Calculation method for bearing capacity of reinforced skew beam joints under combined bending and shear action

Abstract

This application provides a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, including the following steps: S10, determining the shear span ratio λ of the independent secondary beam. a S20, based on the shear span ratio λ of the independent secondary beam. a The load-bearing capacity of the independent secondary beam is calculated; S30, the load-bearing capacity of the independent secondary beam is converted into the load-bearing capacity of the orthogonal beam joint, and the load-bearing capacity of the orthogonal beam joint is calculated; S40, the load-bearing capacity of the orthogonal beam joint is converted into the load-bearing capacity of the reinforced oblique beam joint; S50, the load-bearing capacity of the reinforced oblique beam joint is calculated; it can strengthen the unreinforced oblique beam joint into a reinforced oblique beam joint, thereby enhancing the load-bearing capacity at the acute angle between the second main beam and the second secondary beam, taking into account the beneficial effect of combined bending and shear action; it is applicable to the field of building design.

Description

Technical Field

[0001] This application relates to the technical field of building design, specifically to a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action. Background Technology

[0002] When public buildings are constructed above the throat area of ​​a subway station, skew beams are inevitably used. When the angle between the main beam and the secondary beam of the skew beam is between 30° and 60°, the following problems may occur: 1. There will be a large stress concentration at the acute angle between the main beam and the secondary beam, which will significantly reduce the bearing capacity at the acute angle of the main beam and the secondary beam joint; 2. At present, the bearing capacity of the section at the joint of the main beam and the secondary beam is not considered when calculating the bearing capacity, which will cause the maximum shear force and the maximum bending moment to occur at the same section, which poses a safety hazard.

[0003] To address the aforementioned issues, reinforcement is needed at the joints of the main and secondary beams to enhance the load-bearing capacity at the acute angles of these joints. Simultaneously, the load-bearing capacity of the reinforced joints needs to be calculated, taking into account the combined effects of bending and shear to improve safety. Currently, there is no existing method for calculating the load-bearing capacity of reinforced skew beam joints.

[0004] Currently, there are two common methods for reinforcing skew beams. The first method involves installing oblique haunches on the outside of the main beam and secondary beam joint, with vertical ribs welded to the sides of the haunches. Since both the oblique haunches and vertical ribs are located outside the joint, they are easily damaged, thus making the connection between the main beam and secondary beam unstable. The second method involves installing a large number of stirrups and longitudinal reinforcements inside both the main beam and secondary beam near the joint. While this can stabilize the connection between the main beam and secondary beam, it consumes more materials and is more expensive. Summary of the Invention

[0005] To address one of the aforementioned technical deficiencies, this application provides a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action.

[0006] According to a first aspect of the embodiments of this application, a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action is provided, comprising the following steps:

[0007] S10, calculate the shear span ratio λa of the independent secondary beam;

[0008] S20, the bearing capacity of the independent secondary beam is calculated based on the shear span ratio λa of the independent secondary beam;

[0009] S30 converts the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam joint, and calculates the bearing capacity of the orthogonal beam joint;

[0010] S40 converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint;

[0011] S50, calculate the bearing capacity of the reinforced skew beam joint. Preferably, step S20, which calculates the bearing capacity of the independent secondary beam based on the shear span ratio λa of the independent secondary beam, specifically includes:

[0012] S201, when the shear span ratio of the independent secondary beam is λ a Calculate the maximum bending moment M borne by the independent secondary beam at time 1. max And the corresponding shear force V1;

[0013] S202, when the shear span ratio of the independent secondary beam is λa2, calculate the maximum shear force V borne by the independent secondary beam. max And the corresponding bending moment M2.

[0014] More preferably, in step S201, when the shear span ratio of the independent secondary beam is λa1, the maximum bending moment M borne by the independent secondary beam is calculated. max And the corresponding shear force V1, specifically including:

[0015] S2011, Calculate the maximum bending moment M borne by the independent secondary beam. max ;

[0016]

[0017] In the formula: α0=ξ(1-0.5ξb), ξb=ρf yv / f c The reinforcement ratio ρ = As / bh0, fyv is the yield strength of the steel bars, fc is the compressive strength of the concrete in the compression zone, As is the area of ​​the tensile steel bars, b is the width of the independent secondary beam, and the effective height of the section h0 = section height - distance from the resultant point of the longitudinal steel bars to the near edge of the section.

