Question 4. In your own words, briefly discuss how the Young’s modulus (modulus of elasticity) of concrete is determined. Calculate the Young’s modulus of a concrete specimen weighing 135 lb/ft3 with a 28-days compressive strength of 4,000 psi.

E = 94,5048 lb/ft^2

Explanation:

Given:

- The density of the concrete specimen W = 135 lb/ft^3

- The 28-day compression strength of S = 4,000 psi

Find:

Calculate the Young’s modulus of a concrete specimen

Briefly discuss how the Young’s modulus (modulus of elasticity) of concrete is determined

Solution:

- ACI Committee 318 recommends the following empirical relationship between  Young’s modulus and compressive strength of normal strength concrete:

                                      E = 33*W^1.5*sqrt(S)

- Plug in the values:

                                      E = 33*(135)^1.5*sqrt(4,000/12)

                                      E = 94,5048 lb/ft^2

- Piezoelectric materials can be used as both sensors and actuators. One piezoelectric acts as an actuator and sends high frequency stress waves through a  concrete test cylinder. A second piezoelectric, acting as a sensor, then picks up a signal due to the propagated stress waves at the opposite end of the cylinder. Based on a relation with  the speed of sound in an elastic solid, an approximation of the Young’s modulus, E, can be

made from the equation shown below:

                                     E = V^2 ( ( 1 + v)(1-2v)*W) / ( 1 - v))

Where,

                   V: Speed of sound

                    v: poisson ratio

                    W: Density of concrete

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