Support design method of strong support steel frame based on layer critical stiffness

Abstract

The invention discloses a support design method of a strong support steel frame based on layer critical stiffness, and relates to the technical field of building reinforcement. Comprising the steps of calculating the critical support stiffness of a frame column and drawing a nomogram of the critical support stiffness of the frame column, calculating the critical support stiffness of a shear type support steel frame layer of each floor, calculating the critical support cross-sectional area of the shear type support steel frame of each floor under the action of no horizontal load, and calculating the equivalent support area required for resisting the horizontal load. Calculating the critical support area of each floor frame under the action of a vertical load and a horizontal load; calculating the cross section area of a tension critical support single diagonal rod; and selecting the cross section model of a shear type support. The invention discloses a support design method of a strong support steel frame based on layer critical stiffness, provides design steps of a shear type strong support for the steel frame, and in the method, discloses a calculation formula of the structural layer critical support stiffness of the shear type support steel frame and provides a nomogram convenient for engineering application.

Description

Technical Field

[0001] This invention relates to the field of steel structure design technology, and specifically to a support design method for strongly supported steel frames based on the critical stiffness of the story. Background Technology

[0002] Compared to concrete structures, steel structures have smaller cross-sectional dimensions and slender members. Pure frames generally have relatively weak lateral stiffness, so bracing is often incorporated into engineering designs to improve overall lateral stiffness. Shear-braced steel frames are a commonly used structural form in steel structure engineering. The deformation of the bracing system is mainly shear deformation, commonly achieved through cross bracing and single bracing. Strongly braced shear-type steel frames have sufficiently high lateral stiffness to induce non-lateral buckling of the frame. The calculation length factor for columns in strongly braced frames is determined based on non-lateral buckling frame columns, and deflection is selected in the second-order effect calculation. Effects. How to design the bracing in a shear-braced steel frame to meet the requirements of strong bracing? In structural design, there is always a desire for easy-to-use analytical calculation formulas for strong bracing sections to avoid complex finite element calculations or to verify the correctness and reliability of finite element calculation results.

[0003] There are no clear criteria for distinguishing between strongly braced and weakly braced steel frames in the US steel structure code AISC 360-16, the European steel structure code EN 1993, and the Australian steel structure code AS4100. China's "Steel Structure Design Standard" GB 50017 provides a formula for identifying strongly braced steel frames. In the above formula: To support the lateral stiffness of the structural layers, , The first The sum of the axial compression stability bearing capacity of all frame columns in the story, calculated using the length coefficients for both non-swaying and swaying frame columns. The left side of this expression represents stiffness in N / mm or kN / cm, while the right side represents force in N or kN. The different dimensions on both sides make direct comparison inappropriate.

[0004] How can we design bracing to achieve displacement-free buckling in shear-braced steel frames, thus forming strong shear-braced steel frames? Existing research has proposed various design methods and criteria to address this issue. Current research analyzes the criteria for determining the elastoplastic instability mode of shear-braced frames and proposes a hypothetical load method for determining the stability of shear-braced frames. The main focus is on using finite element method software for strong bracing design and analysis. Strong shear-braced steel frames exhibit displacement-free buckling modes. Therefore, how should the shear bracing be designed to meet the strong bracing requirements? If the design is inaccurate, the bracing section may be too small to meet the strong bracing requirements, leading to an underestimation of the calculated length coefficient of the frame columns and the selection of displacement-free deflection in the second-order effect calculation. Effect without lateral displacement The effect, in turn, makes the calculation of second-order effects unsafe. Summary of the Invention

[0005] To this end, the present invention provides a support design method for a strongly supported steel frame based on the critical stiffness of the story. The method discloses the calculation formula of the critical support stiffness of the story, establishes the relationship between the cross section of the shear support member and the lateral stiffness, and gives the calculation formula of the critical support area of ​​the shear strongly supported steel frame under no horizontal load and with horizontal load.