[0018] S2012, calculate the corresponding shear force V1 borne by the independent secondary beam;

[0019]

[0020] In the formula: average compressive stress σ1=fc, height of the compression zone h1=1.1x1, relative height of the compression zone x1=ξbh0, The shear capacity provided by stirrups within a width range of 0.5h0, A sv s is the area of ​​the stirrups, and s is the spacing between the stirrups.

[0021] More preferably, in step S202, when the shear span ratio of the independent secondary beam is λa2, the maximum shear force V borne by the independent secondary beam is calculated. max and the corresponding bending moment M2; specifically including:

[0022] S2021, Calculate the maximum shear force V borne by the independent secondary beam. max ;

[0023]

[0024] In the formula: τ2max=0.2fc, x2=0.5h0, The shear support force provided for the stirrups within the h0 width range;

[0025] S2022, calculate the corresponding bending moment M2 borne by the independent secondary beam;

[0026] M2 = P2d2;

[0027] In the formula, the normal pressure provided by the concrete in the compression zone is P2 = Pn1, calculated according to the triangular distribution. σ2max=0.6fc, the amplification factor n1=1.2 for P2 when the normal stress curve is distributed, and the distance d2=h0-0.4x2 from the point of application of the resultant force to the tensile reinforcement.

[0028] Preferably, the orthogonal beam includes a first main beam and a first primary beam, and the intersection of the first main beam and the first primary beam is an orthogonal beam node;

[0029] Step S30 involves converting the bearing capacity of the independent secondary beams into the bearing capacity of the orthogonal beam joints, and calculating the bearing capacity of the orthogonal beam joints, specifically including:

[0030] S301, when the first main beam provides support with infinite stiffness to the first beam, the first beam has no displacement at the orthogonal beam joint, thus the bearing capacity of the independent secondary beam can be converted into the bearing capacity of the orthogonal beam joint.

[0031] S302, Calculate the shear span ratio of orthogonal beam nodes;

[0032] The shear span ratio λ of an orthogonal beam joint is: λ = M 1-1 / (V1-1h0);

[0033] In the formula, M1-δ and Vδ-c are the bending moment and shear force acting at the root section of the first beam, respectively.

[0034] Preferably, the reinforced skew beam includes an unreinforced skew beam and a reinforcing component. The unreinforced skew beam includes a second main beam and a second secondary beam. The reinforcing component is disposed between the second main beam and the second secondary beam, so that the unreinforced skew beam node at the intersection of the second main beam and the second secondary beam is reinforced into a reinforced skew beam node.

[0035] Step S40, which converts the bearing capacity of the orthogonal beam node into the bearing capacity of the reinforced skew beam node, specifically includes: correcting the shear span ratio at the root section of the second beam of the unreinforced skew beam until the equivalent shear span ratio λe is the same as the shear span ratio λ of the orthogonal beam node, so that the bearing capacity of the orthogonal beam node can be converted into the bearing capacity of the reinforced skew beam node.

[0036] The corrected equivalent shear span ratio λe is the shear span ratio of the second beam in the reinforced skew beam joint;

[0037] The equivalent shear span ratio λe is: λ e =βM2-2 / (V2-2h0);

[0038] In the formula, the oblique angle correction coefficient M2-2 and V2-2 are the bending moment and shear force acting at the root section of the second beam of the unreinforced skew beam, respectively. h0 is the effective height of the second beam section, and θ is the angle between the second main beam and the second beam that is less than 90°.

[0039] More preferably, step S50 involves calculating the bearing capacity of the reinforced skew beam joint; specifically including:

[0040] When λe>λ a At time 1, the bending moment at the joint of the reinforced skew beam is M = M max The shear force at the reinforced skew beam joint is:

[0041] When λa2<λe<λ al When the bending moment at the joint of the reinforced skew beam is: M = λ e Vh0, according to the linear expression: The shear force V at the joint of the reinforced skew beam can be calculated.

[0042] Preferably, the reinforcing assembly includes two reinforcing components centrally symmetrically arranged at both ends of the intersection of the second main beam and the second beam. Each reinforcing component includes: a haunch, a diagonal bar, at least one short stirrup, and at least one long stirrup. The haunch is located at the acute angle between the second main beam and the second beam. The diagonal bar is located between the haunch and the acute angle between the second main beam and the second beam, with one end of the diagonal bar connected to the second main beam and the other end connected to the second beam. The short stirrup is located between the root of the second beam and the second main beam. The long stirrup connects the second beam and the diagonal bar.

