Method for determining flexural capacity of high-strength steel-UHPC composite beam

Abstract

The invention relates to a method for determining the flexural capacity of a high-strength steel-UHPC composite beam. The method is characterized by comprising the following steps that (1) the corresponding section curvature k when UHPC reaches crushing serves as the section curvature of the steel-concrete composite beam, and the strain distribution rule of the section of the composite beam is determined; 2) aiming at two conditions that a neutralizing shaft is positioned in a UHPC plate and the neutralizing shaft is positioned in a steel beam, simplifying a UHPC stress diagram of a pressed area into a triangle, and by considering the strain hardening characteristic of high-strength steel, simplifying a steel beam web stress diagram into a trapezoid, and determining internal force distribution of the section of the main beam under the two conditions; and (3) according to the bending moment balance equation of the section of the main beam, the method for determining the flexural capacity of the high-strength steel-UHPC composite beam is established. According to the method, the problem that a method for calculating the flexural capacity of the high-strength steel-UHPC composite beam is lacked is solved, and technical support is provided for promoting application of the high-strength steel-UHPC composite beam in bridge engineering.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge and culvert engineering in the transportation industry, and specifically relates to a method for determining the bending bearing capacity of a high-strength steel-UHPC composite beam. Background Art

[0002] In recent years, steel-concrete composite beams have been widely used in bridge engineering. With the continuous development of new material technologies, concrete has gradually developed from high-performance concrete to ultra-high-performance concrete (Ultra High Performance Concrete, referred to as UHPC, compressive strength ≥ 150MPa), and high-performance steel has gradually developed towards higher-strength steel (High-Strength Steel, referred to as HSS, yield strength ≥ 460MPa). However, the traditional calculation of the bending bearing capacity of steel-concrete composite beams uses a plastic method to simplify the stress distribution of concrete and steel beams into rectangles. This simplified method is used to calculate high-strength steel-UHPC composite beams, which often leads to conservative calculation results and cannot fully reflect the bending performance of the structure.

[0003] The current design specifications and technical standards are mainly applicable to high-performance concrete and steel below C60 and below Q420. The design and application of high-strength steel-UHPC composite beams exceed the requirements of design specifications and technical standards. Therefore, the present invention aims at the stress distribution characteristics of the cross-section of the high-strength steel-UHPC composite beam, simplifies the stress distribution in the compression zone of the UHPC bridge deck under the limit state into a triangle, and simplifies the stress distribution in the tension zone of the steel web into a trapezoid, and proposes a method for determining the bending bearing capacity of the high-strength steel-UHPC composite beam, which provides a theoretical basis for the design and application of the high-strength steel-UHPC composite beam in bridge engineering. Summary of the invention

[0004] The purpose of the present invention is to provide a method for determining the flexural bearing capacity of a high-strength steel-UHPC composite beam, and a calculation formula is proposed for the two cases where the neutral axis is inside the concrete slab and inside the steel beam. The method can accurately determine the flexural bearing capacity of the high-strength steel-UHPC composite beam.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for determining the bending resistance of a high-strength steel-UHPC composite beam, which is characterized by comprising the following steps:

[0006] A method for determining the bending bearing capacity of a high-strength steel-UHPC composite beam comprises the following steps:

[0007] S1. Determine the basic parameters of the UHPC composite beam and the position of the neutral axis when the composite beam reaches the ultimate bending state, wherein the neutral axis is located inside the UHPC plate or the steel beam;

[0008] S2. Conduct static bending mechanical properties test of UHPC composite beams, study the bending mechanical properties and bearing capacity of UHPC composite beams, and determine the bending mechanical properties of UHPC composite beam structures;

[0009] Step S2 includes:

[0010] K1. Based on the flat section assumption, the section curvature k corresponding to the concrete reaching the crushing state is used as the section curvature of the steel-concrete composite beam, and the strain values ​​at various locations of the high-strength beam-UHPC composite beam are calculated, including the strain ε at the center of the upper flange plate of the steel beam. ft , the strain at the top of the web of the steel beam ε wt , the strain at the bottom of the web of the steel beam ε wb And the strain ε at the center of the lower flange plate of the steel beam fb , ε wb and ε fb

