Integrated Strength and Serviceability Assessment of Doubly Reinforced Concrete Beams: An ACI 318-19 Case Study

Abstract

Doubly reinforced concrete beams are commonly adopted when architectural constraints limit beam depth and the required flexural resistance exceeds the practical capacity of a tension-controlled singly reinforced section. This study presents an integrated strength and serviceability procedure for doubly reinforced beams using force equilibrium, strain compatibility, the Whitney rectangular stress block, and ACI 318 provisions. A beam from a 12-storey multifunctional building in Sihanoukville, Cambodia, is used as the numerical case. For the 300 × 400 mm section, the selected reinforcement of six 22 mm tension bars and two 22 mm compression bars provides adequate design flexural strength and a tension-controlled response. The manuscript extends the original ultimate-strength analysis by introducing a reproducible deflection procedure based on the gross and cracked moments of inertia, cracking moment, effective moment of inertia, service-load moment, and the time-dependent deflection multiplier. For the selected beam, the compression reinforcement ratio is 0.00722 and the ACI long-term multiplier for a sustained-load duration of five years or more decreases from 2.00 for an equivalent section without compression reinforcement to approximately 1.47, a 26.5% reduction in the multiplier. This reduction does not automatically mean that total deflection is 26.5% lower because immediate deflection also depends on span, support condition, service loading, cracking and section depth. Final deflection in millimetres therefore requires the project clear span and service-load data, which should be reported before code compliance is claimed.