[0006] To achieve the above-mentioned technical effects, the present invention is implemented through the following technical solution: A bracing design method for a strongly braced steel frame based on the critical stiffness of a story includes the following steps: S1. Calculate the critical support stiffness of the frame columns and draw the nomograph of the critical support stiffness of the frame columns: S11. The critical support stiffness of the frame column is calculated using the separated column method. The calculation formula is as follows: (1) In the formula, It is the ratio of the sum of the stiffness of the beams at the top of the column to the sum of the stiffness of the column. It is the ratio of the sum of the stiffness of the crossbeams at the bottom of the column to the sum of the stiffness of the column lines, that is... , , and The rotational spring stiffness for the top and bottom of the separating column. The height of the steel column. For the bending stiffness of the steel column, The dimensionless characteristic coefficient of the non-lateral-slip frame column can be calculated using the following formula: (2) S12, draw respectively Take the sum of 0.05-0.5 Take the critical support stiffness nomograph of the frame columns between 0.5 and 20; S2. Calculate the critical support stiffness of the shear-braced steel frame layer at each floor. It can be calculated using the following formula: (3) In the formula, For the first Layer The critical support stiffness of the root column can be calculated by equation (1) or obtained from the critical support stiffness nomograph of the frame column. It can be obtained by interpolation between two adjacent lines. For the first Layer Bending stiffness of the root column; For shear-type braced steel frame structures Total number of columns in the floor, For the first Layer upon layer; S3. Formula for calculating the critical support section area of ​​shear-braced steel frames on each floor under no horizontal load: S31, Calculation of shear-type braced steel frame The lateral stiffness of the layer bracing is calculated using the following formula: (4) In the formula, For the first The area of ​​the layer support, For the first The span of the layer support, The length of the supporting rod; Combining equations (3) and (4), we can obtain the first... Layer The area of ​​the support rods in the support span is used to calculate the first shear-type braced steel frame under no horizontal load. Critical support cross-sectional area of ​​the layer : (5) (6) In the formula, For the first Layer The area of ​​the support rod supporting the span. No. Layer Support span width, For the first Layer The length of the diagonal brace supporting the span, For the first The total number of spans supported by each layer; S4. Calculate the equivalent support area required to resist horizontal loads. The calculation formula is as follows: (7) In the formula, For the first The horizontal load on the columns of the multi-story frame For the first The yield strength of the layer support steel, The angle between the support rod and the crossbeam; S5. Calculate the vertical load. and horizontal load During operation, the critical support area of ​​the frame on each floor for: (8); S6. Calculate the cross-sectional area of ​​a critically tensioned single diagonal bar. The calculation formula is as follows: (9) In the formula, For the first The total number of single diagonal bracing members per layer; for cross bracing, two single diagonal bracing members are used. For the first The total number of single diagonal bracing members under tension in each layer, with only one cross bracing member being a diagonal bracing member under tension; For the first The length of the diagonal brace supporting the layer. To support the elastic modulus of the steel; S7. Based on the calculation results of step S6, select the required cross-sectional specifications for the shear support.

[0007] Furthermore, this invention also discloses the application of this method in the stability calculation of the calculated length factor of frame columns: when the cross-sectional area of ​​the shear brace is greater than the critical brace area, it belongs to a shear-type strong-braced steel frame, and buckling without lateral displacement occurs. In the stability calculation, the calculated length factor of the frame column without lateral displacement is selected, and in the second-order effect calculation, the deflection factor is selected. Effect; conversely, if it is less than the critical support area, lateral buckling occurs. In stability calculations, the calculation length factor for lateral buckling frame columns is selected, and in second-order effect calculations, the lateral buckling factor is selected. effect.