[0011] K2. Using the stress equivalence principle, determine the bending bearing capacity of the UHPC composite beam when it yields, consider the tensile effect of UHPC in the tension zone, simplify the stress distribution of the beam web into a trapezoid, and simplify the stress distribution of the UHPC compression zone into a triangle, and calculate the internal force F at the UHPC plate c and bending moment M c 、UHPC plate tensile zone internal force F ct and bending moment M ct 、Internal force F on the upper flange of the steel beam ft and bending moment M ft , Steel beam web internal force F w and bending moment M w , Internal force F of the lower flange of the steel beam fb and bending moment M fb ;

[0012] K3. Based on the force balance equation and the moment balance equation, the ultimate bending bearing capacity M of the high-strength steel-UHPC composite beam is calculated u In step S1, based on the flat section assumption, the cross-sectional curvature k corresponding to the concrete reaching the crushing state is measured as the cross-sectional curvature of the steel-concrete composite beam, and the ultimate compressive strain ε of the UHPC when it is crushed is measured. cu , calculate the height x of the upper flange plate from the neutral axis of the UHPC concrete according to the calculation formula of the cross-sectional curvature k:

[0013]

[0014] Where: h a is the height of the steel beam; h c is the thickness of the UHPC concrete slab, h f1 h is the thickness of the upper flange of the steel beam; f2 is the thickness of the lower flange of the steel beam.

[0015] In step K1: the strain values ​​at various locations of the composite beam are obtained from the cross-sectional strain diagram, where:

[0016] ε wb = k(h c +h a -h f2 -x)

[0017]

[0018] ε wb is the strain at the bottom of the web of the steel beam, ε fb is the strain at the center of the lower flange plate of the steel beam.

[0019] When the neutral axis is inside the UHPC board:

[0020]

[0021] ε wt = k(h c +h f1 -x)

[0022] When the neutral axis is inside the steel beam:

[0023]

[0024] ε wt =k(xh c -h f1 )

[0025] Where: hc is the thickness of the UHPC concrete slab; ha is the height of the steel beam; h f1 h is the thickness of the upper flange of the steel beam; f2 is the thickness of the lower flange of the steel beam.

[0026] In step K2, the internal force F of the UHPC plate is calculated. c and bending moment M c 、UHPC plate tensile zone internal force F ct and bending moment M ct 、Internal force F on the upper flange of the steel beam ft and bending moment M ft , Steel beam web internal force F w and bending moment M w , Internal force F of the lower flange of the steel beam fb and bending moment M fb include:

[0027] M1. Internal force F at UHPC plate c and bending moment M c :

[0028] When the neutral axis is inside the UHPC board:

[0029]

[0030]

[0031] When the neutral axis is inside the steel beam:

[0032]

[0033]

[0034] Where: b e is the effective width of the UHPC concrete slab; f0 is the stress at the lower edge of the UHPC concrete slab; f c is the compressive strength value of UHPC concrete;

[0035] M2. Internal force F in the tensile zone of UHPC plate ct and bending moment M ct , at this time the neutral axis is located inside the UHPC board:

[0036] F ct =b e ·(h c -x)·f ct

[0037]

[0038] Where: f ct is the tensile strength value of UHPC concrete;

[0039] M3. Internal force F on the upper flange of the steel beam ft and bending moment M ft :

[0040]

[0041] Where: E s is the elastic modulus of steel; E sh is the elastic modulus of high-strength steel at the end of the elastic stage, taken as 0.01E s ; b f1 f is the width of the upper flange of the steel beam; y is the yield strength of steel; ε y is the yield strain value of steel;

[0042] M4. Internal force of steel beam web F w and bending moment M w :

[0043] When the neutral axis is inside the UHPC board:

[0044]

[0045]

[0046]

[0047] The web section is decomposed into four regions, and the internal forces are F w1 、F w2 、F w3 、F w4 , satisfying the following formula:

[0048] F w1 =ε ft ·E s ·t w ·h y

[0049]

[0050] F w3 =f y (h w -h y )·t w

[0051]

[0052] When the neutral axis is inside the steel beam,

[0053]

[0054]

[0055] h z =xh c -h f1

[0056] Where: hy is the height from the bottom of the upper flange to the point where the web of the steel beam just yields when the neutral axis is inside the UHPC plate; hz is the height from the bottom of the upper flange to the point where the web of the steel beam just yields when the neutral axis is inside the steel beam;

[0057] ε wt No greater than ε y When the web section is decomposed into four regions, the internal forces are F w1 、F w2 、F w3 、F w4 , the calculation formula is:

