Continuous beams and one-way slabs pose a unique challenge in structural analysis due to their inherent complexity. Traditional methods fall short, and that’s where the ACI Approximate Analysis Method comes into play. This method, outlined in ACI 318-19, section 6.5, provides a simplified yet effective way to analyze and design these structures.
Continuous beams and one-way slabs are statically indeterminate structures, meaning they defy analysis using the standard three equations of equilibrium. To tackle this, various methods have emerged, including slope deflection, moment distribution, displacement, stiffness matrix, and the ACI Approximate Method.
The ACI Approximate Method, also known as the simplified analysis method, is detailed in ACI 318-19, section 6.5. It employs elastic analysis, considering different live load placements to identify critical sections with maximum positive or negative moments.
Before diving into the method, certain conditions must be met:
The method provides coefficients for calculating shears and moments, as presented in Table-1. The same coefficients are visually represented in Figures 3 to 6. These coefficients are crucial for determining approximate moments and shears in non-prestressed continuous beams and one-way slabs.
| Positive Moment Locations | Conditions | Mu |
|---|---|---|
| End span | Discontinuous end integral with support | wu ℓn2/14 |
| End span | Discontinuous end unrestrained | wu ℓn2/11 |
| Interior spans | All | wu ℓn2/16 |
| Negative Moment Locations | Conditions | Mu |
|---|---|---|
| Interior face of exterior support | Member built integrally with supporting spandrel beam | wu ℓn2/24 |
| Interior face of exterior support | Member built integrally with supporting column | wu ℓn2/16 |
| Exterior face of first interior support | Two spans | wu ℓn2/9 |
| Exterior face of first interior support | More than two spans | wu ℓn2/10 |
| Face of other supports | All | wu ℓn2/11 |
| Face of all supports satisfying (a) or (b) | (a) slabs with spans not exceeding 3m (b) beams where the ratio of the sum of column stiffnesses to beam stiffness exceeds 8 at each end of a span | wu ℓn2/12 |
Shear values are determined based on specific conditions at different locations. For instance, the exterior face of the first interior support has a shear value of 1.15wuℓn/2, while the face of all other supports has a shear value of wuℓn/2.
Once moments and shears are established using the ACI Approximate Method, the subsequent steps involve calculating cross-sections and necessary reinforcements. Practical design considerations include casting beams monolithically with slabs, allowing them to be designed as T-sections at midspans for positive moments and as rectangular beams for negative moments. This approach ensures structural integrity and meets the necessary design specifications outlined in ACI 318-19.
