Question

Problem 2 (PCC) For the corrosion protection of reinforcement in a reinforced concrete structure exposed to seawater, the minimum specified compressive strength (fe) is 30 MPa a) Determine the required average compressive strength (f) for the mix design if the mixing plant has a standard deviation (s) obtained from 20 test samples 3.9 MPa. b) Using the ACI code equation (Equation 7.3 pp 316), estimate the modulus of elasticity of the concrete given the required compressive strength. c) Based on the ACI code equation, how much larger (in percent) is the modulus of elasticity of 40 MPa concrete compared to 30 MPa concrete?

Answer 1

Given:

Compressive strength f'c = 30Mpa

Standard deviation s = 3.9 MPA

(a) Average compressive strength, f'cr:

Average compressive strength is the larger value obtained from the two equations according to ACI 318

f'cr = f'c + 1.34s

f'cr = f'c + 2.33s - 3.45

Equation 1, f'cr = 30 + 1.34 × (1.08 × 3.9) = 35.64 Mpa

Equation 2, f'cr = 30 + 2.33 × (1.08 × 3.9) - 3.45 = 36.36 Mpa

(Note. Modification factor 1.08 is to be multiplied with standard deviation because 20 test samples are used instead of 30.)

Hence, f'cr = 36.36 Mpa

(b) Modulus of elasticity of concrete Es:

Es = 4731 √f'cr = 4731 × √36.36

= 28527.57 Mpa

(c) Average compressive strength for 40 Mpa concrete

f'cr1 = 40 + 1.34 (1.08 × 3.9) = 45.64 Mpa

f'cr1 = 40 + 2.33 (1.08 × 3.9) - 3.45 = 46.36 Mpa

Hence, f'cr1 = 46.36

Es1 = 4731√46.36 = 32212.5 Mpa

Es1 Larger than Es in % = (32212.5 - 28527.57)/28527.57 × 100

= 12.92 %

Elasticity of 40 Mpa concrete is larger than elasticity of 30 Mpa concrete by 12.92%