[0058]

[0059]

[0060]

[0061]

[0062] ε wt Greater than ε y When the internal force is decomposed into five areas, namely F w1 、F w1’ 、F w2 、F w3 、F w4 , where F w2 、F w3 、F w4 With ε wt No greater than ε y Same, web force F w1 、F w1’ , the calculation formula is as follows:

[0063]

[0064]

[0065] M5. Internal force F of lower flange of steel beam fb and bending moment M fb

[0066] F fb =[f y +E sh (ε fb -ε y )]·b f2 ·h f2

[0067]

[0068] Where: t w h is the thickness of the steel beam web; w b is the web height of the steel beam; f2 is the width of the lower flange of the steel beam, F w1 and F w2 is the internal force of the elastic section of the web; F w3 、F w4 and F w1 ' is the internal force of the web hardening section.

[0069] Step K3 includes:

[0070] X1. When the neutral axis is located inside the UHPC board,

[0071] F c =F ct +F ft +F w +F fb

[0072] M u =M c +M ct +M ft +M w +M fb

[0073] X2. When the neutral axis is located inside the UHPC board,

[0074] F c +F ft =F w +F fb

[0075] M u =M c +M ft +M w +M fb

[0076] The mid-span section of the composite beam complies with the flat section assumption during bending, and the curvatures of the UHPC and steel beams are approximately equal.

[0077] In step K1, the loading process of UHPC composite beams is divided into three stages: elasticity, crack development and failure.

[0078] The present invention has the following main advantages:

[0079] This scheme carried out static bending tests on high-strength steel-UHPC composite beam components, studied the bending mechanical properties of this composite beam, and then considered the stress characteristics of UHPC and high-strength steel, and established a calculation method for the bending bearing capacity of high-strength steel-UHPC composite beams based on plastic design theory.

[0080] 1. The characteristics of UHPC compression and high-strength steel strain hardening in the ultimate state of high-strength steel-UHPC composite beams can be considered, and the influence of UHPC in the tensile zone can be considered to accurately determine the stress distribution characteristics of the mid-span section of the high-strength steel-UHPC composite beam, and a calculation method for the flexural bearing capacity of high-strength steel-UHPC composite beams is proposed.

[0081] 2. The calculation method provided by the present invention comprehensively considers the position distribution of the two neutral axes and can accurately determine the bending bearing capacity of the high-strength steel-UHPC composite beam.

[0082] 3. The ratio of the calculated value obtained by the calculation formula of the flexural bearing capacity of the high-strength steel-UHPC composite beam of the present invention to the test value is 0.95, which can reasonably and accurately calculate the flexural bearing capacity of the high-strength steel-UHPC composite beam and has good engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1This is a flow chart for calculating the bending bearing capacity of the high-strength steel-UHPC composite beam of the present invention;

[0084] Figure 2 This is the stress distribution diagram of the cross section where the neutral axis is located in the UHPC plate in the present invention;

[0085] Figure 3 The stress distribution diagram of the cross section in which the neutralization axis is located in the steel beam in the present invention;

[0086] Figure 4 It is a schematic diagram of the size and structure of high-strength steel-UHPC composite beam components;

[0087] Figure 5 It is the layout of loading device and strain gauge;

[0088] Figure 6 It is the load-deflection relationship curve at the mid-span of the component.

[0089] In the figure: 1. Load distribution beam; 2. Concrete strain gauge; 3. Steel beam strain gauge; 4. Displacement meter; 5. Steel beam section strain gauge; 6. Concrete flange plate; 7. Steel beam; 8. Flange; 9. Support. DETAILED DESCRIPTION

[0090] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0091] Explanation of terms

[0092] Neutral Axis (NA) is a concept in structural mechanics, especially in the bending theory of beams. When a beam is subjected to a bending moment, the cross section of the beam will bend, and a line will divide the cross section into two parts, the upper part is under compression and the lower part is under tension. This line is the neutral axis, which means that during the bending process of the beam, the material on the neutral axis is neither under tension nor under pressure, that is, it is in a neutral state.

