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Flexural strength calculator: modulus of rupture (ASTM C78 and C293)
Choose third-point or center-point loading, then enter the maximum load, the span and the average width and depth of the beam. For third-point loading, say whether the fracture is inside the middle third; if it is outside, enter the distance from the fracture to the nearest support.
By ProofGrit Editorial TeamLast reviewed:
Results update as you typeUnits: psi, in, lbfRuns in your browser. Nothing is saved.
Key takeaways
- Match the formula to the loading: third-point (C78) or center-point (C293).
- C78 fracture outside the middle third by no more than 5 % of the span: R = 3 × P × a ÷ (b × d²).
- Use the measured average width and depth, not the nominal size.
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How it's calculated
How is the result calculated?
C78 inside the middle third: R = P × L ÷ (b × d²). C78 outside (≤ 5 % of span): R = 3 × P × a ÷ (b × d²). C293: R = 3 × P × L ÷ (2 × b × d²).
- 01P = maximum applied load (lbf), L = span length (in), b = average width (in), d = average depth (in) of the specimen
- 02ASTM C78 third-point loading, fracture inside the middle third: R = P × L ÷ (b × d²)
- 03ASTM C78, fracture outside the middle third by no more than 5 % of the span: R = 3 × P × a ÷ (b × d²), where a is the average distance from the fracture line to the nearest support
- 04ASTM C293 center-point loading: R = 3 × P × L ÷ (2 × b × d²)
- 05Report the modulus of rupture R to the nearest 5 psi
Rounding: modulus of rupture to the nearest 5 psi. Full precision is kept between steps.
FAQ
Frequently asked questions about the flexural strength calculator
What is the modulus of rupture?
It is the flexural strength of a plain concrete beam: the calculated stress at the extreme tension fiber when the beam breaks in bending.
What is the difference between C78 and C293?
ASTM C78 loads the beam at two points, at the third points of the span. ASTM C293 loads it at one point at mid-span. The formulas differ, so use the one that matches how the beam was tested.
What if the beam breaks outside the middle third?
Under C78, if the fracture is outside the middle third by no more than 5 % of the span, use R = 3 × P × a ÷ (b × d²). If it is further out, the calculator does not report a result; follow the current standard.
Which width and depth should I enter?
The average measured width and depth of the specimen at the fracture, not the nominal mold size.
Why round to 5 psi?
The modulus of rupture is reported to the nearest 5 psi. The calculator keeps full precision and rounds only the reported value.
Related guides and pages
- ASTM C39: compressive strength of concrete cylindersHow a cylinder break works, how strength is calculated from two diameters and the maximum load, when the L/D correction applies, and what to check.
- ASTM C42: concrete core testing guideHow concrete cores are obtained and tested, how length-to-diameter correction applies, and how ACI core criteria are evaluated.
- Construction materials testing: a practical lab guideA practical overview of construction materials testing: how field observations, laboratory methods, calculations and reviewed reports fit together.
- Concrete testing softwareHow ProofGrit handles this test in the lab.
- Standards indexEvery standard explained on this site, with plain-English purpose.
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Sources and further reading
- ASTM InternationalASTM International
- American Concrete InstituteACI
- FHWA pavement programFederal Highway Administration
Standards are summarized in our own words. Read the current edition from the publisher before you test.
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