---
title: "Various strengths of concrete"
subject: "Concrete Technology and Masonry Structure"
chapter: 5
key: "semester_5/concrete_technology_and_masonry_structure:various-strengths-of-concrete"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/various-strengths-of-concrete
site: BCT Engineering
---

# Various strengths of concrete

Concrete Technology and Masonry Structure · Chapter 5: Testing of concrete and quality control

- Asked in: 2078 Bhadra, 4 marks; 2069 Chaitra, 6 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/various-strengths-of-concrete
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-5

## Question

Explain the various strengths of concrete (required for design of concrete structures, with their relation to the compressive strength).

## Short answer

Key strengths: compressive (fck, basis of design), flexural (fcr = 0.7 sqrt(fck)), splitting tensile (approx 0.5-0.6 sqrt(fck)), direct tensile (approx 0.35-0.45 sqrt(fck)), shear (tau_c from IS 456 Table 19), bond (tau_bd = 1.2 N/mm^2 for M20 plain bars), and bearing (0.45 fck sqrt(A1/A2) up to 0.9 fck). All increase with fck, roughly proportional to sqrt(fck).

## Answer

Concrete strength is not a single value; it depends on the type of stress. All are related to the compressive strength, which is the basic one measured.

| Strength | Typical value | Relation (IS 456) |
|---|---|---|
| Compressive | $f_{ck}$ (cube, 28 days) | Basis of design; grade M20, M25 etc. |
| Flexural (modulus of rupture) | 10 to 15% of $f_c$ | $f_{cr} = 0.7\sqrt{f_{ck}}$ (Cl. 6.2.2) |
| Splitting tensile | 8 to 12% of $f_c$ | $\approx 0.5\sqrt{f_{ck}}$ to $0.6\sqrt{f_{ck}}$ |
| Direct tensile | 7 to 10% of $f_c$ | $\approx 0.35\sqrt{f_{ck}}$ to $0.45\sqrt{f_{ck}}$ |
| Shear | about 20% of $f_c$ (pure shear), design $\tau_c$ | Table 19: $\tau_c = 0.28$ to 0.82 N/mm$^2$ for M20 depending on steel percentage |
| Bond | $\tau_{bd}$ | Cl. 26.2.1.1: 1.2 N/mm$^2$ (M20 plain bars); 1.6 times higher for deformed bars |
| Bearing | Higher than $f_c$ when the loaded area is smaller than the supporting area (confinement) | Cl. 34.4: $0.45 f_{ck}\sqrt{A_1/A_2}$, with $\sqrt{A_1/A_2}\le 2$ |

#### Compressive strength
Measured on 150 mm cube (IS 516) or 150 × 300 cylinder; $f_{cyl} \approx 0.8 f_{cube}$. Needed for column, beam compression zone and slab design.

#### Tensile strength
Governs cracking and is found by splitting or flexure tests. Concrete is weak in tension, so steel carries it.

#### Shear strength
Resistance to sliding failure. Pure shear is difficult to test; diagonal tension controls beam design, with $\tau_v = V/bd$ compared to $\tau_c$ (Table 19) and $\tau_{c,max}$ (Table 20).

#### Bond strength
Adhesion and friction between steel and concrete that transfers force through the development length $L_d = \phi\sigma_s/(4\tau_{bd})$ (Cl. 26.2.1). It depends on bar surface, concrete strength, cover and bar position.

As the compressive strength rises, the other strengths also rise, but at a lower rate, in proportion to $\sqrt{f_{ck}}$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which strength is measured as basis of other strengths?
   A. Compressive strength
   B. Shear
   C. Bond
   D. Bearing
   Answer: A. All others relate to compressive strength. (Key point: Basic strength)

2. IS 456 flexural strength is:
   A. 0.7 f_ck
   B. 0.7 sqrt(f_ck) N/mm^2
   C. 0.35 sqrt(f_ck)
   D. 0.45 f_ck
   Answer: B. Cl. 6.2.2. (Key point: Flexural)

3. Cylinder strength relates to cube strength as about:
   A. 1.25 x cube
   B. 0.5 x cube
   C. 0.8 x cube
   D. equal
   Answer: C. f_cyl is approx 0.8 f_cube. (Key point: Cylinder relation)

4. Development length formula is:
   A. L_d = phi sigma_s/(4 tau_bd)
   B. L_d = phi tau_bd/(4 sigma_s)
   C. L_d = 4 phi/ sigma_s
   D. L_d = sigma_s/ phi
   Answer: A. Bond transfers force over development length. (Key point: Bond)

5. As compressive strength rises, other strengths rise:
   A. Proportionally
   B. At a lower rate, in proportion to sqrt(f_ck)
   C. Faster
   D. Not at all
   Answer: B. Tensile, flexural strengths scale with sqrt(f_ck). (Key point: Scaling)

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