[0093] A method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam comprises the following steps:

[0094] Step 1: Based on the plane section assumption, k is used as the cross-sectional curvature of the steel-concrete composite beam, that is, the cross-sectional curvature corresponding to the concrete reaching the crushing state, which satisfies formula (1):

[0095]

[0096] Where: εcu is the ultimate compressive strain of UHPC concrete slab; h c is the thickness of the UHPC concrete slab; h a is the height of the steel beam; x is the height of the UHPC concrete upper flange plate from the neutral axis.

[0097] Step 2: According to Figure 2-3 The cross-sectional strain diagram shown in the figure is used to calculate the strain values ​​of each part of the high-strength steel-UHPC composite beam according to equations (2) to (7), including the strain ε at the center of the upper flange plate of the steel beam. ft , the strain at the top of the web of the steel beam ε wt , the strain at the bottom of the web of the steel beam ε wb And the strain ε at the center of the lower flange plate of the steel beam fb , ε wb and ε fb Satisfying formulas (2) to (3):

[0098] ε wb = k(h c +h a -h f2 -x) (2)

[0099]

[0100] When the neutral axis is inside the UHPC board, ε ft With ε wt Satisfying formulas (4) to (5):

[0101]

[0102] ε wt = k(h c +h f1 -x) (5)

[0103] When the neutral axis is inside the steel beam, ε ft With ε wt Satisfying formulas (6) to (7):

[0104]

[0105] ε wt =k(xh c -h f1 ) (7)

[0106] Where: h c is the thickness of the UHPC concrete slab; h a is the height of the steel beam; h f1 h is the thickness of the upper flange of the steel beam; f2 is the thickness of the lower flange of the steel beam;

[0107] Calculation of internal force F at UHPC plate c and bending moment M c .

[0108] When the neutral axis is inside the UHPC plate, the stress in the UHPC compression zone is simplified into a triangle and calculated according to stress diagram 2: c With M c Satisfying formulas (8) to (9):

[0109]

[0110]

[0111] When the neutral axis is inside the steel beam, the stress in the UHPC compression zone is simplified into a trapezoid and calculated according to stress diagram 3: c With M c Satisfying formulas (10) to (11):

[0112]

[0113]

[0114] Where: b e is the effective width of the UHPC concrete slab; f0 is the stress at the lower edge of the UHPC concrete slab; f c is the compressive strength value of UHPC concrete;

[0115] Considering the tensile performance of UHPC when the neutral axis is located in the concrete slab, the internal force F in the tensile zone of the UHPC slab is calculated according to stress diagram 2. ct and bending moment M ct , as shown in formulas (12) to (13):

[0116] F ct =b e ·(h c -x)·f ct (12)

[0117]

[0118] Where: f ct is the tensile strength value of UHPC concrete;

[0119] Calculation of internal force F on the upper flange of steel beam ft and bending moment M ft , internal force F ft Satisfies formula (14):

[0120]

[0121] Where: E sis the elastic modulus of steel; E sh is the elastic modulus of high-strength steel at the end of the elastic stage, taken as 0.01E s ; b f1 f is the width of the upper flange of the steel beam; y is the yield strength of steel; ε ft is the strain value of the upper flange plate of the steel beam; ε y is the yield strain value of steel.

[0122] Calculation of the internal force F of the web of the steel beam w and bending moment M w .

[0123] When the neutral axis is inside the UHPC board, F w With M w Satisfying formulas (15) to (16):

[0124]

[0125]

[0126] hy is the height from the bottom of the upper flange to the point where the web of the steel beam just yields, satisfying formula (17):

[0127]

[0128] The web section is decomposed into four regions, and the internal forces are F w1 、F w2 、F w3 、F w4 , satisfying formulas (18) to (21) as follows:

[0129] F w1 =ε f t·E s ·t w ·h y (18)

[0130]

[0131] F w3 =f y (h w -h y )·t w (20)

[0132]

[0133] When the neutral axis is inside the steel beam, F w With M w Satisfying formulas (22) to (23):

[0134]

[0135]

[0136] h z is the height from the bottom of the upper flange to the point where the web of the steel beam just yields, satisfying formula (24):

[0137] h z =xh c -h f1 (twenty four)

[0138] M W3 and M w4 is the internal force F in the web hardening section W3 and F W4 The bending moment satisfies the formula:

[0139]

[0140]

[0141] ε wt No greater than ε y When the web section is decomposed into four regions, the internal forces are F w1 、F w2 、F w3 、F w4 , the calculation formula is (27)~(30)

[0142]

[0143]

[0144]

[0145]

