JP7475777B2 - How to design a composite slab - Google Patents

Description

This invention relates to a composite slab in which a deck plate and concrete are integrated, and in particular to a composite slab constructed using an end-closed deck plate (hereinafter, "end-closed deck plate" will be abbreviated to "encro deck plate"), in which the longitudinal ends of the deck plate are crushed to form end-closed beam placement sections at the height of the mountain surface, i.e., an inverted encro deck plate.

Deck plates, in which the peaks and valleys are continuous at the slope to form a trapezoidal wave-shaped cross section and which have flat sections at the height of the valleys on both sides in the width direction, are widely used when using them as formwork to pour concrete and construct floor slabs.

When a load is applied to a floor slab (concrete floor slab) made of a deck plate that is not embossed or specially bent, bending occurs in the deck plate and concrete. Cracks occur in the concrete in the area where tension is applied due to the bending (area below the neutral line), and a force is generated that causes the deck plate and concrete to shift relative to each other in the longitudinal direction. This shift also causes peeling.

In contrast, in a composite slab made of a deck plate for composite slabs that has been embossed or specially folded (for example, deck plate 1 in Figure 1 (however, the deck plate is not embossed in the illustration)), the misalignment is reduced, allowing the combined effect of both to be exerted, and a high-performance floor can be constructed.
In FIG. 1, reference numeral 2 denotes a peak (or peak surface), 3 denotes a valley (or valley surface), 4 denotes a slope, and 7 and 8 denote flat portions at the valley surface height on both sides in the width direction.

When a load is applied to a composite slab, cracks begin to appear in the concrete on the tension side, but as long as the cracks are small, the load is supported by an effective equivalent cross section consisting of the concrete on the compression side of the neutral axis and the deck plate on the tension side. As long as this state is maintained, there is no reduction in strength, and the floor load can be supported in a stable manner.

However, as the concrete becomes thicker, the distance from the neutral axis to the tension edge (the bottom edge of the floor slab) increases, which causes a large tension force to be generated in the tension side concrete, making it easier for cracks to grow. In other words, slippage occurs more easily between the deck plate and the concrete, and the theoretical cross-sectional performance cannot be maintained.
Therefore, the "Deck Plate Floor Structure Design and Construction Standards 2018" (Japan Steel Construction Association) states that the effective thickness of the concrete on the top of the deck plate as a composite slab should be between 50mm and 100mm. As stated in the standard, this is a value that was directly confirmed from the performance of past experiments.

Patent Publication 2007-118020

When using a composite slab, making the thickness of the concrete on the top of the deck plate 100 mm or more will improve the cross-sectional performance of the composite slab, and will be able to support a greater load and reduce cracks.
However, under the current design system for composite slabs, the concrete thickness on the top of the deck plate is set at 100 mm or more, and as mentioned above, the concrete thickness on the top of the deck plate is designed to have performance up to 100 mm. Even if a cross section with a concrete thickness of more than 100 mm is used, it is not possible to add additional performance; instead, the allowable load is reduced by the increase in the floor slab's own weight.
As shown in Figures 2(a) and (b) for a 75mm high deck plate, for example, if the thickness of the concrete on the top of the hill is increased by 20mm, for example from 100mm to 120mm, the second moment of area and section modulus are treated as the same without any additional performance, so the allowable load is reduced by the increase in self-weight (weight of the concrete for a thickness of 20mm). In other words, even if the concrete on the top of the hill is 120mm thick, it will be considered as having the cross-sectional performance of a composite slab with a concrete thickness of 100mm.

The reason why the thickness of the concrete on the top of the deck plate in the "Deck Plate Floor Structure Design and Construction Standards 2018" is set at 100 mm or less is because it is assumed that the beam placement part on the beam 10 is at the valley surface height, as shown in Figure 3 (A) and (B).
That is, this assumes the case of a typical deck plate 1A without end blocking as shown in Figure 3 (a), and the case of a typical end-blocked deck plate 1B in which an end-blocked beam support portion 5B is formed at the valley face height position as shown in Figure 3 (b).

