JP3364167B2 - Hollow slab structure design apparatus, method, and recording medium therefor - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a hollow slab structure designing apparatus and method used for structural design of a reinforced concrete floor (hollow slab) having a cylindrical hollow structure, and a recording medium therefor.

[0002]

2. Description of the Related Art Generally, a reinforced concrete floor board structure is assumed to have a fixed load or a load constantly acting thereon, and has an appropriate margin with respect to a structural strength and an allowable limit of use performance.
The structure is designed to ensure its safety. Also,
The conventional design of reinforced concrete floorboard structures is based on the "Construction Standards for Reinforced Concrete Structures-Commentary" of the Architectural Institute of Japan.

[0003]

The calculation related to the structural design is performed under a certain assumption, but in the structural calculation based on the simplified assumption, the correct displacement and stress property of the structure cannot be grasped. Sometimes there is not. This is because the structural system assumed for structural calculation cannot simulate an actual phenomenon. Currently, in reinforced concrete floorboard structures, a method of arranging voids (hollow pipe-shaped members) inside floorboard structures has been put into practical use for the purpose of weight reduction, material saving, and large span structure without beam beams. The floorboard structure made by the construction method is called a hollow slab). However, although the structural design method and computer program of the whole building are generally known, the appropriate structural calculation method of the hollow slab, especially the rational structural calculation method by the finite element method considering the anisotropy is not well known. Has not been done.

The present invention has been made in view of the above points, and in a hollow slab structural design, a hollow slab structure designing apparatus capable of consistently performing optimum structural design, a method thereof, and a recording medium thereof. It is provided.

[0005]

The present invention is a hollow slab structure.
Used in the structural design of hollow slabs in building design equipment.
A computer for calculating a physical quantity to be stored, wherein an input device for inputting input data used for calculating strain and stress generated in a hollow slab and a displacement and strain of the hollow slab are calculated based on a load applied to the hollow slab. a distortion calculating means for further viewing including the stress calculating means for calculating the stress generated in the hollow slabs based on distortion of the hollow slabs calculated by the distortion calculating means, a central processing unit and main
Comprising a processing unit comprising a memory, a storage unit for storing the data calculated by the input data and pre-Symbol processor, and an output device for outputting the results calculated from the thus the input data to the processing unit , Divided into multiple elements
For each element of the empty slab, the strain calculation means is configured to generate {P} = [K] {δ}, (where {P} is a load vector, [K] is an orthogonal anisotropy) according to the boundary condition. Stiffness matrix obtained by using the bending stiffness matrix [D] considering
{Δ}: Displacement vector) Using the relational expression between the load vector and the displacement vector, the load vector and the stiffness matrix are set based on the input data, and the displacement is calculated. Calculate the distortion in
The stress calculating means is {M} = [D] {ε}, (where, {M} is a stress vector, [D] is a bending rigidity matrix in consideration of orthogonal anisotropy, and {ε} is a strain vector). By using the relational expression between the stress vector and the strain vector that can be expressed by, based on the strain calculated by the input data and the strain calculation means,

[Equation 7]

[Equation 8] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: Poisson's ratio, in particular, the coefficient k _y, the boundary element method From the horizontal displacement d _p of the cross-section end of the solid slab and the horizontal displacement d _y of the cross-section end of the hollow slab due to the bending moment calculated using k _y = d _p / d _y The value is calculated as, and the stress is calculated by setting.

The present invention considers the orthogonal anisotropy of a hollow slab containing voids (hollow pipe structure) arranged in one direction, and calculates stress in two directions, a void parallel direction and a void orthogonal direction. There is. A direction parallel to the void is called a void parallel direction, and a direction orthogonal to the void is called a void orthogonal direction.

The boundary condition mentioned here includes the degree of fixing in consideration of the bending back of pin support / fixed support / fixed end moment. According to the present invention, it is possible to calculate the displacement, strain and stress generated in the hollow slab according to the boundary conditions.

[0008]

Further, in the computer , the processing section compares a value obtained by multiplying the maximum displacement of the hollow slab calculated by the strain calculating means by a safety factor in consideration of creep with a reference value, and bends the hollow slab. It is characterized by further including a first determining means for determining the safety according to. ADVANTAGE OF THE INVENTION According to this invention, the safety | security regarding the bending of a hollow slab can be determined automatically.

Further, in the computer , the processing unit may calculate the maximum stress generated in the hollow slab by the stress calculating unit and Mc = k · (Fc) ^1/2 Z, where
k: coefficient, Fc: concrete design strength, Z: sectional modulus, which is compared with the crack moment Mc, and further comprises second judging means for judging the safety related to the crack of the hollow slab. . The coefficient k is determined separately, and for example, the unit of Fc is [kg /
When the unit of cm ² ] and Z is [cm ³ / m], 1.8 is used as the value. ADVANTAGE OF THE INVENTION According to this invention, the safety regarding the crack of a hollow slab can be determined automatically.

Further, in the computer , the storage unit further stores a stress concentration coefficient α relating to the element shape of the reinforcing bar in the direction orthogonal to the void, and the processing unit determines the reinforcing bar amount N required for the hollow slab as the stress. It is characterized by further including a reinforcing bar amount calculating means for calculating using the concentration coefficient α. Specifically, N ′ = αM × 10 ² / (f _t ja _s B), where α is the stress concentration factor relating to the element shape, M is the maximum value of stress [tm / m], and f _{t is the} rebar allowance. Tensile stress [t /
cm ² ], j: distance between stress centers [cm], a _s : cross-sectional area [cm ² ] per rebar used, B: unit width [c
m], the rebar amount N is calculated as a value N obtained by rounding up the decimal value of N ′.

According to the present invention, the required amount of reinforcing bar is determined in consideration of stress concentration on the void in the reinforcing bar arrangement in the direction orthogonal to the void. That is, the calculation suitable for the structure of the hollow slab is performed. The stress center distance is, for example, d × 7 /
8 (however, d is the distance between the rebar and the floor underside)
Is set as. According to the present invention, the amount of rebar required for a hollow slab can be automatically calculated. Also, by dividing the hollow slab into elements and calculating the amount of rebar required for each element,
The required minimum bar arrangement can be performed.

