Modulus of rupture and flexural test

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)

      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.