Modulus of elasticity and modulus of rupture, calculated
f′c
Ec = 57,000√f′c
Ec = wc1.5·33√f′c (ksi)
fr = 7.5λ√f′c (psi)
psi
MPa
ksi
GPa
wc = 100 lb/ft³
120 lb/ft³
145 lb/ft³
λ = 1.0
λ = 0.75
Calculated from Eqs. (19.2.2.1.a), (19.2.2.1.b) and (19.2.3.1) [1]: the density form for wc of 90 to 160 lb/ft³, the 57,000√f′c form for normalweight concrete only.
λ by equilibrium density (Table 19.2.4.1(a))
wc (lb/ft³)
λ
λ by composition of aggregates (Table 19.2.4.1(b))
Concrete
Fine aggregate
Coarse aggregate
λ
Ranges may be interpolated by the normalweight share of the aggregate volume; λ = 0.75 may be used for any lightweight concrete and is 1.0 for normalweight (19.2.4.2, 19.2.4.3).
Exposure Classes & Mixture Requirements
Class
Condition
Max. w/cm
Min. f′c (psi)
Additional requirements
Tables 19.3.1.1 and 19.3.2.1 [1]; sulfate in soil is percent by mass, in water ppm. Max. w/cm does not apply to lightweight concrete, and the table’s footnotes allow some other cements for seawater and sulfate exposure.
Air Content
Concrete (Table 19.3.3.1)
Nominal max. aggregate
Target air content (%)
in.
mm
F1
F2
Shotcrete (Table 19.3.3.3)
Mixture
Sampling
Target air content (%)
F1
F2
F2 and C2
Concrete in F1 or F2 must be air entrained [1]. For f′c ≥ 5000 psi the air content may be 1.0 percentage point lower (19.3.3.6).
Development Length of Straight Bars in Tension
Bar
db (in)
Tension
Hook ℓdh
Compression
ℓd
Class A lap
Class B lap
ℓdc
Lap ℓsc
Simplified development length (Table 25.4.2.3)
Spacing and cover
No. 6 and smaller bars, deformed wires
No. 7 and larger bars
Modification factors, straight bars in tension (Table 25.4.2.5)
Factor
Condition
Value
ℓd is at least 12 in. (25.4.2.1), √f′c is limited to 100 psi (25.4.1.4) and ψtψe need not exceed 1.7 [1]. The lengths above are calculated; the Code tabulates only the equations.
Hooked, Headed & Compression Bars
Standard hooks in tension: ℓdh = (fyψeψsψccψr / 50λ√f′c) db, at least 8db and 6 in. (25.4.3.1, Table 25.4.3.2)
Factor
Condition
Value
Headed bars in tension: ℓdt = (fyψeψpψoψc / 90√f′c) db1.5, at least 8db and 6 in. (25.4.4.2, Table 25.4.4.3)
Factor
Condition
Value
Headed bars: No. 11 and smaller, normalweight concrete, clear cover ≥ 2db, spacing ≥ 3db, head bearing area ≥ 4Ab (Grade 60) or 6Ab (Grades 80 and 100) (25.4.4.1).
Bars in compression: ℓdc = greater of (fyψr / 50λ√f′c) db and 0.0003fyψrdb, at least 8 in. (25.4.9, Table 25.4.9.3)
Factor
Condition
Value
Lap Splices
Tension lap splices (Table 25.5.2.1)
As,provided/As,required over splice
Max. % of As spliced within lap
Type
ℓst
Compression lap splices, No. 11 and smaller (25.5.5.1)
fy (psi)
ℓsc
ℓd in Table 25.5.2.1 is taken before its 12 in. minimum; bars larger than No. 11 are not lap spliced (25.5.1.1), and compression laps are one-third longer where f′c < 3000 psi.
Spiral lap length, at least 12 in. (Table 25.7.3.6)
Reinforcement
Coating
Ends of lapped bar or wire
Lap length
Standard Hooks & Bar Spacing
Hooks for development of bars in tension (Table 25.3.1)
Hook
Bar size
Min. inside bend diameter
Straight extension ℓext
Stirrup, tie and hoop hooks (Table 25.3.2)
Hook
Bar size
Min. inside bend diameter
Straight extension ℓext
Hook dimensions by bar size, calculated (in)
Bar
db
Development hooks
Stirrups, ties and hoops
Bend dia.
90° ℓext
180° ℓext
Bend dia.
90° ℓext
135° ℓext
180° ℓext
Nominal bar diameters from ASTM A615 [2]; bend diameters are inside diameters. Stirrup and tie hooks are limited to No. 8 and smaller.