10Flexural Design of Reinforced Concrete Beams and Slab Sections Analysis Versus Design:Analysis: Given a cross-section, fc , reinforcement sizes, location, fy compute resistance or capacityDesign: Given factored load effect (such as Mu) select suitable section(dimensions, fc, fy, reinforcement, etc.)
11Flexural Design of Reinforced Concrete Beams and Slab Sections ACI Code Requirements for Strength DesignBasic Equation: factored resistance factored load effectEx.
12ACI Code Requirements for Strength Design Mu = Moment due to factored loads (required ultimate moment)Mn = Nominal moment capacity of the cross-section using nominal dimensions and specified material strengths.f = Strength reduction factor (Accounts for variability in dimensions, material strengths, approximations in strength equations.
13Flexural Design of Reinforced Concrete Beams and Slab Sections Required Strength (ACI 318, sec 9.2)U = Required Strength to resist factored loadsD = Dead LoadsL = Live loadsW = Wind LoadsE = Earthquake Loads
14Flexural Design of Reinforced Concrete Beams and Slab Sections Required Strength (ACI 318, sec 9.2)H = Pressure or Weight Loads due to soil,ground water,etc.F = Pressure or weight Loads due to fluids with well defined densities and controllable maximum heights.T = Effect of temperature, creep, shrinkage, differential settlement, shrinkage compensating.
15Factored Load Combinations U = 1.2 D +1.6 L Always check even if other load types are present.U = 1.2(D + F + T) + 1.6(L + H) (Lr or S or R)U = 1.2D (Lr or S or R) + (L or 0.8W)U = 1.2D W + 1.0L + 0.5(Lr or S or R)U = 0.9 D + 1.6W +1.6HU = 0.9 D + 1.0E +1.6H
16Resistance Factors, f - ACI Sec 9.3.2 Strength Reduction Factors  Flexure w/ or w/o axial tensionThe strength reduction factor, f, will come into the calculation of the strength of the beam.
17Resistance Factors, f - ACI Sec 9.3.2 Strength Reduction Factors  Axial Tension f = 0.90 Axial Compression w or w/o flexure (a) Member w/ spiral reinforcement f = 0.70 (b) Other reinforcement members f = 0.65*(may increase for very small axial loads)
18Resistance Factors, f - ACI Sec 9.3.2 Strength Reduction Factors  Shear and Torsion f = 0.75 Bearing on Concrete f = 0.65ACI Sec f factors for regions of high seismic risk
19Background Information for Designing Beam Sections 1.Location of Reinforcement locate reinforcement where cracking occurs (tension region) Tensile stresses may be due to : a ) Flexure b ) Axial Loads c ) Shrinkage effects
20Background Information for Designing Beam Sections 2.Constructionformwork is expensive - try to reuse at several floors
21Background Information for Designing Beam Sections 3.Beam DepthsACI Table 9.5(a) min. h based on l (span) (slab & beams)Rule of thumb: hb (in) l (ft)Design for max. moment over a support to set depth of a continuous beam.
22Background Information for Designing Beam Sections 4.Concrete CoverCover = Dimension between the surface of the slab or beam and the reinforcement
23Background Information for Designing Beam Sections 4.Concrete CoverWhy is cover needed? [a] Bonds reinforcement to concrete [b] Protect reinforcement against corrosion [c] Protect reinforcement from fire (over heating causes strength loss) [d] Additional cover used in garages, factories, etc. to account for abrasion and wear.
24Background Information for Designing Beam Sections Minimum Cover Dimensions (ACI 318 Sec 7.7)Sample values for cast in-place concreteConcrete cast against & exposed to earth - 3 in.Concrete (formed) exposed to earth & weather No. 6 to No. 18 bars - 2 in. No. 5 and smaller in
25Background Information for Designing Beam Sections Minimum Cover Dimensions (ACI 318 Sec 7.7)Concrete not exposed to earth or weather - Slab, walls, joists No. 14 and No. 18 bars in No. 11 bar and smaller in - Beams, Columns in
26Background Information for Designing Beam Sections 5.Bar Spacing Limits (ACI 318 Sec. 7.6)- Minimum spacing of bars- Maximum spacing of flexural reinforcement in walls & slabsMax. space = smaller of
28Minimum Cover Dimension Reinforcement bar arrangement for two layers.
29Minimum Cover Dimension ACI 3.3.3Nominal maximum aggregate size.- 3/4 clear space /3 slab depth /5 narrowest dim.
30Example - Singly Reinforced Beam Design a singly reinforced beam, which has a moment capacity, Mu = 225 k-ft, fc = 3 ksi, fy = 40 ksi and c/d = 0.275Use a b = 12 in. and determine whether or not it is sufficient space for the chosen tension steel.
31Example - Singly Reinforced Beam From the calculation of Mn
32Example - Singly Reinforced Beam Select c/d =0.275 so that f =0.9. Compute k’ and determine Ru
33Example - Singly Reinforced Beam Calculate the bd 2
34Example - Singly Reinforced Beam Calculate d, if b = 12 in.Use d =22.5 in., so that h = 25 in.
35Example - Singly Reinforced Beam Calculate As for the beam
36Example - Singly Reinforced Beam Chose one layer of 4 #9 barsCompute r
37Example - Singly Reinforced Beam Calculate rmin for the beamThe beam is OK for the minimum r
38Example - Singly Reinforced Beam Check whether or not the bars will fit into the beam. The diameter of the #9 = in.So b =12 in. works.
39Example - Singly Reinforced Beam Check the height of the beam.Use h = 25 in.