Method for calculating punching bearing capacity of composite beam and slab structure

Abstract

The invention discloses a method for calculating punching bearing capacity of a composite beam and slab structure. At present, a design method for punching bearing capacity of a composite beam plate structure does not exist. The punching bearing capacity of the composite beam plate is approximately equivalent to the sum of the shear bearing capacities of the longitudinal and transverse beams of the composite beam plate at the front, rear, left and right end parts of the reinforced concrete pile; punching bearing capacity of the composite beam plate structure is decomposed into punching bearing capacity (shear bearing capacity) of a front part, a rear part, a left part and a right part, and the punching bearing capacity of each part is matched with load borne by each part. According to the method, the problem that the calculation of the punching bearing capacity in different directions in the existing reinforced concrete specification (GB50010-2010) is not matched with the actual loading condition is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of reinforced concrete structures, and in particular relates to a method for calculating the shear bearing capacity of a composite beam-slab structure. Background Art

[0002] The karst phenomenon is strongly developed in the DK49+556.00-DK49+913.22 section of the Qianzhangchang Railway, with sinkholes, rising springs, etc. on the surface. Among the 45 drill holes that have been implemented, 10 drill holes have revealed caves, with the largest size of about 3.0m, a cave encounter rate of 22.2%, and a linear karst rate of 1.6%. It is an area with strong karst development, and the roadbed is filled up by 6-8m. In order to prevent foundation collapse, engineering measures need to be taken to deal with it. This section is adjacent to a Class I water source, and grouting cannot be used to treat the karst foundation; at the same time, this section has reserved railway connection points and reserved turnouts, and bridge structure treatment cannot be used. After comparing multiple technical options, such as Figure 1 , Figure 2 As shown in the figure, a pile-slab structure is proposed, with a reinforced concrete slab thickness of 1m, a reinforced concrete pile diameter of 1m, a pile longitudinal spacing of 7.0m, and a transverse spacing of 5.5m. After calculation, the shear force of the reinforced concrete pile on the reinforced concrete is 9172KN, which is greater than the shear bearing capacity of the reinforced concrete slab of 6614KN, and does not meet the requirements.

[0003] Regarding the problem that the shear bearing capacity of reinforced concrete slab is less than the shear force of reinforced concrete slab, such as Figure 1 , Figure 2 As shown in the figure, a pile-composite beam-slab structure is used. In the pile-composite beam-slab structure, longitudinal and transverse beams are set inside the reinforced concrete slab to resist concentrated shear force, which is equivalent to setting a "cross" reinforced node at the intersection of the pile top and the reinforced concrete slab. At present, there is no design method for the shear bearing capacity of composite beam-slab structure. Summary of the invention

[0004] In order to make up for the deficiencies of the prior art, the present invention provides a method for calculating the shear bearing capacity of a composite beam-slab structure, so as to calculate the shear bearing capacity of the composite beam-slab structure.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for calculating the punching shear bearing capacity of a composite beam-slab structure, characterized by:

[0007] The punching shear bearing capacity of the composite beam-slab is approximately equivalent to the sum of the shear bearing capacities of the longitudinal and transverse beams of the composite beam-slab at the front, rear, left and right ends of the reinforced concrete piles.

[0008] Furthermore, the shear bearing capacity of the composite beam-slab structure is decomposed into four parts: front, rear, left and right. The shear bearing capacity of each part should match the size of the load borne by each part.

[0009] Further, the method specifically includes the following steps:

[0010] Step 1: Using the pile as the fulcrum, divide the load-bearing area of ​​the longitudinal and transverse beams of the composite beam-slab according to the 45° line;

[0011] Step 2: Establish the mechanical calculation model of longitudinal and transverse beams, calculate the shear force of the transverse beam according to the four-span continuous beam with fixed support, and calculate the shear force of the longitudinal beam according to the multi-span continuous beam with fixed support;

[0012] Step 3: Establish a simplified calculation model of fixed support 1 span and calculate the shear force of longitudinal and transverse beams;

[0013] Step 4: Draw the shear force diagram of the longitudinal beam and transverse beam in the composite beam-slab structure;

[0014] Step 5: Determine the cross-sectional dimensions of the longitudinal and transverse beams and the configuration of stirrups according to the shear forces of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles;

[0015] Step 6: Arrange stirrups in two areas along the longitudinal direction of the beam. One area is the stirrup reinforcement density area, which is located near the pile ends on both sides. The shear force on the beam is large and the stirrup spacing is small; the other area is the stirrup general area, which is located near the middle of the beam span. The shear force on the beam is small and the stirrup spacing is large.

