Rectangular Stress Distribution I In 111219305 Whitney proposed the use at a remnguier compressive sress dismbumn Whitney Rectangular Stress Distribution I In 111219305 Whitney proposed the use at a rectangular compressive sress dismbumn 0 Ban r l Whitney Rectangular Stress Distribution I Assume that the eaneree eanribues nothing w the Tensile strength cf the beam 05a 0 85f r i Whitney Rectangular Stress Distribution I Assume thatthe complex distribution cf compressive swess m the meme can be approximated by a rectangle b Whitney Rectangular Stress Distribution I The heigm cf the swess box a is defined as a pereemge mm depth e the neural axis CIVL1112 Introduction to Reinforced Concrete Beams 610 Whitney Rectangular Stress Distribution I The height of the stress box a is defined as a percentage of the depth to the neural axis f39cg 4000 psi A 085 f 2 4000 psi 2 065 31 0857 005 1000 Whitney Rectangular Stress Distribution I The values of the tension and compression forces are 185639c 05 639 085f39c ba 72157 My Zon quot 085fb Whitney Rectangular Stress Distribution I If the tension force capacity of the steel is too high than the value of a is large 02m 05 474 085f395b If a gt d then you have too much steel Whitney Rectangular Stress Distribution I The internal moment is the value of either the tension on compression force multiplied the distance between t em 185639c 05 Whitney Rectangular Stress Distribution I The internal moment is the value of either the tension on compression force multiplied the distance between t em 085f39 c 05a l39 39l a M 441 75 Substitute the value for a Whitney Rectangular Stress Distribution I The internal moment is the value of either the tension on compression force multiplied the distance between t em 42 M f a e 059 y 4 r f b We know that the moment in our reinforced M4P concrete beans is CIVL 1112 Introduction to Reinforced Concrete Beams 710 Reinforced ConcreTe Beams Reinforced ConcreTe Beams I There is a quotbalancedquot condiTion where The sTress in The sTeel reinforcemenT and The sTress in The concreTe are boTh aT The r I The llmlls of The remforcemenl rallo are y eld poinTs esTablished as I The amounT of sTeel required To reach The balanced sTrain condiTion C B f I H d b is defined in Terms of The reinforcemenT raTio gt O 80m C rte 393 comm 3 Y 0 compressvon 0375 lt i lt 0600 TransiTion beTween Tension and compression conTrol g lt Beam failure is conTrolled by d fanson Reinforced ConcreTe Beams Reinforced ConcreTe Beams I The limiTs of The reinforcemenT ratio are I LeTs consider shear failure in unreinforced concreTe esTablished as V6 z bd 12 PAW gm Reinforced ConcreTe Beams Reinforced ConcreTe Beams I LeTs consider shear failure in reinforced concreTe I LeTs consider compression failure in over reinforced f 0 concreTe W 4 y I FirsT leT define an equaTion ThaT given The sTress in The Tr V5 lCr Tensile sTeel when concreTe reaches iTs ulTimaTe sTrain lllllllll L L 5 dc PM My 0 fsfee 87 105 V l l d l V 2 I If fsfee fy39rhen or gt o 600 a l 39 a c a IDS780W 2 5 2 f C Mompres s ion A5 c P57 CIVL 1112 Introduction to Reinforced Concrete Beams 810 Reinforced Concrete Beams I LeTs consider campressian failure h aver reinfarced cancr efe I Firs leT defhe ah equcmah ThaT given The sTress h The ehsiie sTeel wheh cancreTe reaches Ts ulTimaTe sTrain M4P onlyi l 2 5ltfy Reinforced Concrete Beam Analysis I LeT s use The failure madels n predicT The ulTimaTe sTrengThTaweighT swu cf she cf W reinferced cancreTe beams ram lab I Cahsider abeam wiTh The fallawihg chameTerisTics Cuncrele slrenglh r 5000 psi Sleel slrenglh r 00000 psi The lensiun reinfurcemem Will be 2 4 rebars The shear 7 2 nfurcemem Will be 3 rebars bem m a Ushape spa m4 inches Uselhe m h mum wmh m accummudave The reinfurcemem Reinforced Concrete Beam Analysis I Reihfarcmg bars are dehaTed by The bar number The diameTer and area cf sTahdard rebars are shawh belaw In Reinforced Concrete Beam Analysis I Based sh The chaice cf reinfercemenT we can campuTe ah esTimaTe cf band a i b 1 b 2 205 in 2075 in 