[0146] ε wt Greater than ε y When the internal force is decomposed into 5 areas, the internal forces are F w1 、F w1’ 、F w2 、F w3 、F w4 , where F w2 、F w3 、F w4 With ε wt No greater than ε y Same, web force F w1 、F w1’ , the calculation formula is as follows (31)~(32):

[0147]

[0148]

[0149] Calculate the internal force F of the lower flange of the steel beam fb and bending moment M fb , as shown in formulas (33) to (34):

[0150] F fb =[f y +E sh (ε fb -ε y )]·b f2 ·h f2 (33)

[0151]

[0152] Where: t w h is the thickness of the steel beam web; w b is the web height of the steel beam; f2 F is the width of the lower flange of the steel beam; w1 and F w2 is the internal force of the elastic section of the web; F w3 、F w4 and F w1 ' is the internal force of the web hardening section;

[0153] Use the force balance equation to find the value of x.

[0154] When the neutral axis is inside the UHPC plate, the force balance equation satisfies formula (35):

[0155]

[0156] When the neutral axis is inside the steel beam, the force balance equation satisfies formula (36):

[0157]

[0158] Step 3: Calculate the ultimate bending bearing capacity M of the high-strength steel-UHPC composite beam from the moment equilibrium equation u .

[0159] When the neutral axis is inside the UHPC board, M u Satisfies formula (37):

[0160] M u =M c +M ct +M ft +M w +M fb (37)

[0161] When the neutral axis is inside the steel beam, Mu Satisfies formula (38):

[0162] M u =M c +M ft +M w +M fb (38)

[0163] A method for calculating the bending capacity of high-strength steel-UHPC composite beams, such as Figure 5 (n) and (o) in the figure are used to design the components first. To study the bending performance of high-strength steel-UHPC composite beams, a bending test was carried out on this type of simply supported beam using a four-point loading method. The steel material used is Q500 high-strength steel, and the concrete is 180MPa grade UHPC.

[0164] The component structure is as follows:

[0165] The length of the test beams is 2300mm, with a 100mm transition section at both ends. The calculated span is 2100mm. The width of the concrete slab 6 (UHPC slab) of the test beam section is 450mm and the thickness is 80mm. The width of the upper and lower flanges 8 of the steel beam 7 is 100mm, the flange thickness is 10mm, the web thickness is 10mm, the web height is 130mm, and the total height is 150mm. In order to prevent local buckling of the web at the loading and support locations, vertical stiffeners with a thickness of 10mm are welded there. HRB400 hot-rolled threaded steel bars are used for symmetrical reinforcement in the slab. The longitudinal reinforcement is 4C10@130, evenly arranged in two layers, and the reinforcement ratio of the tensile longitudinal reinforcement section is 1.7%; the transverse reinforcement is 38C8@60 evenly arranged in two layers. The composite beams are all set with shear nails according to the full shear connection, using ML15 material, with a diameter of 13mm and a height of 50mm. Before pouring concrete, the specimen is first supported by formwork, and then the steel mesh is arranged according to the design requirements, and then the concrete is poured. The specimen is steam cured and the formwork is removed after 72 hours of curing.

[0166] The test contents are as follows:

[0167] Load

[0168] The test load value is collected by a 300t force sensor placed above the steel distribution beam 1, and the load data is recorded by a TDS530 dynamic data acquisition instrument.

[0169] Deflection

[0170] The deflection is mainly measured by 4 displacement meters at the mid-span, loading point and 9 vertical displacements of the support, and the displacement data is recorded by TDS530. Among them, the displacement meter at the support of the test beam is used to monitor the support settlement to eliminate the test error. The test has 6 LVDT displacement meters arranged symmetrically, and 2 displacement meters are arranged at 9 supports, with a range of 100mm.

[0171] strain

[0172] At the mid-span position, eight concrete strain gauges 2 are arranged symmetrically along the height direction of the concrete slab 6 to measure the deformation of the mid-span section of the concrete slab 6. At the same time, three strain gauges are arranged at the mid-span position of the top of the concrete slab 6 to monitor the change of concrete strain under each level of load; seven steel beam strain gauges 3 are arranged at the mid-span section of the steel beam 7 to monitor the deformation of the steel beam.

