A method and computer device for calculating the stiffness of the negative moment zone of a steel-concrete composite beam

Abstract

The present invention relates to the field of calculation of negative moment zone stiffness, and specifically to a method and computer device for calculating the stiffness of a steel-concrete composite beam in the negative moment zone, which improves the accuracy of the calculation of the stiffness of the negative moment zone. The present invention provides a method for calculating the stiffness of a steel-concrete composite beam in the negative moment zone, including determining the section moment of inertia of the negative moment zone of the composite beam based on a linear stiffness reduction method, calculating the deflection of the composite beam in the negative moment zone considering concrete cracking, calculating the additional deflection of the composite beam in the negative moment zone considering interface slip, calculating the total deflection of the composite beam in the negative moment zone, and finally calculating the stiffness of the composite beam in the negative moment zone. The present invention is applicable to the calculation of the stiffness of a steel-concrete composite beam in the negative moment zone.

Description

Technical Field

[0001] The invention relates to the field of negative moment zone stiffness calculation, and in particular to a negative moment zone stiffness calculation method and a computer device for a steel-concrete composite beam. Background Art

[0002] The steel-concrete composite continuous beam is a low-carbon bridge construction structure suitable for assembly. According to the stress state of the composite continuous beam, it includes positive moment zone and negative moment zone. For the positive moment zone of the steel-concrete composite continuous beam structure, the steel-concrete composite beam fully utilizes the material advantages of steel and concrete. For the negative moment zone of the steel-concrete composite continuous beam structure, the steel beam is compressed and the concrete is tensile, and the concrete is prone to cracking. In addition, the interface slip between the steel beam and the concrete slab causes the cross-sectional stiffness of the composite beam to decrease. The determination of the stiffness of the negative moment zone of the composite beam is the premise for the deformation calculation of the continuous beam. The current calculation method is to take the bending stiffness within the 15% span range of the mid-span support of the continuous beam as the stiffness of the cracked section, and the bending stiffness of the remaining part is still taken as the stiffness when it is not cracked. This method causes a sudden change in the cross-sectional stiffness, and does not consider the influence of cross-sectional slip, so the calculation accuracy is not high. The invention provides a method for calculating the stiffness of a composite beam in a negative moment zone, which can simultaneously consider the influence of concrete cracking and interface slippage, has accurate calculation, and can be used for calculating the stiffness of a composite continuous beam in a negative moment zone. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method and a computer device for calculating the stiffness of a steel-concrete composite beam in a negative moment zone, thereby improving the accuracy of the calculation of the stiffness of the negative moment zone.

[0004] The present invention adopts the following technical solutions to achieve the above-mentioned purpose. In a first aspect, the present invention provides a method for calculating the stiffness of a steel-concrete composite beam in a negative moment zone, comprising:

[0005] S1. Determine the section inertia moment I of the composite beam in the negative moment zone based on the linear stiffness reduction method m ;

[0006] The moment of inertia of the section in the negative moment zone of the composite beam is linearly reduced. The moment of inertia of the support section after concrete cracking is I eff , the section moment of inertia at the inflection point is the initial moment of inertia I 0 , the moment of inertia between the two points is linearly interpolated, then the section moment of inertia is:

[0007]

[0008] Where M cr is the cracking moment, M is the actual bending moment of the section, I 0 is the converted moment of inertia of the entire section before concrete cracking, I crIn order to consider only the section moment of inertia of the steel beam and reinforcement, a represents the distance from the middle support to the load application point, and b represents the distance between the two supports at the bottom of the steel beam;

[0009] S2. Calculate the deflection f(x) of the negative moment zone of the composite beam considering concrete cracking;

[0010] Considering the boundary conditions, the deflection of the negative moment zone of concrete cracking is obtained as follows:

[0011]

[0012] In the formula E s is the elastic modulus of the steel beam;

[0013] S3. Calculate the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip;

[0014]

[0015] in

[0016]

