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ELEMENTS OF ARCHITECTURAL STRUCTURES:FORM, BEHAVIOR, AND DESIGNConcrete Beam Design composite of concrete and steel American Concrete Institute (ACI)ARCH 614DR. ANNE NICHOLSSPRING 2014– design for maximum stresses– limit state designlecturetwenty onehttp:// nisee.berkeley.edu/goddenconcrete construction:Elements of Architectural StructuresARCH 614service loads x load factorsconcrete holds no tensionfailure criteria is yield of reinforcementfailure capacity x reduction factorfactored loads reduced capacity– concrete strength f’cmaterials & beamsConcrete Beams 1Lecture 21 S2009abnConcrete Beams 2Lecture 21Elements of Architectural StructuresARCH 614Concrete ConstructionConcrete low strength to weight ratio relatively nsioningS2007abn– Portland cement– aggregate– water hydration fire resistant creep & shrinkConcrete Beams 3Lecture 21http://nisee.berkeley.edu/goddenElements of Architectural StructuresARCH 614S2007abnConcrete Beams 4Lecture 21Elements of Architectural StructuresARCH 614S2007abn1

ReinforcementBehavior of Composite Members deformed steel bars (rebar) plane sections remain plane stress distribution changes– Grade 40, Fy 40 ksi– Grade 60, Fy 60 ksi - most common– Grade 75, Fy 75 ksi– US customary in # of 1/8” longitudinally placed– bottom– top for compression reinforcement– spliced, hooked, terminated.Concrete Beams 5Lecture 21Elements of Architectural StructuresARCH 614f1 E1 S2007abnTransformation of Material n is the ratio of E’sn Elements of Architectural StructuresARCH 614 f 2 E 2 Elements of Architectural StructuresARCH 614E2 y S2007abnStresses in Composite Section with a sectiontransformed to onematerial, new IE2E1 effectively widens a material to getsame stress distributionConcrete Beams 7Lecture 21Concrete Beams 6Lecture 21E1 yn – stresses in thatmaterial aredetermined as usual– stresses in the othermaterial need to beadjusted by nS2007abnConcrete Beams 8Lecture 21Elements of Architectural StructuresARCH 614EE2 steelE1 Econcretefc fs MyI transformedMynI transformedS2007abn2

Reinforced Concrete - stress/strainReinforced Concrete Analysis for stress calculations– steel is transformed to concrete– concrete is in compression above n.a. andrepresented by an equivalent stress block– concrete takes no tension– steel takes tension– force ductile failureConcrete Beams 9Lecture 21Elements of Architectural StructuresARCH 614S2007abnConcrete Beams 10Lecture 21Elements of Architectural StructuresARCH 614S2007abnLocation of n.a.T sections ignore concrete below n.a. transform steel same area moments, solve for x n.a. equation is different if n.a. belowflangeffhfhfbwbwbx Concrete Beams 11Lecture 21x nA s ( d x ) 02Elements of Architectural StructuresARCH 614 x hf nA ( d x ) 0bf hf x hf x hf bws2 2 S2007abnConcrete Beams 12Lecture 21Elements of Architectural StructuresARCH 614S2007abn3

ACI Load Combinations*Reinforced Concrete Design stress distribution in bending1.4D1.2D 1.6L 0.5(Lr or S or R)1.2D 1.6(Lr or S or R) (1.0L or 0.5W)1.2D 1.0W 1.0L 0.5(Lr or S or R)1.2D 1.0E 1.0L 0.2S0.9D 1.0W0.9D 1.0E*can also use oldACI factorsConcrete Beams 13Lecture 21Elements of Architectural StructuresARCH 614S2007abnForce Equations C 0.85 f cba T A s fy whereConcrete Beams 15Lecture 21a 1xElements of Architectural StructuresARCH 614CxdhAsNAa 1xTactual stressa/2 CTWhitney stressblockWang & Salmon, Chapter 3Concrete Beams 14Lecture 21Elements of Architectural StructuresARCH 614S2007abnEquilibrium0.85f’c– f c concrete compressivestrength– a height of stress block– 1 factor based on f c– x location to the n.a.– b width of stress block– fy steel yield strength– As area of steel reinforcement0.85f’cba/2 C T C Mn T(d-a/2)0.85f’ca 1xa/2 C– d depth to the steel n.a. dT with As–a TAs f y0.85 f c b– Mu Mn 0.9 for flexure– Mu T(d-a/2) Asfy (d-a/2)S2007abnConcrete Beams 16Lecture 21Elements of Architectural StructuresARCH 614S2007abn4

Over and Under-reinforcementAs for a Given Section over-reinforced several methods– steel won’t yield– guess a and iterate under-reinforced1. guess a (less than n.a.)2. A 0.85 f c ba– steel will yields reinforcement ratioA– ρ sbdhttp://people.bath.ac.uk/abstji/concrete video/virtual lab.htm– max is found with steel 0.004 (not bal)Elements of Architectural StructuresARCH 6143. solve for a from Mu Asfy (d-a/2) M u a 2 d As f y – use as a design estimate to find As,b,dConcrete Beams 17Lecture 21fy4. repeat from 2. until a from 3. matches a in 2.S2009abnConcrete Beams 18Lecture 21Elements of Architectural StructuresARCH 614As for a Given Section (cont)Reinforcement chart method min for crack control3 f c required– Wang & Salmon Fig. 3.8.1 Rn vs. 1. calculate Rn S2007abnAs (bd )fy not less than200As (bd )fy As-max : a (0.375d )1Mnbd 22. find curve for f’c and fy to get 3. calculate As and a simplify by setting h 1.1dcover typical cover– 1.5 in, 3 in with soil bar spacingConcrete Beams 19Lecture 21Elements of Architectural StructuresARCH 614S2007abnConcrete Beams 20Lecture 21spacingElements of Architectural StructuresARCH 614S2007abn5

Approximate DepthsConcrete Beams 21Lecture 21Elements of Architectural StructuresARCH 614S2009abn6

Concrete Beams 9 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete - stress/strain Concrete Beams 10 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete Analysis for stress calculations steel is transformed to concrete concrete is in compression above n.a. and

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