Structural Concrete - Hassoun

2.8 Poisson’s Ratio 23
For practical applications, the secant modulus can be used. The secant modulus is represented
by the slope of a line drawn from the origin to a specific point of stress (B) on the stress–strain curve
(Fig. 2.4). Point B is normally located at f ′ c∕2.
The ACI Code, Section 19.2.2.1, gives a simple formula for calculating the modulus of elasticity
of normal and lightweight concrete considering the secant modulus at a level of stress, f c ,
equal to half the specified concrete strength, f ′ c,
E c = 33w 1.5√ f ′ c psi(w in pcf) =0.043w 1.5√ f ′ c N∕mm 2 (2.5)
where w = unit weight of concrete [between 90 and 160 lb/ft 3 (pcf) or 1400 to 2600 kg/m 3 ]and
f ′ c = specified compressive strength of a standard concrete cylinder. For normal-weight concrete,
w is approximately 145 pcf (2320 kg/m 3 ); thus,
E c = 57,600 √ f ′ c psi = 4780 √ f ′ c MPa (2.6)
The ACI Code allows the use of E c = 57,000 √ f ′ c (psi) =4700 √ f ′ c MPa. The module of elasticity,
E c , for different values of f ′ c are shown in Table A.10.
2.8 POISSON’S RATIO
Poisson’s ratio μ is the ratio of the transverse to the longitudinal strains under axial stress within
the elastic range. This ratio varies between 0.15 and 0.20 for both normal and lightweight concrete.
Poisson’s ratio is used in structural analysis of flat slabs, tunnels, tanks, arch dams, and other
statically indeterminate structures. For isotropic elastic materials, Poisson’s ratio is equal to 0.25.
An average value of 0.18 can be used for concrete.
Test on a standard concrete cylinder to determine the modulus of elasticity of concrete.