[0017] Where, d cs A is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab. c and A s are the cross-sectional areas of the concrete slab and the steel beam, E c and E s are the elastic moduli of concrete and steel beam, I c and I s are the section inertia moments of the concrete slab and the steel beam, respectively; h is the section height; K is the shear stiffness of a row of studs; p is the spacing between two rows of studs; λ is the relative stiffness coefficient; A 1 , A 2 , B 1 , B 2 、E 1 、E 2 、E 3 , E4 is the calculation coefficient;

[0018] S4. Calculate the total deflection f of the composite beam in the negative moment zone t (x);

[0019] f t (x) = deflection f(x) considering concrete cracking + additional deflection Δf(x) caused by interface slip;

[0020] S5. Calculate the stiffness of the composite beam in the negative moment zone;

[0021] The stiffness B is:

[0022] In the formula, f t (a) is the total deflection of the outrigger, calculated according to step S4.

[0023] Furthermore, when the mid-span of the inverted simply supported beam is subjected to concentrated load, the calculation method of the section inertia moment in S1 is replaced by the following formula:

[0024]

[0025] Furthermore, when the mid-span of the inverted simply supported beam is subjected to concentrated load, the calculation method of the deflection in the negative moment zone considering concrete cracking obtained by solving the boundary conditions in S2 is replaced by the following formula:

[0026]

[0027] Furthermore, when the mid-span of the inverted simply supported beam is subjected to concentrated load, the calculation method of the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip in S3 is replaced by the following formula:

[0028]

[0029] In a second aspect, the present invention provides a computer device, including a memory, wherein the memory stores program instructions, and when the program instructions are executed, the method for calculating the stiffness of the negative moment zone of the steel-concrete composite beam as described above is executed.

[0030] The beneficial effects of the present invention are:

[0031] In order to make the stress state of the test beam closer to that of an actual bridge, the present invention is based on a steel-concrete composite cantilever beam, applies a concentrated load on the concrete surface of the cantilever end, and arranges a support at the bottom of the steel beam, and proposes a stiffness calculation method for the composite beam under the factors of concrete cracking in the negative bending moment zone and interface slip between the steel beam and the concrete slab. The factors of concrete cracking and interface slip are taken into account in the calculation. At the same time, a stiffness calculation method for the composite beam under the factors of concrete cracking in the negative bending moment zone and interface slip between the steel beam and the concrete slab is proposed when the mid-span is subjected to a concentrated load on a simply supported beam. The factors of concrete cracking and interface slip are taken into account in the calculation, which greatly improves the accuracy of the stiffness calculation in the negative bending moment zone. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A mechanical calculation model of a steel-concrete composite cantilever beam provided in an embodiment of the present invention;

[0033] Figure 2 Another mechanical calculation model of a steel-concrete composite cantilever beam provided in an embodiment of the present invention;

[0034] Figure 3It is a schematic diagram of the internal force distribution of the micro-segment length of the extended end of the analysis model provided by an embodiment of the present invention;

[0035] Figure 4 It is a schematic diagram comparing the deflection test value and the calculated value when the end of the cantilever composite beam provided by the embodiment of the present invention is loaded with 140 kN;

[0036] Figure 5 is a schematic diagram of the relationship between deflection and movable support distance under different conditions provided by an embodiment of the present invention;

[0037] Figure 6 It is a schematic diagram of comparison between calculated values ​​and test values ​​before yielding of a steel beam provided by an embodiment of the present invention;

[0038] Figure 7 It is a schematic diagram comparing the calculated values ​​and experimental values ​​of deflection and load provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0040] The present invention is based on Figure 1 The mechanical calculation model of the steel-concrete composite cantilever beam shown in the figure provides a method for calculating the stiffness of the negative moment zone of the steel-concrete composite beam taking into account the factors of concrete cracking and interface slip. Figure 1 In the equation, a represents the distance from the middle support to the load application point, b represents the distance between the two supports at the bottom of the steel beam, and F represents the applied concentrated load. The steps of this method are as follows:

[0041] Step S1: Determine the section moment of inertia I of the negative moment region of the composite beam based on the linear stiffness reduction method m

[0042] The moment of inertia of the section in the negative moment zone of the composite beam is linearly reduced. The moment of inertia of the support section after concrete cracking is I eff , the section moment of inertia at the inflection point is the initial moment of inertia I 0 , the moment of inertia between the two points is linearly interpolated, and the section moment of inertia of the test beam is:

[0043]

[0044] Where M cr is the cracking moment, M is the actual bending moment of the section, I 0 is the converted moment of inertia of the entire section before concrete cracking, I cr Only the section moment of inertia of steel beams and reinforcements is considered.

[0045] Step S2: Calculate the deflection f(x) of the negative moment zone of the composite beam considering concrete cracking

[0046] Considering the boundary conditions, the deflection of the negative moment zone of concrete cracking is obtained as follows:

[0047]

[0048] In the formula I eff with I 0 Calculated in step S1, E s is the elastic modulus of the steel beam.

[0049] Step S3: Calculate the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip

[0050] Take the micro-segment length dx of the extended end of the analysis model, and its internal force distribution is shown in Figure 3 shown.

[0051] Under the premise of meeting the basic settings and considering the boundary conditions, we get:

[0052]

[0053]

[0054] Where, d cs A is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab. c and A s are the cross-sectional areas of the concrete slab and the steel beam, E c and E s are the elastic moduli of concrete and steel beam, I c and I s are the section moments of inertia of the concrete slab and the steel beam, respectively. h is the section height, K is the shear stiffness of a row of studs, p is the spacing between two rows of studs, λ is the relative stiffness coefficient, and A 1 , A 2 , B 1 , B 2 、E 1 、E 2 、E 3 , E4 is the calculation coefficient.

[0055] Step S4: Calculate the total deflection f of the composite beam in the negative moment zone t (x)

[0056] f t (x) = deflection of concrete cracking f(x) + additional deflection Δf(x) caused by interface slip

[0057] Step S5: Calculate the stiffness of the composite beam in the negative moment zone

[0058] for Figure 1 The bending stiffness of the cantilever beam shown is:

[0059] In the formula, f t (a) is the total deflection of the outrigger, calculated according to step S4.

[0060] like Figure 2 As shown, the test beam is turned upside down. Figure 2 Where c represents the distance from the supports on both sides to the load application point. The stiffness calculation process of the negative bending moment zone of the composite beam under this model is as follows.

[0061] (1) Based on the linear stiffness reduction method, determine the section inertia moment I of the composite beam in the negative moment zone m

[0062] The moment of inertia of the section in the negative moment zone of the composite beam is linearly reduced. The moment of inertia of the support section after concrete cracking is I eff , the section moment of inertia at the inflection point is the initial moment of inertia I 0 , the moment of inertia between the two points is linearly interpolated, and the section moment of inertia of the test beam is:

[0063]

[0064] Where M cr is the cracking moment, M is the actual bending moment of the section, I 0 is the converted moment of inertia of the entire section before concrete cracking, I cr Only the section moment of inertia of steel beams and reinforcements is considered.

[0065] (2) Calculation of the deflection f(x) in the negative moment zone of the composite beam considering concrete cracking

[0066] Considering the boundary conditions, the deflection of the negative moment zone of concrete cracking is obtained as follows:

[0067]

[0068] In the formula I eff with I 0 Calculated using the formula in part (1) above.

[0069] (3) Calculation of the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip

[0070] Under the premise of meeting the basic assumptions and considering the boundary conditions, we get:

[0071]

[0072] (4) Calculate the total deflection f of the composite beam in the negative moment zone t (x)

[0073] f t (x) = deflection f(x) considering concrete cracking + additional deflection Δf(x) caused by interface slip

[0074] (5) Calculation of the stiffness of the composite beam in the negative moment zone

[0075] for Figure 2 The simply supported beam shown has a bending stiffness of

[0076] In the formula, f t (c) is the total deflection at mid-span of the inverted simply supported beam, calculated according to step (4).

