Hydraulic Universal Flexural Testing Machine
Applies smooth, continuous vertical load with third-point articulated roller loading assembly.
Civil Engineering / Concrete Modulus of Rupture
FREE TO EXPLORELABORATORY 03 · CIVIL ENGINEERING
Flexural Tensile Strength of Concrete Prisms & Modulus of Rupture (Two-Point Loading)
Determine the flexural tensile strength (Modulus of Rupture, f_r) of unreinforced concrete prism beams under third-point symmetrical loading according to ASTM C78 / BS EN 12390-5. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.
STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING
Your virtual civil engineering laboratory.
MODULUS OF RUPTURE F_R—
CIVIL INFRASTRUCTURE TELEMETRY
Ready to sample with Failure Load = 25.0 kN.
Adjust Failure Load, then execute civil engineering measurement.
Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.
Civil engineering assumptions and boundary condition limits
The civil engineering physical models apply within the specified calibrated operational window (15.0 to 40.0 kN). Beam cross-section: b = 150 mm, d = 150 mm, span L = 450 mm. Section modulus Z = b d^2 / 6 = 5.625 x 10^5 mm^3. Conversion slope f_r / P = L / (b d^2) = 450 / (150 x 150^2) = 0.13333 MPa/kN.
Laboratory apparatus & testing equipment.
Articulated Steel Roller Bearing Assembly
Ensures true simply supported boundary conditions without axial thrust or torsional restraint.
Precision Steel Beam Molds (150 x 150 x 500 mm)
Machined steel molds producing square, perpendicular prism specimens compliant with ASTM C78.
Moist Curing Facility (23.0 ± 2.0 °C)
Prevents drying shrinkage microcracks on specimen tensile surfaces prior to testing.
Digital Vernier Calliper & Rule
Measures beam cross-sectional width, depth, and fracture location to 0.1 mm precision.
Deflection Dial Gauge (LVDT)
Monitors midspan elastic flexural deflection up to brittle fracture.
FOLLOW THE METHOD
A reason behind every step.
Determine the flexural tensile strength (Modulus of Rupture, f_r) of unreinforced concrete prism beams under third-point symmetrical loading according to ASTM C78 / BS EN 12390-5. Standardized parameter settings: 15.0, 20.0, 25.0, 30.0, 35.0, 40.0 kN.
01
Specimen Removal & Moist Conditioning
Remove cured prism beam from water bath immediately prior to testing; keep surfaces moist with wet burlap to prevent tensile shrinkage microcracks.
02
Beam Dimensional Verification
Measure cross-sectional width b and depth d at the failure plane to within 0.1 mm across three separate readings.
03
Support & Loading Point Layout
Mark reference support lines at span L = 450 mm and third-point loading lines at 150 mm and 300 mm from left support using a square.
04
Specimen Placement on Articulated Rollers
Turn specimen on its side with respect to its as-cast orientation; center upon support rollers and adjust upper loading rollers to ensure uniform contact.
05
Continuous Flexural Loading
Apply load continuously at a standardized stress rate of 0.86 to 1.21 MPa/min (approximately 0.1 kN/s) until brittle tension rupture occurs.
06
Fracture Location & Modulus Calculation
Inspect the fracture plane; verify that failure occurred within the middle third of the span; record ultimate load P and calculate f_r.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into civil engineering insight.
Points are your recorded observations. The solid regression line validates Concrete Modulus of Rupture mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
f_r = 0.1333 · P
| # | Peak Fracture Load P (kN) | Modulus of Rupture f_r (MPa) | Applied fracture load P (kN) | Modulus of rupture f_r (MPa) | Remove |
|---|
No readings yet. Execute a civil engineering trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the civil engineering metrics mean.
In standard third-point beam flexure testing (ASTM C78), the shear force within the middle third of the span is:
The theoretical maximum bending moment in a third-point loaded beam of span L under total load P is:
According to ACI 318, the nominal modulus of rupture f_r for normal-weight concrete with f'c = 36 MPa is approximately:
What is the standard cross-sectional size of concrete prism beams in ASTM C78?
THEORY AND STRUCTURAL CONTEXT
Civil engineering background & physical principles.
Because concrete is composed of aggregate particles bound by a cementitious paste characterized by microscopic flaws, pores, and interfacial transition zones, its tensile strength is substantially lower than its compressive strength (typically 8% to 12% of f'c). In highway pavements, airport runways, and industrial ground slabs, flexural cracking under repetitive wheel loads represents the primary design governing criterion. The standard flexure test (ASTM C78) utilizes unreinforced prism specimens (150 x 150 x 500 mm) supported across a span L = 450 mm and subjected to symmetrical two-point loading at the third points (spaced L/3 = 150 mm apart). Third-point loading is superior to center-point loading because it establishes a pure bending zone over the central middle third where shear force is exactly zero and bending moment is constant and maximized (M = P L / 6). Consequently, fracture initiates at the weakest critical flaw within the middle third. In this laboratory experiment, concrete prisms are tested to ultimate flexural rupture under controlled loading rates to calculate the Modulus of Rupture f_r and evaluate empirical correlations with compressive strength.
f_r = 0.1333 · P
Beam cross-section: b = 150 mm, d = 150 mm, span L = 450 mm. Section modulus Z = b d^2 / 6 = 5.625 x 10^5 mm^3. Conversion slope f_r / P = L / (b d^2) = 450 / (150 x 150^2) = 0.13333 MPa/kN.