20375 in s 0 El 3 T Reinforced Concrete Beam Analysis I If we allaw amimmum caver under The rebars were can esTimaTe e i b i d 6 70 7075 s Reinforced Concrete Beam Analysis I We haw have values m e e and A I The Agar Twa 4 rebars is 4 l A 2o20 m2 040 m2 I C 7 CIVL1112 Introduction to Reinforced Concrete Beams Reinforced Concrete Beam Analysis I Compute the moment capacity A f A d 05 5 y M 56 9 f b 2 04n260ks 04m sob4625 me 940 k in 235 kips J 910 Reinforced Concrete Beam Analysis I Let39s check the shear model Mema S 7 4011012 60f00 psi4625in 7 mummszsm 35757 Reinforced Concrete Beam Analysis I Let39s check the reinforcement ratio cf39c 2085 P Ag 7 To compute p first we need to estimate 51 Reinforced Concrete Beam Analysis I Check the reinforcement ratio for the maximum steel allowed for tension controlled behavior or cd 0 375 f39 5ksi 085 080 0375 fy 60ks C 085 0 A d 0021 7 i 7 04 m2 p bd 4 n4625 n I The amount of steel in this beam is just a bit over the allowable for tension controlled behavior 0022 Since Pmnsmn lt Pshw therefore Hemquot controls Reinforced Concrete Beam Analysis I An lestimate is given as g 4000 psi A 085 f 2 4000 psi l 085 7 005 2 065 1000 5 085 7005 500074000 7 1IOOO 7 080 Reinforced Concrete Beam Analysis I However the maximum about of steel where compression is in control is cd 0 600 f39 5ksi 085 080 0600 fy 60 ksi C 085 0 A d 0034 7 i 7 04n2 p bd 4m4625m I Therefore the beam is in the lower part of the transition zone and for our purposes is OK 0022 CIVL 1112 Reinforced Concrete Beam Project Introduction 13 Reinforced Concrete Beam Project I Entry to the Herff College of Engineering 2007 Reinforced Concrete Competition requires I The competition is sponsored by Dr Martin E Lipinski Chair Department of Civil Eng neering The University of Memp is Memphis TN 38152 I A researchbased progress report must be submitted to Dr Charles V Camp Contest Coordinator by April 8 2007 Reinforced Concrete Beam Project I Each team should prepare a full formal technical report with a 6 minute presentation supported by recent and relevant research I Final presentation and reports are due Sunday April 8 2007 600 pm Engineering Auditorium Reinforced Concrete Beam Project I The objective of this project is to develop the strongest reinforced concrete beam as measured by the strength to weight ratio SMR U mafe Load lbs R 5W Beam WellthUbs I The strength of the beam is the ultimate load recorded during testing Reinforced Concrete Beam Project I The cost of each beam will be estimated using the following data Reinforced Concrete Beam Project I A cost factor will be computed as follows If cost lt 150 then 6057 Facfor 1 If cost gt 150 then 150 osf Cost Factor Reinforced Concrete Beam Project I Using your cost factor an adjusted 5W computed as follows Swami SWR x Cost Factor CIVL1112 Reinforced ConcreTe Beam ProjecT I The concreTe beam musT be 30 inches long 6 inches hnghT and have a prismaTic crosssecTion Maximum wi Th is 8 inches mm ma Wm l L saw I In designing The reinforced concreTe beam groups may c nsider The use of admixtures various T es o reinforcemenT various Types o cemenTs and aggregaTes and nonrecTangular crosssecTions Reinforced Concrete Beam Project Introduction 23 Reinforced ConcreTe Beam ProjecT I The reinforced concreTe beam problem poses several challenges To The sTudenT 1 seecTion of The shape and size of The crosssecTion beam N design of a concreTe mix based on sTrengTh and worka iliTy 0 design of The reinforcemenT Type of reinforcemenT amounT and posiTion in The beam an 4 The predicTion of The SWR of The beam Reinforced ConcreTe Beam ProjecT I The reinforced concreTe beam projecT schedule concrete mix m concrete beam m rMarch 1 March 03 March 1315 March 2022 devele concrete beam 4 March 2729 Reinforced ConcreTe Beam ProjecT I The cosT of sTeel may be esTimaTed as follows L lb 790 for Cost of steel 4 49 39 3 3 f 2 000 lb 1 7281quot on I where A is The cross secTional area of sTeel rebars L is The lengTh of The sTeel rebars and 490 lbfT3 is The uniT weighT of sTeel