--- title: "Modulus of rupture and flexural test" subject: "Concrete Technology and Masonry Structure" chapter: 5 key: "semester_5/concrete_technology_and_masonry_structure:modulus-of-rupture-determination" source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/modulus-of-rupture-determination site: BCT Engineering --- # Modulus of rupture and flexural test Concrete Technology and Masonry Structure · Chapter 5: Testing of concrete and quality control - Asked in: 2074 Ashwin, 6 marks; 2073 Shrawan, 2+4 marks; 2072 Kartik, 6 marks; 2064 Jestha (old course) (asked 4 times) - Video: [Expt 2. Flexural Strength Test of Concrete Beam](https://www.youtube.com/watch?v=gCj4lP3vNl4) — VIRTUAL LABS - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/modulus-of-rupture-determination - Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-5 ## Question What is modulus of rupture (flexural strength) of concrete? How do you determine it in the laboratory (methods of performing the flexural test)? ## Short answer Modulus of rupture is the maximum tensile stress at the extreme fibre of a plain concrete beam in bending, f_cr = M/Z. It is determined by a flexure test (IS 516) on a 150×150×700 mm beam under third-point loading over 600 mm span; if the crack is in the middle third, f_cr = Pl/(bd²). ## Answer **Modulus of rupture** (flexural strength) is the maximum extreme-fibre tensile stress in a plain concrete beam at failure in bending, calculated by the flexure formula $f_{cr} = M/Z$. It is an indirect measure of the tensile strength, used for cracking moment of RC members (IS 456, Cl. 6.2.2: $f_{cr} = 0.7\sqrt{f_{ck}}$ N/mm$^2$) and for the design of pavements. #### Laboratory determination (IS 516) ```text P/2 P/2 | | ____v____________v____ | beam | d = 150 |______________________| ^ l/3 | l/3 | l/3 ^ |<------- l = 600 ------>| ``` 1. Cast beams 150 × 150 × 700 mm (or 100 × 100 × 500 for 20 mm aggregate), cure in water and test wet, at 28 days. 2. Place the beam on two rollers at 600 mm span, with the cast side turned to the side. Apply the load at the **third points** (two-point loading), without shock at 0.7 N/mm$^2$/min extreme-fibre stress (about 400 kg/min). 3. Record the failure load $P$ (total). 4. If the fracture is within the middle third, then (with $P$ the total load, $b$ the width and $d$ the depth of the beam): $$ f_{cr} = \frac{P\,l}{b\,d^2} $$ 5. If the fracture lies outside the middle third by not more than 5% of the span, $f_{cr} = \dfrac{3Pa}{bd^2}$ with $a$ the distance from the nearest support; if more than that, the result is discarded. With single (centre) point loading $f_{cr} = \dfrac{3Pl}{2bd^2}$. Two-point loading is preferred because a uniform moment acts over the middle third, so the weakest section governs, as in a direct test; centre-point loading gives about 15% higher values. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Modulus of rupture is: A. Compressive strength of a cube B. Max extreme-fibre tensile stress in a plain concrete beam at failure in bending C. Splitting stress of a cylinder D. Stress at first crack in steel Answer: B. It is M/Z at failure of an unreinforced beam. (Key point: Definition) 2. Standard flexure beam and loading are: A. 150 mm cube at centre B. 100x100x500 on 300 mm span, point load C. 150x150x700 mm on 600 mm span, loaded at third points D. 150x150x700 on 700 mm span, UDL Answer: C. IS 516 uses 600 mm span with two-point (third-point) loading. (Key point: Test setup) 3. If fracture lies outside middle third within 5% of span, f_cr is: A. 3Pa/(bd^2), a measured from nearest support B. Pl/(bd^2) C. Rejected always D. 3Pl/(2bd^2) Answer: A. Within 5% use 3Pa/bd^2; beyond it the result is discarded. (Key point: Crack outside) 4. Why is two-point loading preferred? A. Higher values are obtained B. Moment is maximum under one point C. It needs smaller beams D. Uniform moment in middle third, so the weakest section governs Answer: D. Constant moment over the middle third; centre-point test gives about 15% higher values. 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