What Is Slab?
A slab is vital structural element to create flat surfaces, typically horizontal, in building roofs, floors, bridges, and other types of structures. A slab has generally some 150mm thickness in commercial buildings however thickness may change depending upon the structure we are constructing and it is supported by other structural elements like RCC columns, RCC beams, walls, or the ground surface. Thickness of slab is always less than its width and span.
Depending upon the support slab can be of following types
- Simply Supported
- Continuous slab
- Cantilever slab
- One Way Slab
- Two Way Slab
According to IS 456:2000,when the ratio of longer span(L) to shorter span(B) which is (L/B) greater than 2 the slab is called one way slab. In common practices, a one way slab is supported by two parallel walls or beam and this type of slab is not used often.
In structural engineering, a one way slab is any flat plate which is supported underneath by beams. In this case, the load from the slab transfers directly from the top to the bottom of each beam instead of being distributed across a network of members. A common application is in a floor for a single story building where there are no beams running parallel to the length of the building; in this case, the beams are supported by columns.
The span is defined as twice the clear distance between supports. For a uniform beam, this relationship can be expressed as: $$ L = 2D \qquad D = {\text{span}}/{2}L $$
In the case of a one way slab, the beam is resting on two points, so there are three forces acting at each support: $$ W = L \cdot D + {z_1}D + {z_2}D $$ The shear stress at any point in a beam depends on the position within the span and the loading. The shear stress varies linearly with the distance from one end of the span, and it can be expressed as: $$ V \cong \frac{W}{A} = L \cdot D + {z_1}D + {z_2}D $$ The position in the span is found by integrating the curve of the shear stress with respect to distance: $$ z \cong \int_{{\text{near end}}}^{{\text{far end}}} {V} = L + 2D – {\text{span}} $$
The area moment of inertia can be related to the bending stress as well. This relationship is given by: $$ I \cong 2\cdot A \cdot D^2 = 2L \cdot D \qquad D = {\text{span}}/{\sqrt{2}} $$
The bending stress can be expressed as: $$ {s_B} \cong F_{\text{total}}/A = {\text{span}}/{\sqrt{2}} \cdot L + L \cdot {z_1} $$
The critical buckling shear stress, which is the maximum allowable shear stress in the beam when it is in a state of bending and compression can be expressed as: $$ V_{\text{c}} \cong {s_c} = 0.5 \cdot E \cdot {\text{I}}_{\text{c}} $$ The critical shear stress is found by solving for the maximum value of the shear stress: $$ V_{\text{c}} = {s_c} = {2E}/{A_{\text{I}}^2} $$
Two Way Slab
Two way slab is a type of slab and it is supported by beams on all the four sides, which helps in carrying loads along both directions. In two way slab, the ratio of longer span (l) to shorter span (b) is less than 2.
As we know that
For long-span design:
Σ M = M½
For short-span design:
Σ M = M+M
where,
M = Maximum positive Moment
ΣM/ΣL = 1.5 < 2 (condition satisfied) Therefore, it is OK to design two-way slab as a one-way slab.
And at last the conclusion is that,
Two way slab system can be designed as a simple span system.
The main purpose of two way slab design is to complete the analysis and design under only one mode of vibration. During earthquakes, vibrations in structures are generally very complex and cannot be assumed to have only one mode. The selection of two-way slab is made by checking if the condition of ΣM/ΣL>1.5 (condition not satisfied) is satisfied or not.
According to Eurocode 8, Two way slabs are for spans which are less than 2 times the support widths, i.e. L/B≤2. The slab is assumed to be pinned at the supports and therefore only one half of the total load can be carried through these.
According to ACI 318-05, two-way slabs are designed for spans less than twice the clear span between beams or column lines. These require a higher moment capacity due to a more complicated bending pattern in the slab.
According to Indian code IS 1893 (part-1), it is assumed that, in case of two way slabs, the length L should be 2 b or more. For short span design, if the length L is less than 2 b, then M l /M u = 0.5 should be considered in place of cross sectional moment of resistance. If the length L is more than 2 b, then M u = f cu m u (0.4L/b) should be considered in place of cross sectional moment of resistance.
Difference between one way slab vs two way slab
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