10.4 Density, Yield, and Gravimetric Air Calculations
Key Takeaways
- Density calculations start with net concrete mass, not the combined mass of concrete and measure.
- The basic density relationship is net mass divided by measure volume, with units carried through the work.
- Yield and relative yield questions require connecting batch mass, measured density, and design volume.
- Gravimetric air problems compare measured density with theoretical density and are easy to miss if signs or percentages are handled casually.
Build Every C138 Problem From Net Mass and Known Volume
Density, unit weight, yield, relative yield, and gravimetric air questions are manageable if the setup is disciplined. The most common error is using the total filled measure mass as if it were the concrete mass. The empty measure has mass. The concrete mass is the filled measure mass minus the empty measure mass. Only that net mass is divided by the calibrated measure volume.
Write the units beside every number. If the measure volume is in cubic feet and the mass is in pounds, density will be in pounds per cubic foot. If the problem gives SI units, keep the SI units together. Many wrong answers come from mixing units or choosing a plausible number with the wrong unit label.
| Calculation | Plain-language setup | Common trap |
|---|---|---|
| Net mass | Full measure mass minus empty measure mass | Forgetting the tare mass |
| Density | Net mass divided by measure volume | Dividing by the wrong volume |
| Yield | Total batch mass divided by measured density | Using design density instead of measured density |
| Relative yield | Actual yield divided by design yield | Reversing the ratio |
| Gravimetric air | Difference between theoretical and measured density expressed as a percent | Sign error or using wrong density |
Example: an empty measure weighs 18.6 lb. The filled measure weighs 54.1 lb. The measure volume is 0.250 ft3. The net concrete mass is 54.1 minus 18.6, or 35.5 lb. Density is 35.5 divided by 0.250, or 142.0 lb/ft3. If the answer choices include 216.4 lb/ft3 from using full mass divided by volume, that answer is a tare error.
Yield questions add one more step. If the total batch mass is 4000 lb and the measured density is 142.0 lb/ft3, the actual yield is 4000 divided by 142.0, or about 28.17 ft3. If the design yield was 27.0 ft3, the relative yield is 28.17 divided by 27.0, or about 1.043. Whether the question asks for yield or relative yield, identify the required output before touching the calculator.
Gravimetric air content is a comparison problem. It asks how much lower the measured density is than the theoretical density, expressed as a percent of the theoretical density. If the measured density is lower than theoretical density, the air content should be positive. If your calculation produces a negative value for ordinary entrained air, review the subtraction order before selecting an answer.
Use this calculation checklist:
- Circle the required output: density, yield, relative yield, or air content.
- Identify empty measure mass, filled measure mass, and measure volume.
- Compute net concrete mass before any density calculation.
- Carry units through each line.
- Use measured density for actual yield when the problem asks for field yield.
- Check whether a percent answer needs multiplication by 100.
- Compare the final value with normal concrete reasonableness.
The written exam may not use the same numbers you practiced. It will reward the same habits. Separate tare from full mass, protect units, know which density belongs in the formula, and do not let a familiar-looking answer choice pull you away from the method.
An empty measure weighs 18.6 lb, the filled measure weighs 54.1 lb, and the measure volume is 0.250 ft3. What is the concrete density?
Which value should be divided by the measure volume to compute density?
A batch mass is 4000 lb and measured density is 142.0 lb/ft3. What is the approximate actual yield?