The floor usually needs a beam as a bed to stiffen the floor (picture a)
For some reasons such as insufficient floor height, aesthetics, simple formwork (flat bottom), … the design engineer thinks of removing the beam, called a beamless floor or mushroom floor. At that time, to ensure stiffness, the floor must be thicker, leading to more concrete consumption, heavier than a beam floor.
If there is only a flat floor, the risk of being punctured by the column is very high.
🔍Punching Shear:
is a form of shear failure of concrete, occurring when there is a compressive force on a small area on the surface of the slab, such as a column reaction on a flat floor. The form of failure is a 45-degree inclined space pyramid from the column opening to the top of the floor, punching shear (see picture below)
To ensure puncture resistance, the floor thickness on the column must be large enough. If there is only a flat plate with a constant thickness, it will be very wasteful for other floor areas (mid-span), for reinforced concrete materials and heavy on the foundation.
Therefore, except for cases where the height is too limited, the structure is reasonable in terms of design advice, not a flat floor plate but should only locally increase the floor thickness around the column, called the column cap (figure b)
🔲Because a beam-free floor is always heavier than a beam floor when spanning the same span and bearing the same load, it is costly in materials and foundation. That is the price to pay to reduce the height. Therefore, people have come up with ways to reduce the floor weight:
– Reduce the thickness: use prestressing, or
– Reduce the concrete: create a hollow, reduce the weight of the floor itself.
🔲Principle of creating a hollow:
– The floor is a structure that can withstand bending under the effect of its own weight and the load used.
As illustrated above, when bent, the top grain (surface) of the floor is compressed, the bottom grain is subjected to tension. The central axis of the floor thickness is called the neutral axis. On the right is a diagram showing the change in stress on the cross-section (section) along the floor thickness direction. The stress always reaches the maximum value at the top and bottom grains, meaning the farthest from the neutral axis. The closer to the neutral axis, the more the stress gradually decreases to 0.
Therefore, it is more reasonable to concentrate most of the concrete mass at the two ends as far away from the neutral axis as possible, meaning that it is possible to make the middle hollow (low-stress area) to save materials while still ensuring equivalent bending efficiency.
– That is considering pure bending, when bearing the load, the floor is still subject to shear. The high shear area such as at the top of the column (subject to puncture) is returned to a solid floor to withstand shear stress across the entire thickness.
2. Design calculation method
Calculating a flat floor using computer software is a common and simple method in construction design. Therefore, it is necessary to think of hollow floors as equivalent solid flat floors for calculation. The conversion is carried out as follows:
Replace the hollow floor with an equivalent solid floor of the same thickness, but reduce the stiffness and weight to the value of the hollow floor.
– Stiffness:
Consider a typical floor strip limited between 2 adjacent hollow axes (created by boxes, balls, etc.). The cross-section is i-shaped as shown in the figure. Calculate its stiffness Ji.
Compare with the stiffness Jd of the equivalent solid floor (rectangular cross-section with the same width).
So the stiffness reduction factor for the equivalent solid floor is K=Ji/Jd
– Weight:
based on the actual void volume Vr per unit floor area. Compare with the solid floor volume Vd; the weight reduction factor of the equivalent solid floor is 1-Vr/V
– Note the areas that bear large local loads sitting on the hollow part with thin wings: Walls, machinery on the floor
– If using a polished floor, the conversion is difficult, leading to less accuracy because the equivalent cross-section does not have a simple I-shape (not square with sharp edges) as I illustrated in the picture below
3. Notes on construction
The construction of a solid hollow floor is a bit complicated, requiring careful technical supervision with the following notes:
– Should be made in one piece, because it is easy to create shapes, especially with complex floors
– For floor joists (toilets, loggias, etc.), use a different type of ball (box) to make the floor thinner and still have a flat bottom
– The most important thing is to ensure the size and position of the hollow holes in the floor according to the design when pouring concrete. It is necessary to position the ball/box…, push it up, and
– If creating a hollow with a box, it is recommended to use a closed-bottom box, only having to pour concrete once. Hollow boxes such as Ubot, bottomless VRO foam, be careful not to let the mortar rise into the box, reducing the size of the hollow hole and increasing the weight of the floor. Or have to pour twice, slowing down the construction progress: the first time pour concrete to the bottom of the box, have to wait for the concrete to harden and seal the bottom of the box before pouring the next round to the top of the floor.
– After construction, conduct load testing for some of the most dangerous floor cells according to the design load, check the load-bearing indexes, deflection, cracking, … to ensure that the floor works according to the forecast of the structural design.
– The reinforcement is placed relatively complicatedly in terms of diameter and distance, ensuring optimal economic requirements and according to the structure of the hollow material (box, ball …).
4. Actual project
The project we consulted on in 2019, the Smart Terminal Manufacturing Factory, is phase 2 of the VSmart complex manufacturing electronic equipment in Hoa Lac High-Tech Park, Hanoi.
Scale of over 200,000m2 total floor area, 3 floors high.
Due to the limitation of floor height according to the planning, the monolithic reinforced concrete flat floor plan was chosen, using VRO foam boxes to create hollow.
The load used is relatively large, due to the production line requirements, 1.5 tons/m2. The floor spans 9×12.5m (distance from column to column).
Hollow floor 530mm thick using 350mm thick VRO foam, solid floor column caps 750mm and 900mm thick. Floor size 160x260m, expansion joints divided in 2 directions with a maximum distance of 63m.
🔲Economic comparison with conventional beam floor plan:
– Floor height is reduced by 0.6m;
– In terms of progress: Flat floor construction is faster than beam floor, especially reducing formwork work for beams
– In terms of cost: The cost per 1m2 of VRO flat floor plan is equivalent to beam floor plan. In terms of total cost, calculated for the entire factory, it is cheaper (due to reduced column costs, covering the vertical surface).
🔲 Load testing work:
Conducted immediately after removing the floor formwork, on the area of 3×3 floor cells with a span of 9×12.5m. Load according to the total design load with brick pallets with a total weight of 20 kN/pallet.
The survey content is determined based on the objectives of the experiment, specifically:
– Measure the deflection of the floor when bearing the test load. Based on that, compare with the allowable displacement limit value according to the regulations of current construction standards and the deflection value according to the design calculation. The average deflection value measured at the characteristic cross-sections must not be greater than the calculated design consulting value.
– Cracks appearing before and during the loading process will be monitored during the test, the parameters of the cracks including the location of appearance, length and width will be monitored and recorded during the experiment.
– During the loading process at all levels, observe the floor parts and related structures for signs of other local deformation if any.
The load test results are consistent with the calculations and ensure the design requirements. The deflection at the center of the floor panel is 6.10 mm, smaller than the limit deflection of 6.89 mm; the crack width does not exceed 0.2 mm.
Experimental loading of floor structure on site
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🍺Conclusion:
– Hollow flat slab structure shows its cost advantage💸, promoting many of its advantages, especially when the floor height is limited.
– Structural engineering design and calculation of this slab are also simple and easy to explain.
– To confirm the competitiveness of Hollow flat slab when applied to each project, design consultants need to establish and compare with other floor structure options so that customers have a basis for deciding to choose.