The deck plate in Figure 3 (c) was not taken into account in the standards.

The present invention was made against the background described above, and aims to obtain a composite slab that can increase performance by the amount of the increase in thickness of the concrete on the top of the hill, if the thickness is increased beyond the current 100 mm.

The design method for a composite slab of the invention of claim 1 that solves the above problems is a design method for a composite slab in which a deck plate and concrete are integrated, the deck plate being constructed using an inverted end-closed deck plate in which the crests and valleys are continuous at the slope to form a trapezoidal wave-shaped cross section and flat parts at the valley height on both sides in the width direction are crushed at the longitudinal ends of the deck plate to form beam placement parts with closed ends at the crest height,
In designing composite slabs, they are considered to be unidirectional reinforced concrete beams.
A step of setting a tensile reinforcement ratio (r) when the beam is made into a reinforced concrete beam;
A step of setting a coefficient (α) to be multiplied by the tensile reinforcement ratio (r);
The method includes a step of setting the cross-sectional dimensions of each member of the composite slab using the following formulas (1 ) and (2).
H = S / (α · r) - d ... (1)
2≦α≦2×1.1 (2)
however,
H = concrete thickness on top of hill (mm)
S = Cross-sectional area of deck plate per 1000 mm width (mm ² )
α = Coefficient for tensile reinforcement ratio (r)
r = tensile reinforcement ratio of the part of the reinforced concrete beam that receives the maximum bending moment during long-term loading d = average concrete thickness in the deck plate height area (mm)

Claim 2 is characterized in that the tensile reinforcement ratio ( r ) in the design method of the composite slab of claim 1 is 0.004.
[Effect of the invention]

The deck plate in the composite slab of the present invention is an enclosing deck plate with the longitudinal ends crushed to form a beam support part with closed ends at the height of the mountain surface, i.e., the inverted enclosing deck plate 1C shown in Figure 3 (C). The beam support part is indicated by the symbol 5C.
When a load is applied to the floor slab formed by the deck plate, bending occurs in the deck plate and concrete, and cracks occur in the concrete in the area where tension acts due to the bending (the area below the neutral line).
If cracks occur in the concrete below, the bending force will cause the concrete to slip relative to the deck plate,
In the case of a normal end-closed deck plate 1B in which the end-closed beam placement portion is formed at the valley height position as shown in Fig. 3(b), the concrete 6 shifts as shown in Fig. 4(b). In addition, peeling also occurs due to this shift.
However, in the case of the inverted enclosing deck plate 1C with the end-blocked beam placement portion 5C formed at the mountain surface height as shown in Fig. 3(C), by being an inverted enclosing deck plate as shown in Fig. 4(A), i.e. by having the beam placement portion 5C at the mountain surface height, the end-blocking portion of the deck plate effectively acts as a slip-stop for the concrete 6 in the valley of the composite slab. Therefore, the mutual slippage and the accompanying peeling between the deck plate 5C and the concrete 6 are prevented, resulting in an effectively integrated composite slab.

The present invention has discovered that by using an inverted enclosing deck plate, the deck plate and concrete are prevented from slipping from each other as described above, and an effectively integrated composite slab is obtained. In addition, under conditions that satisfy formulas (1) and (2), if the thickness of the concrete on the top of the hill is increased beyond the current 100 mm, it is possible to obtain a composite slab that can achieve an increase in performance by the amount of the increase.

In formula (1), r is the "tensile reinforcement ratio (ratio of the rebar cross-sectional area to the beam cross-sectional area) of the part of the reinforced concrete beam that receives the maximum bending moment during long-term loading." In the "Reinforced Concrete Structure/Calculation Standards and Commentary," it is stated that "The tensile reinforcement cross-sectional area of the part that receives the maximum positive and negative bending moment during long-term loading is,
It shall be equal to or greater than the smaller of "0.004 x beam width x beam effective depth" (i.e., tensile rebar ratio r is 0.004) or 4/3 times the amount required by the existing stress."
It is said that.

