Cheatsheet: Concrete Design

1. Material Properties and Mix Design

1.1 Concrete Strength Properties

1.2 Reinforcing Steel Properties

1.3 Concrete Weight and λ Modification Factor

2. Design Principles and Load Factors

2.1 Strength Reduction Factors (φ)

2.2 Load Combinations (ACI 318)

• U = 1.4D
• U = 1.2D + 1.6L + 0.5(Lr or S or R)
• U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.5W)
• U = 1.2D + 1.0W + 1.0L + 0.5(Lr or S or R)
• U = 1.2D + 1.0E + 1.0L + 0.2S
• U = 0.9D + 1.0W
• U = 0.9D + 1.0E

3. Flexural Design of Beams

3.1 Rectangular Beam Design Equations

3.2 T-Beam Design

3.3 Doubly Reinforced Beams

• Check if compression steel yields: fs' = 87,000(c - d')/c ≥ fy
• If compression steel yields: Mn = (As - A's)fy(d - a/2) + A'sfy(d - d')
• Where a = (As - A's)fy/(0.85f'cb)
• Net tensile strain must satisfy tension-controlled requirements

4. Shear Design

4.1 Shear Strength Equations

4.2 Stirrup Spacing Requirements

4.3 Critical Sections

• Critical section at distance d from face of support for non-prestressed members
• Vu may be calculated at d from support if: support reaction introduces compression, no concentrated load within d
• For deep beams (ln/h < 4):="" use="" strut-and-tie="">

5. Development Length and Splices

5.1 Development Length for Deformed Bars in Tension

5.2 Development Length in Compression

5.3 Splice Lengths

5.4 Standard Hooks (Tension)

• ldh = (0.02fyψe)/(λ√f'c) × db for #11 and smaller
• ψe = 1.0 for uncoated; 1.2 for epoxy-coated
• Modification factors: 0.7 for side/top cover ≥ 2.5 in and #11 hook cover ≥ 2 in; 0.8 for ties/stirrups
• ldh ≥ max(8db, 6 in)

6. Column Design

6.1 Column Load Capacity

6.2 Reinforcement Limits

6.3 Lateral Reinforcement

6.3.1 Tied Columns

• Minimum tie size: #3 for longitudinal bars #10 and smaller; #4 for #11 and larger
• Vertical spacing: s ≤ min(16db,long, 48db,tie, least column dimension)
• Ties must enclose all longitudinal bars with corner bars enclosed by tie corners
• Every corner and alternate longitudinal bar must have lateral support ≤ 6 in clear

6.3.2 Spiral Columns

6.4 Slenderness Effects

7. Slab Design

7.1 One-Way Slab Design

7.2 Two-Way Slab Minimum Thickness

7.3 Two-Way Slab Moment Distribution (Direct Design Method)

7.4 Punching Shear in Slabs

8. Footings

8.1 Spread Footing Design

8.2 Transfer of Force at Base of Column

• Bearing on concrete: φPn = φ0.85f'cA1√(A2/A1) where φ = 0.65
• √(A2/A1) ≤ 2 where A2 is supporting area geometrically similar to A1
• If bearing inadequate, use dowels: As = (Pu - φPn)/φfy
• Minimum dowel area: 0.005Ag of supported column
• Dowel diameter ≤ longitudinal bar diameter + 1/16 in

8.3 Combined Footings

• Resultant of loads should coincide with centroid of footing for uniform bearing
• Design for moment and shear at critical sections
• Check one-way and two-way shear at each column

9. Reinforcement Details

9.1 Standard Bar Sizes

9.2 Concrete Cover Requirements

9.3 Crack Control

• Spacing of reinforcement closest to tension face: s ≤ 15(40,000/fs) - 2.5cc
• Not to exceed s ≤ 12(40,000/fs) where fs = 2fy/3
• For beams with h > 36 in, distribute skin reinforcement along both faces in tension zone
• Ask ≥ 0.012(d - 30)/2 on each face, spacing ≤ min(d/6, 12 in)

10. Deflection Control

10.1 Immediate Deflection

10.2 Long-Term Deflection

• λΔ = ξ/(1 + 50ρ') where ξ = time-dependent factor
• ξ = 1.0 for 3 months; 1.2 for 6 months; 1.4 for 12 months; 2.0 for 5 years or more
• ρ' = As'/(bd) (compression reinforcement ratio)
• Additional long-term deflection = λΔ × immediate sustained load deflection

10.3 Deflection Limits

11. Special Design Considerations

11.1 Torsion Design

11.2 Brackets and Corbels

• a/d ≤ 1.0 where a = shear span
• Avf (friction steel) ≥ Nuc/(φμfy) where Nuc = factored normal force, μ = 1.4λ for monolithic
• As ≥ (Vua/φfyd) + Nuc(h - d)/(φfyd) + An
• An = Nuc/(φfy) minimum for tension reinforcement
• As,min = max(0.04f'c/fy, As,calculated) × bd
• Closed stirrups Ah ≥ 0.5(As - An)

11.3 Deep Beams

• Deep beam when ln/h ≤ 4 or clear span ≤ 4d
• Use strut-and-tie model for design
• Minimum vertical reinforcement: Av ≥ 0.0025bws
• Minimum horizontal reinforcement: Avh ≥ 0.0025bws2
• Maximum spacing: min(d/5, 12 in)

12. Prestressed Concrete

12.1 Prestressing Steel Properties

12.2 Prestress Losses

12.3 Flexural Strength

12.4 Service Load Stresses

• Compression at transfer: ≤ 0.60f'ci
• Tension at transfer (no bonded reinforcement): ≤ 3λ√f'ci (may exceed if shown acceptable)
• Compression at service: ≤ 0.45f'c
• Tension at service (Class U): ≤ 7.5λ√f'c
• Tension at service (Class T): ≤ 6λ√f'c (precompressed zone)

13. Retaining Walls

13.1 Design Requirements

13.2 Lateral Earth Pressure

13.3 Design Considerations

• Check stem for flexure and shear as cantilever from base
• Check heel and toe slabs for flexure and shear
• Increase active pressure by 20% if backfill is sloped or surcharged
• Provide drainage to prevent hydrostatic pressure buildup
• Temperature and shrinkage steel: same as one-way slabs

14. Seismic Design Provisions

14.1 Special Moment Frame Requirements

14.2 Transverse Reinforcement in Beams

• First hoop at 2 in from column face
• Spacing ≤ min(d/4, 8db, 24db,tie, 12 in) for distance 2h from face
• Hoops required where Vu > φVc/2
• Minimum hoop size: #3 for longitudinal bars ≤ #9; #4 for longitudinal bars > #9

14.3 Special Moment Frame Columns

14.4 Confinement Requirements

• Confine over lo from joint face where lo = max(h, ln/6, 18 in)
• Spacing: min(h/4, 6db, 4 + (14 - hx)/3 in) but ≤ 6 in initially
• Ash = 0.09shcf'c/(fytkbc) or Ash = 0.3(shcf'c/fyt)(Ag/Ach - 1) whichever is greater
• Every corner and alternate longitudinal bar must have seismic hook support