[0043] More preferably, the acute angle between the second main beam and the second secondary beam is 30°-60°; the end of the armhole that is close to the second main beam is 200mm away from the vertex of the acute angle, and the end of the armhole that is close to the second secondary beam is 400mm away from the vertex of the acute angle.

[0044] The method for calculating the bearing capacity of a reinforced skew beam under combined bending and shear action provided in this application takes into account the combined bending and shear action, solving the problem in the prior art where the maximum shear force and maximum bending moment occur at the same cross section, thus improving safety. The embodiment of this application converts the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam node, and then converts the bearing capacity of the orthogonal beam node into the bearing capacity of the reinforced skew beam node. This allows for convenient and accurate calculation of the bearing capacity at the reinforced skew beam node, transforming an unreinforced skew beam node into a reinforced skew beam node, thereby enhancing the bearing capacity of the reinforced skew beam. Attached Figure Description

[0045] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0046] Figure 1 A flowchart illustrating a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, provided in an embodiment of this application;

[0047] Figure 2 A schematic diagram of step S201 of a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, provided in an embodiment of this application;

[0048] Figure 3 A schematic diagram of step S202 of the method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action provided in an embodiment of this application;

[0049] Figure 4 This is a schematic diagram of the orthogonal beam provided in an embodiment of this application;

[0050] Figure 5 This is a structural schematic diagram of an unreinforced skew beam provided in an embodiment of this application;

[0051] Figure 6 A diagram showing the linear expression of the bearing capacity of a reinforced skew beam joint under combined bending and shear action, provided in an embodiment of this application;

[0052] Figure 7 This is a structural schematic diagram of the reinforced skew beam provided in an embodiment of this application;

[0053] Figure 8This is a schematic diagram of the unreinforced skew beam in a specific embodiment of the present application.

[0054] In the picture:

[0055] 10 is an orthogonal beam, 101 is the first main beam, 102 is the first beam, and 1-1 is the root of the first beam;

[0056] 20 is an unreinforced skew beam, 201 is the second main beam, 202 is the second beam, and 2-2 is the root of the second beam of the unreinforced skew beam;

[0057] 30 is a reinforcing component, 301 is a haunch, 302 is a diagonal bar, 303 is a short stirrup, and 304 is a long stirrup. Detailed Implementation

[0058] To make the technical solutions and advantages of the embodiments of this application clearer, the exemplary embodiments of this application will be described in further detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0059] Figure 1 A flowchart illustrating a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear loads, as provided in this application embodiment, is shown below. Figure 1 As shown, to address the above problems, this application provides a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, including the following steps:

[0060] S10, Calculate the shear span ratio λ of the independent secondary beam. a ;

[0061] S20, based on the shear span ratio λ of the independent secondary beam. a Calculate the load-bearing capacity of the independent secondary beams;

[0062] S30 converts the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam joint, and calculates the bearing capacity of the orthogonal beam joint;

[0063] S40 converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint;

[0064] S50, Calculate the bearing capacity of the reinforced skew beam joint. The method for calculating the bearing capacity of the reinforced skew beam joint under combined bending and shear action provided in this application takes into account the combined bending and shear action, solving the problem in the prior art where the maximum shear force and maximum bending moment occur at the same cross section, thus improving safety. In this embodiment, by converting the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam joint, and then converting the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint, the bearing capacity of the reinforced skew beam joint can be calculated conveniently and accurately. This reinforces the unreinforced skew beam joint into a reinforced skew beam joint, thereby enhancing the bearing capacity of the reinforced skew beam.

[0065] More specifically, under concentrated load, the shear span ratio of the most unfavorable stress section of the independent secondary beam is as follows: the concentrated load acts at the mid-span, and the most unfavorable stress occurs on both sides of the mid-span section. When L / h0 = 8, λ = 4; when L / h0 = 12, λ = 6. At this time, the shear span ratio of the independent secondary beam is between 4 and 6, which is taken as the upper limit range of the shear span ratio of the independent secondary beam.