[0016] Step 7: Calculate the shear bearing capacity of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles based on their cross-sectional dimensions and the configuration of the stirrups.

[0017] Furthermore, the shear bearing capacity V of the longitudinal and transverse beams is calculated as follows:

[0018] V=α cv ×f t ×b×h0+f yv ×A sv ×h0 / s

[0019] α cv —The shear bearing capacity coefficient of inclined section concrete is 0.7 for this type of project;

[0020] h0—effective section height of longitudinal and transverse beams;

[0021] b—width of longitudinal and transverse beam sections;

[0022] f t —Design value of concrete axial tensile strength;

[0023] f yv—Design value of stirrup tensile strength;

[0024] A sv —The total cross-sectional area of ​​each leg of the stirrups arranged in the same section;

[0025] s—Stirrup spacing along the length of the member.

[0026] Beneficial effects of the present invention:

[0027] The punching shear failure of the composite beam-slab of the present invention is calculated according to the longitudinal and transverse beam modes, and the punching shear bearing capacity is the sum of the shear bearing capacities of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles. According to the distribution of loads and the longitudinal and transverse spacing of the piles, the shear forces in different directions are calculated by using the structural mechanics analysis method, and the structural section dimensions and steel bars in different directions are configured according to the shear forces, thereby solving the problem that the calculation of the shear bearing capacities in different directions in the current "Specification for Reinforced Concrete" (GB50010-2010) does not match the actual load conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a cross-sectional view of the pile-composite beam-slab structure of the present invention;

[0029] Figure 2 It is a plan view of the pile-composite beam-slab structure of the present invention;

[0030] Figure 3 This is a calculation diagram of the punching shear bearing capacity of the composite beam-slab of the present invention;

[0031] Figure 4 The calculation model of the longitudinal and transverse beams of the composite beam-slab of the present invention;

[0032] Figure 5 A simplified calculation model for the longitudinal beam of the composite beam slab of the present invention;

[0033] Figure 6 A simplified calculation model for the composite beam-slab crossbeam of the present invention;

[0034] Figure 7 This is the shear force diagram of the longitudinal and transverse beams of the composite beam-slab of the present invention;

[0035] Figure 8 The cross-sectional dimensions of the longitudinal and transverse beams of the composite beam-slab of the present invention and the arrangement of stirrups;

[0036] Fig. 9 This is a diagram of stirrup arrangement along the length of the beam according to the present invention. DETAILED DESCRIPTION

[0037] The present invention is described in detail below in conjunction with specific implementation modes.

[0038] The current "Specification for Reinforced Concrete" (GB50010-2010) calculates the punching shear bearing capacity of reinforced concrete slabs according to the equivalent inverted cone model. The present invention proposes that the punching shear bearing capacity of reinforced concrete slabs can be calculated according to the longitudinal and transverse beam models, which is helpful for technicians in this field to understand the essence of punching shear resistance and is beneficial for structural design.

[0039] The current "Reinforced Concrete Code" (GB50010-2010) calculates the shear resistance of reinforced concrete slabs according to the equivalent inverted cone model. The equivalent cylinder is divided into four parts: front, back, left, and right. Each part is a fan-shaped cylinder with a central angle of 90°. The total shear resistance of the equivalent cylinder is decomposed into the four parts of front, back, left, and right. The shear resistance of each part of the equivalent cylinder is equal. The distribution of load on the reinforced concrete slab is different. In different directions at the reinforced concrete pile, the shear force of the reinforced concrete pile on the reinforced concrete slab is different. On the side with large load distribution, the shear force of the reinforced concrete pile on the reinforced concrete slab must be large. Therefore, the current "Reinforced Concrete Code" (GB50010-2010) has the problem that the calculation of the shear resistance in different directions does not match the actual load conditions.

