Ce334 Exam Resources Fall 2019 Design Aids And Charts

Ce334examresourcesfall2019designaidschartsreinforcingsteelba

Ce334examresourcesfall2019designaidschartsreinforcingsteelba

CE 334 Exam Resources Fall 2019 DESIGN AIDS & CHARTS Reinforcing steel Bar # Diameter (in) Area (in.375 0..500 0..625 0..750 0..875 0..00 0..13 1..27 1..41 1..69 2..26 4.00 Minimum Concrete Cover Concrete exposure Member Reinforcement Specified cover, in. Cast against and permanently in contact with ground All All 3 Exposed to weather or in contact with ground All No. 6 through No. 18 bars 2 No. 5 bar, W31 or D31 wire, and smaller 1-1/2 Not exposed to weather or in contact with ground Slabs, joists, and walls No. 14 & No. 18 bars 1-1/2 No. 11 bar & smaller 3/4 Beams, columns, pedestals, and tension ties Primary reinforcement, stirrups, ties, spirals, and hoops 1-1/2 ACI Moment and Shear Coefficients Moment Location Condition Mu Positive End span Discontinuous end integral with support wuâ„“n 2 /14 Discontinuous end unrestrained wuâ„“n 2 /11 Interior spans All wuâ„“n2/16 Negative [1] Interior face of exterior support Member built integrally with supporting spandrel beam wuâ„“n 2 /24 Member built integrally with supporting column wuâ„“n 2 /16 Exterior face of first interior support Two spans wuâ„“n 2 /9 More than two spans wuâ„“n 2 /10 Face of other supports All wuâ„“n2/11 Face of all supports satisfying (a) or (b) (a) slabs with spans not exceeding 10 ft (b) beams where ratio of sum of column stiffnesses to beam stiffness exceeds 8 at each end of span wuâ„“n 2 /12 Shear Exterior face of first interior support All 1.15wuâ„“n/2 All other supports wuâ„“n/2 T Beam Overhangs Effective Flange Width Flange location Effective overhanging flange width, beyond face of web Each side of web Least of: 8h sw/2 â„“n/8 One side of web Least of: 6h sw/2 â„“n/12 Minimum Thickness of BEAMS AND SLABS for no Deflection Calculations Support condition BEAM Minimum h[1] SLAB Minimum h[1] Simply supported â„“/16 â„“/20 One end continuous â„“/18.5 â„‘/24 Both ends continuous â„“/21 â„‘/28 Cantilever â„“/8 â„‘/10 Coefficient of Resistance Rn  EQUATIONS Basic Load Combinations U = 1.4D U = 1.2D+1.6L U = 1.2D+1.6L+0.5(Lr or S or R) U = 1.2D+1.0W+1.0L+0.5(Lr or S or R) Basic Design Equations φMn  Mu φVn  Vu φPn  Pu φTn  Tu Strength Reduction Factors φ = 0.9 for tension controlled sections when εt  0.005 φ = 0.65 for compression controlled sections when εt  εy φ is linearly interpolated when εt is between εy and 0.005 φ = 0.65 + (εt – 0./3) for fy = 60 ksi φ = 0.75 for shear and torsion φ = 0.65 for tied columns φ = 0.75 for spiral columns Concrete Modulus of Elasticity Ec = 33(wc1.5) = 57,000 for normal weight concrete Concrete Density Normal weight reinforced concrete = 150 lb/ft3 Normal weight unreinforced concrete = 144 lb/ft3 Concrete Tensile Strength Modulus of rupture fr = 7.5λ Splitting (split cylinder) tensile strength fct = 6.7λ Lightweight Concrete Factor Normal weight λ = 1.0 sand lightweight λ = 0.85 all lightweight λ = 0.75 Cracking Moment Mcr = Moment Strength T = Asfy C = 0.85f’cAc T = C to find depth of stress block a Asfy = 0.85f’c Ac if stress block is rectangular Mn = T x jd = C x jd jd = d – a/2 if stress block is rectangular Neutral axis location c = a/β1 εt from strain linearity εt = εcu εcu = 0.003 β1 = 0.85 for f’c  4000 psi β1 = 0.65 for f’c  8000 psi β1 = 0.85 – 0.05 between 4000 and 8000 psi Minimum Area if Steel in a Beam Section As, min = bwd 3 not less than 200 psi Statically determinate T beams with flange in tension use smaller of be or 2bw for bw in the As, min equation vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text vlbrown Typewritten Text One Way Slabs – Design Based on a 12 Wide Section (b=12) Spacing of reinforcement = or s = 12 Shrinkage and temperature reinforcement: required perpendicular to main steel provided for moment strength As&t = 0.0018bh for Grade 60 As&t = 0.002bh for Grade 40 As&t = 0.0018bh ,  0.0014 for higher strengths As, min for main steel = As&t Spacing limits are the smaller of 3h or 18 for main steel and the smaller of 5h or 18 for temperature & shrinkage steel Shear Equations φVn = φVc + φVs φ= 0.75 for shear Vc = 2λ Vs = Av min = . but 0.75  50 psi Vs max = 8 Maximum stirrup spacing = d/2 or 24 when Vs  4 d/4 or 12 when Vs  4 Stirrups required if Vu  ½ φVc for most members Stirrups not required if Vu  φVc for slabs and for beams with h  10 Maximum shear for design of beams is at distance = d from face of support if there is a compression reaction at support Shear from pattern loading at midspan of uniformly loaded beams Vu, midspan = Development of Reinforcement Equations but not less than 12 not greater than 2..3 for bars with 12 of fresh concrete cast below them = 1.5 for epoxy coated bars unless cover > 3d and clear spacing > 6db when 1.2 can be used 0.8 for No. 6 bars and smaller but not less than 8db or 6 For standard hooks, = 1.2 when rebar is epoxy-coated = 0.7 for No. 11 bars and smaller with side cover  2.5 = 0.8 for No. 11 bars and smaller with ties or stirrups placed along the hooked bar at spacing 3db vlbrown Typewritten Text b Critical sections for development of bars is at points of maximum moment and at the cut off point for continuing bars. Actual cut off point must extend d or 12db beyond the theoretical cut off point For positive moment bars: At least 1/3As must extend at least 6 into a simple support and at least 1/4As must extend 6 into a continuous support At simple supports with a compression reaction, 1.3 At inflection points, = distance bars extend beyond support centerline at a simple support, or the larger of d, 12db at an inflection point For negative moment bars: At least 1/3As must extend the largest of d, 12db or past the inflection point into the positive moment zone Limits on Crack Widths Bar spacing s  15 ( , 2.5 but not greater than 12 ( , where fs can be approximated as 2/3fy Deflection Calculations Ieff = 1 δLL = δDL+LL  δDL δLT = δLL + λΔ δDL + λΔ δSL λΔ= Time-Dependent Factor for sustained loads Sustained load duration, months Time-dependent factor ξ 3 1... or more 2.0 Maximum permissible calculated deflections Member Condition Deflection to be considered Deflection limitation Flat roofs Not supporting or attached to nonstructural elements likely to be damaged by large deflections Immediate deflection due to maximum of Lr, S, and R      /180 [1] Floors Immediate deflection due to L      /360 Roof or floors Supporting or attached to nonstructural elements Likely to be damaged by large deflections That part of the total deflection occurring after attachment of nonstructural elements, which is the sum of the time-dependent deflection due to all sustained loads and the immediate deflection due to any additional live load[2]      /480[3] Not likely to be damaged by large deflections      /240[4] Ieff = Ig when Ma