[0066] More specifically, under uniformly distributed load, the shear span ratio of the most unfavorable stress section of an independent secondary beam fixed at both ends is as follows: the most unfavorable stress section is located on the inner side of the support. When L / h0 = 6, λ = 1.0; when L / h0 = 6, λ = 1.67. In this case, the shear span ratio of the independent secondary beam is between 1.0 and 1.67, which is taken as the lower bound of the shear span ratio of the independent secondary beam.

[0067] In summary, the shear span ratio λ of the independent secondary beam a The upper limit range is 4-6; the shear span ratio λ of the independent secondary beam. a The lower bound range is 1.0-1.67.

[0068] In this application, the upper and lower bounds of the shear span ratio of independent secondary beams are derived under both concentrated and uniformly distributed loads, so that the shear span ratio of independent secondary beams can be used to determine whether bending failure or shear failure occurs first.

[0069] Further, in step S20, based on the shear span ratio λ of the independent secondary beam... a The load-bearing capacity of the independent secondary beams is calculated, specifically including:

[0070] S201, when the shear span ratio of the independent secondary beam is λ a1 When calculating the maximum bending moment M borne by the independent secondary beam. max And the corresponding shear force V1;

[0071] S202, when the shear span ratio of the independent secondary beam is λ a2 When calculating the maximum shear force V borne by the independent secondary beam. max And the corresponding bending moment M2.

[0072] In this application, when the shear span ratio of the independent secondary beam is λ a1 When the shear span ratio is large, bending failure occurs first, and the maximum bending moment borne by the independent secondary beam can be calculated. When the shear span ratio of the independent secondary beam is λ... a2 When the shear span is relatively small, bending failure occurs first, and the maximum shear force borne by the independent secondary beam can be calculated at this time.

[0073] Specifically, when the shear span ratio of the independent secondary beam is λ a1 At this time: (1) Since the magnitude of concrete shear stress is small, its influence on the distribution of normal stress in concrete on the cross section is ignored; (2) Due to insufficient compressive strength fc of concrete in the compression zone, the independent secondary beam undergoes bending failure. At this time, both stirrups and tie bars enter the yield state; the plane section assumption is valid, the crack is a vertical crack, and the compressive stress of concrete in the compression zone is equivalent to a rectangular distribution, with an average compressive stress of σ1 = fc; (3) Ignoring the tensile properties of concrete in the compression zone, the concrete shear stress is distributed in a quadratic parabola, and the maximum shear stress is equal to 1.5 times the average shear stress; (4) Since the tensile reinforcement enters the yield state, and the cross section of the independent secondary beam is mainly bent, the dowel force provided by the tensile reinforcement and the interlocking force of the crack are ignored; (5) The maximum shear stress and the maximum compressive stress in the compression zone are not in the same position, and the strong circumferential action of the stirrups on the concrete in the compression zone after reaching the yield point will increase the compressive strength of the concrete, and the maximum shear stress τ in the compression zone 1max =0.1fc;

[0074] Figure 2 This is a schematic diagram of step S201 of a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, as provided in an embodiment of this application. Figure 2 As shown, further, in step S201, when the shear span ratio of the independent secondary beam is λa1, the maximum bending moment M borne by the independent secondary beam is calculated. max And the corresponding shear force V1, specifically including:

[0075] S2011, Calculate the maximum bending moment M borne by the independent secondary beam. max ;

[0076]

[0077] In the formula: α0=ξb(1-0.5ξb), ξb=ρfy v / fc, reinforcement ratio ρ=A s / bh0,fy v Where fc is the yield strength of the steel reinforcement, As is the area of ​​the tensile reinforcement, b is the width of the independent secondary beam, and the effective height of the section h0 = section height - distance from the resultant point of the longitudinal reinforcement to the nearest edge of the section.

[0078] S2012, calculate the corresponding shear force V1 borne by the independent secondary beam;

[0079]

[0080] In the formula: average compressive stress σ1=fc, height of the compression zone h1=1.1x1, relative height of the compression zone x1=ξbh0, The shear capacity provided for stirrups with a width of 0.5h0, where Asv is the stirrup area and s is the stirrup spacing.

[0081] The formula provided in this application can be used to quickly calculate the maximum bending moment and the corresponding shear force V1 when bending failure occurs, which facilitates subsequent calculations.