[0040] Pile-composite beam-slab structure Figure 1 , 2 as shown; Figure 3 As shown, the punching force of the reinforced concrete pile on the composite beam-slab is mainly borne by the longitudinal and transverse beams of the composite beam-slab, and the punching bearing capacity of the composite beam-slab is approximately equivalent to the sum of the shear bearing capacities of the longitudinal and transverse beams of the composite beam-slab at the front, rear, left and right ends of the reinforced concrete pile. The present invention specifically includes the following steps:

[0041] Step 1: When the two-way slab is subjected to vertical load, the adjacent supporting beams intersecting at right angles are divided into load-bearing ranges according to the 45° line; with the pile as the fulcrum and the longitudinal and transverse beams as the unit, the load-bearing areas of the composite beam-slab longitudinal and transverse beams are divided according to the 45° line; the transverse beam bears the triangular distributed linear load transmitted from the slab surface; the longitudinal beam bears the trapezoidal distributed linear load transmitted from the slab surface, such as Figure 4 As shown;

[0042] Step 2: With piles as fixed supports, establish mechanical calculation models for longitudinal and transverse beams, calculate the shear force of transverse beams according to the 4-span (span 5.5m) continuous beam with fixed supports, and calculate the shear force of longitudinal beams according to the multi-span (span 7.0m) continuous beam with fixed supports; the spans and loads of longitudinal and transverse continuous beams are consistent. Through structural mechanics analysis, the support bending moment, mid-span bending moment, and support shear force of longitudinal and transverse beams with 1 span, 5 spans, 10 spans, and 20 spans are calculated to be the same;

[0043] Step 3: To facilitate the calculation of internal forces, Figure 5 , Figure 6As shown, a simplified calculation model of fixed support for one span is established to calculate the shear forces of the longitudinal and transverse beams;

[0044] Step 4: Draw the shear force diagram of the longitudinal beam and transverse beam in the composite beam-slab structure, such as Figure 7 As shown;

[0045] Step 5: According to the shear force of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete pile, determine the cross-sectional dimensions of the longitudinal and transverse beams and the configuration of the stirrups, such as Figure 8 As shown;

[0046] Step 6: According to the shear force diagram of the longitudinal and transverse beams, stirrups are arranged in two zones along the longitudinal direction of the beam, such as Fig. 9 As shown in the figure, one area is the stirrup reinforcement density area, which is located near the pile ends on both sides. The shear force on the beam is large and the stirrup spacing is small; the other area is the stirrup general area, which is located near the mid-span of the beam. The shear force on the beam is small and the stirrup spacing is large; the specific stirrup diameter, spacing and length of the stirrup density area and the stirrup general area are determined according to calculation;

[0047] Step 7: Calculate the shear bearing capacity of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles based on their cross-sectional dimensions and the configuration of the stirrups.

[0048] According to the cross-sectional dimensions and stirrup configuration of the longitudinal and transverse beams at the ends of reinforced concrete piles, and in accordance with Article 6.3.4 of the Code for Reinforced Concrete (GB50010-2010):

[0049] The calculation method of the shear bearing capacity V of the longitudinal and transverse beams is as follows:

[0050] V=α cv ×f t ×b×h0+f yv ×A sv ×h0 / s

[0051] α cv —The shear bearing capacity coefficient of inclined section concrete is 0.7 for this type of project;

[0052] h0—effective section height of longitudinal and transverse beams;

[0053] b—width of longitudinal and transverse beam sections;

[0054] f t —Design value of concrete axial tensile strength;

[0055] f yv —Design value of stirrup tensile strength;

[0056] A sv —The total cross-sectional area of ​​each leg of the stirrups arranged in the same section;

[0057] s—Stirrup spacing along the length of the member.