[0077] The following is further explanation with reference to specific data.

[0078] (1) In the case of an extended beam

[0079] Table 1 shows the calculation parameters of the cantilever beam stiffness determined based on the static load test of the cantilever beam.

[0080] Table 1 Calculation parameter values ​​of steel-concrete composite cantilever beams

[0081] parameter Value a(mm) 1200 b(mm) 2400 K(N / mm) 3.4E+05 p(mm) 140 <![CDATA[A s (mm 2 )]]> 4540 <![CDATA[A c (mm 2 )]]> 45000 <![CDATA[E s (N / mm 2 )]]> 2.000E+05 <![CDATA[E c (N / mm 2 )]]> 4.113E+04 <![CDATA[I s (mm 4 )]]> 3.171E+07 <![CDATA[I c (mm 4 )]]> 3.038E+07 λ 0.003359 F(N) 200000 h(mm) 290

[0082] The concrete cracking moment of the test beam is calculated according to the following formula, and the calculated cracking moment and the actual cracking moment are compared.

[0083]

[0084] In the formula, f t is the standard value of tensile strength of concrete, n E is the ratio of the elastic modulus of the steel beam to the elastic modulus of the concrete, z 0 is the distance between the centroid of the concrete slab and the centroid of the composite beam section, I 0 is the moment of inertia of the composite beam section.

[0085] The calculation results are shown in Table 2.

[0086] Table 2 Comparison of concrete cracking moment

[0087]

[0088] It can be seen from the table that the calculated value of the cracking moment is in good agreement with the test value, which indicates that the method proposed in the present invention can accurately calculate the cracking moment in the negative moment zone of the composite beam.

[0089] Using f t (x) = f(x) + Δf(x) The calculated deflection value is compared with the test value, such as Figure 4As shown in the figure, before the load value of 180kN, the calculated value is in good agreement with the test value, but after 180kN, the difference between the two is large. The main reason is that after 180kN, the composite beam enters the yield stage, the steel beam gradually buckles, and the nonlinear characteristics of the composite beam become more obvious. These nonlinear characteristics are not considered in the calculation. In the normal use stage, this method can calculate the deflection of the composite beam more accurately.

[0090] Figure 5 The figure shows the comparison between the test value and the calculated value of the deflection when the end of the cantilever composite beam is loaded with 140kN. It can be seen from the figure that when concrete cracking and interface slip are not considered, the calculated deflection is smaller than the test value, and the difference in the deflection of the cantilever end is 59.994% of the test value, which is a large error; when only concrete cracking is considered without considering interface slip, the calculated deflection is smaller than the test value, and the difference in the deflection of the cantilever end is 11.421% of the test value; when both concrete cracking and interface slip are considered, the calculated deflection is larger than the test value, and the difference in the deflection of the cantilever end is 3.957% of the test value, which is the smallest error. Therefore, this method has a high accuracy in calculating the negative bending moment of the composite beam with concrete cracking and interface slip.

[0091] The test beam was inverted to test the static performance of the composite beam in the negative moment zone. This method was used to calculate the slip and deflection of the inverted beam, and the calculation results were compared with the test data in the literature. The calculation parameters are shown in Table 3.