[0008] The beneficial effects of this invention are as follows: This invention discloses a bracing design method for strongly braced steel frames based on story critical stiffness, and provides design steps for shear-type strongly braced steel frames. The method discloses the calculation formula for the story critical bracing stiffness of shear-type strongly braced steel frame structures and provides a nomograph for easy engineering application. It also discloses the calculation formula for story critical bracing stiffness and establishes the relationship between the cross-section of shear-type braced members and lateral stiffness. Based on this, it provides calculation formulas for the critical bracing area of ​​shear-type strongly braced steel frames under no horizontal load and with horizontal load. The story critical bracing stiffness, as a key indicator for determining whether a shear-type strongly braced steel frame has lateral buckling or non-lateral buckling, can provide a direction for choosing between the calculation coefficient of non-lateral frame columns and the calculation length coefficient of lateral frame columns during stability calculations. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a design flowchart of a support design method for strongly supported steel frames based on the critical stiffness of the story. Figure 2 This is a simplified diagram of a shear-type strongly braced steel frame and its equivalent simplified diagram. Figure 2 a is a simplified diagram of a shear-type strong-braced steel frame. Figure 2 b is a simplified equivalent diagram of a shear-type strongly braced steel frame; Figure 3 This is a diagram showing the relationship between the area of ​​a single diagonal brace angle steel and the critical force of the structure. Figure 4 This is a nomograph of the critical support stiffness of the frame column when R1 is between 0.05 and 0.5. Figure 5 This is a nomograph of the critical support stiffness of the frame column when R1 takes values ​​of 0.5-20; Figure 6 This is a simplified diagram of a five-span, four-story shear-type strong-braced steel frame. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0012] (I) The concept of shear-type strong-braced steel frame mentioned in this invention When a pure steel frame structure experiences lateral instability, adding shear braces gradually increases the critical load-bearing capacity of the structure as the lateral stiffness provided by the braces increases. If the lateral stiffness provided by the shear braces is sufficiently large, it can lead to a situation like... Figure 2 The shear-type strong-braced steel frame shown in diagram a causes the frame to buckle in a non-lateral displacement mode. The bracing can be equivalent to horizontal springs at the floor beams, such as... Figure 2 As shown in b.

[0013] Pick Figure 2 Figure a shows a three-span, four-story supported steel frame with a story height and span of 4000mm. The frame beams and columns are all HW200×200×8×12, with a modulus of elasticity of [missing information]. The support system employs a single diagonal brace, with the frame bearing loads only at the beam-column joints. The load at each joint on each floor is 200kN. Assuming that each column simultaneously reaches its critical load upon instability, the angle steel specifications of the diagonal braces are varied. Elastic buckling calculations are performed using the finite element method (Ansys) to analyze the variation of the critical force in this supported steel frame. In the Ansys solution, BEAM188 elements are used for both columns and beams, and LINK1 elements are used for the cross-braces. All joints are rigidly connected.

[0014] Table 1 Comparative Analysis of Critical Bearing Capacities of Shear-Bound Steel Frames type Single diagonal angle steel specifications <![CDATA[Area of single supporting diagonal bar / mm 2 > Ansys Critical Force / N Critical force increment calculation formula Incremental Ratio Flexibility type ① Not set 0 1050 Lateral displacement ② L20x4 146 1698 ∣②-①∣ / ① 0.617 Lateral displacement ③ L30x4 228 2031 ∣③-①∣ / ① 0.934 Lateral displacement ④ L36x4 276 2219 ∣④-①∣ / ① 1.113 Lateral displacement ⑤ L45x4 349 2496 ∣⑤-①∣ / ① 1.377 Lateral displacement ⑥ L56x5 541 3172 ∣⑥-①∣ / ① 2.021 Lateral displacement ⑦ L63x5 614 3389 ∣⑦-①∣ / ① 2.228 Lateral displacement ⑧ L63x6 729 3588 ∣⑧-①∣ / ① 2.417 No lateral displacement ⑨ L90x8 1394 3589 ∣⑨-①∣ / ① 2.417 No lateral displacement ⑩ L150x10 2937 3590 ∣⑩-①∣ / ① 2.417 No lateral displacement As shown in Table 1, when no diagonal bracing is provided (Type ①), the lateral stiffness of the bracing is zero, classifying it as a free-slip steel frame. At this point, the critical load-bearing capacity of the structure is minimal, and lateral buckling occurs. As the specifications of the bracing angle steel are gradually increased, the area of ​​the bracing diagonal members and the lateral stiffness provided by the bracing also increase. From Types ② to ⑦, the critical load-bearing capacity of the braced steel frame gradually increases, and lateral buckling occurs in all cases. From Types ⑧ to ⑩, the area of ​​the bracing diagonal members increases fourfold, and the lateral stiffness of the bracing also increases significantly, but the critical load remains essentially unchanged, resulting in buckling without lateral buckling. To more intuitively illustrate the relationship between the changes in the single diagonal bracing and the critical load of the structure, a plot is drawn... Figure 3 .

