Flexural Strength of Concrete – Modulus of Rupture Test and Formula

If you’re designing a road, the compressive strength of concrete barely matters. What matters is how well the concrete resists bending. That’s flexural strength. The modulus of rupture (MOR) — the technical name for flexural tensile strength — is what engineers use to design rigid pavements, airport runways, and precast beams. This guide explains it in a way that makes sense, with a solved numerical and the IS 456 formula you absolutely need for RTMNU exams.

1. What is Flexural Strength (Modulus of Rupture)?

The modulus of rupture (MOR) is the maximum tensile stress calculated at the extreme bottom fibre of a simply supported concrete beam at the instant of fracture under a transverse load. It tells you how much bending stress the concrete can take before it cracks and breaks in tension.

A quick clarification that trips up many students: MOR is called “modulus of rupture” because it’s calculated using the linear-elastic bending stress formula (Mc/I), which assumes the stress distribution remains linear right up to failure. In reality, concrete behaves non-linearly near failure — so MOR actually overestimates the true tensile strength slightly. That’s why MOR is always the highest of the three tensile strength values.

IS Code: IS 516:2018 – Method of Tests for Strength of Concrete (Section on Flexure)

Typical range: 3.0–6.5 MPa for normal concrete (M20–M50)

2. Apparatus and Specimen

• Test beam specimen: 150 mm × 150 mm × 700 mm long (standard per IS 516)
• Two knife-edge supports: Placed at a span of 450 mm = 3 × depth (3 × 150 mm)
• Two loading nose pieces: Applied at the one-third points of the span (at 150 mm from each support)
• Flexural testing machine or UTM with load application jig

The beam dimensions follow the rule: span = 3 × depth. For a 150 mm deep beam, the span is always 450 mm.

3. Test Procedure (IS 516:2018)

1. Casting: Cast 150 mm × 150 mm × 700 mm beams. Fill in 2 equal layers, each compacted by 62 tamping strokes distributed uniformly over the cross-section. Alternatively, use a vibrating table.
2. Curing: Demould after 24 hours. Immerse in water at 27 ± 2°C until the day of testing.
3. Marking: Mark the centre and one-third points of the 450 mm span on the beam. Mark load application lines at 150 mm from each support.
4. Positioning: Place the beam on the knife-edge supports with the cast face on the sides (not on the tension face). This ensures the smoothest, most uniform surfaces are the tension and compression faces.
5. Load application: Apply load through the two loading noses at the third-points at a rate of 400 kg/min for two-point loading. Apply continuously without shock until failure.
6. Record: Note the maximum failure load P and, critically, the location of the fracture line relative to the middle third of the span.

4. Two-Point (Third-Point) Loading Formula

Two loads are applied at L/3 from each support. The middle third of the beam experiences pure bending with no shear — this is the ideal test condition because failure is due purely to bending stress.

Case A: Fracture within middle third (a ≥ L/3)

Case B: Fracture outside middle third but within 5% of span

Important: If the fracture occurs outside the middle third by more than 5% of the span (more than 22.5 mm from the L/3 point), the test result is rejected and the test must be repeated with a fresh beam.

5. Centre-Point Loading Formula

When a single load is applied at the midpoint of the span:

Centre-point loading is simpler to set up but gives slightly higher MOR values than two-point loading for the same beam because the maximum bending moment is concentrated at a single point (not distributed over the middle third).

6. Solved Numerical Example

Problem: A 150 mm × 150 mm × 700 mm beam is tested under two-point loading on a 450 mm span. The beam fails at P = 22.5 kN. Fracture occurs within the middle third. Find f_r.

7. IS 456:2000 Empirical Formula

This is the formula you’ll use most often in design and exams. IS 456:2000 Clause 6.2.2 gives:

8. MOR Values for Common Grades

9. Where is Flexural Strength Used in Practice?

• Rigid Pavement Design (IRC:58): The entire design methodology for concrete road pavements is based on MOR, not compressive strength. The pavement slab must resist bending under wheel loads without cracking. Typical design MOR: 4.0–4.5 MPa (using M40 concrete for highways).
• Airport Runways and Taxiways: Similar to road pavements but for much heavier aircraft loads. MOR governs slab thickness.
• Industrial Floor Slabs: Warehouse floors under forklift and racking loads experience significant bending. MOR used for thickness design.
• Cracking Moment (M_cr) in IS 456: M_cr = f_r × I_g / y_t, where I_g is gross section inertia and y_t is distance to tension face. Used for deflection calculations and crack width control.
• Railway Sleepers: Pre-tensioned concrete sleepers resist bending under wheel loads. MOR governs sleeper design.

