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Estimation of preliminary sizes of concrete elements is crucial for the design of structural concrete elements. Initially, the designer has to determine the loads to proceed with the design works that involve calculating the dimensions of concrete members and required reinforcement area.
Self-weight is one of the significant loads that a structure must support. The calculation of the self-weight needs dimensions of the concrete member. Moreover, the purpose of the design is to determine the geometrical dimension and reinforcement area. That is why rapid preliminary sizing of concrete members is required to be developed to enable the designer to start the design process.
The preliminary dimensions are not exact, but one can assume values that are quite accurate and prevent extensive iteration of the calculation procedure to achieve good design values.
How to Estimate Preliminary Sizes of Concrete Elements?
1. One-way Slab
Table-1, which is taken from ACI 318-19, provide a minimum thickness for solid one-way slabs not supporting or attached to partitions or other construction likely to be damaged by large deflections.
If these values are considered, the calculation of deflection is not required. However, when the assumed slab thickness is smaller than the values in Table-1, then the slab's deflection should be checked to ensure that it does not exceed the acceptable deflection limits.
Another method of assuming a preliminary size of a one-way solid slab is dividing the smaller span of the slab by 40, but the slab thickness should not be less than 7 cm for common floor slabs and 12 cm for slabs supporting vehicle' traffic.
Table 1 Minimum one-way Solid Slab Thickness, as per ACI 318-19
|Support condition||Minimum, h|
|One end continuous||ℓ/24|
|Both ends continuous||ℓ/28|
- Use value in Table-1 provided that steel yield stress is fy= 420 MPa.
- If steel yield stress is not equal to 420 MPa, multiply the values in Table-1 by (0.4+fy/700).
- For lightweight concrete slab having a unit weight ranging from 1440 kg/m3 to 1840 kg/m3, and composite slab made of a combination of lightweight and normal-weight concrete, multiply values in Table-1 by the greater of the two (1.09 or 1.65-0.0003*concrete unit weight).
2. Composite Slab
For composite slab constructed with lightweight and normal weight concrete, shored during construction, and where the lightweight concrete is in compression, multiply values in Table-1 by the greater of the two (1.09 or 1.65-0.0003*concrete unit weight) to achieve preliminary thickness.
3. Prefabricated and Ribbed Slab
The preliminary thickness of the prefabricated and ribbed slab can be assumed by dividing the slab's smaller span by 20. Unified Building Code (UBC) specified the minimum thickness of the ribbed slab to be 1/12 distance between the ribs or 51mm.
4. Two-way Solid Slab
As a rule of thumb, the thickness of a simply supported two-way concrete slab can be taken as 4 cm per meter of span, and 3.5 cm per meter of span for a continuous slab.
Alternatively, divide the perimeter of the slab panel by 180 to achieve a preliminary thickness of a two-way solid slab. For more detailed computation of the minimum thickness of the two-way slab, please click here.
5. Slab with embedded Objects
UBC recommends the minimum thickness of slabs with embedded conduits and pipes to be 25mm greater than the total overall depth of conduits or pipes.
ACI 318-14 specifies that conduits and pipes shall not be larger in exterior dimension than 1/3 the overall thickness of slab, wall, or beam in which they are embedded.
6. Slab on the Ground
UBC recommends a minimum thickness of concrete floor slabs supported directly on the ground to be 89mm.
7. Drop Panel
In flat slabs, sometimes drop panels are used at the top of columns to improve the shear strength. The drop panel shall project below the slab at least one-fourth of the slab thickness.
The length and width of a drop panel is one-sixth the span length measured from center-to-center of supports in the direction of the drop panel length and depth, respectively.
Like one-way solid slab, ACI 318-19 provides the minimum height for a non-prestressed concrete beam not supporting or attached to partitions or any other structure likely to be damaged by large deflections.
If the designer chooses the minimum height of the concrete beam suggested by ACI 318-19, checking beam deflection is unnecessary. However, a detailed calculation of beam deflection should be carried out if the beam's height is smaller than the values provided in Table-2.
As far as the beam's width is concerned, it can be assumed to be 0.3 to 0.6 times the beam height.
Table-2: Minimum height of non-prestressed beam, as per ACI 318-19
|Support condition||Minimum, h|
|One end continuous||ℓ/18.5|
|Both ends continuous||ℓ/21|
- Use the value in Table-2 provided that steel yield stress is fy= 420 MPa.
- If steel yield stress is not equal to 420 MPa, multiply the values in Table-2 by (0.4+fy/700).
- For lightweight concrete slab having a unit weight ranging from 1440 kg/m3 to 1840 kg/m3, and composite slab made of a combination of lightweight and normal weight concrete, multiply values in Table-2 by the greater of the two (1.09 or 1.65-0.0003*concrete unit weight).
The imposed loads govern the size of the column. Therefore, the first step is to transfer loads from the slab and beams to columns. After that, specify a reinforcement ratio equal to or greater than the minimum reinforcement ratio (0.01) and equal to or less than the maximum reinforcement ratio (0.08).
It is preferable to select a reinforcement ratio that is not greater than 0.04 to avoid possible steel congestions at joints and column splice positions. Now, when both the reinforcement and imposed loads are known, use the following equation to determine the area of columns and then decide the shape and dimensions.
phi*Pn(max): designed load on the column
phi: strength reduction factor which is 0.65 for tie columns and 0.75 for spiral column
Ag: gross area of column
Ast: area of steel in column
fy: yield stress in steel
Equation 1 used for the tied column, whereas Equation-2 used for the spiral column.
Alternatively, based on axial load, the dimension of the column can be taken from Table-3:
Table-3: Dimensions of a Column Based on Axial load
|Equivalent axial column load with moment factor (KN)||column size (mm)|
|Up to 500||230 x 230|
|Above 500 to 800||230 x 300|
|Above 800 to 1200||230 x 450|
|Above 1200 to 1500||230 x 600|
|Above 1500 to 1950||300 x 750|
10. Shear Wall
The thickness of shear wall varies from 150 mm to 500 mm, based on the number of stories, building age, and thermal insulation requirements. A minimum thickness of 150 mm should be used to build up to two storeys in height. The minimum thickness of 150 mm should be increased by 25 mm for each storey below the top two storeys.
The minimum depth of footings below the surface of undisturbed soil, compacted fill material, or controlled low strength material should be 305 mm. The minimum width of footings shall be 305 mm. The depth of the foundation can also be determined using Rankine theory.
12. Raft foundation
The minimum thickness of raft foundation is 300mm.
The preliminary sizing is the process by which rough dimensions of concrete elements are determined using design code guidelines and rules of thumbs. The estimated dimensions may be refined during the detailed design process.
The preliminary size of concrete elements are used to compute self-weight of the concrete member which is a major load that needs to be supported.
The size of the concrete column is controlled by the imposed loads. Initially, compute the imposed load, then assume a reinforcement ratio in a range of 0.01 to 0.08, preferably not greater than 0.04. After that, one can estimate the column dimensions.