[0015] from Figure 3It can be seen that as the area of ​​the supporting angle steel increases, the critical force of the structure also gradually increases. When the area of ​​the supporting angle steel increases to a certain extent, that is, when the support stiffness increases to a certain extent, further increasing the area of ​​the supporting angle steel or increasing the support stiffness cannot improve the critical bearing capacity of the structure. The shear-type supported steel frame also gradually transitions from lateral buckling to non-lateral buckling. At this time, the supported steel frame also becomes a strongly supported steel frame. The critical point at the end of the rising section corresponds to the critical load with lateral buckling, and the starting point at the front end of the platform section corresponds to the critical load without lateral buckling. The load values ​​at these two points are equal, and the corresponding support stiffness is called the critical support stiffness, and the corresponding supporting angle steel area is called the critical support area. When the stiffness provided by the shear brace is less than the critical brace stiffness, the structure experiences lateral buckling instability, and the calculation length factor of the lateral buckling frame column is used in the stability calculation. When it is greater than the critical brace stiffness, the structure experiences non-lateral buckling instability. At this time, it is a shear-braced steel frame, and the calculation length factor of the non-lateral buckling frame column is used in the stability calculation. Therefore, finding this critical stiffness point is of great significance and can be used as a criterion for determining whether the shear-braced steel frame will experience lateral buckling or non-lateral buckling.

[0016] (II) The present invention proposes a support design method for a strongly supported steel frame based on the critical stiffness of the story, such as... Figure 1 As shown, the specific steps include: S1. Calculate the critical support stiffness of the frame columns and draw the nomograph of the critical support stiffness of the frame columns: S11. The critical support stiffness of the frame column is calculated using the separated column method. The calculation formula is as follows: (1) In the formula, It is the ratio of the sum of the stiffness of the beams at the top of the column to the sum of the stiffness of the column. It is the ratio of the sum of the stiffness of the crossbeams at the bottom of the column to the sum of the stiffness of the column lines, that is... , , and The rotational spring stiffness for the top and bottom of the separating column. The height of the steel column. For the bending stiffness of the steel column, The dimensionless characteristic coefficient of the non-lateral-slip frame column can be calculated using the following formula: (2) S12, draw respectively Take the sum of 0.05-0.5 Take the critical support stiffness nomograph of the frame column between 0.5 and 20, as shown in the figure. Figure 4 and Figure 5 As shown; S2. Calculate the critical support stiffness of the shear-braced steel frame layer at each floor. It can be calculated using the following formula: (3) In the formula, For the first Layer The critical support stiffness of the root column can be calculated by equation (1) or obtained from the critical support stiffness nomograph of the frame column. It can be obtained by interpolation between two adjacent lines. For the first Layer Bending stiffness of the root column; For shear-type braced steel frame structures Total number of columns in the floor, For the first Layer upon layer; S3. Formula for calculating the critical support section area of ​​shear-braced steel frames on each floor under no horizontal load: S31, Calculation of shear-type braced steel frame The lateral stiffness of the layer bracing is calculated using the following formula: (4) In the formula, For the first The area of ​​the layer support, For the first The span of the layer support, The length of the supporting rod; Combining equations (3) and (4), we can obtain the first... Layer The area of ​​the support rods in the support span is used to calculate the first shear-type braced steel frame under no horizontal load. Critical support cross-sectional area of ​​the layer : (5) (6) In the formula, For the first Layer The area of ​​the support rod supporting the span. No. Layer Support span width, For the first Layer The length of the diagonal brace supporting the span, For the first The total number of spans supported by each layer; S4. Calculate the equivalent support area required to resist horizontal loads. The calculation formula is as follows: (7) In the formula, For the first The horizontal load on the columns of the multi-story frame For the first The yield strength of the layer support steel, The angle between the support rod and the crossbeam; S5. Calculate the vertical load. and horizontal load During operation, the critical support area of ​​the frame on each floor for: (8); S6. Calculate the cross-sectional area of ​​a critically tensioned single diagonal bar. The calculation formula is as follows: (9) In the formula, For the first The total number of single diagonal bracing members per layer; for cross bracing, two single diagonal bracing members are used. For the first The total number of single diagonal bracing members under tension in each layer, with only one cross bracing member being a diagonal bracing member under tension; For the first The length of the diagonal brace supporting the layer. To support the elastic modulus of the steel; S7. Based on the calculation results of step S6, select the required cross-sectional specifications for the shear support.

