Effective Section Stiffness per ASCE 7-16 §12.7.3
Notation
A_{g }= gross area of concrete section
b_{w} = web width of section
h = overall thickness, height, or depth of member, in.
I_{g }= moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement
The mathematical model is created with cracked sections to determine seismic design forces and displacements according to 12.7.3.
The effective section stiffness of the reinforced concrete structural elements is accounted by using the effective section stiffness factors given in Table 6.6.3.1.1(a) in ACI 318-19. Effective cross-section stiffness factors are applied only in the calculations under the loads included in earthquake effects. Effective cross-section stiffness multipliers are not used in the calculation under loads included in load combinations that do not have earthquake effects.
Member and Condition | Moment of inertia | Cross-sectional area for axial deformations | Cross-sectional area for shear deformations | |
---|---|---|---|---|
Columns | 0.70I_{g} | 1.0A_{g} | b_{w}h | |
Walls | Uncracked | 0.70I_{g} | ||
Cracked | 0.35I_{g} | |||
Beams | 0.35I_{g} | |||
Flat plates and flat slabs | 0.25I_{g} |
Dead load and live load effects, from which internal forces and displacements are obtained, calculated using the effective cross-section stiffness factors, are represented by symbols G ' and Q' in combinations. Effective cross-section stiffness multipliers are not used in load combinations without seismic effects. In this case, dead load and live load effects, from which internal forces and displacements are obtained, calculated without using the effective cross-section stiffness multipliers, are shown with symbols G and Q in combinations. Earthquake effects are taken into account using effective cross-section stiffness factors and the results of the analysis made using these factors in load combinations are taken into account.