Concrete
Basic mix: Cements + Aggregate (gravel,sand) + Water
To produce stronger concrete, less water is added to the mix (without “starving” it = too little water), which makes the concrete mixture less workable and difficult to mix, necessitating the use of plasticizers, water reducers, superplasticizers or dispersants.
Various Binders Used in Concrete
Pozzolonic
Pozzolanic ash – a fine volcanic ash. historically mixed in a 2:1 ratio with lime before hydrated. Modern pozzolanic cement some form of natural or industrial pozzolans together with Portland Cement.
Cementitious
Cement is “a finely pulverized, dry, material that …develops the binding property as a result of hydration.” -Paulo Monteiro
Portland cement is a binder produced by grinding Portland cement clinker (>90%), and mixing with calcium sulfate (~5%), with the addition of other specialized particulate as standards require. Hydraulic cement is stable in an aqueous environment (due to presence of hydraulic calcium silicates)
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Basic formula
7 – 15% Cement
60-70% Additives (gravel, sand, expanded clay granules, glass ‘beads’, recycled materials such as concrete, bricks and rubble, wood chips or polystyrene aggregates)
water (~ w/c ratios)
less than 2% admixtures (plasticizers, accelerators, retarders, water reducers, air entrainers, anti-freeze admixtures, superplasticizers…)
1-6% air (in volume)
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* Water/cementitious materials ratio (w/c)
used for strength analysis (tensile + compressive)
w/c = w(m) / w(c)
with
w(m) = weight of mixing water in batch [lb]
w(c) = weight of cementitious materials in batch [lb]
ACI Code (refer to the ACI Code for the appropriate w/c value when preparing designs or concrete analyses):
* Ratio for non-air entrained concrete between 0.41 & 0.82 – (0.41 | 28 day compressive strength of 6000 lb/in² (41 MPa) <> 0.82 | 2000 lb/in² (14 MPa))
* Ratio for air-entrained concrete between 0.40 & 0.74 (0.40 | 28 day compressive strength of 5000 lb/in² (34 MPa) <> 0.74 | 2000 lb/in² (14 MPa))
* Maximum w/c ratios when strength data is not available: absolute w/c ratios between 0.67 & 0.38 for non-air-entrained concrete (2500 lb/in² – 17 MPa) <> 0.54 & 0.35 for air-entrained concrete (5000 lb/in² – 34 MPa)
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* Determine volume of batch
= Sum of all the V(a)
Find the V(a) for each element of the mix (cement/gravel/sand/water)
V(a) = W(L) / [(SG)*W(u)]
with
V(a) = absolute volume [ft³]
W(L) = weight of material [lb]
(SG) = specific gravity of the material
W(u) = density of water at atmospheric conditions = 62.4 lb/ft³
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* Modus of Elasticity E(c)
E(c) = 33*[w(c)^(1.5)]*[sq rt (f(c)' ]
in lb/in²
E(c) = 0.043 *[w(c)^(1.5)]*[sq rt (f(c)' ]
in MPa
with f(c)’ = specified 28-day compressive strength of concrete [lb/in²]
* Tensile Strength
in normal-weight, normal density concrete:
f(r) = 7.5 * [sq rt (f(c)' ]
in lb/in²
f(r) = 0.7 * [sq rt (f(c)' ]
in MPA
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from Chapter 5 ‘Concrete formulas’ of Civil Engineering formulas pdf