[0017] Furthermore, this invention also discloses the application of this method in the stability calculation of the calculated length factor of frame columns: when the cross-sectional area of ​​the shear brace is greater than the critical brace area, it belongs to a shear-type strong-braced steel frame, and buckling without lateral displacement occurs. In the stability calculation, the calculated length factor of the frame column without lateral displacement is selected, and in the second-order effect calculation, the deflection factor is selected. Effect; conversely, if it is less than the critical support area, lateral buckling occurs. In stability calculations, the calculation length factor for lateral buckling frame columns is selected, and in second-order effect calculations, the lateral buckling factor is selected. effect.

[0018] (III) Specific Calculation Examples In this embodiment, the following is selected: Figure 6 The five-span, four-story shear-braced steel frame building shown uses equilateral angle steel for the shear bracing, arranged in a combination of cross bracing and single diagonal bracing. The frame columns are 200x8mm square box-shaped columns. The top-floor beams are HN248×124×5×8, and the beams on other floors are HN300×150×6×9. The modulus of elasticity is... The first and second floors have a floor height of 3900mm, and the third and fourth floors have a floor height of 3000mm. The width of each span is 4800mm. The load is applied to the beam-column joints. The horizontal loads acting on each floor are shown in the figure. The support section design of the shear-type strong-braced steel frame of this building is carried out using the method of the present invention. The specific steps are as follows: (1) The critical support stiffness of the frame column is determined by the nomograph ( Figure 4 and Figure 5 As shown), the critical support stiffness of each column can be found, and the critical support stiffness of each floor can be obtained by substituting it into equation (3). The desired results are listed in Table 2. (2) Obtain the critical support area of ​​each floor under no horizontal load by equations (5) and (6). The equivalent support area required to resist the horizontal load can be obtained from equation (7). Substituting into equation (8), the critical support area under vertical and horizontal loads on each floor is obtained. The calculation results are listed in Table 2; (3) The cross-sectional area of ​​the critical tensile support single diagonal bar is obtained from equation (9). Based on this, the required cross-sectional specifications for shear supports are selected, and the results are listed in Table 2. For ease of comparison and analysis, the displacement of each floor of the building under load was calculated using the finite element method Ansys and elastic buckling analysis was performed. When using Ansys to solve the problem, BEAM188 elements were used for columns and beams, and LINK1 elements were used for cross bracing and single diagonal bracing. All nodes were rigidly connected. The relevant calculation results are listed in Table 2.

[0019] Table 2. Calculation process and results for the bracing design of shear-type strongly braced steel frame columns. floor Critical stiffness of edge column support Critical support stiffness of the central column Critical stiffness of layer / N / cm <![CDATA[Critical supporting area of layer / cm 2 > <![CDATA[Horizontal force equivalent support area / cm 2 > <![CDATA[Critical support surface for non-sway buckling / cm 2 > <![CDATA[Critical tension-bearing area of single angle steel for critical support / cm 2 > Equal angle steel specifications Slenderness ratio of single angle steel brace Ansys calculates inter-layer lateral displacement in cm. buckling mode 4 10.161 12.353 189.726 7.250 23.810 31.059 14.321 L100x8 184 0.891 No lateral displacement 3 10.289 12.661 193.773 7.404 47.619 55.023 26.278 L125x12 148 1.082 No lateral displacement 2 10.586 13.364 92.421 4.606 80.952 85.559 42.012 L160x14 126 1.738 No lateral displacement 1 19.723 21.647 156.081 7.779 114.286 122.065 59.736 L200x16 100 1.863 No lateral displacement Finite element analysis revealed that the inter-story lateral displacement of the shear-braced steel frame building was very small, meeting the requirements for a strong-braced steel frame, and that buckling without lateral displacement occurred, thus verifying the correctness and reliability of the algorithm of this invention.