[0082] Specifically, when the shear span ratio of the independent secondary beam is λa2: (1) due to the small value of the bending moment, the concrete in the compression zone has not entered the plastic state; (2) the value of the shear force is large, the plane section assumption does not hold, and the normal stress on the section satisfies the linear expression: (3) Ignoring the tensile and shear properties of the concrete in the tension zone, the shear stress in the compression zone is distributed according to a quadratic parabola, and the maximum shear stress is equal to 1.5 times the average shear stress; (4) When the height of the compression zone x2 = 0.5h0, the shear bearing capacity of the section is the maximum, and the maximum shear stress τ in the compression zone is at this time. 2max =0.2fc, the corresponding maximum compressive stress σ 2max =0.6fc.

[0083] Figure 3 This is a schematic diagram of step S202 of a method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, as provided in an embodiment of this application. Figure 3 As shown, further, in step S202, when the shear span ratio of the independent secondary beam is λa2, the maximum shear force V borne by the independent secondary beam is calculated. max and the corresponding bending moment M2; specifically including:

[0084] S2021, Calculate the maximum shear force V borne by the independent secondary beam. max ;

[0085]

[0086] In the formula: τ2max=0.2fc, x2=0.5h0, The shear support force provided for the stirrups within the h0 width range;

[0087] S2022, calculate the corresponding bending moment M2 borne by the independent secondary beam;

[0088] M2 = P2d2;

[0089] In the formula, the normal pressure provided by the concrete in the compression zone is P2 = Pn1, calculated according to the triangular distribution. σ2max=0.6fc, the amplification factor n1=1.2 for P2 when the normal stress curve is distributed, and the distance d2=h0-0.4x2 from the point of application of the resultant force to the tensile reinforcement.

[0090] The formula provided in this application can be used to quickly calculate the maximum shear force and the corresponding bending moment M2 when shear failure occurs, which facilitates subsequent calculations.

[0091] Figure 4 This is a schematic diagram of the orthogonal beam provided in the embodiments of this application, such as... Figure 4 As shown, further, the orthogonal beam 10 includes a first main beam 101 and a first secondary beam 102, and the intersection of the first main beam 101 and the first secondary beam 102 is an orthogonal beam node. Step S30 converts the bearing capacity of the independent secondary beams into the bearing capacity of the orthogonal beam node, and calculates the bearing capacity of the orthogonal beam node, specifically including:

[0092] S301, when the first main beam 101 provides support for the first beam 102 with infinite stiffness, the first beam 102 has no displacement at the orthogonal beam node, thus converting the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam node.

[0093] S302, Calculate the shear span ratio of orthogonal beam nodes;

[0094] The shear span ratio λ of the orthogonal beam joint is: λ=M1-1 / (V1-1h0);

[0095] In the formula, M 1-1 and V 1-1 These are the bending moment and shear force acting at section 1-1 at the root of the first beam, respectively.

[0096] The above method can convert the bearing capacity of independent secondary beams into the bearing capacity of orthogonal beam joints, and accurately calculate the shear span ratio of orthogonal beam joints.

[0097] Figure 5 This is a schematic diagram of the unreinforced skew beam provided in an embodiment of this application, as shown below. Figure 5 As shown, further, the reinforced skew beam includes an unreinforced skew beam 20 and a reinforcing component 30. The unreinforced skew beam 20 includes a second main beam 201 and a second secondary beam 202. The reinforcing component 30 is disposed between the second main beam 201 and the second secondary beam 202, so that the unreinforced skew beam node at the intersection of the second main beam and the second secondary beam is reinforced into a reinforced skew beam node.

[0098] Step S40 converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint. Specifically, this includes: correcting the shear span ratio at section 2-2 at the root of the second beam of the unreinforced skew beam; when the equivalent shear span ratio λe is the same as the shear span ratio λ of the orthogonal beam joint, the bearing capacity of the orthogonal beam joint can be converted into the bearing capacity of the reinforced skew beam joint.

[0099] The corrected equivalent shear span ratio λe is the shear span ratio of the second beam in the reinforced skew beam;

[0100] The equivalent shear span ratio λe is: λ e =βM 2-2 / (V2-2h0);

[0101] In the formula, the oblique angle correction coefficient M2-2 and V2-2 are the bending moment and shear force acting at section 2-2 at the root of the second beam in the unreinforced skew beam, respectively. h0 is the effective height of section 202 of the second beam, and θ is the angle between the second main beam and the second beam that is less than 90°.

