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The minimum reinforcement ratio is the lowest possible quantity of steel that should be embedded in structural concrete elements to prevent premature failure after losing the tensile strength. The minimum reinforcement ratio controls the cracking of concrete members.
The maximum reinforcement ratio is the largest steel area that can be put into concrete members like columns and beam. In a reinforced concrete beam, the provision of extra reinforcement above the maximum reinforcement ratio would not be beneficial since the concrete would get crushed before the full strength of steel is used.
The collapse of a concrete structure is sudden and does not show any signs before failure. The maximum reinforcement ratio ensures concrete members' economy and provides safety against brittle failure of concrete.
Finally, the required reinforcement area of the designed concrete member should not exceed the maximum reinforcement ratio and should be less than the minimum reinforcement ratio. Therefore, the designed member should be checked for this requirement.
- Minimum Reinforcement Ratio
- Maximum Reinforcement Ratio
- Minimum Reinforcement Ratio for Shear
Minimum Reinforcement Ratio
The purpose of the minimum reinforcement ratio is to control cracking and prevent sudden failure by equipping the member with adequate ductility after the loss of concrete's tensile strength due to cracking.
Building construction codes such as ACI 318-19, provides minimum reinforcement ratio for different reinforcement concrete members such as beams and columns.
1. Minimum Reinforcement Ratio in Beams
In reinforced concrete beams, if the cracked section's flexural strength is lower than the moment that produced cracking of the previously uncracked section, then the beam would fail upon the formation of the first flexural crack, without showing any distress.
The minimum reinforcement ratio, which can be computed using the equation provided by ACI 318-19, can prevent a concrete beam's premature failure. The minimum reinforcement for beams can be computed using the following expression:
As,min: minimum area of steel, mm2
fc': compressive strength of concrete, MPa
fy: steel yield stress, MPa
bw: width of web in T-beam, and width of beam in rectangular beam, mm
d: effective depth measured from extreme concrete compression fiber to the center of steel bars, mm
2. Minimum Reinforcement Ratio in Slabs
The minimum reinforcement area for slab is the temperature and shrinkage reinforcement installed to control cracks due to shrinkage in concrete and temperature variations. It is not required to provide a reinforcement area more than the temperature and shrinkage reinforcement.
As= ρbd Equation 2
As: shrinkage and temperature reinforcement, mm2
b: width of slab strip considered for design purpose which is 1 m
d: effective depth, mm
3. Minimum Reinforcement Ratio in Uniform Footing
The minimum reinforcement ratio for uniform footing is similar to that of a slab i.e temperature and shrinkage reinforcement ratio.
4. Minimum Reinforcement Ratio in Columns
The minimum reinforcement ratio for columns is required to provide resistance against bending, which may occur irresective of analytical results. It is also needed to decrease the effect of shrinkage and creep of the concrete under sustained compressive stresses.
The minimum reinforcement ratio in the column prevents steel bars from yielding under sustained service load. ACI 318-19 specifies the minimum longitudinal reinforcement ratio for a column as 0.01 times the column's gross area.
5. Minimum Reinforcement for Connections between Cast-in-place Members and Foundation
The minimum reinforcement area that crosses the cast-in-place column or pedestal and foundation interface should be 0.005 times the gross area of the supported member.
Maximum Reinforcement Ratio
The maximum reinforcement ratio is an upper limit of steel quantity that can be put into concrete members. It is commonly provided for various reasons, which are discussed below:
1. Maximum Reinforcement Ratio in Beams
The maximum reinforcement ratio for beams is provided to prevent concrete crushing, which is an undesired mode of failure and prevented by the ACI code. It also avoids the use of excessive steel area that does not offer real benefits. Therefore, it helps to bring economy in the design of concrete beams.
If a beam possesses a higher reinforcement ratio than the maximum reinforcement ratio, it is called an over-reinforced concrete beam and usually fails in compression.
Over-reinforced concrete beam fails in compression before utilizing the full-strength potential of steel bars. The maximum reinforcement ratio for beams can be calculated using Equation 3.
2.Maximum Reinforcement Ratio in Columns
The maximum reinforcement has been established to make sure that the concrete can be compacted adequately around steel bars and to ensure that the designed columns are similar to the test specimens, as per ACI 318.19.
The maximum reinforcement ratio for columns is 0.08 times the gross area of the column. It brings economy to the design of columns and prevent steel congestion, which otherwise hinders proper concrete placement.
Practically, it is recommended to consider a maximum reinforcement ratio of 0.04 times the column's gross area to avoid over-reinforcement at steel bars' splicing locations.
Minimum Reinforcement Ratio for Shear
Similar to minimum flexural reinforcement discussed above, ACI 318-19 sets minimum reinforcement ratio for shear in beams, etc.
1. Minimum Shear Reinforcement Ratio in Beams
A minimum area of shear reinforcement should be provided in all regions of a beam where applied shear is greater than half the designed shear strength of concrete.
The minimum shear reinforcement (Av,min) in beams should be the greater of the following:
Av,min=0.062*fc'(0.5)*(bw*s/fyt) Equation 4
Av,min=0.35*(bw*s/fyt) Equation 5
s: center-to-center spacing of stirrups, mm
fyt: yield stress of stirrup steel bar, MPa
2. Minimum Longitudinal and Transverse Reinforcement in Cast-in-place Walls
If the in-plane applied shear (Vu) of the cast-in-place wall is equal to or less than the value derived from Equation 6, use values provided in Table-1 as a minimum reinforcement for both longitudinal and transverse direction.
However, if the in-plane applied shear (Vu) is greater than the value derived from Equation 6, then (ρt= 0.0025) and the value of (ρℓ) is the greatest of 0.0025 and the result from Equation 7.
hw: height of entire wall from base to top, mm
lw: length of entire wall, mm
Table-1: Minimum Longitudinal and Transverse Reinforcement for Walls
|Type of non-prestressed reinforcement||Bar/wire size||fy, MPa||Minimum longitudinal reinforcement ratio, ρℓ||Minimum transverse reinforcement ratio, ρt|
|Deformed bars||≤ No. 16||≥420||0.0012||0.0020|
|Deformed bars||> No. 16||<420||0.0015||0.0025|
|Welded-wire reinforcement||≤ MW200 or MD200||Any||0.0015||0.0025|
|Deformed bars or welded-wire reinforcement||Any||Any||0.0012||0.0020|
Minimum reinforcement is the lowest steel area that prevents early ductile failure of a beam when concrete loses its tensile strength due to imposed loads.
1. To prevent any sudden failure of a beam when concrete cover bursts and the bond to the tension steel is lost.
2. To avoid brittle shear failure that may occur without shear reinforcement
3. Prevent tension failure due to shrinkage and thermal stresses and internal cracking in a beam
4. To hold longitudinal steel bars at their position during concreting.
The minimum reinforcement ratio for column is 0.01.
The minimum reinforcement area in a column is equal to gross column area times 0.01.
Concrete slab expands and contracts with temperature fluctuations. When fresh concrete sets and loses moisture rapidly, the concrete would shrink and create stress in concrete. Contraction and expansion of concrete leads to crack development if it is not accounted for during design.
So, temperature and shrinkage reinforcement are provided to control cracks due to temperature variations and shrinkage of concrete