In this invention, the tensile reinforcement ratio R in a composite slab is considered to be α times the tensile reinforcement ratio r of a reinforced concrete beam, but is basically understood to be "α = 2" (i.e., twice the tensile reinforcement ratio r of a reinforced concrete beam). The reason for this is that the entire circumference of the reinforcement in a reinforced concrete beam is attached to the concrete, integrating the concrete and the reinforcement, whereas the deck plate in a composite slab exerts a composite effect by attaching only one side of it, so it is basically set to twice the tensile reinforcement ratio r in the case of a reinforced concrete beam. α is a numerical value used as a coefficient for the tensile reinforcement ratio r, and in this invention, the range of α is used, which is greater than 2 and less than 2.1.

The reason why the "tensile reinforcement ratio of a beam (reinforced concrete beam)" is utilized even though the present invention relates to a floor (floor slab) is because a composite slab is a one-way slab.
In other words, in a composite slab, the cross section of the deck plate becomes the tensile reinforcement, but unlike a reinforced concrete floor slab, which is a bidirectional slab with reinforcement bars arranged in two perpendicular directions, in a composite slab the deck plate, which functions as a reinforcement bar, is unidirectional, and structurally it can be treated as a series of unidirectional beams similar to "reinforced concrete beams."

The effect of the composite slab of the present invention, that is, the possibility of increasing the performance by the amount of the increase when the thickness of the concrete on the top of the hill is increased beyond the current 100 mm, will be explained in the examples of the "Form for carrying out the invention" described below, using a reverse-enclosed deck plate with specific shape and dimensions as an example, in line with the ideas described in the "Reinforced Concrete Structure/Calculation Standards and Commentary" above.

FIG. 2 is a diagram showing the shape/dimensions of a deck plate adopted in a composite slab according to an embodiment of the present invention. This figure compares the case where the concrete thickness on the top of the deck plate is 100 mm (a) with the case where it exceeds that, 120 mm (b), in the case of a composite slab made of a typical deck plate (including the case of a normal end-closed deck plate with an end-closed beam placement portion formed at the valley surface height) in which the valley surface is placed on the beam, and explains that even if the thickness exceeds 100 mm, the performance cannot be improved by that amount. This explains end-closed deck plates, where (a) shows a typical deck plate 1A with a beam support portion that does not have a closed end, (b) shows a normal end-closed deck plate 1B with an end-closed beam support portion 5B formed at valley surface height, and (c) shows a reverse-enclosed deck plate 1C, which is the subject of this invention, with an end-closed beam support portion 5C formed at peak surface height. (a) shows a composite slab constructed using a reverse-enclosed deck plate 1C, and (b) shows a composite slab constructed using a normal-enclosed deck plate 1B, and is a figure that explains how the concrete is less likely to slip relative to the deck plate in the case of a composite slab using a reverse-enclosed deck plate 1C. FIG. 2 is a schematic diagram showing a composite slab constructed using the deck plate of FIG. 1, and is a diagram for explaining the effect of the composite slab of the present invention as a numerical example.

Below, we will explain the form for implementing the composite slab of the present invention with reference to the drawings.

The effect of the composite slab of the present invention, that is, the fact that if the thickness of the concrete on the top of the hill is made thicker than the current 100 mm, it is possible to improve performance by the amount of the increase, will be explained by taking a deck plate with the cross-sectional shape and dimensions shown in Figure 1.
In the present invention, the composite slab is treated as a reinforced concrete beam, and in the embodiment, the composite slab is treated as a reinforced concrete beam having a width of 1000 mm and a depth of H mm.
h = thickness of concrete on top of hill (mm)
d = average concrete thickness of the deck plate height area mm
S = cross-sectional area of deck plate ^mm2
Then,
The cross-sectional area of the beam corresponds to 1000 x H (= 1000 x (h + d)),
The cross-sectional area of the reinforcing bar corresponds to the cross-sectional area of the deck plate S,
It is.
Therefore, the tensile reinforcement ratio R in the composite slab is:
R = S / 1000 (h + d) ... Equation (3)
It is.