[0020] In the description of this specification, references to terms such as "an embodiment," "example," and "specific example" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A support design method for a strong braced steel frame based on layer critical stiffness, characterized by, The method comprises the following steps: S1, calculating critical support stiffness of the frame column and drawing a critical support stiffness nomogram of the frame column: S11, calculating the critical support stiffness of the frame column by using the separation column method, and the calculation formula is as follows: c w T ' = ε 1 3 ε 1 2 - 36 R 1 R 2 t a n ε 1 - 6 R 1 + R 2 ε 1 / ε 1 3 t a n ε 1 + 36 R 1 R 2 2 t a n ε 1 / 2 - ε 1 t a n ε 1 + 6 R 1 + R 2 ε 1 t a n ε 1 - ε 1 （1） wherein is the ratio of the sum of the lateral beam stiffnesses at the top of the column to the sum of the column stiffnesses, is the ratio of the sum of the lateral beam stiffnesses at the bottom of the column to the sum of the column stiffnesses, i.e. , , and is the rotational spring stiffness of the column top and column bottom of the split column, is the height of the steel column, is the flexural stiffness of the steel column, is the dimensionless characteristic factor of the sway frame column, which can be calculated by the following formula: （2） S12, draw respectively Take 0.05-0.5 and Take 0.5-20 between the frame column critical support stiffness nomogram; S2, calculate the critical support stiffness of each floor shear-type support steel frame layer may be calculated according to the following formula: （3） In the formula, the critical support stiffness of the first floor column is calculated by formula (1) or is obtained from the nomogram of critical support stiffness of frame column, and is obtained by interpolation between two adjacent lines; the critical support stiffness of the first floor column is calculated by formula (1) or is obtained from the nomogram of critical support stiffness of frame column, and is obtained by interpolation between two adjacent lines; the bending stiffness of the first floor column; the total number of columns of the shear type support steel frame structure of the first floor is calculated by formula (2); the total number of columns of the shear type support steel frame structure of the first floor is calculated by formula (2); S3, calculating the critical support section area of each floor of the shear type support steel frame under the action of no horizontal load, and the calculation formula is as follows: S31、calculate the shear type support steel frame the layer support lateral stiffness, the calculation formula is: （4） wherein is the first area of the layer support, is the first span of the layer support, is the length of the support strut; Substitution of equation (3) into equation (4) gives the first floor critical support cross-sectional area supporting the support beam area and thus calculating the first floor critical support cross-sectional area : （5） （6） wherein is the number of stories is the number of stories is the area of the support strut across the support span, is the number of stories is the width of the support span is the number of stories is the length of the diagonal strut across the support span, is the number of stories is the length of the diagonal strut across the support span, is the number of stories is the total number of support spans S4, calculate the equivalent support area required to resist horizontal loads The formula is as follows: （7） wherein is the horizontal load on the is the yield strength of the steel material of the is the angle between the support rod and the crossbeam S5, the critical support area of each floor frame under vertical load and horizontal load is: ​ （8）； S6, calculate the critical support of the tensile monoclinal rod section area The calculation formula is as follows: （9） In the formula, Total number of diagonal bracings in the 1st Total number of diagonal bracings in the 1st Total number of diagonal bracings in the 1st Total number of diagonal bracings in the 1st Length of diagonal bracings in the 1st Length of diagonal bracings in the 1st Elastic modulus of the bracing steel S7, according to the calculation result of step S6, the required section size of the shear type support is selected.

2. The method for support design of a steel frame based on the critical stiffness of layers of a strong braced steel frame in the calculation of the stability of the frame column length coefficient, according to claim 1, characterized in that, When the shear type support sectional area is greater than the critical support area, it belongs to the shear type strong support steel frame, no lateral displacement buckling occurs, the lateral displacement frame column calculation length coefficient is selected for stability calculation, and the lateral displacement effect is selected for second-order effect calculation effect.

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