[0173] The test loading scheme is as follows:

[0174] The test adopts graded loading, load-controlled loading within the elastic range, each load level is 1 / 10 of the expected ultimate load, and each load level lasts for about 3 minutes. When the component enters the elastic-plastic stage, displacement-controlled graded loading is used instead, with each load level being 0.5mm. When approaching the ultimate load, slow displacement-controlled continuous loading is used until the specimen is destroyed.

[0175] The test phenomena are as follows:

[0176] In the elastic loading stage, the composite beam components have a large stiffness and the mid-span displacement increases slowly, so the steel beam and UHPC board show a good combination effect. When loaded to 560kN, cracks first appear on the bottom surface of the UHPC board. As the load increases, a slight sound of steel fibers being pulled out can be heard. The cracks in the bottom plate continue to increase and develop until 979kN, when the UHPC top plate collapses and penetrates the top surface. The crack width is thin and the depth is shallow. The added load value decreases, and the test beam is damaged.

[0177] The test results are analyzed as follows:

[0178] During the test, the mid-span deflection of the specimen changes with the load. Figure 6 . It shows three stages, namely the elastic stage, the crack development stage and the destruction stage. In the elastic stage, the mid-span deflection of the composite beam component increases linearly with the load, and a short and fine crack of 0.05mm width appears in the mid-span concrete bottom plate. The composite beam component cracks and enters the crack development stage. The bending stiffness of the component decreases, and the cracks in the concrete slab develop rapidly. The structural stress enters the plastic stage. The lower flange of the steel beam yields in tension until most of the entire cross-section of the steel beam yields. After loading to the ultimate bearing capacity, it enters the destruction stage, the concrete slab collapses, and the mid-span deflection increases rapidly with the decrease of load until the bearing capacity is completely lost.

[0179] The following assumptions are made when establishing the calculation formula for the ultimate bending bearing capacity of high-strength steel-UHPC composite beams:

[0180] The high-strength steel-UHPC composite beam is set up as a fully shear-resistant connection, and the cross-sectional strain distribution conforms to the flat section assumption;

[0181] The stress-strain relationship of steel is analyzed based on the bilinear model, which simplifies the stress distribution of the web of the steel beam into a trapezoid.

[0182] The UHPC in the compression zone of the test beam is always in an elastic working state during the entire loading process, and the stress distribution in the compression zone of the UHPC is simplified into a triangle;

[0183] Consider the influence of UHPC in the tension zone.

[0184] The calculation is as follows:

[0185] According to the structural characteristics of the high-strength steel-UHPC composite beam, it was found that when the bending bearing capacity limit was reached, the plastic neutral axis of the cross-section was located inside the UHPC plate, part of the UHPC was under tension, and the entire cross-section of the steel beam was under tension.

[0186] Step 1: Measure the cross-sectional curvature k corresponding to the concrete reaching the crushing state as the cross-sectional curvature of the steel-concrete composite beam and calculate it according to formula (1):

[0187]

[0188] Where:

[0189] ε cu is the ultimate compressive strain of UHPC when it is crushed, and its value is 3679με; h c is the thickness of the UHPC concrete slab h c =80mm;h a is the height of the steel beam h a =150mm; x is the height of the upper flange plate of UHPC concrete from the neutral axis.

[0190] Step 2: Since the neutral axis is inside the UHPC board, the height x of the equivalent compression zone of the UHPC is calculated according to the force balance equation. At this time, the formula should be satisfied:

[0191]

[0192] Substituting each data into the calculation, the x value obtained is 73.70 mm; the neutral axis is inside the UHPC board;

[0193] b e b is the effective width of the UHPC concrete slab e =450mm; f c is the compressive strength value of UHPC concrete c=180MPa; f ct is the tensile strength value of UHPC concrete ct =XXMPa; F ft is the internal force of the upper flange of the steel beam; F w is the internal force of the web of the steel beam; f y is the yield strength of steel; E sh is the elastic modulus of high-strength steel at the end of the elastic stage, taken as 0.01E s ; E s is the elastic modulus of steel; b f2 b is the width of the lower flange of the steel beam f2 =100mm; ε y is the yield strain value of steel; ε fb h is the strain at the center of the lower flange plate of the steel beam; f2 is the thickness of the lower flange of the steel beam h f2 =10mm;

[0194] ε wb = k(h c +h a -h f2 -x)

[0195]

[0196]

[0197] ε wt = k(h c +h f1 -x)

[0198]

[0199]