[0102] The above method can convert the bearing capacity of orthogonal beam joints into the bearing capacity of reinforced skew beam joints and calculate the corrected equivalent shear span ratio λe, which facilitates the subsequent calculation of the bearing capacity of reinforced skew beam joints.

[0103] Figure 6 A diagram illustrating the linear expression of the bearing capacity of a reinforced skew beam joint under combined bending and shear action, provided in an embodiment of this application, is shown below. Figure 6 As shown, further, step S50 calculates the bearing capacity of the reinforced skew beam joint; specifically including:

[0104] When λe>λ a At time 1, the bending moment at the joint of the reinforced skew beam is M = M max The shear force at the reinforced skew beam joint is:

[0105] When λa2<λe<λ a1 When the bending moment at the joint of the reinforced skew beam is: M = λ e Vh0, according to the linear expression: The shear force V at the joint of the reinforced skew beam can be calculated.

[0106] In this application, based on the different equivalent shear span ratios, that is, the different shear span ratios of the second beam in the reinforced skew beam joint, the bending moment and shear force that the section can withstand under different conditions can be calculated. The calculation is faster and more accurate, thus improving the safety of the reinforced skew beam joint.

[0107] It should be noted that, in calculating the bearing capacity of the reinforced skew beam joint in this application, due to λe <λ a2 Diagonal compression failure may occur, which does not meet the specifications. Therefore, only the bearing capacity of the reinforced skew beam joints outside the specified range is calculated.

[0108] Figure 7 This is a structural schematic diagram of the reinforced skew beam provided in the embodiments of this application, as shown below. Figure 7 As shown, the reinforcing component 30 further includes two reinforcing parts centrally symmetrically arranged at both ends of the intersection of the second main beam 201 and the second beam 202. Each reinforcing part includes: a armhole 301, a diagonal bar 302, at least one short stirrup 303, and at least one long stirrup 304. The armhole 301 is located at the acute angle between the second main beam 201 and the second beam 202. The diagonal bar 302 is located between the armhole 301 and the acute angle between the second main beam 201 and the second beam 202, and one end of the diagonal bar 302 is connected to the second main beam 201, and the other end of the diagonal bar 302 is connected to the second beam 202. The short stirrup 303 is located between the root 2 of the second beam and the second main beam 201. The long stirrup 304 is connected between the second beam 202 and the diagonal bar 302.

[0109] Specifically, when there are multiple short stirrups, they are arranged in parallel to each other; when there are multiple long stirrups, they are arranged in parallel to each other.

[0110] Furthermore, the acute angle between the second main beam 201 and the second beam 202 is 30°-60°; the end of the armhole 301 that is close to the second main beam 201 is 200mm away from the vertex of the acute angle, and the end of the armhole 301 that is close to the second beam 202 is 400mm away from the vertex of the acute angle.

[0111] In this application, the unreinforced skew beam joint was reinforced using reinforcing components. Short stirrups were used to strengthen the root of the secondary beam; the connection between the secondary beam and the second main beam was made more stable through the use of haunches and diagonal reinforcements; and the stability of the connection structure between the secondary beam and the second main beam was further enhanced by connecting long stirrups between the secondary beam and the diagonal reinforcements. The reinforced skew beam joint has increased load-bearing capacity and is safer than the unreinforced skew beam joint.

[0112] In this application, a reinforcing component is used to connect the interior of the second main beam and the interior of the second beam near the node, and a haunch is provided on the outside of the node to make the connection between the second main beam and the second beam more stable. This solves the problem of unstable connection structure between the second main beam and the second beam caused by the setting of inclined haunch plates and vertical ribs on the outside of the node of the second main beam and the second beam in the prior art, and does not require a large amount of material, thus effectively saving costs.

[0113] Figure 8This is a schematic diagram of the structure of the unreinforced skew beam in a specific embodiment of this application, as shown below. Figure 8 As shown, specifically, taking a concrete skew beam joint with concrete grade C40 and HRB400 grade steel reinforcement as an example, the bearing capacity of the reinforced skew beam joint under the above-mentioned combined bending and shear action is calculated using the above-mentioned calculation method.

[0114] Specifically, the secondary beam of the skew beam is 400mm wide and 500mm high, with an effective height h0 = 0.465m; the reinforcing bars are 5 steel bars with a diameter of 28mm, and the stirrups are 4-legged steel bars with a diameter of 10mm, spaced 400mm apart; the acute angle between the second main beam and the secondary beam is 60°; two loads N of the same magnitude act on both sides of the secondary beam node, with the loading point 100mm from the edge.