Further, in the computer, the processing unit, with respect to volume id parallel τ = Qx × (B / b ) /
(7/8 × (H-d _t )), τ =
Qy / (7/8 × (H-φ)), where Qx: maximum shear force [t / m] in the void parallel direction, Qy: maximum shear force [t / m] in the void orthogonal direction, B: void center Distance, b: distance between void outer diameters, H: floor thickness, φ: void diameter, d _t : distance from the tensile edge of the floor to the barycenter of the reinforcing bar, and the shear stress τ and the allowable shear stress Compare
It is characterized by further including a third judging means for judging the safety of the shearing force generated in the hollow slab. According to the present invention, it is possible to automatically judge the safety related to the shearing force generated in the hollow slab.

The present invention relates to a hollow slab structure designing apparatus.
The strain and stress used in the structural design of hollow slabs
Is it a procedure that the computer will execute to calculate?
A method for calculating strain stress consisting of : a procedure for calculating a geometrical moment of inertia I _x in a void parallel direction in a slab having a hollow cross section, and a geometrical moment of inertia I ₀ in a void parallel direction in a slab having no hollow cross section. And the second moment of area I _x is divided by I ₀ to obtain a coefficient k _x
And the boundary element method to calculate the horizontal displacement d _p of the cross-section end of the slab having no hollow cross section and the horizontal displacement d _y of the cross-section end of the hollow slab by the bending moment. According to the calculation procedure and the bending moment,
A procedure for dividing the horizontal displacement d _p of the cross-section end of the slab having no hollow cross section by the horizontal displacement d _y of the cross-section end of the hollow slab to calculate a coefficient k _y , and the coefficients k _x , k _The procedure of taking the average of _y and setting the average values as the coefficients k ₁ and k _xy , {P} = [K] {δ}, (where {P}: load vector, [K]: orthogonal difference) A stiffness matrix obtained by using a bending stiffness matrix [D] considering the directionality,
{Δ}: Displacement vector) Using the relational expression between the load vector and the displacement vector, the load vector and the stiffness matrix are set based on the input data, and the displacement is calculated. And a procedure for calculating strain, {M} = [D] {ε}, (where, {M} is a stress vector, [D] is a bending rigidity matrix in which orthogonal anisotropy is considered, and {ε} is strain. Vector), using a relational expression of a stress vector and a strain vector, based on the strain calculated by the input data and the strain calculation means,

[Equation 9]

[Equation 10] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: a step of calculating the Poisson's ratio, set the stress, the It is characterized by including.

The present invention is a recording medium recording a strain stress calculation program in a hollow slab structure designing apparatus,
Cross section of void parallel direction in slab with hollow cross section
The procedure for calculating the second moment I _x , the procedure for calculating the second moment of inertia I ₀ in the void parallel direction in the slab having no hollow cross section, and the second moment of inertia I _x for the section are I
_Using the procedure of dividing by ₀ to calculate the coefficient k _x and the boundary element method, the horizontal displacement d _p of the cross-section end of the slab having no hollow section and the cross-section end of the hollow slab due to the bending moment are calculated. The procedure for calculating the horizontal displacement d _y and the horizontal displacement d _p of the cross-section end of the slab having no hollow cross section due to the bending moment are _defined as the horizontal displacement d _y of the cross-section end of the hollow slab. A procedure of dividing and calculating a coefficient k _y , a procedure of taking an average of the coefficients k _x and k _y and setting the average value as coefficients k ₁ and k _xy , {P} = [K] {δ}, (Where, {P} is a load vector, [K] is a stiffness matrix obtained by using a bending stiffness matrix [D] in consideration of orthogonal anisotropy, and {δ} is a displacement vector). Based on the input data, the load vector And a stiffness matrix are set to calculate the displacement, and a procedure for calculating the strain based on the calculated displacement, {M} = [D] {ε}, (where,
{M}: Stress vector, [D]: Bending rigidity matrix considering orthotropic anisotropy, {ε}: Strain vector). Based on the distortion calculated by the means,

[Equation 11]

[Equation 12] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: a procedure of calculating the Poisson's ratio, set the stress computer It is a computer-readable recording medium in which a strain stress calculation program to be executed by is recorded.

As described above, the program for causing the computer to realize the function of the hollow slab structure designing device is recorded in the recording medium, and the program is read from the recording medium to the computer, whereby the hollow slab structure designing can be easily performed using the computer. The device can be realized.

[0017]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a hollow slab structure designing device according to an embodiment of the present invention.

The hollow slab structure designing apparatus 1 includes a processing unit 2 described below, a storage unit 3 for storing input data and a calculation result by the processing unit 2, and an input unit (not shown) to which the input data is input. And an output unit (not shown) that outputs the calculation result by the processing unit 2. The processing unit 2 includes a dividing unit 20 that equally divides the hollow slab into a plurality of elements (rectangular elements) according to the number of divisions input to the input unit, and a strain calculation unit that calculates displacement and strain due to a load applied to the hollow slab. (Strain calculation unit) 21, a stress calculation unit (stress calculation unit) 22 that calculates the stress generated in the hollow slab, and a deflection determination unit (first determination unit) 23 that determines the safety of deflection of the hollow slab. A crack determination unit (second determination unit) 24 that determines the safety of cracking of the hollow slab, a rebar amount calculation unit (rebar amount calculation unit) 25 that calculates the amount of rebar required for the hollow slab, and a hollow slab Force determination unit (third determination means) 26 for determining the safety of the shear force generated in the
Composed of and.

The processing unit 2 is composed of a memory, a CPU (central processing unit), etc., and a program (not shown) for realizing each function of the processing unit 2 is loaded into the memory and executed. The function shall be realized. The storage unit 3 is configured by a storage device such as a memory, a hard disk, a magneto-optical disk, or the like. An input device such as a keyboard or a mouse is used for the input unit. The output section has a CRT (Cathode Ray Tub).
e) or an output device such as a liquid crystal display device or a printer.

First, the hollow slab structure designing apparatus 1 of this embodiment will be described with respect to the hollow slab to be structurally designed and the force acting on the hollow slab. FIG. 2 shows the structure of the hollow slab and the forces acting on it. The hollow slab structure design device 1 targets the slab in which the voids shown in FIG. This hollow slab has
As shown in the figure, a stress composed of bending moments: Mx, My and shearing forces: Qx, Qy is generated. The hollow slab structure designing device 1 takes into account these forces and the structure peculiar to the hollow slab, and inputs the materials (reinforcing bar, concrete), load, dimensions, the number of divisions, etc. required for the hollow slab used in the building to be designed. By doing so, the displacement and strain generated in the hollow slab,
Stresses (bending moment, shearing force, reaction force) etc. are automatically calculated and output.

