# Concrete Mix Design

Concrete is made from different proportions of cement, fine aggregate (sand), coarse aggregate, and water. Cement usually comes in 94 lb sacks, water is measured by gallons (volume), and coarse and fine aggregate by weight. These are all over the place.

There are two main methods of measuring concrete ingredients, the Absolute Volume Method, and a method using Proportion ratio of components

### Absolute Volume

With Absolue Volume the components are measured out using their densities or specific gravities to calculate the volume that each ingredient will use in a given unit of concrete.

$$V_a = \frac{W}{G_s \gamma_{water}}$$

W is the weight (mass if SI)

$$G_s$$ is specific gravity of the material

$$\gamma_{water}$$ is specific weight of water, 62.4 lb/cuft (for SI use density, $$\rho$$, 100 kg/m^3)

Note: $$G_s \gamma_{water}$$ gives the *specific weight* or *solid density *of the material, if you are given that in the prompt, use it straight off.

The general method is to convert all of the materials to absolute volume and then compare those in the mix, that way you will get correct ratios between components.

If any of these values are not given, use the values provided in table 49.2 of the CERM.

### Proportioning Component Ratio

Proportion mixes are specified by a ratio of **weights** of cement, sand, and coarse aggregate, in that order.

Cement : Sand : Coarse

For example in a mix with a ratio of 1:2:3 the sand weighs twice as much as the cement, and the amount of coarse aggregate weighs three times as much as the cement. You can use this information, combined with knowledge of densities of the materials, to determine how much volume of material of each to use in a mix.

### Water-Cement Ratio

The strength of a concrete mix is determined by how much water versus how much cement are in it. Less water will yield a higher strength concrete. Typical values for this ratio are 5-7 gallons to each 94 lb sack of cement, or around 45-60% by weight.

$$! w = \frac{water}{cement} $$

### Yield

Yield is the volume of concrete produced in a batch. A “batch” is the amount of concrete mix you get when you use one (1) 94 lb sack of cement.

Example:

Find the yield of the mix. The weight component ratio is 1:1.8:3. 6 gallons of water per sack.

Component | Ratio | Weight/Sack | Specific Weight | Absolute Volume ($$ft^3$$) |

Cement | 1 | 94 | 195 | 0.48 |

Sand | 1.8 | 178.6 | 165 | 1.082 |

Coarse | 3 | 282 | 165 | 1.709 |

Water | – | – | 6 gal/7.48 gal/ft^3 | 0.802 |

Sum | 4.073 $$ft^3$$ |

Weight/Sack – the component ratio multiplied by 94 lbs

Density – Common densities of materials ($$\frac{lb}{ft^3}$$)

Absolute Volume – Weight/Sack divided by Density (see equation above)

If you are asked to find how much of a component is needed for some volume of concrete, first divide the of concrete by the yield, the volume produced by one sack of cement. The result is the number of 1-sack batches needed.

Take this number of batches and multiply it by the ratio of the component asked for.

If you determined that you need 100 batches to produce 380 cubic feet of concrete, and your ratio for sand is 2, then you need $$100 \bullet 2 \bullet 94lb = 18800 lbs$$ of sand!

Work with the ratios and use the sack of cement as your base unit, then convert it to the component you need.

### Air/Water Entrainment

A percentage of air entrainment may be specified for some concrete mixes to allow for some “breathing room” for water when it is freezing and thawing in cold areas. Calculate the absolute volume of all of the other materials for a batch just like usual in some cases and then work with that number.

If 3% air entrainment is required, divide your absolute batch volume by 0.97, watch the number increase. This is your actual absolute volume for the given solids after including air.

This article/topic is getting huge, and is complicated, please comment if something looks incorrect. I am still trying to wrap my head around this and unfortunately it is portrayed differently in the CERM and AIO books.

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