3.1 Testing Apparatus & Specimen Setup

ASTM C78 — Flexural Strength of Concrete (Third-Point Loading)

3.1 Testing Apparatus & Specimen Setup

Significance of Flexural Strength Testing

Flexural strength is a measure of the tensile strength of concrete. Unlike compressive strength tests (ASTM C39), which subject concrete cylinders to axial crushing, flexural strength tests evaluate the ability of concrete beams to resist bending forces. In structural design, concrete is assumed to have zero tensile strength, and steel reinforcement is designed to carry all tensile loads. However, in pavement engineering—specifically for highways, airport runways, and industrial floor slabs—concrete slabs are subjected directly to wheel loads that induce bending stresses. In these applications, the modulus of rupture (MR or R) is used for thickness design, quality control, and concrete acceptance. Flexural strength is typically 10% to 15% of the compressive strength of the concrete, but it is highly sensitive to specimen preparation, moisture conditioning, and testing alignment.

The Mechanics of Third-Point Loading

ASTM C78 utilizes third-point loading (also referred to as two-point loading on a simple span). In this configuration, the support span length ($L$) is set to exactly three times the specimen depth ($d$), or $L = 3d$. The total load ($P$) applied by the testing machine is split equally into two loads ($P/2$) applied at the third points of the span (each load-applying block is located at a distance of $L/3$ from the nearest support block).

The primary advantage of third-point loading over center-point loading (ASTM C293) is the distribution of bending moment. Under center-point loading, the maximum bending moment occurs at a single point directly beneath the load. In third-point loading, the bending moment is constant and maximum throughout the entire middle-third section of the span, while the shear force is zero in this region. This uniform moment distribution means that the entire middle-third volume of the beam is subjected to the maximum tensile stress. Because concrete is a heterogeneous material, the fracture will naturally initiate at the weakest spot (e.g., a localized void, weak aggregate interface, or microcrack) within this middle-third zone. Consequently, third-point loading provides a more realistic and conservative measure of the concrete's actual flexural strength than center-point loading, which forces failure at the center and tends to overestimate flexural strength by 15% to 20%.

Testing Apparatus & Bearing Blocks

The testing machine must be capable of applying loads vertically, continuously, and without shock. The loading and support apparatus must be designed to ensure that forces are applied perpendicular to the face of the specimen and without eccentricity. The bearing blocks in contact with the specimen must meet the following ASTM C78 specifications:

1. Dimensions: The bearing blocks must be at least as wide as the specimen (typically 6 in. or 150 mm).
2. Hardness: The contact surfaces of the bearing blocks must be case-hardened with a hardness of not less than 30 HRC.
3. Flatness Tolerance: The bearing surfaces must be flat to within 0.002 inches (0.05 mm) along any line of contact.
4. Height Constraint: The height of the blocks, measured from the pivot axis to the contact surface, must be no greater than 2.5 inches (64 mm).
5. Freedom of Rotation: The load-applying and support blocks must be designed to rotate and pivot. A standard setup consists of one fixed support block, one rolling support block, and two load-applying blocks that are free to tilt. This configuration allows the apparatus to maintain uniform contact across the full width of the beam, compensating for minor surface irregularities, twisting, or warping of the specimen.

Specimen Preparation & Moisture Conditioning

Concrete beams are highly susceptible to moisture loss. When a concrete specimen dries, moisture evaporates from its outer surfaces faster than from its core, inducing tensile drying shrinkage stresses in the outer fibers. Since concrete is weak in tension, these shrinkage stresses create invisible microcracks on the surface. When the beam is tested, these shrinkage stresses combine with the applied bending stresses, causing the specimen to rupture prematurely at a lower load. To prevent this, ASTM C78 mandates strict moisture conditioning rules:

• Specimens must be stored in a moist condition (in a curing tank or a moist room) until the moment of testing.
• The specimen must be tested as soon as possible after removal from moist storage.
• If there is any delay between removal from curing and testing, the technician must cover the specimen with a damp cloth, wet burlap, or plastic sheeting to prevent surface drying. Even 15 minutes of exposure to dry air can significantly reduce the measured modulus of rupture.

Specimen Setup & Gap Tolerances

To perform the test, the technician follows a precise sequence:

1. Orientation: The beam must be turned on its side relative to its molded position. This 90-degree rotation is critical because the top surface of the concrete beam is finished with a trowel, which is rarely flat or parallel to the bottom. Turning the beam on its side places the smooth, parallel sides that were cast against the metal mold in direct contact with the loading and support blocks, ensuring uniform load distribution.
2. Centering: Center the beam on the support blocks so that the span length ($L$) is exactly three times the depth ($d$) of the beam. For a standard 6 in. x 6 in. beam, the support span is 18 inches, and the beam's overall length must be at least 20 inches (providing at least 1 inch of overhang at each end).
3. Checking for Gaps: Visually inspect the contact between the beam surfaces and the bearing blocks. Slide a feeler gauge along the lines of contact to measure any gaps.
   • Gaps $\le 0.004$ in. (0.10 mm): No action is required. The test can proceed.
   • Gaps between 0.004 in. (0.10 mm) and 0.015 in. (0.38 mm): The gaps must be eliminated. The technician can choose to grind the specimen surface, cap the contact points, or use leather shims. If leather shims are used, they must be of uniform thickness (typically 1/4 in. or 6 mm), 1 to 2 inches (25 to 50 mm) wide, and must extend across the full width of the specimen.
   • Gaps $> 0.015$ in. (0.38 mm): The contact surface must be corrected by grinding or capping. Leather shims are strictly prohibited for gaps larger than 0.015 inches. Capping must be performed in accordance with ASTM C617 or using sulfur mortar, ensuring the caps are thin and flat.