[0058] The specific embodiments are as follows:

[0059] The following is a detailed description of the specific implementation steps and methods of the present invention in conjunction with the Qianzhangchang DK49+556.00~DK49+913.22 section karst foundation treatment test project, which specifically includes the following steps:

[0060] Step 1: The reinforced concrete piles in the middle share the area of ​​the reinforced concrete slab 37.5m 2 (7×5.5m), the design load is 9172KN, and the uniform load strength of the reinforced concrete slab is 244.6KN / m 2 ;

[0061] Step 2: Divide the load range according to the total 45° line of adjacent supporting beams intersecting at right angles when the two-way slab is subjected to vertical load; divide the load borne by the reinforced concrete slab into regions using piles as supports and longitudinal and transverse beams as units, and determine the force calculation model of longitudinal and transverse beams according to multi-span continuous beams with fixed supports, see Figure 4 , where l 01 =5m,l 02 =7m, p=1345.3KN / m;

[0062] l 01 -- Transverse spacing of reinforced concrete piles, l 02 -- longitudinal spacing of reinforced concrete piles, p-- linear loads of longitudinal and transverse beams, SV(Max)-- shear forces of longitudinal and transverse beams at the ends of reinforced concrete piles, l-- beam length within a single span;

[0063] Step 3: Calculation model of longitudinal beam shear force Figure 5 . Calculate and draw the shear force diagram of the longitudinal beam, see Figure 7 , the front end of the longitudinal beam l = 0m, SV = 2858.8KN, the middle part of the longitudinal beam l = 3.5m, SV = 0KN, the rear end of the longitudinal beam l = 7m, SV = -2858.8KN;

[0064] Step 4: Calculation model of shear force on beam Figure 6 . Calculate and draw the shear force diagram of the beam, see Figure 7 , l = 0m, SV = 1949.8KN at the left end of the beam, l = 2.75m, SV = 0KN at the middle of the beam, l = 5.5m, SV = -1949.8KN at the right end of the beam;

[0065] Step 5: The cross-sectional dimensions of the longitudinal and transverse beams are set to be 1.2m high and 1.0m wide. Figure 8. According to the shear force diagram of the longitudinal and transverse beams, stirrups are configured. The maximum shear force of the longitudinal beam at the pile end is 2858.8KN. Based on this, 6 stirrups with a diameter of 12mm and HRB400 are configured. The length of the stirrup reinforcement area is 1.5m, the stirrup spacing is 0.15m, the length of the stirrup general area is 4.0m, and the stirrup spacing is 0.2m. Fig. 9 The maximum shear force of the beam at the pile end is 1949.8KN. Based on this, 4 HRB400 stirrups with a diameter of 12mm are configured. The length of the stirrup reinforcement area is 1.5m, the stirrup spacing is 0.15m, the length of the stirrup general area is 2.5m, and the stirrup spacing is 0.2m.

[0066] Step 7: According to Article 6.3.4 of the Code for Reinforced Concrete (GB50010-2010), calculate the shear bearing capacity of the longitudinal and transverse beams in front, back, left and right of the reinforced concrete pile end.

[0067] According to the cross-sectional dimensions of the longitudinal beam at the front and rear ends of the pile and the stirrups configured, the following parameters can be obtained:

[0068] h0—effective cross-sectional height of longitudinal and transverse beams (1200-70) mm;

[0069] b—The width of the longitudinal and transverse beam sections is 1000mm;

[0070] f t —Concrete axial tensile strength design value, C40 concrete axial tensile strength design value 1.71 (N / mm 2 );

[0071] f yv — Design value of tensile strength of stirrups, design value of tensile strength of HRB400 stirrups 360 (N / mm 2 );

[0072] A sv — Six stirrups are arranged on the same section of the longitudinal beam, with a total cross-sectional area of ​​678mm 2 ;

[0073] s—The spacing of stirrups along the length of the longitudinal beam near the pile is 150 mm;

[0074] α cv —The shear bearing capacity coefficient of inclined section concrete is 0.7 for this type of project;

[0075] Shear bearing capacity of the longitudinal beam at the front and rear ends of the pile:

[0076] V 前 =V 后 =α cv ×f t ×b×h0+f yv ×A sv ×h0 / s

[0077] =0.7×1.71×1000×1130+360×678×1130 / 150

[0078] =3191.35KN

[0079] Similarly, the shear bearing capacity of the beam at the left and right ends of the pile is:

[0080] V 左 =V 右 =2578.43KN

[0081] Punching shear bearing capacity CQ of composite beam-slab structure:

[0082] CQ=V 前 +V 后 +V 前 +V 后 =3277+3277+2648+2648=11540KN;

[0083] V 左 -- Shear capacity of the beam on the left side of the reinforced concrete pile end, V 右 -- Shear capacity of the beam at the right side of the reinforced concrete pile end, V 前 -- Shear capacity of the longitudinal beam in front of the reinforced concrete pile end, V 后 --The shear bearing capacity of the longitudinal beam behind the end of the reinforced concrete pile, CQ--the punching shear bearing capacity of the composite beam-slab.

[0084] The shear bearing capacity of the composite beam-slab structure is 11540KN, which is greater than the shear force of reinforced concrete piles on the composite beam-slab 9172KN, meeting the shear resistance requirements.

[0085] The content of the present invention is not limited to the embodiments listed, and any equivalent changes made to the technical solution of the present invention by ordinary technicians in this field after reading the description of the present invention are covered by the claims of the present invention.

Claims

1. A method for calculating the shear bearing capacity of a composite beam-slab structure, characterized in that: The punching shear bearing capacity of the composite beam-slab is approximately equivalent to the sum of the shear bearing capacities of the longitudinal and transverse beams of the composite beam-slab at the front, rear, left and right ends of the reinforced concrete piles.

2. The method for calculating the punching shear bearing capacity of a composite beam-slab structure according to claim 1, characterized in that: The shear bearing capacity of the composite beam-slab structure is decomposed into four parts: front, rear, left and right. The shear bearing capacity of each part should match the size of the load borne by each part.

3. The method for calculating the punching shear bearing capacity of a composite beam-slab structure according to claim 2, characterized in that: The specific steps include: Step 1: Using the pile as the fulcrum, divide the load-bearing area of ​​the longitudinal and transverse beams of the composite beam-slab according to the 45° line; Step 2: Establish the mechanical calculation model of longitudinal and transverse beams, calculate the shear force of the transverse beam according to the four-span continuous beam with fixed support, and calculate the shear force of the longitudinal beam according to the multi-span continuous beam with fixed support; Step 3: Establish a simplified calculation model of fixed support 1 span and calculate the shear force of longitudinal and transverse beams; Step 4: Draw the shear force diagram of the longitudinal beam and transverse beam in the composite beam-slab structure; Step 5: Determine the cross-sectional dimensions of the longitudinal and transverse beams and the configuration of stirrups according to the shear forces of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles; Step 6: Arrange stirrups in two areas along the longitudinal direction of the beam. One area is the stirrup reinforcement density area, which is located near the pile ends on both sides. The shear force on the beam is large and the stirrup spacing is small; the other area is the stirrup general area, which is located near the middle of the beam span. The shear force on the beam is small and the stirrup spacing is large. Step 7: Calculate the shear bearing capacity of the longitudinal and transverse beams at the front, rear, left and right ends of the reinforced concrete piles based on their cross-sectional dimensions and the configuration of the stirrups.

4. The method for calculating the punching shear bearing capacity of a composite beam-slab structure according to claim 3, characterized in that: The calculation method of the shear bearing capacity V of the longitudinal and transverse beams is as follows: V=α cv ×f t ×b×h0+f yv ×A sv ×h0 / s α cv —The shear bearing capacity coefficient of inclined section concrete is 0.7 for this type of project; h0—effective section height of longitudinal and transverse beams; b—width of longitudinal and transverse beam sections; f t —Design value of concrete axial tensile strength; f yv —Design value of stirrup tensile strength; A sv —The total cross-sectional area of ​​each leg of the stirrups arranged in the same section; s—Stirrup spacing along the length of the member.

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