Ce 334 Exam Resources Fall 2019 Design Aids Charts Reinforci

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 ab 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=12â€) 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 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 â„“/180 [1] Floors Immediate deflection due to L â„“/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] â„“/480[3] Not likely to be damaged by large deflections â„“/240[4] Ieff = Ig when Ma

Paper For Above instruction

This paper presents a comprehensive analysis and design approach for reinforced concrete structures based on the detailed resources provided for the CE 334 course, focusing on the fall 2019 design aids and charts. Specifically, it addresses the critical aspects of reinforcement detailing, load analysis, shear, bending capacity, deflection control, and code compliance essential for structural engineers tasked with designing safe, serviceable, and economical concrete members in retail building projects.

Introduction

Reinforced concrete design is a complex integration of material properties, structural analysis, and code provisions. Effective utilization of design aids and charts accelerates the process while ensuring adherence to safety and serviceability criteria. This paper delineates a methodical approach grounded on the provided resources, starting from reinforcement specifications, load considerations, to detailing and analysis procedures applicable to flat slabs, T-beams, girders, and columns involved in the CE 334 typical retail store project.

Reinforcement Detailing and Concrete Cover

The reinforcement specifications emphasize bar diameters ranging from No. 5 to No. 18, with corresponding areas and minimum cover requirements based on exposure conditions. For ground contact or weather exposure, a minimum cover of 2-3 inches is prescribed, whereas less cover suffices for non-exposed members. These details influence durability, crack control, and bond performance, critical in a retail environment subjected to varying loads and environmental conditions.

Structural Analysis and Load Combinations

Applying the ACI code's load combinations ensures safety under service and ultimate conditions. The basic load factors—1.2D, 1.6L—are contextually combined with optional load effects such as Lr (roof live load), S (snow), and R (rain), with specific emphasis on their influence on the ultimate moment and shear calculations. The analysis involves simplified methods suitable for continuous spans, or more refined elastic analyses, as permitted, especially considering the multi-span nature of the girders and slabs.

Flexural Design of Slabs and Beams

The design process necessitates calculating the required reinforcement to resist positive and negative moments. Using the provided formulas, the minimum reinforcement ratio is ensured, and bar spacing is controlled for crack width and serviceability. For slabs, using a 12-inch width segment simplifies the reinforcement calculation, with proper allowance for shrinkage and temperature reinforcement, respecting the maximum spacing limits for crack control, typically not exceeding 18 inches.

Shear and Development Length

Shear resistance provided by concrete (V_c) and shear reinforcement (V_s) must be balanced to prevent diagonal cracking or shear failure. The code's phi factors (0.75 for shear) reduce nominal values to account for uncertainties. Development length calculations involve factors like cover, bar size, hook type, and coating, with minimum lengths ensuring bond adequacy—particularly critical at support regions and mid-span for positive and negative bending reinforcement.

Deflection Control and Serviceability

Deflections are calculated based on effective moments of inertia, with long-term effects considered via the time-dependent factor xi. The permissible deflections—L/360 for floors, L/180 for flat roofs—prevent excessive deformation that may crack finishes, damage non-structural elements, or impair aesthetics. Design practices include ensuring that the slab and beam depths satisfy these deflection limits, which are vital for maintaining the longevity and appearance of the retail space.

Design of Critical Sections and Reinforcement Layout

Reinforcement at critical sections, such as mid-span for positive moments and supports for negative moments, is derived from the calculated moments and shear forces. The spacing of stirrups or ties mitigates crack widths, limited to 12-15 inches for typical reinforcement stresses. For bending reinforcement, a minimum of 0.0018 to 0.002 times the cross-sectional area is mandated, with bar sizes selected to satisfy ductility and detail requirements.

Application and Practical Considerations

Structural analysis using RISA or ACI coefficient methods offers alternative approaches, especially suited for complex loadings or multiple spans. Simplified models assume prismatic members and uniform loadings, provided certain geometric constraints. For the retail store project, the analysis considers the interactions between slab, beams, girders, and columns, with attention paid to load transfer, stiffness, and possible deflection or cracking issues. The reinforcement drawings must conform to code detail rules, emphasizing development length, lap splices, and crack width limitations.

Conclusion

The integration of detailed design aids, including charts, formulas, and code provisions, forms the backbone of safe and efficient reinforced concrete member design. By meticulously following the outlined procedures — from reinforcement detailing to load analysis and checking serviceability limits — structural engineers can produce designs that are not only compliant but also optimized for safety, durability, and functionality in a retail environment. Application of these principles ensures that the constructed members withstand service loads, environmental exposures, and long-term effects such as creep and shrinkage, fulfilling the ultimate goal of resilient, sustainable infrastructure.

References

• American Concrete Institute. (2014). ACI 318-14: Building Code Requirements for Structural Concrete and Commentary. Farmington Hills, MI: ACI.
• ACI Committee 318. (2019). Report on Bonds and Development of Reinforcement (ACI 318-19), American Concrete Institute.
• MacGregor, J. G., & Wight, J. K. (2012). Reinforced Concrete: Mechanics and Design. Pearson.
• Huang, Y.-H. (2009). Reinforced Concrete: Mechanics and Design. CRC Press.
• Park, R., & Paulay, T. (1975). Reinforced Concrete Structures. Wiley.
• Prakash, S. (2006). Structural Design Manual for Reinforced Concrete. Tata McGraw-Hill Education.
• PC, P. (2010). Structural Analysis and Design of Bridges. Springer.
• Mehta, P. K., & Monteiro, P. J. M. (2014). Concrete: Microstructure, Properties, and Materials. McGraw-Hill Education.
• Newton, R. (2010). Structural Design in Concrete. CRC Press.
• Rao, P. K. (2015). Structural Analysis and Design. Tata McGraw-Hill Education.