Next, an outline of the operation of the hollow slab structure designing apparatus 1 configured as described above will be described, and the details thereof will be described later. When the hollow slab structure designing device 1 of the present embodiment receives input of predetermined input data, as shown in the operation flowchart of FIG. 36, first, the displacement / strain is calculated (step S0). Then, the stress is calculated using the strain data calculated in step S0 (step S1).
Further, in accordance with the request of the user (designer), the determination of flexure safety (step S2), the determination of bending crack safety (step S3), the calculation of the required reinforcing bar amount (step S)
4), the safety of shearing force is determined (step S5).

Next, the operation of the hollow slab structure designing device 1 will be described in detail. First, from the input section (not shown),
Concrete design strength Fc which is the analysis condition (see Fig. 3)
[Kg / cm ² ], reinforcing bar design strength Fs [kg / cm ² ],
Floor thickness H [mm], void diameter [mm], cover thickness [mm], concrete specific gravity [kg / cm ³ ], finishing load [kg / m ² ], Poisson's ratio ν (for ordinary concrete: 1 / 6), short side length [mm], long side length [m
m], data such as separately defined load, concentrated load, line load (due to walls, etc.), and the boundary condition of the degree of fixing considering the pin support, fixed support, and bending back of the fixed end moment (see Fig. 5). Is entered. Furthermore, when the hollow slab model to be structurally designed is divided into a plurality of elements, the number of divisions corresponding to the short side and the long side of the floor surface is input so that each element becomes a substantially square shape. In FIG. 3, the floor thickness is 4
An example is shown in which the void diameter is 00 [mm], the void diameter is 250 [mm], the fog thickness is 75 [mm], and the void center-to-center distance is 400 [mm]. In addition, as the degree of fixing considering the bending back of the fixed end moment, which is one of the boundary conditions, a value can be set from a degree of fixing of 100% assuming a fixed end to a degree of fixing of 0% assuming a pin end. Is.

Numerical examples shown in the respective figures referred to in the following description, as analysis conditions, these values, concrete design strength Fc = 210 [kg / cm ² ] and concrete Poisson's ratio ν = 1 / 6, reinforcing bar design strength Fs = 20
00 [kg / cm ² ], short side length 4248 [mm], long side length 9098 [mm], loading load 100.0 [kg /
m ² ] and the like relating to the material strength, and the boundary condition that the pin support exists at the position of Δ shown in FIG. Further, the void parallel direction will be referred to as the X direction, and the void orthogonal direction will be referred to as the Y direction.

The dividing unit 20 divides the model of the hollow slab in the X direction and the Y direction parallel to the floor surface based on the input number of divisions.
Multiple (almost square) with equal division in each direction
Divide into rectangular elements and assign numbers to each divided node and each element. As shown in FIG. 4, a node number is assigned to each node, and an element number is assigned to each element as shown in FIG. Each unit of the processing unit 2 (strain calculation unit, stress calculation unit, first to third determination unit, reinforcing bar amount calculation unit) will be described below for each element of the model of the hollow slab divided by the division unit 20. Perform processing.

The strain calculation unit 21 uses the relational expression {P} = [K] {δ}, which represents the relationship between the load and the displacement, (where, {P}: load vector, [K]: stiffness matrix, {δ}. : Displacement vector), the displacement at the node of each element is calculated. Where the stiffness matrix [K] is
It is obtained by the following equation using a bending stiffness matrix [D] in consideration of orthogonal anisotropy described later.

[Equation 13] (Here, [C]: coefficient matrix by shape,
[Q]: Distortion conversion matrix) Further, the components of the load vector are set based on the analysis conditions input as the above-mentioned input data. Further, the strain, which is the displacement per unit length, is calculated from the calculated displacement. Next, the stress calculation unit 22 expresses a relational expression {σ} = {M} = [D] {ε} ... (1) indicating the relationship between stress and strain, where {σ}, {M}: stress vector, [ D]: Bending rigidity matrix, {ε}: Bending rigidity matrix [D] used for strain vector is calculated. In the case of an isotropic plate (floor), the bending stiffness matrix [D] is
Formula (2)

[Equation 14] It can be expressed as (2). Where E is the longitudinal elastic modulus (Young's modulus), t
Represents the plate thickness (floor thickness), and ν represents the Poisson's ratio. In the case of ordinary concrete, the longitudinal elastic modulus E is calculated by the following equation (3). E = 2.1 × 10 ⁵ (Fc / 200) ^1/2 [kg / cm ² ] ... (3), (Fc: concrete design strength)

The hollow slab which is the object of structural design by the hollow slab structure designing apparatus 1 has orthogonal anisotropy in which the principal axes of anisotropy coincide with the X and Y axes. The bending stiffness matrix [D] can be expressed by equation (4).

[Equation 15] (4) In the present embodiment, the coefficients k _x , k representing the ratio of D ₁ , D _x , D _y, D _xy to the elements of the flexural rigidity matrix equation [D] in the case of an isotropic plate. _{Using y} , k ₁ and k _xy :

[Equation 16] Among these coefficients, k _x and k _y are I _x or I _y shown below.
And the normal second moment of area I ₀ (= I
_p )). ^{_{I 0 = bt 3/12 ...}} (5) Here, b is a unit width of the hollow slabs, t represents the floor thickness. In the following, the direction that coincides with the void axis is assumed to be the X axis, and the coefficient
_x, k _y, a k _1, k _xy How to find the show.

[0027] 1) coefficient k calculated X-plane of _x, has a cross section having a hollow diameter phi, expression of the bending moment about the X-plane normal second moment ^{_{(6) I x = bt 3}} /12 -πφ obtained by the ^4/64 ... (6). The coefficient k _x is obtained _by the ratio of this value to the above-mentioned second moment of area I ₀ , that is, the equation (7) (see FIG. 6). k _x = I _x / I ₀ (7)

2) Calculation of coefficient k _{y In} the Y plane, since the defective portion (hollow portion) of the cross section due to the void changes along the Y axis, it is not possible to adopt the usual method of calculating the second moment of area. . In this embodiment, considering the rigidity decreases due to the hollow structure, the in-plane pure bending analysis of a flat plate with a hollow cross section with a boundary element method, calculating the coefficient k _y as follows. The strain calculation unit 21 applies a bending moment of the same magnitude as an external force to a flat plate having a hollow cross section that is simply supported and a flat plate that does not have a hollow cross section,
The horizontal displacement of the end portion (d _p , d _y shown in FIG. 7) is calculated. For the boundary element, for example, the left and right surfaces are divided into 20, the horizontal surface is divided into 30, and the circumference is divided into 80, and the horizontal displacement of the end is obtained.

