10.2 : Dynamic Modulus of Elasticity of Concrete

The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.

The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x4 x20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by a variable-frequency oscillator. A pick-up device at the other end detects these vibrations, which are then amplified and measured using an indicator.

The vibrations at varying frequencies are transmitted through the specimen till it starts to resonate at its fundamental frequency. The dynamic modulus of elasticity (E_d) in pounds per inch is computed mathematically by substituting the beam's fundamental frequency (n) in Hertz, length (L) in inches and density (⍴) in pounds per cubic feet.

Another method to estimate the dynamic modulus involves the stress-strain curve of concrete. By drawing a tangent at the curve's origin and calculating its slope, the initial tangent modulus is determined. This value is approximately equal to the dynamic modulus of elasticity.