βt - Concrete Property
For one of the concrete slab design methods (aka, the Direct Design Method) βt will be used as a ratio of relative torsional stiffness of the edge beam to the flexural stiffness of a width of slab equal to the span of beam (center to center of supports)
How to Calculate βt:
βt can be calculated the following way:
C = {\sum{\left(1-.063\left({x\over y}\right)\right)\left({x^3y\over 3}\right)}}
\beta_t = {E_{cb}C\over {2E_{cs}I_s}}
where:
x = The horizontal length of the shapes (both interior and exterior) shown in FIgure 1.
y = The vertical height of the shapes (both interior and exterior) shown in Figure 1.
Ecb = Modulus of Elasticity of the concrete beam.
Ecs = Modulus of Elasticity of the concrete slab.
ls = The Moment of Intertia? of the slab.
y = The vertical height of the shapes (both interior and exterior) shown in Figure 1.
Ecb = Modulus of Elasticity of the concrete beam.
Ecs = Modulus of Elasticity of the concrete slab.
ls = The Moment of Intertia? of the slab.
References:
- American Concrete Institute, "ACI 318", 2005
- This equation can be found in ACI 318 13.6.4.2