Minimum Depth-Span Ratio of Beams in order to Control Maximum Permissible Deflection

ACI code and other building codes and standards include the provisions for deflection control and depth-span limitations, also including the maximum permissible deflection for specified concrete and steel reinforcement strength. In this study, the effects of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρ_b), concrete strength (f_c' ) and beam width on the depth-span ratio of the beam with different types (simply supported, fixed ended, propped and cantilever) were investigated.

This study aimed to study the effect of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρ_b), concrete strength (f_c' ) and beam width on the depth-span ratio of the beam of different types (simply supported, fixed ended, propped and cantilever).

This study theoretically investigates the effect of applied load intensity, steel reinforcement index amount as a ratio to the balancing reinforcement index (ρ/ρ_b), concrete strength (f_c' ) and beam width on the depth-span ratio of the beam of different types (simply supported, fixed ended, propped and cantilever).

The results show that the effect of the ratio (ρ/ρ_b) is small on the depth-span ratio, and the required depth of the beam increased with increasing the applied distributed load value and decreased with increasing the concrete strength for all beam types.

Deflection of slabs and beams can be controlled by the addition of steel reinforcement bars or using pre-stressing concrete, loading type and value, material properties (E), section properties (I), and the type of the member. The results showed that the effect of the ratio (ρ/ρ_b) was small on the depth-span ratio, and the required depth of the beam increased with increasing the applied distributed load value and decreased with increasing the concrete strength for all beam types.

- A modification of ACI Code span-depth ratio is suggested to include the effect of tension reinforcement area which is represented by the reinforcement indices ratio (ρ/ρ_b), applied distributed load (w), concrete compressive strength (f_c' ) and cross section width (b) in order to control the maximum deflection of the beam within the ACI limit of the maximum permitted deflection.

- The value of span-depth ratio (N = L / h) is determined for four types of beam (simply supported, fixed ended, propped and cantilever) for concrete strengths (f_c' = 21, 28, 35, 42, 63 & 84 MPa), applied distributed load (w = 14.6, 29.2, 43.8 & 58.4 kN/m), cross width (b = 150, 200, 250 & 300 mm) and (ρ/ρ_b = 0, 0.5 & 1) in addition to (ρ_t /ρ_b & ρ_max /ρ_b).

- The effect of the reinforced indicia ratio (ρ/ρ_b) is small on the span-depth ratio (N = L / h) for all values of applied load and concrete compressive strength.

- The span-depth ratio (N = L / h) decreased with increasing the applied load, or in other words, the required depth increased with increasing the applied load for all values of concrete strength and beam width.

- The span-depth ratio (N = L / h) increased with increasing the concrete strength (f_c' ), i.e. the required depth decreased with increasing concrete strength for all values of applied loads and beam width.

- The same behavior and conclusions are obtained for all beam types (simply supported, fixed ended, propped and cantilever).