A specific numerical example is described below.
As shown in Figure 1, the calculation is based on the cross-sectional shape and dimensions of one deck plate being 1.0 mm thick, 75 mm high, 600 mm wide, and a cross-sectional area of 880 mm ² (cross-sectional area S per meter (1000 mm) = 1480 mm ² ).
The "average concrete thickness d in the deck plate height region" in formula (1) is, more specifically, a value d such that "the width dimension of the deck plate × d = the total cross-sectional area of the valley space and the valley equivalent space", and is also called the groove equivalent slab thickness.
The valley space here refers to the space in the joint area when deck plates are connected together in the width direction. Usually, the valley space and the joint area space are the same size.
The "average concrete thickness d in the deck plate height region" of the exemplary deck plate is 36 mm (d = 36 mm).

The specific calculation is as follows:
Here, the tensile reinforcement ratio r of the reinforced concrete beam is set to "r = 0.004" in accordance with the concept described in the above-mentioned "Reinforced Concrete Structure/Calculation Standards and Commentary."
As described in [0018], in the present invention, the value of the coefficient α is basically understood to be 2, so that "α=2.0".

As mentioned above, if r = 0.004 and α = 2.0,
The tensile reinforcement ratio of the composite slab is R = α × r = 0.008.
The cross-sectional area per meter of the above cross-sectional shape and dimensions is S = 1480 ^mm2 and d = 36 mm, so
Substituting into equation (3),
0.008 = 1480/1000 (h + 36)
therefore,
h = 1480/(2 x 0.004) x 1000-36
= 149 mm (≒ 150 mm)
It becomes.
In other words, by using the reverse enclosing deck plate, the mutual slippage between the deck plate and the concrete is prevented, so even if the thickness h of the concrete on top of the composite slab exceeds 100 mm, it is possible to effectively exert the composite effect as long as it is up to about 150 mm (calculated as a reinforced concrete beam, because the tensile reinforcement ratio R of the composite slab of the present invention meets the tensile reinforcement ratio requirements in the "Reinforced Concrete Structure/Calculation Standards").

As described above, by making it possible to make the thickness h of the concrete on the top of a composite slab using an inverted enclosing deck thicker than before, it is possible to solve the problem of the allowable load being reduced by the increase in dead weight without any increase in cross-sectional performance. In other words, compared to conventional composite slabs of 100 mm or less, the cross-sectional performance of the composite slab is improved, and in addition to increasing the burden of live loads, it is expected to have the effect of reducing cracks.

1 (1A, 1B, 1C) Deck plate 2 ridge (or ridge face)
3. Valley (or valley surface)
4 Slope portion 5 (5B, 5C) Beam placement portion 6 Concrete 7, 8 Flat portion 10 at valley height on both sides of deck plate width direction Beam

Claims (2)

A design method for a composite slab in which a deck plate and concrete are integrated, the deck plate having a trapezoidal wave-shaped cross section with continuous peaks and valleys on the slopes and flat portions at the valley height on both sides in the width direction, the longitudinal ends of which are crushed to form beam placement portions with closed ends at the peak height, and the composite slab is constructed using an inverted end closed deck plate,
In designing composite slabs, they are considered to be unidirectional reinforced concrete beams.
A step of setting a tensile reinforcement ratio (r) when the beam is made into a reinforced concrete beam;
A step of setting a coefficient (α) to be multiplied by the tensile reinforcement ratio (r);
and setting the cross-sectional dimensions of each member of the composite slab using the following formulas (1 ) and (2).
H = S / (α · r) - d ... (1)
2≦α≦2×1.1 (2)
however,
H = concrete thickness on top of hill (mm)
S = Cross-sectional area of deck plate per 1000 mm width (mm ² )
α = Coefficient for tensile reinforcement ratio (r)
r = tensile reinforcement ratio of the part of the reinforced concrete beam that receives the maximum bending moment during long-term loading d = average concrete thickness in the deck plate height area (mm) The method for designing a composite slab according to claim 1, characterized in that the tensile reinforcement ratio ( r ) is 0.004.

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