As if you are familiar with the structural design software such as SAP2000, ETABS, STAAD PRO, SAFE, and other design software, then you already know that these all designs on the basis of hit and trial. If you go through the preliminary design, then you will reach the target in a first or second trial in most cases.
Before detailed design of slab, it will be the better practice to know about the preliminary design. It is just an initial procedure to find out the depth of slab.
Note: All my design procedure are based on Indian Standard codes but if you use other codes that your country accepts, then also it would not be wrong for the preliminary case.
Table of Contents
Preliminary design of Slab:
For deflection control, as per IS456:2000, Clause 23.2.1,
L/d ≤ αβγδλ
Where,
L = length of the beam
d = Effective depth of the beam
α = basic value
= 20, for simply supported
= 26, for continuous
β = modification factor for length more than 10m
= 10/span
γ = modification factor for tensile reinforcement
δ = modification factor for compression reinforcement
λ = modification faction for web-flanged ratio
Assumptions:
i. Percentage of steel = 0.3% so modification factor β = 1.4 (for fe415 steel)
ii.Modification factor δ and λ = 1
For span less than 10 m;
i. For simply supported case
αβγδλ = 20*1.4 =28
ii. For continuous case
αβγδλ = 26*1.4=36.2
or, simply from IS 456:2000, clause 24.1 ; Notes
For a two-way slab of shorter span (up to 3m) with the mild steel reinforcement, the span to overall depth ratio given below may be generally be assumed to satisfied vertical deflection limits for loading cases up to 3KN/m2.
Simply supported slabs = 35
Continuous slabs = 40
For the high strength deformed bar of grade fe415, the values given above should be multiplied by 0.8.
ie.
Simply supported slabs = 35*0.8=28
Continuous slabs = 40*0.8=32
For numerical of slab,
For all sides discontinuous, l/d = 28
For all sides continuous, l/d = 32
For two sides discontinuous and two continuous, l/d =30
But for the economic design, Designers mostly prefer the ratio of span to depth in the range from 32 to 40.
Note: No matter one-way or two-way slab, The preliminary design is the same.
Example1. Let’s take a simple plan for each room of inner dimension 3m * 4m with beam support of width 230mm
Solution,
from deflection criteria, as per IS456:2000, Clause 23.2.1,
L/d ≤ αβγδλ
From clause 24.1, IS 456:2000
Since two sides continuous and two sides discontinuous
l/d =30
d= shorter span/30
d= 3000/30
d=100mm
For mild exposure and diameter of steel bar = 10mm
clear cover = 15mm
so, overall depth = effective depth + clear cover + half the diameter of the bar
= 100 + 15 + 10/2
= 120mm
Example 2: Preliminary depth design of internal panel slab of interior dimension 6m * 8m supported on the beam of 300mm.
Solution,
From deflection criteria, as per IS456:2000, Clause 23.2.1,
L/d ≤ αβγδλ
Since the shorter span is greater than 3m so we can’t use the clause 24.1, so
For the internal panel, ie. Continuous slab
Basic value α = 26
Assumptions:
i. Percentage of steel = 0.3% so modification factor β = 1.4 (for fe415 steel)
ii.Modification factor δ and λ = 1
Depth = shorter span /36.2
= 6000/36.2
= 165.75mm
Assuming the diameter of the steel rod = 10mm and clear cover = 15mm
Overall depth = 165 + 15+10/2 = 185mm
Since it is not advisable to use the slab depth greater than 150 mm so the secondary beam is necessary.
The secondary beam should be placed such that longer span divides into two. So the dimension of the slab to be designed become 6m * 4m.
Depth = shorter span /36.2
= 4000/36.2
= 110.5mm
Assuming diameter of steel rod = 10mm and clear cover = 15mm
Overall depth = 110 + 15+10/2 = 130mm, ok
Point should be known before the design of the slab:
a. Thickness of slab
i. For all types of building, the overall depth of the slab should not be less than 100 mm or 4’’.
ii. It is advisable that the practice of using a slab of overall depth greater than 150 mm or 6’’ should be avoided, if possible by the use of secondary beam.
b. Minimum reinforcement
The percentage of reinforcement in either direction should be
i. 0.15 percent where plain bars are used, and
ii. 0.12 percent where high yield strength (hot rolled and cold twisted) deformed bars
c. Spacing cover and diameter
i. Spacing
- The pitch of main tensile reinforcement bars shall be not more than thrice the effective depth or 300 mm, whichever is smaller.
- The pitch of the distribution bars shall not be more than 5 times the effective or 450 mm, whichever is smaller.
ii. Cover
- No matter the member is in tension, compression or shear, the minimum cover to reinforcement shall be neither less than 15 mm, nor less than the diameter of bar.
- The clear cover can be derived for durability criteria, as specified in IS456:2000 Table 16.
iii. Bar Diameters
- The diameter of main bars in the slab shall not be less than 8 mm if high yield strength bar or 10 mm if plain bars and distribution steel shall not be less than 6 mm diameter bars.
- The diameter of the bar shall not also be more than one-eighth of the slab thickness.
d. Reinforcement
- For main reinforcement, at least 50 percent of the tension reinforcement provided at mid-span should extend to the supports. The remaining 50 percent should extend to within 0.1lx, or 0.1ly, of the support.
- For distribution bar, it is not necessary to calculate reinforcement, it is advisable to use 50% of the main bar despite it contributes to load transfer.
- The reinforcement for the torsion shall be provided at any corner of the slab, that is, if the slab is simply supported on both edges meeting at that corner and is prevented from lifting. There is no need to provide where the consequences of cracking are negligible. It shall consist of top and bottom reinforcement, each with a layer of bars placed parallel to the sides of the slab and extending from the edges a minimum distance of one-fifth of the shorter span.
- The area of torsional reinforcement per unit width in each of top and bottom layers shall be three-quarters of the area required for the maximum mid-span moment per unit width in the slab
Note: The distribution or transverse steel assist in the distribution of the stresses caused by the superimposed loading, temperature changes and shrinkage during the hardening process. These bars are placed in the upper layer and tied with the main steel bars to keep them in the correct position during concreting.
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