From the bending moment-curvature relational expression M = EIκ of the beam element subjected to bending (8), the second moment of area and curvature of the slab having a hollow cross section, I _y and κ _y , and I _p and κ _p are hollow. Assuming the second moment of area and curvature of a slab having no cross section, M = EI _y κ _y = EI _p κ _p (9) From the equation (9), the equation (10) is calculated as follows using the horizontal displacements d _p and d _y of the coefficient k _y at the ends. k _y = I _y / I _p = κ _p / κ _y ≈d _p / d _y (10)

3) The calculation coefficients k ₁ and k _{xy of} k ₁ = k _xy take the arithmetic mean (equation (11)) of the coefficients k _x and k _y . k ₁ = k _xy is = (k _x + k _y ) / 2 (11)

From the above, the bending stiffness matrix [D] is calculated. The stress calculation unit 22 uses the calculated bending rigidity matrix [D] and the strain data calculated by the strain calculation unit 21 to calculate the stress from the relational expression (1) indicating the relationship between the stress and the strain. Then, the strain calculation unit 21 and the stress calculation unit 22
The data calculated by is output to the output unit 4. 8 to 12 show output examples calculated by the strain calculation unit 21 and the stress calculation unit 22 and output to the output unit (not shown).

FIG. 8 is a displacement diagram showing the displacement (strain) of the hollow slab and showing the maximum displacement (node number (19
9), -1.033 [mm], node number (7
8) shows 1.556 [mm]). FIG. 9 is a bending moment diagram in the X direction, showing the X of the hollow slab.
The bending moment generated in the direction is shown, and at the maximum bending moment (node number (156), -0.4
1 [tm / m], 0.36 at the node number (83)
[Tm / m]) is shown. FIG. 10 is a bending moment diagram in the Y direction, showing bending moments generated in the Y direction of the hollow slab, and showing the maximum bending moment (at the node number (156), -1.88 [tm / m]],
The node number (88) indicates 3.88 [tm / m)].

FIG. 11 is a shear force diagram in the X direction, showing the shear force generated in the X direction of the hollow slab, and at the maximum shear force (at the node number (155), -0.90).
At [tm / m], the node number (165) is 0.90
[Tm / m)]) is shown. FIG. 12 is a shear force diagram in the Y direction, showing the shear force generated in the Y direction of the hollow slab, as well as the maximum shear force (at the node number (145), -2.73 [tm / m]] and the node number. (23)
Shows 2.30 [tm / m]). The data calculated by the strain calculation unit 21 and the stress calculation unit 22 is temporarily stored in the memory included in the processing unit 2 and is also stored in the storage unit 3 according to conditions.

Next, the operation of the deflection determination unit 23 will be described. The deflection determination unit 23 first acquires the maximum value of the displacement data calculated by the strain calculation unit 21 from the memory or the storage unit 3 included in the processing unit 2. Then, using a safety factor that takes creep into consideration and a reference value related to the safety of deflection (separately determined) that are separately input and set from the input section, the maximum value of displacement data is multiplied by the previous safety factor and the reference value. The safety of the deflection is judged by comparing the value with the value.

For example, the maximum displacement of the slab (elastic deflection)
Long-term deflection obtained by multiplying δ _E = 0.156 [cm] (see the displacement diagram in FIG. 8) by a safety factor (= 4.0) considering creep δ δ = 0.156 × 4.0 = 0.622 [ cm] was divided by the short side of the floor (see FIG. 4) = 424.8 [cm] and the value per unit length [cm] (1/682) was compared with the reference value (= 1/250) to determine ing. In this example,
Since the calculated value is equal to or less than the reference value, it is determined that the safety regarding the deflection is OK. The result of this determination is output to the output unit.

Next, the operation of the crack determination unit 24 will be described. The crack determination unit 24 first acquires the maximum value (maximum bending moment) of the stress data calculated by the stress calculation unit 22 from the memory or the storage unit 3 of the processing unit 2. Then, the crack moment Mc Mc = 1.8 (Fc) ^1/2 Z (11) (where Fc is the concrete design strength and Z is the section modulus) and the maximum stress are expressed by the following equation (11). By comparing, the safety of cracking is judged.

For example, the section modulus in the X direction is 25474.
[Cm ³ / m], concrete design strength Fc = 210
When [kg / cm ² ], the crack moment Mc in the X direction is 6.64 [tm / m]. The maximum bending moment shown in FIG. 9 is 0.41 [tm / m], and this value is equal to or less than the crack moment Mc. Therefore, the safety regarding the crack in the X direction is judged to be OK. Further, when the section modulus in the Y direction is 24270 [cm ³ / m], the crack moment Mc in the Y direction is 6.33 [tm / m].
Becomes Maximum bending moment 3.8 shown in FIG.
It is 8 [tm / m], and this value is less than or equal to the crack moment Mc in the Y direction. Therefore, the safety regarding the crack in the Y direction is determined to be OK. The result of the determination is output to the output unit.

Next, in explaining the operation of the reinforcing bar amount calculating section 25, a method of evaluating the reinforcing bar amount will be described first.

The amount of rebar required in each element divided by the dividing unit 20 is determined by using the maximum value of the moment of the node belonging to the element. However, perforated slab (hollow slab)
In case of, unlike the non-perforated slab (a slab that does not have a hollow structure), stress concentration must be considered. Therefore, the reinforcing bar amount calculation unit 25 calculates the reinforcing bar amount in each element based on the maximum value of the moment of the node belonging to each element calculated by the finite element method multiplied by the stress concentration factor shown in Table 1. It is carried out. (In the table, h indicates the plate thickness (floor thickness), and r indicates the diameter of the hole (void))

[Table 1]

This stress concentration factor is 2 according to the boundary element method.
It was obtained by dimensional elasticity analysis, and the outline of the analysis is described below. The square two-dimensional plate with holes shown in FIG. 13 is simply supported at the centers of both ends, a simple bending unit moment (see FIG. 14) is applied from both ends, and the stress (σ _x ) at each point generated is calculated. In FIG. 13, 1 to 96 are points for obtaining stress, 1 to 31 are element lower ends, 32 to 62 are element upper ends, and 63 to 96 are points inside the element. The border element is
Primary element, divided into 30 equal parts in the width direction and 20 parts in the height direction
Evenly divided, the circumference of the hole is equally divided into 80. Plate thickness (h = width)
And the diameter (r) difference is 125 [mm] and 150 [mm], and the plate thickness (h = width) is 250 [m].
Calculation was performed from m] to 700 [mm] in steps of 25 [mm].

