varepsilon_{x}^{i} = psi^{i} d -varepsilon_{c}^{i} (2 Figure 2a shows a linear strain distribution in a typical reinforced concrete cross section of a simple beam under arbitrary static loading.
Open image in new window Fig. 2 a Details of reinforced concrete cross section used; b discretization of one-half reinforced concrete cross section used for computing theoretical strength; c schematic concrete stress strain curves used for computing theoretical strength; and d schematic reinforcing steel stress strain curves used for computing theoretical strength.
Note that, for reinforced concrete columns examined in this study, P o was computed from 0.8[ 0.85 f c ′ )(A g − A rs ) + f y A rs ], as permitted by ACI 318-11 (2011), where f c ′, f y = specified compressive and yield strengths of concrete and reinforcing steel, and A g, A rs = areas of the gross concrete cross section and of the longitudinal reinforcing steel.
The gathered results revealed that employing functionally graded reinforced concrete leads to more reduction in penetration depth, and destroyed front and back area, compared to entirely reinforced concrete cross section slabs with equal fiber volume fractions.
For strut and tie modeling for deep beams, the reduction in effective concrete compressive strength because of corrosion cracks was considered along with the reduction in geometry of concrete cross section.
For sectional design method of slender beams, the reduction in cross-sectional area of steel stirrups due to corrosion was considered along with the reduction in geometry of concrete cross section due to spalling.
Area of gross concrete cross section and of longitudinal reinforcing steel bars.
Moment of inertia of gross concrete cross section of member, beam and column.
Total area of longitudinal reinforcing bars divided by gross area of concrete cross section of member, beam, and column.
The effective moment of inertia was initially proposed by Branson (1977), with the intention of reflecting the loss of concrete cross section according to crack propagation.