U = strength of a member or cross section required to resist factored loads or related internal moments and forces in such combinations as stipulated in this Code Vc = nominal shear strength provided by concrete, lb Vn = nominal shear strength, lb Vs = nominal shear strength provided by shear reinforcement, lb Vu = factored shear force at section, lb wc = density, unit weight, of normalweight concrete or equilibrium density of lightweight concrete, lb/ft3 wu = factored load per unit length of beam or oneway slab, lb β1 = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis δDL = immediate deflection from service dead load δLL = immediate deflection from service live load δSL = immediate deflection from sustained live load δLT = long-term deflection εcu = concrete crushing strain εt = net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature εty = value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section λ = modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normalweight concrete of the same compressive strength λ = multiplier used for additional deflection due to long-term effects ξ = time-dependent factor for sustained load Ï = ratio of As to bd Ï = ratio of As to bd Ïw = ratio of As to bwd Ï• = strength reduction factor ψe = factor used to modify development length based on reinforcement coating ψr = factor used to modify development length based on confining reinforcement ψs = factor used to modify development length based on reinforcement size ψt = factor used to modify development length for casting location in tension WIDENER UNIVERSITY Department of Civil Engineering CE 334 Term Design Project Fall 2019 Phase I – Flexural Design A floor plan for the first floor of a retail store is shown below. The one-way slab is continuous on 12 foot spans over the 27 foot long supporting beams. The slab forms the flange of the beams, resulting in a T beam construction where the T beams are 27 feet long with simple supports provided by the girders. The girders, which are rectangular in cross section, are supported by the columns on 36 foot spans. Assume that columns are 24" square with 20 ft height between stories. Floor loading includes 100 psf live load based on the ASCE 7-10 minimum live load requirements for a retail building. Dead load (not including slab, beam or girder weights) is 25 psf (5 psf for ceiling, 13 psf mechanical and electrical, and 7 psf miscellaneous). Normal weight concrete with a 28 day compressive strength of 6,000 psi and Grade 60 steel rebar are to be used. The floor does not support partitions or other construction likely to be damaged by large deflections, so you can avoid deflection calculations if your design meets ACI minimum height requirements. Use clear cover requirements for cast in place concrete with interior exposure conditions (1.5" for beams and 3/4" for slabs). By the end of the semester the slab, T beams, girders and columns will be completely designed. The first phase of the project will be the flexural design of the slab, T beams, and girders. Design reinforcement for both positive moment and negative moment where appropriate. RISA 2D can be used to aid in the structural analysis of the girders. RISA 2D OR the ACI coefficient method can be used for the structural analysis of the slab; if you use RISA for the slab you must consider pattern loading. The T beams are analyzed as simply supported beams. Find the required reinforcement and select bar arrangements at all critical sections; e.g. at ends of beams and middle of span. Make sure that code requirements for As min, ductility (εt > 0.005), and bar spacing for crack control are satisfied. Include CAD drawings of all critical cross sections. Reduce live loads on both the T beams and the girders based on the size of the influence area for the T beams; for slabs, AT is calculated as 1.5L2 so the slab's live load won't be reduced.