The calculation result is shown in FIG. 15 (hr = 125). The horizontal axis represents the point numbers shown in FIG. 4, and the vertical axis represents the absolute value of stress (σ _x ) when there is a hole divided by the maximum value of stress (σ _x ) that occurs when there is no hole. Is shown (for each pipe size shown at the right end). The legend in FIG. 15 indicates h, and it can be seen that as h increases (that is, as the ratio of the diameter to the height increases), stress concentration occurs. From this calculation result, the one with the maximum stress concentration factor was taken out for the plate thickness (h) and the difference between the plate thickness and the diameter of the hole (hr). Table 1 shows the stress concentration factors related to the difference between the thickness and the diameter of the hole (hr).

Next, the operation of the reinforcing bar amount calculating section 25 will be described. Rebar amount calculating section 25, a reinforcement amount N necessary for hollow slabs, but the following equation N '= αM × 10 ² / of _{(f t ja s B) ...} (12), α: stress concentration factor for element shapes, M: maximum value of the stress _{[tm / m], f t} : allowable tensile stress of the rebar ^{[t / cm 2], j} : stress center distance (= d × 7/8) [cm], a s: using The cross-sectional area per rebar [cm ² ], B: unit width [cm], and the decimal value N ′ calculated from N ′ are rounded up to calculate the value N. The stress concentration coefficient α is calculated by the above-mentioned method, and the allowable tensile stress degree f _{t of} the reinforcing bar, the distance d between the reinforcing bar and the floor lower surface, the cross-sectional area a _s per reinforcing bar used, The unit width B is input from the input unit 3 in advance and is stored in the storage unit 3.

The reinforcing bar amount calculation unit 25 acquires the maximum value of the moment (stress) calculated by the stress calculation unit 22 from the memory of the processing unit 2 or the storage unit 3, and further acquires the required data from the storage unit 3. Then, the amount of rebar is calculated from the equation (12). The amount of reinforcing bars calculated here is the distance d (four types) between the reinforcing bars arranged in each direction and vertically and the floor underside (FIG. 16).
Unit width B (unit width [cm] in the direction orthogonal to the void (see FIG. 17) and 100 in the void parallel direction).
[Cm]), and is calculated for each of the top and bottom in the void parallel direction and the top and bottom in the void orthogonal direction. The calculation result is output to the output unit. It should be noted that the maximum moment of the node forming each element is defined as the maximum value of the moment (stress) of the element.

18 to 21 show examples of output. In this example, H = 40 [cm], d _x = 34.0 [cm], d _y =
35.0 [cm], (j _x = 29.8 [cm], j _y = 3
0.6 [cm]), α _x = 1.208, α _y = 1 and a _s =
It is 1.27 [cm ² ] and f _t = 2.0 [t / cm ² ]. In these figures, the number of reinforcing bars required for each divided element is shown in the grid corresponding to each element. In the present calculation example, D13 rebar (a _s = 1.27
[Cm ² ] and ft = 2.0 [t / cm ² ]) are used. In addition, the number written on the white background of the figure is 1
It is the number of required rebars per [m], and is the number per unit width in the shaded area.

Next, the operation of the shearing force judging section 26 will be described. The shear force determination unit 26 determines a reference value (allowable stress level) fs separately determined for the shear force generated in each cross section of the hollow slab and the shear stress level τ calculated by the following equations (13) and (14). And to determine its safety. (1) Void parallel direction τ = Q _i × 1000 × (B / 100) / (b × j _i ) = Q _i × 10 × (B / b) / (7/8 × (H-5)) [kg / Cm ² ] (13) (2) Void orthogonal direction τ = Q _i × 1000 × (100 × j _i ) = Q _i × 10 / (7/8 × (H-φ)) [kg / cm ² ] (14) Here, i = x, y, and Q _i and j _i represent shear force and stress center distance in the void parallel direction (X direction) or the void orthogonal direction (Y direction). B is the distance between void centers, b is the distance between void outer diameters, H is the floor thickness, and φ is the void diameter (see FIG. 22).

For example, in the X direction, the shearing force Q _x is 0.90 [t / m] and the shearing stress τ is 0.69 [kg].
/ Cm ² ], and the reference value fs is 7.00 [kg / cm ² ], τ <fs and the determination is OK. Further, when the shearing force Q _y is 2.73 [t / m] and the shearing stress τ is 2.38 [kg / cm ² ] in the Y direction, τ <fs and the determination is OK. The result of the determination is output to the output unit.

Next, by the hollow slab structure designing device 1,
A structural calculation example of a reinforced concrete floorboard structure having steps will be described.

This structural calculation example is a hollow structure shown in FIG.
In the floorboard having the floorboard structure S1 which is a slab, FIG.
Step with floorboard structure S2 that is a non-perforated slab shown in (B)
It is an example when there is a part. Analysis conditions for this structural calculation example
Then, the floor plate structure S1 has a plate thickness of 25.0 [cm] and a hole diameter.
12.5 [cm], finishing load is 50.0 [kg /
m²], The slab own weight is 482.2 [kg / m²], Loaded load
180.0 [kg / m²] And the floor plate structure S2
Has a plate thickness of 20.0 [cm] and a finishing load of 50.0 [k]
g / m²], Slab dead weight 480.0 [kg / m²]
I shall. Also, using concrete, concrete
Design strength of 240 [kg / cm ²], Young's modulus
(E) is 320.04 [t / cm²], Poisson's ratio
(Ν) is set to 1/6 and the reinforcing bar design strength (Fs) is 2000
[Kg / cm²]] And the short side length of the floorboard is 6
Floor length of 800 [mm] and long side length of 8400 [mm]
Divide the plate into 16 equal parts along the short side and 20 equal parts along the long side.
(See FIG. 24). Furthermore, as a boundary condition,
The outer circumference is fixed and supported, and the degree of fixing is 85% and 60
FIG. 25 shows that there is a% portion.