[0200] F c and M c are the internal force and bending moment at the UHPC plate respectively;

[0201] F ct =b e ·(h c -x)·f ct

[0202]

[0203] F ct and M ct are the internal force and bending moment in the tension zone of the UHPC plate;

[0204]

[0205] Where: Es is the elastic modulus of steel; E sh is the elastic modulus of high-strength steel at the end of the elastic stage, taken as 0.01E s ; b fl b is the width of the upper flange of the steel beam f1 =100mm; f y is the yield strength of steel; ε y is the yield strain value of steel; h f1 h is the thickness of the upper flange of the steel beam f1 =10mm; ε ft is the strain at the center of the upper flange plate of the steel beam; wb is the strain at the bottom of the web of the steel beam; wt is the strain at the top of the web of the steel beam.

[0206]

[0207]

[0208] hy is the height from the bottom of the upper flange to the point where the web of the steel beam just yields, satisfying the formula:

[0209]

[0210] F fb =[f y +E sh (ε fb -ε y )]·b f2 ·h f2

[0211]

[0212] F fb and M fb are the internal force and bending moment of the lower flange of the steel beam respectively;

[0213] Step 3: Take the moments of the UHPC in the compression zone, the UHPC in the tension zone, and each part of the steel beam, and obtain the ultimate bending bearing capacity M of the high-strength steel-UHPC composite beam according to the moment equilibrium equation. u , then the formula is satisfied.

[0214] M u =M c +M ct +M ft +M w +M fb

[0215] Comparison between formula and test results

[0216] Table 1 shows the comparison between the test results of the flexural performance of high-strength steel-UHPC composite beams and the calculation results of the formula. u1 Bending test results The agreement is good, with an error of only 4.4%.

[0217] Table 1 Comparison of test values ​​and calculation formula results (unit: kN·m)

[0218]

[0219] Comparison between formula value and finite element results

[0220] Four geometric construction parameters, namely, UHPC plate width, UHPC plate thickness, steel beam lower flange thickness, and steel beam web thickness, were selected to establish the finite element model of 13 high-strength steel-UHPC composite beams. The comparison between the formula value and the finite element results is shown in Table 2:

[0221] Table 2 Finite element results and calculation formula results (unit: kN·m)

[0222]

[0223] The calculation results show that the average ratio of the finite element calculation value to the formula value is 0.95, and the error is 5.6%. Overall, the calculation formula is consistent with the finite element calculation results and has good accuracy.

Claims

1. A method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam, characterized in that: The following steps are involved: S1. Determine the basic parameters of the UHPC composite beam and the position of the neutral axis when the composite beam reaches the ultimate bending state, wherein the neutral axis is located inside the UHPC plate or the steel beam; S2. Conduct static flexural mechanical properties tests on UHPC composite beams, study the flexural mechanical properties and bearing capacity of UHPC composite beams, and determine the flexural mechanical properties of UHPC composite beam structures.

2. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 1 is characterized in that: Step S2 includes: K1. Calculate the strain values ​​at various locations of the high-strength beam-UHPC composite beam, including the strain ε at the center of the upper flange plate of the steel beam ft , the strain at the top of the web of the steel beam ε wt , the strain at the bottom of the web of the steel beam ε wb And the strain ε at the center of the lower flange plate of the steel beam fb , ε wb and ε fb K2. Using the stress equivalence principle, determine the bending bearing capacity of the UHPC composite beam when it yields, consider the tensile effect of UHPC in the tension zone, simplify the stress distribution of the beam web into a trapezoid, and simplify the stress distribution of the UHPC compression zone into a triangle, and calculate the internal force F at the UHPC plate c and bending moment M c 、UHPC plate tensile zone internal force F ct and bending moment M ct 、Internal force F on the upper flange of the steel beam ft and bending moment M ft , Steel beam web internal force F w and bending moment M w , Internal force F of the lower flange of the steel beam fb and bending moment M fb ; K3. Calculate the ultimate bending bearing capacity M of high-strength steel-UHPC composite beam from the moment equilibrium equation u .

3. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 1 is characterized in that: In step S1, based on the plane section assumption, the section curvature k corresponding to the concrete reaching the crushing state is measured as the section curvature of the steel-concrete composite beam, and the ultimate compressive strain ε of the UHPC at the crushing state is measured. cu , calculate the height x of the upper flange plate from the neutral axis of the UHPC concrete according to the calculation formula of the section curvature k: Where: h a is the height of the steel beam; h c is the thickness of the UHPC concrete slab, if x is not greater than h c , the neutral axis is located inside the UHPC plate, otherwise it is located inside the steel beam.

4. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 2, characterized in that: In step K1: ε wb =k(h c +h a -h f2 -x) ε wb is the strain at the bottom of the web of the steel beam, ε fb is the strain at the center of the lower flange plate of the steel beam. When the neutral axis is inside the UHPC board: ε wt =k(h c +h f1 -x) When the neutral axis is inside the steel beam: ε wt =k(x-h c -h f1 ) Where: hc is the thickness of the UHPC concrete slab; ha is the height of the steel beam; h f1 h is the thickness of the upper flange of the steel beam; f2 is the thickness of the lower flange of the steel beam.

5. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 2, characterized in that: In step K2, the internal force F of the UHPC plate is calculated. c and bending moment M c 、UHPC plate tensile zone internal force F ct and bending moment M ct 、Internal force F on the upper flange of the steel beam ft and bending moment M ft , Steel beam web internal force F w and bending moment M w , Internal force F of the lower flange of the steel beam fb and bending moment M fb include: M1. Internal force F at UHPC plate c and bending moment M c : When the neutral axis is inside the UHPC board: When the neutral axis is inside the steel beam: Where: b e is the effective width of the UHPC concrete slab; f0 is the stress at the lower edge of the UHPC concrete slab; f c is the compressive strength value of UHPC concrete; M2. Internal force F in the tensile zone of UHPC plate ct and bending moment M ct , at this time the neutral axis is located inside the UHPC board: F ct =b e ·(h c -x)·f ct Where: f ct is the tensile strength value of UHPC concrete; M3. Internal force F on the upper flange of the steel beam ft and bending moment M ft : Where: E s is the elastic modulus of steel; E sh is the elastic modulus of high-strength steel at the end of the elastic stage, taken as 0.01E s ; b f1 f is the width of the upper flange of the steel beam; y is the yield strength of steel; ε ft is the strain value of the upper flange plate of the steel beam; ε y is the yield strain value of steel; M4. Internal force of steel beam web F w and bending moment M w : When the neutral axis is inside the UHPC board: The web section is decomposed into four regions, and the internal forces are F w1 、F w2 、F w3 、F w4 , satisfying the following formula: F w1 =ε ft ·E s ·t w ·h y F w3 =f y (h w -h y )·t w When the neutral axis is inside the steel beam, h z =x-h c -h f1 Where: hy is the height from the bottom of the upper flange to the point where the web of the steel beam just yields when the neutral axis is inside the UHPC plate; hz is the height from the bottom of the upper flange to the point where the web of the steel beam just yields when the neutral axis is inside the steel beam, M W3 and M w4 is the internal force F in the web hardening section W3 and F W4 The bending moment satisfies the formula: ε wt No greater than ε y When the web section is decomposed into four regions, the internal forces are F w1 、F w2 、F w3 、F w4 , the calculation formula is: ε wt Greater than ε y When the internal forces are F w1 、F w1’ 、F w2 、F w3 、F w4 , where F w2 、F w3 、F w4 With ε wt No greater than ε y Same, F w1 、F w1’ , the calculation formula is as follows: M5. Internal force F of lower flange of steel beam fb and bending moment M fb Where: t w h is the thickness of the steel beam web; w b is the web height of the steel beam; f2 F is the width of the lower flange of the steel beam; w1 and F w2 is the internal force of the elastic section of the web; F w3 、F w4 and F w1’ is the internal force of the web hardening section.

6. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 1 is characterized in that: Step K3 includes: X1. When the neutral axis is located inside the UHPC board, F c =F ct +F ft +F w +F fb M u =M c +M ct +M ft +M w +M fb X2. When the neutral axis is located inside the UHPC board, F c +F ft =F w +F fb M u =M c +M ft +M w +M fb 7. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 1 is characterized in that: The mid-span section of the composite beam complies with the flat section assumption during bending, and the curvatures of the UHPC and steel beams are approximately equal.

8. The method for determining the ultimate bending bearing capacity of a high-strength steel-UHPC composite beam according to claim 1, characterized in that: In step K1, the loading process of UHPC composite beams is divided into three stages: elasticity, crack development and failure.

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