[0115] More specifically, the concrete compressive strength fc = 26.8 N / mm². 2 The beam width b = 0.4m, the stirrup spacing s = 0.2m, and the steel yield strength fyv = 400N / mm². 2 The radius of the stirrup Asv = 0.005m, and the radius of the tensile reinforcement A s =0.014m;

[0116] According to the calculation formula λe=βM / (Vh0) provided in this application, we can obtain:

[0117]

[0118] In the formula: L is the distance from the point of application of the concentrated load to the center of the node; Le is the distance from the center of the node to the root of the secondary beam.

[0119] S10, calculate the shear span ratio λa of the independent secondary beam as: λ a1 =4.57, λa2 = 1.15;

[0120] S20, the bearing capacity of the independent secondary beam is calculated based on the shear span ratio λa of the independent secondary beam;

[0121] When the shear span ratio of the independent secondary beam is λa1 = 4.57, calculate the maximum bending moment M borne by the independent secondary beam. max And the corresponding shear force V1;

[0122] The maximum bending moment is: M max =501.7kN·m, and the corresponding shear force is: V1=236.3kN;

[0123] When the shear span ratio of the independent secondary beam is λa2 = 1.15, calculate the maximum shear force V borne by the independent secondary beam. max and the corresponding bending moment M2;

[0124] The maximum shear force is: Vm ax =624.3kN, and the corresponding bending moment is: M2 =333.8kN·m.

[0125] S30 converts the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam joint, and calculates the bearing capacity of the orthogonal beam joint;

[0126] S40 converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint;

[0127] λ e =βM 2-2 / (V2-2h0):

[0128] S50, calculate the bearing capacity of the reinforced skew beam joint;

[0129] Since λa2<λe<λ a1 The bending moment of the reinforced skew beam joint is: M = 409.5 kN·m, according to the linear expression: The shear force V at the reinforced skew beam joint can be calculated: V = 449.3 kN.

[0130] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0131] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0132] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0133] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0134] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action, characterized in that, Includes the following steps: S10, Calculate the shear span ratio λ of the independent secondary beam. a ; S20, based on the shear span ratio λ of the independent secondary beam. a Calculate the load-bearing capacity of the independent secondary beams; S30 converts the bearing capacity of the independent secondary beam into the bearing capacity of the orthogonal beam joint, and calculates the bearing capacity of the orthogonal beam joint; S40 converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint; S50, calculate the bearing capacity of the reinforced skew beam joint; The reinforced skew beam includes an unreinforced skew beam (20) and a reinforcing component (30). The unreinforced skew beam (20) includes a second main beam (201) and a second secondary beam (202). The reinforcing component (30) is disposed between the second main beam (201) and the second secondary beam (202), thereby reinforcing the unreinforced skew beam node at the intersection of the second main beam and the second secondary beam into a reinforced skew beam node. Step S40, which converts the bearing capacity of the orthogonal beam joint into the bearing capacity of the reinforced skew beam joint, specifically includes: The shear span ratio at the root section of the second beam of the unreinforced skew beam is corrected; the correction is made to the equivalent shear span ratio λ. e When the shear span ratio λ of the orthogonal beam joint is the same, the bearing capacity of the orthogonal beam joint can be converted into the bearing capacity of the reinforced skew beam joint. Corrected equivalent shear span ratio λ e This refers to the shear span ratio of the second beam in a reinforced skew beam; Equivalent shear span ratio λ e for: ; In the formula, the oblique angle correction coefficient M 2-2 and V 2-2 These are the bending moment and shear force acting at the root section of the second beam of the unreinforced skew beam, respectively; h0 is the effective height of the section of the second beam (202); and θ is the angle between the second main beam and the second beam that is less than 90°. Step S50, calculating the bearing capacity of the reinforced skew beam joint, specifically includes: When λ e >λ a1 At that time, the bending moment M at the reinforced skew beam joint is M = M max The shear force at the reinforced skew beam joint is: ; When λ a2 <λ e <λ a1 When the bending moment at the joint of the reinforced skew beam is: M = λ e Vh0, according to the linear expression: The shear force V at the joint of the reinforced skew beam can be calculated.

2. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action as described in claim 1, characterized in that, In step S20, based on the shear span ratio λ of the independent secondary beam... a The load-bearing capacity of the independent secondary beams is calculated, specifically including: S201, when the shear span ratio of the independent secondary beam is λ a1 When calculating the maximum bending moment M borne by the independent secondary beam. max And the corresponding shear force V1; S202, when the shear span ratio of the independent secondary beam is λ a2 When calculating the maximum shear force V borne by the independent secondary beam. max And the corresponding bending moment M2.

3. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action according to claim 2, characterized in that, In step S201, when the shear span ratio of the independent secondary beam is λ a1 When calculating the maximum bending moment M borne by the independent secondary beam. max And the corresponding shear force V1, specifically including: S2011, Calculate the maximum bending moment M borne by the independent secondary beam. max ; ； In the formula: , reinforcement ratio , For the yield strength of the steel reinforcement, A represents the compressive strength of the concrete in the compression zone. s Where b is the area of ​​the tensile reinforcement, b is the width of the independent secondary beam, and h0 is the effective height of the section = section height - distance from the resultant point of the longitudinal reinforcement to the nearest edge of the section. S2012, calculate the corresponding shear force V1 borne by the independent secondary beam; ； Where: average compressive stress Height of the pressure zone relative pressure zone height , The shear capacity provided for stirrups within a width range of 0.5 h0. s is the area of ​​the stirrups, and s is the spacing between the stirrups.

4. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action as described in claim 3, characterized in that, In step S202, when the shear span ratio of the independent secondary beam is λ a2 When calculating the maximum shear force V borne by the independent secondary beam. max and the corresponding bending moment M2; specifically including: S2021, Calculate the maximum shear force V borne by the independent secondary beam. max ; ； In the formula: , , The shear support force provided for the stirrups within the h0 width range; S2022, calculate the corresponding bending moment M2 borne by the independent secondary beam; ； In the formula, the normal pressure provided by the concrete in the compression zone is... Normal force calculated according to a triangular distribution , The amplification factor n1 = 1.2 for P2 when the normal stress curve is distributed, and the distance from the point of application of the resultant force to the tensile reinforcement is... .

5. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action according to claim 4, characterized in that, The orthogonal beam (10) includes a first main beam (101) and a first beam (102), and the intersection of the first main beam (101) and the first beam (102) is an orthogonal beam node; Step S30 involves converting the bearing capacity of the independent secondary beams into the bearing capacity of the orthogonal beam joints, and calculating the bearing capacity of the orthogonal beam joints, specifically including: S301, when the first main beam (101) provides support for the first beam (102) with infinite stiffness, the first beam (102) has no displacement at the orthogonal beam node, and the bearing capacity of the independent secondary beam can be converted into the bearing capacity of the orthogonal beam node. S302, Calculate the shear span ratio of orthogonal beam nodes; The shear span ratio λ of the orthogonal beam joint is: ; In the formula, M 1-1 and V 1-1 These are the bending moment and shear force acting at the (1-1) section at the root of the first beam, respectively.

6. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action as described in claim 5, characterized in that, The reinforcing component (30) includes two reinforcing parts centrally symmetrically arranged at both ends of the intersection of the second main beam (201) and the second beam (202). Each reinforcing part includes: a armhole (301), a diagonal bar (302), at least one short stirrup (303), and at least one long stirrup (304). The armhole (301) is located at the acute angle between the second main beam (201) and the second beam (202). The diagonal bar (302) is located between the armhole (301) and the acute angle between the second main beam (201) and the second beam (202), and one end of the diagonal bar (302) is connected to the second main beam (201), and the other end of the diagonal bar (302) is connected to the second beam (202). The short stirrups (303) are placed between the root (2) of the second beam and the second main beam (201); the long stirrups (304) are connected between the second beam (202) and the diagonal bars (302).

7. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action as described in claim 6, characterized in that, The acute angle between the second main beam (201) and the second beam (202) is 30°-60°.

8. The method for calculating the bearing capacity of a reinforced skew beam joint under combined bending and shear action as described in claim 7, characterized in that, The end of the armpit (301) that is close to the second main beam (201) is 200mm away from the vertex of the acute angle, and the end of the armpit (301) that is close to the second beam (202) is 400mm away from the vertex of the acute angle.

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