[0092] parameter Reference 1 Reference 2 Reference 3 Reference 4 a(mm) 1800 1800 1750 2000 K(N / mm) 2.44E+05 2.44E+05 5.55E+05 5.70E+05 p(mm) 120 120 100 150 <![CDATA[A s (mm 2 )]]> 3392 3392 9764 27200 <![CDATA[A c (mm 2 )]]> 42000 42000 90000 200000 <![CDATA[E s (N / mm 2 )]]> 2.06E+05 2.06E+05 2.06E+05 2.06E+05 <![CDATA[E c (N / mm 2 )]]> 3.28E+04 3.28E+04 3.47E+04 3.35E+04 <![CDATA[I s (mm 4 )]]> 1.498E+07 1.498E+07 1.956E+08 1.621E+09 <![CDATA[I c (mm 4 )]]> 1.715E+07 1.715E+07 1.688E+08 1.042E+09 λ 0.003536 0.003536 0.003622 0.001983 F(N) 100000 100000 700000 2000000 h(mm) 250 250 500 891

[0093] The calculation results are shown in Figure 6 and Figure 7 ,from Figure 6 It can be seen from the results that before the steel beam yields, the calculated value is consistent with the test value, which proves that this method can be used to calculate the deflection of steel-concrete composite beams in normal use. Figure 7 It can be seen that the calculated slip value is in good agreement with the experimental value, and this method can calculate the steel-concrete interface slip more accurately.

[0094] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. A method for calculating the stiffness of a steel-concrete composite beam in the negative moment zone, characterized in that: include: S1. Determine the section inertia moment I of the composite beam in the negative moment zone based on the linear stiffness reduction method m ; The moment of inertia of the section in the negative moment zone of the composite beam is linearly reduced. The moment of inertia of the support section after concrete cracking is I eff , the moment of inertia between the two points is linearly interpolated, then the section moment of inertia is: Where M cr is the cracking moment, M is the actual bending moment of the section, I0 is the converted moment of inertia of the entire section before the concrete cracks, I cr In order to consider only the section moment of inertia of the steel beam and reinforcement, a represents the distance from the middle support to the load application point, and b represents the distance between the two supports at the bottom of the steel beam; S2. Calculate the deflection f(x) of the negative moment zone of the composite beam considering concrete cracking; Considering the boundary conditions, the deflection of the negative moment zone of concrete cracking is obtained as follows: In the formula E s is the elastic modulus of the steel beam; S3. Calculate the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip; in Where, d cs A is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab. c and A s are the cross-sectional areas of the concrete slab and the steel beam, E c and E s are the elastic moduli of concrete and steel beam, I c and I s are the section inertia moments of the concrete slab and the steel beam, respectively; h is the section height; K is the shear stiffness of a row of studs; p is the spacing between two rows of studs; λ is the relative stiffness coefficient; A1, A2, B1, B2, E1, E2, E3, and E4 are calculation coefficients; S4. Calculate the total deflection f of the composite beam in the negative moment zone t (x); f t (x) = deflection f(x) considering concrete cracking + additional deflection Δf(x) caused by interface slip; S5. Calculate the stiffness of the composite beam in the negative moment zone; The stiffness B is: In the formula, f t (a) is the total deflection of the outrigger, calculated according to step S4.

2. The method for calculating the stiffness of the steel-concrete composite beam in the negative moment zone according to claim 1 is characterized in that: When the inverted simply supported beam is subjected to concentrated load at the mid-span, the calculation method of the section inertia moment in S1 is replaced by the following formula:

3. The method for calculating the stiffness of the steel-concrete composite beam in the negative moment zone according to claim 2 is characterized in that: When the mid-span of the inverted simply supported beam is subjected to concentrated load, the calculation method of the deflection in the negative moment zone of concrete cracking obtained by considering the boundary conditions in S2 is replaced by the following formula:

4. The method for calculating the stiffness of the steel-concrete composite beam in the negative moment zone according to claim 3 is characterized in that: When the mid-span of the inverted simply supported beam is subjected to concentrated load, the calculation method of the additional deflection Δf(x) in the negative moment zone of the composite beam considering interface slip in S3 is replaced by the following formula:

5. A computer device, comprising a memory, wherein the memory stores program instructions, characterized in that: When the program instructions are executed, the method for calculating the stiffness in the negative moment zone of a steel-concrete composite beam as described in any one of claims 1 to 4 is executed.

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