RESEARCH ARTICLE
Minimum Depth-Span Ratio of Beams in order to Control Maximum Permissible Deflection
Mereen H. Fahmi Rasheed1, Ayad Zeki Saber Agha1, *
Article Information
Identifiers and Pagination:
Year: 2020Volume: 14
First Page: 402
Last Page: 414
Publisher ID: TOCIEJ-14-402
DOI: 10.2174/1874149502014010402
Article History:
Received Date: 07/08/2020Revision Received Date: 02/11/2020
Acceptance Date: 21/11/2020
Electronic publication date: 31/12/2020
Collection year: 2020
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Abstract
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).