When the above-mentioned analysis conditions are input to the hollow slab structure designing apparatus 1, the dividing section 20 divides the floor board into equal parts as shown in FIG. 24, assigning node numbers to the respective nodes, and further referring to FIG.
An element number is assigned to each element as shown in FIG. Then, the strain calculation unit 21 calculates the displacement and strain from the above analysis conditions. The calculated displacement data is output to the output unit as a displacement diagram shown in FIG. This figure shows that the maximum displacement (1.830 [mm]) occurs at the node number 179 with the node number 1 as the reference (0000 [mm]).

The stress calculator 22 sets a bending stiffness matrix (equation (4)) based on the input analysis conditions. Under the above analysis conditions, the components of the bending stiffness matrix for the floorboard structure S1 are D1 = 499.8 [tm], Dx =
2967.5 [tm], Dy = 3030.5 [tm],
Dxy = 1249.6 [tm], and the component of the bending rigidity matrix for the floor plate structure S2 is D1 = 262.9.
[Tm], Dx = 1577.4 [tm], Dy = 157
It becomes 7.4 [tm] and Dxy = 657.3 [tm].
Then, based on the strain data calculated by the strain calculation unit 21, the stress generated in the floorboard is calculated. The calculated stress data is output to the output section as a moment diagram, a shear force diagram, and a fulcrum reaction force diagram. 27 to 31 show output examples of stress data in this structural calculation example. 27 to 31 respectively,
A bending moment diagram in the X direction, a bending moment diagram in the Y direction, a shear force diagram in the X direction, a shear force diagram in the Y direction, and a fulcrum reaction force diagram are shown.

The maximum displacement (elastic deflection) δ _E calculated by the strain calculating means 21 is δ _E = 0.183 [cm] occurring at the node number 179 as shown in FIG.
The deflection determination unit 23 determines the long-term deflection δ considering creep.
To calculate. In this example, δ = 0.183 × 4.0 = 0.
It becomes 732 [cm]. This value and the short side length of the floorboard (l
_min ) of 680.0 [cm], the long-term deflection per unit length in the short side direction (δ / l _min ) of 1/929 is calculated, and this value and the reference value 1/250 are compared and determined. .
In this example, the long-term deflection per unit length in the short side direction is equal to or less than the reference value and is determined to be OK.

The crack determination unit 24 calculates the crack moment from the equation (11). The concrete design strength (Fc) under the analysis conditions is 240 [kg / cm ² ].
The section coefficient Z in the X direction of the floor plate structure S1 is 10033 [cm
³ / m], the crack moment (Mc) in the X direction, 2.80 [tm], is calculated from equation (11). On the other hand, the maximum value of the bending moment in the X direction is -1.75 [tm / at node number 103 as shown in FIG.
m]. The crack determination unit 24 compares and determines the calculated X direction crack moment (Mc) and the maximum value of the X direction bending moment calculated by the stress calculation unit 22. In this example, the maximum value of the bending moment in the X direction is equal to or less than the crack moment (Mc), so it is determined to be OK. The crack determination unit 24 further determines that the floorboard structure S1 has Y
For the direction and for each of the X and Y directions of the floor plate structure S2, the same determination of the safety regarding cracking is performed.

The reinforcing bar amount calculating section 25 calculates the required reinforcing bar amount using the equation (12) for each element of the divided floorboard structure. In this structural calculation example, in the case of the floor plate structure S1, the plate thickness is 25
[Cm], the distance (d _x ) from the reinforcing bar to the bottom surface of the floor to the X direction is 20.0 [cm], the stress concentration factor (α _y ) is 1, and the direction to the Y direction is The distance (d _y ) between the reinforced bars and the floor lower surface is 19.0 [cm], and the stress concentration coefficient (α _y ) is 1.0771. Further, in the case of the floor plate structure S2, the plate thickness is 20 [cm], and the distance (d _x ) from the reinforcing bar to be reinforced to the floor lower surface is 1 in the X direction.
5.0 [cm], the stress concentration factor (α _x ) is 1, and Y
With respect to the direction, the distance (d _y ) from the reinforcing bar to be arranged to the bottom surface of the floor is 14.0 [cm], and the stress concentration factor (α _y ) is 1
Is.

The required amount of rebar calculated based on these values is output to the output section. FIG. 32 is a diagram of the required number of upper end streaks in the X direction. In this example, D13 rebar (a _s = 1.27
[Cm ² ] and ft = 2.0 [t / cm ² ]) are used for calculation. The white background indicates the required number per 1 [m], and the shaded portion indicates the required number per unit width. FIG. 33 is a diagram showing the required number of lower end streaks in the X direction. FIG. 33 also shows the number of reinforcing bars required under the same conditions as in FIG. 34 and 35 are Y-direction upper muscle necessary number view and Y-direction lower muscle necessary number views, respectively, D13 rebar ^{_{(a s = 1.27 [cm 2}} ], ft = 2.
0 [t / cm ² ]) is used. The numerical value in the square is the number of required reinforcing bars per 1 [m].

The shearing force determining section 26 first calculates the equation (1
The shear stress degree τ is calculated using 3) and the equation (14). In this example, the shearing force Q _x calculated by the stress calculator 22 is 0.90 [t / t with respect to the X direction of the floor plate structure S1.
m], 0.69 [kg / cm ² ] is calculated as the shear stress degree τ from the equation (13). When the reference value (allowable stress level) fs is 7.40 [kg / cm ² ], τ <
It becomes fs and the determination regarding the shear force is determined to be OK. Similarly, the shear stress degree τ is calculated for each of the Y direction of the floor plate structure S1 and each of the X and Y directions of the floor plate structure S2, and each shear stress degree τ is compared and determined with a reference value (allowable stress degree) fs. To do. The result of the determination is output to the output unit. The operation of the hollow slab structure design device 1 has been described above in detail.

A program for causing a computer to realize the function of structural calculation in the hollow slab structure designing apparatus of the present invention is recorded in a computer-readable recording medium, and the program recorded in this recording medium is recorded in a computer system. The hollow slab structure designing device may be realized by reading and executing. That is, this program has a function of dividing the hollow slab into a plurality of elements, a function of strain calculating means, a function of stress calculating means, a function of first determining means, and a function of second determining means. A computer is made to realize the function of the reinforcing bar amount calculating means and the function of the third determining means.