10. Comparison: Three Types of Tensile Strength

11. Diagram – Flexural Test Setup and Formulas

12. Exam Tips (RTMNU)

• ✅ IS 516:2018 = flexural test. Beam: 150 × 150 × 700 mm. Span: 450 mm (= 3 × depth). These numbers are always asked.
• ✅ Two-point formula: f_r = PL ÷ (BD²) for fracture in middle third — most common case, most common formula.
• ✅ IS 456 formula: f_r = 0.7√f_ck (Clause 6.2.2) — memorise and practice computations for M20, M25, M30.
• ✅ If fracture occurs outside middle third by >5% of span → test rejected — this distinction earns marks.
• ✅ Rigid pavement design uses MOR, not compressive strength — a very commonly asked fact.
• ✅ Ranking: Direct tensile < Split tensile < MOR — always explain why (stress gradient in flexure allows redistribution).
• ✅ Practice the numerical: given P and beam dimensions, compute f_r and then back-calculate f_ck using IS 456 formula.

13. Key Takeaways

• Modulus of Rupture (MOR) = tensile stress at extreme bottom fibre of beam at failure in bending.
• Beam: 150 × 150 × 700 mm. Span: 450 mm. Two-point loading at L/3 points (IS 516:2018).
• Two-point formula: f_r = PL ÷ (BD²) when fracture is in middle third.
• Centre-point formula: f_r = 3PL ÷ (2BD²).
• IS 456:2000 Clause 6.2.2: f_r = 0.7√f_ck.
• MOR is used for rigid pavement design (IRC:58), cracking moment calculations, and railway sleeper design.

14. Frequently Asked Questions (FAQs)

Q1. What is the beam size for the flexural strength test?

The standard beam for flexural testing is 150 mm × 150 mm × 700 mm long, tested over a span of 450 mm (= 3 × depth = 3 × 150 mm). Two loads are applied at the one-third points (150 mm from each support), as per IS 516:2018.

Q2. What is the IS 456 formula for modulus of rupture?

IS 456:2000 Clause 6.2.2 gives the formula as f_r = 0.7√f_ck, where f_ck is the characteristic compressive strength in MPa. For M25 concrete: f_r = 0.7 × √25 = 0.7 × 5 = 3.5 MPa.

Q3. What happens if the fracture occurs outside the middle third?

If the fracture line falls outside the middle one-third of the span by more than 5% of the span length (5% × 450 = 22.5 mm), the test result is rejected and the test is repeated with a fresh beam. If within 5%, the formula f_r = 3Pa/(BD²) is used where a = distance from fracture to nearest support.

Q4. Why is MOR used for pavement design rather than compressive strength?

A concrete pavement slab acts as a beam on an elastic foundation. Under vehicle wheel loads, the slab bends, creating tensile stress at the bottom fibre. Pavement failure is by cracking in tension (bending fracture), not by crushing in compression. So it makes physical sense to design against the failure mode, which is governed by flexural (tensile) strength — the modulus of rupture.

Q5. Why is MOR higher than split tensile strength for the same concrete?

In flexural testing, tensile stress builds up gradually from zero at the neutral axis to maximum at the extreme bottom fibre. As the extreme fibre begins to crack, stress can redistribute to adjacent fibres that haven’t yet reached their tensile limit. This redistribution and the stress gradient effect result in a higher apparent strength compared to the split tensile test where the tensile stress is more uniform across the splitting plane.

🔗 Related: Tensile Strength of Concrete – Split Test and IS Formula

🔗 Related: Factors Affecting Strength of Concrete – Complete Guide

📚 Reference: IS 516:2018 – Method of Tests for Strength of Concrete, BIS