Minimum Depth-Span Ratio of Beams in order to Control Maximum Permissible Deflection
Authors: Rasheed Mereen H. Fahmi , Agha Ayad Zeki Saber 
Published: January 2021

Background:
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/ρb), concrete strength (fc' ) and beam width on the depth-span ratio of the beam with different types (simply supported, fixed ended, propped and cantilever) were investigated.

Objective:

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

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

Results:
The results show that the effect of the ratio (ρ/ρb) 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.

Discussion:
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/ρb) 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.

Conclusion:
- 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/ρb), applied distributed load (w), concrete compressive strength (fc' ) 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 (fc' = 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/ρb = 0, 0.5 & 1) in addition to (ρt /ρb & ρmax /ρb).
- The effect of the reinforced indicia ratio (ρ/ρb) 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 (fc' ), 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).