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Various strengths of concrete

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).

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

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.

StrengthTypical valueRelation (IS 456)
Compressivefckf_{ck} (cube, 28 days)Basis of design; grade M20, M25 etc.
Flexural (modulus of rupture)10 to 15% of fcf_cfcr=0.7fckf_{cr} = 0.7\sqrt{f_{ck}} (Cl. 6.2.2)
Splitting tensile8 to 12% of fcf_c≈0.5fck\approx 0.5\sqrt{f_{ck}} to 0.6fck0.6\sqrt{f_{ck}}
Direct tensile7 to 10% of fcf_c≈0.35fck\approx 0.35\sqrt{f_{ck}} to 0.45fck0.45\sqrt{f_{ck}}
Shearabout 20% of fcf_c (pure shear), design τc\tau_cTable 19: τc=0.28\tau_c = 0.28 to 0.82 N/mm2^2 for M20 depending on steel percentage
Bondτbd\tau_{bd}Cl. 26.2.1.1: 1.2 N/mm2^2 (M20 plain bars); 1.6 times higher for deformed bars
BearingHigher than fcf_c when the loaded area is smaller than the supporting area (confinement)Cl. 34.4: 0.45fckA1/A20.45 f_{ck}\sqrt{A_1/A_2}, with A1/A2≤2\sqrt{A_1/A_2}\le 2

Compressive strength

Measured on 150 mm cube (IS 516) or 150 × 300 cylinder; fcyl≈0.8fcubef_{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 τv=V/bd\tau_v = V/bd compared to τc\tau_c (Table 19) and τc,max\tau_{c,max} (Table 20).

Bond strength

Adhesion and friction between steel and concrete that transfers force through the development length Ld=ϕσs/(4τbd)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 fck\sqrt{f_{ck}}.

✓ Answer checked by Claude Sonnet 5.5

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