Reinforced ConcreTe Beam ProjecT I For example if one 5 rebar in placed in The beam The sTeel cosT is esTimaTed as Cost of steel 104 70 31in230in 490i 790 m 17287 73 my 20001 fr 1 Reinforced ConcreTe Beam ProjecT I Consider The following mix for a yd3 of concreTe developed using The ACI mix design procedure CIVL 1112 Reinforced Concrete Beam Project Description 14 Reinforced Concrete Beam Project I Entry to the Herff College of Engineering 2009 Reinforced Concrete Competition requires I The competition is sponsored by Dr Shahram Pezeshk Chair Department of Civil Eng neering The University of Memphis MemphisTN 38152 I A researchbased progress report must be submitted to Dr Charles V Camp Contest Coordinator by April 12 9 Reinforced Concrete Beam Project I Each team should prepare a full formal technical report with a 6 minute presentation supported by recent and relevant research I Final presentation and reports are due Sunday April 12 2009 600 pm Engineering Auditorium Reinforced Concrete Beam Project I The objective of this project is to develop the strongest reinforced concrete beam as measured by the strength to weight ratio SMR U mafe Load lbs R 5W Beam WellthUbs I The strength of the beam is the ultimate load recorded during testing Reinforced Concrete Beam Project I The cost of each beam will be estimated using the following data Reinforced Concrete Beam Project I A cost factor will be computed as follows If cost lt 300 then 6057 Facfor 1 If cost gt 300 then 3 00 Cost Cost Factor Reinforced Concrete Beam Project I Using your cost factor an adjusted 5W computed as follows Swami SWR x Cost Factor CIVL 1112 Reinforced Concrete Beam Project Description 24 Reinforced Concrete Beam Project Tne concrete beam must be 30 incnes long 6 incnes nei nt and nave aprismatic crosssection Maximum ni tn is 5 inc es In designing tne relnfarced concrete beam grou s may consider tne use of admixtu s various es o reinforcement various types of cements and aggregates and nonrectangular crosssections Reinforced Concrete Beam Project The reinforced concrete beam problem poses several challenges to the student 1 selection affl39te shape and sin of the crasssection of the beam 2 design at a concrete mix based on strengtn and warka ili design ottne relnfarcemenf type at relnfarcemenf amount andposition intne beam and 4 tne prediction ct tne SWR ct tne beam Reinforced Concrete Beam Project Tiie reinforced concrete beam project schedule Reinforced Concrete Beam Project The cost of steel may be estimated as follows 05r07 5r22 4 490 E 7 17mm ft ten uuuD where Axis the cross sectional area of stee rebars L is the length of the steel rebars and 490 lbft3 is the unit weight of steel Reinforced Concrete Beam Project For example if one 5 rebar in placed in the beam the steel cost is estimated as am 07 sree e 7031in1x30in 490i E96 tan 39 172w f1 tan 2000 fr ellE Reinforced Concrete Beam Project Consider the followin mix for ayd3 of concrete eveloped using the CI mix design procedure CIVL 1112 Reinforced Concrete Beam Project Description 34 Reinforced Concrete Beam Project The cost of the concrete required for a 4quot by 639 by 30quot beam is estimated as mEnema 4m6md0m70b 102J tun J 172EMW 1M 2 000 b 0 56 am it Wm Meown 1 EMij m 172E 7 27 f1 1M 2 000b 0 20 J Reinforced Concrete Beam Project The cost of the concrete required for a 4quot by 6quot b 3 d as y oquot beam isestimate iiaib w 1M 27ft 1M 2000b Amema i751 of fine a re ate 7 9 172E e 0 09 The cost concrete is estimated as 085 The cost reinforced concrete beam is estimated as 203 Reinforced Concrete Beam Project The cost adjustment for the reinforced concrete beam is If cost lt 300 then Cosf Facfor 1 If cost gt 300 then C39an Facfar 300 C39an Reinforced Concrete Beam Project For example if the unadjusted SWRfor a beam 39 0 and the cost is 203 then the cost adjusted swms 5WPA4ww 5W x C39an Facfar 5W9Aduaed 510X1 510 Reinforced Concrete Beam Project For example if the unadjusted SWRfor a beam is 510 and the cost is 331 then the cost adjusted swms 5WPA4ww SWIZX