The "computer system" referred to here includes an OS and hardware such as peripheral devices. In addition, the “computer system” includes a homepage providing environment (or display environment) if a WWW system is used. Also,
"Computer-readable recording medium" means a floppy disk, a magneto-optical disk, a ROM, a CD-ROM.
It means a storage medium such as a portable medium such as a hard disk built in a computer system. Furthermore, "computer-readable recording medium" means, for a short time, such as a communication line for transmitting a program through a network such as the Internet or a communication line such as a telephone line.
A program that dynamically holds a program (transmission medium or wave), and a program that holds a program for a certain period of time, such as a volatile memory inside a computer system that serves as a server or a client in that case, are also included. Further, the program may be for realizing a part of the functions described above. Further, it may be a so-called difference file (difference program) that can realize the above-mentioned functions in combination with a program already recorded in the computer system.

Although the embodiment of the present invention has been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and the design etc. within the scope not departing from the gist of the present invention. Is also included.

[0059]

As described above in detail, according to the present invention, in designing the structure of a hollow slab in consideration of the orthotropic anisotropy peculiar to the hollow slab and the stress concentration applied to the hollow portion.
Since the physical quantities used are calculated automatically, structural design suitable for hollow slabs can be performed easily and consistently, and safety can be automatically judged. Further, according to the present invention,
It is possible to automatically calculate the amount of rebar required for each part (element) of the hollow slab.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a hollow slab structure designing device according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating a structure of a hollow slab and a force acting thereon.

FIG. 3 is a diagram showing dimensions of a hollow slab as an example of analysis conditions.

FIG. 4 is an example of a model diagram of a hollow slab.

FIG. 5 is an example of a model diagram of a hollow slab.

FIG. 6 is a diagram showing a floor pressure and a unit width of a hollow slab and a non-perforated slab.

FIG. 7 is a diagram showing horizontal displacements d _p and d _y of an end portion due to stress applied to a hollow slab and an ineffective slab.

FIG. 8 is an example of a displacement diagram output by the distortion calculation unit.

FIG. 9 is an example of a bending moment diagram in the X direction output by the stress calculation unit.

FIG. 10 is an example of a bending moment diagram in the Y direction output by the stress calculation unit.

FIG. 11 is an example of a shear force diagram in the X direction output by the stress calculation unit.

FIG. 12 is an example of a shear force diagram in the Y direction output by the stress calculation unit.

FIG. 13 is a diagram showing a simple bending state of the hollow slab.

FIG. 14 is a diagram showing inner points for evaluating the value of stress applied to the hollow slab.

FIG. 15 is a diagram showing an X-direction stress concentration factor (when h−r = 125 [mm]) applied to the hollow slab.

FIG. 16 is a diagram illustrating a distance d between a reinforcing bar to be reinforced and a floor lower surface.

FIG. 17 is a diagram illustrating a unit width B of a hollow slab.

FIG. 18 is an example of a diagram showing the required number of X-direction upper end bars output by the reinforcing bar amount calculation unit.

FIG. 19 is an example of a diagram showing the required number of X-direction lower end bars output by the reinforcing bar amount calculation unit.

FIG. 20 is an example of a diagram showing the required number of Y-direction upper end bars output by the reinforcing bar amount calculation unit.

FIG. 21 is an example of a diagram showing the required number of Y-direction lower end bars output by the reinforcing bar amount calculation unit.

FIG. 22 is a diagram illustrating a void center distance B, a void outer diameter distance b, a floor thickness H, and a void diameter φ.

FIG. 23 is a structural example of an example of a floorboard structure having steps.

FIG. 24 is a diagram showing dimensions and node numbers of an example of a floorboard structure having steps.

FIG. 25 is a diagram showing an element number and boundary conditions (fixed support) of an example of a floorboard structure having steps.

FIG. 26 is a displacement diagram of analysis results for an example of a floorboard structure having steps.

FIG. 27 is a bending moment diagram in the X direction as an analysis result for an example of a floorboard structure having a step.

FIG. 28 is a Y-direction bending moment diagram of an analysis result of an example of a floorboard structure having a step.

FIG. 29 is a shear force diagram in the X direction as an analysis result for an example of a floorboard structure having a step.

FIG. 30 is a shear force diagram in the Y direction as an analysis result for an example of a floorboard structure having a step.

FIG. 31 is a fulcrum reaction force diagram of analysis results for an example of a floorboard structure having a step.

FIG. 32 is a diagram of the required number of X-direction upper end streaks as an analysis result for an example of a floorboard structure having a step.

FIG. 33 is a diagram showing the required number of X-direction bottom streaks as an analysis result for an example of a floorboard structure having steps.

FIG. 34 is a Y-direction upper end streak count diagram of an analysis result of an example of a floorboard structure having a step.

FIG. 35 is a diagram showing the required number of lower end streaks in the Y direction as an analysis result of an example of a floorboard structure having steps.

FIG. 36 is a flowchart illustrating a process of the hollow slab structure design device.

[Explanation of symbols]

1. Hollow slab structure design device 2 ... Processing unit 3 ... Storage unit 20 ... Dividing part 21 ... Distortion calculation unit (distortion calculation means) 22 ... Stress calculation unit (stress calculation means) 23 ... Deflection determination unit (first determination means) 24: Crack determination unit (second determination means) 25 ... Reinforcing bar amount calculation unit (reinforcing bar amount calculation means) 26 ... Shearing force judging section (third judging means)

Continuation of the front page (56) Reference JP-A-5-89209 (JP, A) Building Technology, Japan, Building Technology, April 1, 1984, August 1984, p. 55-56 (58) Fields surveyed (Int.Cl. ⁷ , DB name) G06F 17/50 E04B 5/43

Claims (7)

