Concrete Technology — Worked Examples

These examples follow the concrete quality chain from fresh testing and mixture proportioning through hardened strength and nonconformance investigation. Acceptance decisions always defer to the governing project specification and code.

Example 1 — Water-cementitious materials ratio

A concrete mixture contains 300 kg300\text{ kg} Portland cement, 60 kg60\text{ kg} fly ash, and 162 kg162\text{ kg} effective mixing water. Determine w/cmw/cm.

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Example 2 — Interpret an invalid slump observation

During a slump test, the concrete mass shears markedly to one side rather than subsiding uniformly. The technician records the largest vertical difference as 160 mm. Decide how the observation should be handled.

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Example 3 — Absolute-volume fine-aggregate calculation

For 1.00 m31.00\text{ m}^3 of trial concrete: cement = 360 kg with relative density 3.15; water = 180 kg; SSD coarse aggregate = 1050 kg with bulk SSD relative density 2.65; air = 1.5%; SSD fine-aggregate relative density = 2.60. Determine SSD fine-aggregate mass.

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Example 4 — Aggregate moisture correction

The SSD trial proportions require 1050 kg coarse aggregate and 766 kg fine aggregate. Coarse aggregate absorption is 0.5% and total moisture is 2.0%; fine aggregate absorption is 1.2% and total moisture is 6.0%. All percentages are on an OD basis. Design mixing water is 180 kg. Determine wet aggregate masses and added water.

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Example 5 — Concrete density and measured yield

A trial batch uses a total batched mass of 2300 kg2300\text{ kg} and fills a calibrated 0.0500 m30.0500\text{ m}^3 measure with 118.0 kg118.0\text{ kg} of concrete. The batch was intended to produce exactly 1.00 m31.00\text{ m}^3. Estimate fresh-concrete density and actual yield.

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Example 6 — Cylinder compressive strength

A 150 mm150\text{ mm} diameter concrete cylinder fails at a maximum load of 620 kN620\text{ kN} during a valid cylindrical compression test. Determine measured compressive strength.

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Example 7 — Investigate an unexpectedly low strength test

A valid project strength report is unexpectedly below the acceptance trend. Determine the investigation sequence before changing the mixture or condemning the structure.

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Example 8 — Placement and segregation control in a congested wall

Concrete is discharged from high above its final location, repeatedly striking reinforcement, while workers add unauthorized water to make it flow. Identify the material-quality risks and controls.

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