C39an Facfar 3 0 5Widum 510x 331 462 Reinforced Concrete Beam Project CIVL 1112 Reinforced Concrete Beam Project Description 14 Reinforced Concrete Beam Project I Entry to the Herff College of Engineering 2008 Reinforced Concrete Competition requires I The competition is sponsored by Dr Shahram Pezeshk Chair Memphis TN 38152 I A researchbased progress report must be submitted to Dr Charles V Camp Contest Coordinator by April 6 2007 Reinforced Concrete Beam Project I Each team should prepare a full formal technical report with a 6 minute presentation supported by recent and relevant research I Final presentation and reports are due Sunday April 6 2008 600 pm Engineering Auditorium Reinforced Concrete Beam Project I The objective of this project is to develop the strongest reinforced concrete beam as measured by the strength to weight ratio SMR U mafe Load lbs R 5W Beam WellthUbs I The strength of the beam is the ultimate load recorded during testing Reinforced Concrete Beam Project I The cost of each beam will be estimated using the following data Reinforced Concrete Beam Project I A cost factor will be computed as follows If cost lt 200 then 6057 Facfor 1 If cost gt 200 then 200 Cost Factor Cost Reinforced Concrete Beam Project I Using your cost factor an adjusted 5W computed as follows Swami SWR x Cost Factor CIVL1112 Reinforced ConcreTe Beam ProjecT I The concreTe beam musT be 30 inches long 6 inches hnghT and have a prismaTic crosssecTion Maximum wi Th is 8 inches mm ma Wm l L saw I In designing The reinforced concreTe beam groups may c nsider The use of admixtures various T es o reinforcemenT various Types o cemenTs and aggregaTes and nonrecTangular crosssecTions Reinforced Concrete Beam Project Description 24 Reinforced ConcreTe Beam ProjecT I The reinforced concreTe beam problem poses several challenges To The sTudenT 1 seecTion of The shape and size of The crosssecTion beam N design of a concreTe mix based on sTrengTh and worka iliTy to design of The reinforcemenT Type of reinforcemenT amounT and posiTion in The beam an 4 The predicTion of The SWR of The beam Reinforced ConcreTe Beam ProjecT I The reinforced concreTe beam projecT schedule concrete mix m concrete beam st March 46 March 11713 March 1320 devele concrete beam 34 March 2527 173 Reinforced ConcreTe Beam ProjecT I The cosT of sTeel may be esTimaTed as follows L b 810 for c r f r 4 4 o 05 o 2 Hes 9 ail 0quot ll 000 I where A is The cross secTional area of sTeel rebars L is The lengTh of The sTeel rebars and 490 lbfT3 is The uniT weighT of sTeel Reinforced ConcreTe Beam ProjecT I For example if one 5 rebar in placed in The beam The sTeel cosT is esTimaTed as Cost of steel 7 o 31in230in490 lb 810 m J 39 3 W t 2 000 lb 1 mamr an 107 Reinforced ConcreTe Beam ProjecT I Consider The following mix for a yd3 of concreTe developed using The ACI mix design procedure Water Cement CIVL 1112 Reinforced Concrete Beam Project Description 34 Reinforced Concrete Beam Project The cost of the concrete required for a 4quot by 6quot b 3 t d s 01233311 y 0quotbeamisestima e a rustufmneme 46 j3 7 1 723 0 55 am 12 Wm 4quot16n130n1 12wij m 172W 7 27 f1 1177 2 0001 0 20 Reinforced Concrete Beam Project The cost of the concrete required for a 4quot by 6quot b 3 t s y oquot beam isestima eda 11311 w m 27ft m 20001 The cost concrete is estimated as 084 1751 a f ne aggregate e 46 j3 1 72B 009 The cost reinforced concrete beam is estimated as 191 Reinforced Concrete Beam Project The cost adjustment for the reinforced concrete beam is If cost lt 200 then Cost Factor 1 If cost gt 200 then 200 C39an Facfar C39an Reinforced Concrete Beam Project For example if the unadjusted SWRfor a beam is 510 and the cost is 191 then the cost adjusted swms SWRAdungd 5W X Can Facfar 5WPWW 510X1 510 Reinforced Concrete Beam Project For example if the unadjusted SWRfor a beam is 510 and the cost is 231 then the cost adjusted swms 5WPWMW SWIZX C39an Facfar 2 O 5 an 510x 2231 442 Reinforced Concrete Beam Project

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