(57) [Claims] 1. A hollow slab in a hollow slab structure design device.
A computer that calculates the physical quantities used in the structural design of a lab.
A computer, an input device to which input data used for calculation of strain and stress generated in the hollow slab is input, and strain calculation means for calculating displacement and strain of the hollow slab based on the load applied to the hollow slab And a stress calculating means for calculating the stress generated in the hollow slab based on the strain of the hollow slab calculated by the strain calculating means.
Look, a processing unit comprising a central processing unit and a memory, the input data and the previous SL and a storage unit for storing <br/> the data calculated by the processing unit, thus the input data to the processing unit
Output device that outputs the result calculated from the data, and for each element of the hollow slab divided into multiple elements, the boundary
Depending on the conditions, the strain calculation means is: {P} = [K] {δ}, (where {P} is a load vector, [K] is a bending stiffness matrix [D] in consideration of orthogonal anisotropy. Using a relational expression of a load vector and a displacement vector that can be represented by a stiffness matrix, {δ}: displacement vector) obtained by using, the load vector and the stiffness matrix are set based on the input data, and the displacement is calculated. Further, the strain is calculated based on the calculated displacement, and the stress calculating unit is: {M} = [D] {ε}, (where, {M}: stress vector, [D]: orthogonal anisotropy Bending stiffness matrix considering, {ε}: Strain vector) Using the relational expression of stress vector and strain vector,
Based on the input data and the distortion calculated by the distortion calculating means, [Equation 2] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: Poisson's ratio, in particular, the coefficient k _y, the boundary element method Song calculated using
By lower moment hollow without the cross-sectional end portion of the slab horizontal displacement d _p and the medium
From the horizontal displacement d _y of the cross-section end of the empty slab , k _y =
A computer characterized by setting a value calculated as d _p / d _y , and calculating stress.
Ta . 2. The processing unit compares a value obtained by multiplying the maximum displacement of the hollow slab calculated by the strain calculating unit by a safety factor in consideration of creep with a reference value, and the safety related to the deflection of the hollow slab. The computer according to claim 1, further comprising first determining means for determining. 3. The maximum stress generated in the hollow slab calculated by the stress calculating means and Mc = k · (Fc) ^1/2 Z, where k: coefficient, Fc: concrete design strength, Z:
Comparing the cracking moment Mc shown in section modulus, claim, further comprising a second determination means for determining the safety of the cracking of the hollow slabs 1 or claim 2
The computer described in. 4. The storage unit further stores a stress concentration factor α related to the element shape of the reinforcing bar in the void orthogonal direction, and the processing unit determines the amount N of reinforcing steel required for the hollow slab and the stress concentration factor α. The computer according to any one of claims 1 to 3 , further comprising a reinforcing bar amount calculating means for calculating by using the reinforcing bar amount calculating means. 5. The processing unit comprises τ = Qx × (B / b) / (7/8 × (H- _dt )) in the void parallel direction, and τ = Qy / (7 / in the void orthogonal direction. 8x (H-φ)), where Qx: maximum shear force in the void parallel direction, Qy: maximum shear force in the direction orthogonal to the void, B: distance between void centers, b: distance between void outer diameters, H: floor thickness , Φ: Void diameter, _dt : Distance from the tensile edge of the floor to the barycenter of the reinforcing bar, and compare the shear stress τ with the allowable shear stress to determine the safety of the shear force generated in the hollow slab. The computer according to any one of claims 1 to 4 , further comprising third determining means for determining.
Ta . 6. A hollow slab in a hollow slab structure design device.
Calculate the strain and stress used in the structural design of a lab
Distortion, which consists of processing steps that a computer
A method for calculating stress, which is a cross section 2 in a void parallel direction in a slab having a hollow cross section.
The procedure of calculating the second moment I _x , the procedure of calculating the second moment of inertia I ₀ in the void parallel direction in the slab having no hollow cross section, and the second moment of area I _x being divided by I ₀ to obtain a coefficient k _x. And the boundary element method to calculate the horizontal displacement d _p of the cross-section end of the slab without a hollow cross section and the horizontal displacement d _y of the cross-section end of the hollow slab due to the bending moment. The calculation procedure and the horizontal displacement d _p of the cross-section end of the slab having no hollow section due to the bending moment are divided by the horizontal displacement d _y of the cross-section end of the hollow slab to calculate the coefficient k _y . And the mean of the coefficients k _x and k _y , and the mean value is taken as the coefficient k ₁ ,
Using the procedure of setting as k _xy and {P} = [K] {δ}, (where, {P}: load vector, [K]: bending stiffness matrix [D] considering orthogonal anisotropy Using the relational expression of the load vector and the displacement vector that can be represented by the required stiffness matrix, {δ}: displacement vector), the load vector and the stiffness matrix are set based on the input data, and the displacement is calculated. And a procedure for calculating strain based on the displacement, {M} = [D] {ε}, (where {M} is a stress vector, [D] is a bending stiffness matrix in which orthogonal anisotropy is considered, {Ε}: strain vector) Using the relational expression of the stress vector and strain vector,
Based on the input data and the distortion calculated by the distortion calculating means, [Equation 4] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: a step of calculating the Poisson's ratio, set the stress, the A strain stress calculation method comprising: 7. A recording medium in which a strain stress calculating program in a hollow slab structure designing device is recorded, wherein a cross section 2 in a void parallel direction in a slab having a hollow cross section.
The procedure of calculating the second moment I _x , the procedure of calculating the second moment of inertia I ₀ in the void parallel direction in the slab having no hollow cross section, and the second moment of area I _x being divided by I ₀ to obtain a coefficient k _x. And the boundary element method to calculate the horizontal displacement d _p of the cross-section end of the slab without a hollow cross section and the horizontal displacement d _y of the cross-section end of the hollow slab due to the bending moment. The calculation procedure and the horizontal displacement d _p of the cross-section end of the slab having no hollow section due to the bending moment are divided by the horizontal displacement d _y of the cross-section end of the hollow slab to calculate the coefficient k _y . And the mean of the coefficients k _x and k _y , and the mean value is taken as the coefficient k ₁ ,
Using the procedure of setting as k _xy and {P} = [K] {δ}, (where, {P}: load vector, [K]: bending stiffness matrix [D] considering orthogonal anisotropy Using the relational expression between the load vector and the displacement vector that can be represented by the required stiffness matrix, {δ}: displacement vector), the load vector and the stiffness matrix are set based on the input data, and the displacement is calculated, and further calculated. And a procedure for calculating strain based on the displacement, {M} = [D] {ε}, (where {M} is a stress vector, [D] is a bending stiffness matrix in which orthogonal anisotropy is considered, {Ε}: strain vector) Using the relational expression of the stress vector and strain vector,
Based on the input data and the distortion calculated by the distortion calculating means, [Equation 6] _{However, k x, k y, k} 1, k xy: coefficient considering the orthotropic, E: Young's modulus, t: a bed depth, [nu: a procedure of calculating the Poisson's ratio, set the stress computer A computer-readable recording medium recording a strain-stress calculation program to be executed by.