2.4 Specimen End Tolerances & Dimensional Measurements

2.4 Specimen End Tolerances & Dimensional Measurements

For the compressive strength test to yield accurate, representative results, the axial load must be distributed uniformly across the entire cross-section of the cylinder. If the ends of the concrete cylinder are not flat, or if the cylinder axis is not perpendicular to the bearing blocks, the applied load will concentrate in localized areas (stress concentrations). This causes premature cracking and local crushing, resulting in a false, low compressive strength reading.

This section covers the geometric tolerances for cylinder end planeness and perpendicularity, the standard methods for measuring cylinder dimensions, and the calculations for determining aspect ratios and applying length-to-diameter ($L/D$) correction factors.

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End Geometric Tolerances

ASTM C39 establishes two critical geometric requirements for the ends of cylindrical concrete specimens: planeness (flatness) and perpendicularity.

1. Planeness (Flatness) Tolerance

The bearing surfaces of the cylinder must be exceptionally flat to ensure complete contact with the testing machine platens.

• Flatness Limit: The ends of the specimen must be flat within $0.05\text{ mm}$ [$0.002\text{ inches}$].
• Checking Flatness: Technicians verify flatness using a precision steel straightedge and a $0.002\text{ in.}$ feeler gauge. The straightedge is laid across the diameter of the cylinder end in several directions. If the feeler gauge can slide under the straightedge at any point, the end is not plane.
• Remedies for Out-of-Flat Ends: If a cylinder end exceeds the $0.002\text{ in.}$ flatness limit, it cannot be tested in that condition. It must be:
  • Ground flat using a specialized concrete grinding machine.
  • Capped with sulfur mortar or high-strength gypsum paste in accordance with ASTM C617.
  • Tested using an unbonded neoprene capping system in accordance with ASTM C1231.

2. Perpendicularity Tolerance

The ends of the specimen must be perpendicular to the longitudinal axis of the cylinder to prevent eccentric, off-center loading.

• Perpendicularity Limit: The ends of the specimen must not depart from perpendicularity to the axis by more than $0.5^\circ$.
• Physical Equivalent: A $0.5^\circ$ deviation is approximately equivalent to a slope of 1:100 (or $1\text{ mm}$ in $100\text{ mm}$ of height).
  • For a standard $6 \times 12\text{ inch}$ cylinder, this translates to a maximum end tilt of $0.12\text{ inches}$ [3.0 mm] across the $12\text{ in.}$ height.
  • For a standard $4 \times 8\text{ inch}$ cylinder, this translates to a maximum end tilt of $0.08\text{ inches}$ [2.0 mm] across the $8\text{ in.}$ height.
• Remedies for Out-of-Square Ends: Cylinders exceeding the perpendicularity tolerance must be saw-cut or ground to bring them within tolerance before testing. Capping or neoprene pads cannot correct a cylinder that is severely out of perpendicular.

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Dimensional Measurements and Area Calculation

To convert the maximum load (force) sustained by the specimen into compressive strength (stress), the technician must accurately calculate the cross-sectional area. This requires precise measurements of the cylinder's diameter.

Measuring the Cylinder Diameter

• Location of Measurement: The diameter must be measured at the mid-height of the specimen.
• Measurement Method: Take two measurements of the diameter at right angles ($90^\circ$) to each other at mid-height.
• Averaging: Average the two measurements to determine the average diameter ($d$).
• Measurement Precision Rules:
  • Nearest $0.25\text{ mm}$ [$0.01\text{ inches}$]: This high-precision measurement is required if the average diameter of the cylinder is less than $150\text{ mm}$ [$6\text{ inches}$], or if the expected concrete strength is $35\text{ MPa}$ [$5000\text{ psi}$] or greater.
  • Nearest $0.5\text{ mm}$ [$0.02\text{ inches}$]: This standard measurement is permitted if the average diameter is $150\text{ mm}$ [$6\text{ inches}$] or greater and the expected concrete strength is less than $35\text{ MPa}$ [$5000\text{ psi}$].
• Averaging Precision: The two diameters are averaged and rounded to the same precision (nearest $0.01\text{ in.}$ or $0.02\text{ in.}$).

Calculating the Cross-Sectional Area ($A$)

Once the average diameter ($d$) is determined, the cross-sectional area is calculated using the formula:

ight)^2 = \frac{\pi \times d^2}{4}$$ - If the diameter was measured to the nearest $0.01\text{ in.}$ [$0.25\text{ mm}$], calculate the area to the nearest **$0.01\text{ in.}^2$ [$10\text{ mm}^2$]**. - If the diameter was measured to the nearest $0.02\text{ in.}$ [$0.5\text{ mm}$], calculate the area to the nearest **$0.1\text{ in.}^2$ [$100\text{ mm}^2$]**. --- ## Specimen Length and Aspect Ratio ($L/D$) The length of the specimen is also critical, particularly for determining the aspect ratio (length-to-diameter ratio, or $L/D$). - **Length Measurement:** The length of the specimen must be measured to the **nearest 0.05D** (where $D$ is the nominal diameter) if the $L/D$ ratio is suspected to be less than 1.80 or greater than 2.20. For a $6\text{ in.}$ cylinder, this means measuring length to the nearest $0.3\text{ inches}$. ### The Aspect Ratio Effect A standard concrete cylinder has an $L/D$ ratio of **2.00** (e.g., $6\text{ in.}$ diameter by $12\text{ in.}$ length). - **Why shorter cylinders appear stronger:** When a short concrete cylinder is compressed, the frictional restraint between the steel bearing blocks of the machine and the ends of the concrete cylinder creates a confining stress. This confining stress acts as a lateral pressure, holding the concrete together and preventing lateral expansion. In a standard $L/D = 2.00$ cylinder, this confining stress dissipates towards the mid-height of the cylinder, allowing a true uniaxial compression failure. In shorter cylinders, the confining stress overlaps throughout the entire height, artificially increasing the measured compressive strength. - **The Core Correction Rule:** To compare the strength of short specimens (often drilled cores or cut specimens) to standard cylinders, a correction factor must be applied. --- ## Length-to-Diameter ($L/D$) Correction Factors If the length-to-diameter ratio ($L/D$) of the specimen is **1.75 or less**, the measured compressive strength must be multiplied by a correction factor: | Length-to-Diameter ($L/D$) Ratio | ASTM C39 Correction Factor | | :--- | :--- | | **2.00** | 1.00 (No Correction) | | **1.75** | 0.98 | | **1.50** | 0.96 | | **1.25** | 0.93 | | **1.00** | 0.87 | ### Application Rules - **Linear Interpolation:** For $L/D$ ratios that fall between the values listed in the table, the technician must use linear interpolation to find the exact correction factor. - **Prohibition:** Specimens with an $L/D$ ratio **less than 1.00** are not permitted to be tested under ASTM C39. Shorter specimens exhibit extreme confinement, and the test no longer represents a compressive strength test.