Design method of FRP rib seawater and sea sand concrete beam with midspan deflection control

Abstract

The invention belongs to the technical field of structural engineering, and discloses a design method of a mid-span deflection controlled FRP rib seawater and sea sand concrete beam, which comprises the following steps: inputting a design bending moment and a mid-span deflection limit value; primarily selecting sectional dimensions and material attributes; determining the edge compressive strain of the concrete, and calculating the width coefficient and the height coefficient of an equivalent rectangular stress diagram of the concrete in a normal use limit state; determining the strain of the FRP ribs in the tensile area, and calculating the reinforcement ratio of the FRP ribs in the tensile area; judging whether suitable tendon damage is met or not; judging whether the minimum reinforcement ratio is met or not; the stainless steel bars and the FRP stirrups in the pressed area are arranged according to the construction requirements; determining a safety reserve coefficient; outputting a result; according to the method, the problem of corrosion of the steel bars is effectively solved, meanwhile, it is guaranteed that the mid-span deflection of the steel bars in the normal use limit state meets the service performance, and the safety and rationality of the FRP bar concrete beam in engineering practice are further guaranteed.

Description

TECHNICAL FIELD

[0001] The application relates to a design method of a FRP (Fiber Reinforced Polymer) rebar seawater-sea sand concrete beam with cross-mid deflection control and belongs to the technical field of structural engineering. BACKGROUND

[0002] As a kind of building alternative material with great potential, the large-scale application of seawater-sea sand concrete helps to alleviate the shortage of river sand and the exhaustion of fresh water. However, there are corrosive ions in the material, which can destroy the passivation film on the surface of the steel bar, and then induce and accelerate the electrochemical corrosion of the steel bar, eventually leading to a significant decrease in the structural durability.

[0003] The FRP (Fiber Reinforced Polymer) rebar has become an ideal steel bar replacement material due to its light weight, high strength and good corrosion resistance. However, the elastic modulus of the FRP rebar is relatively low, which causes the FRP rebar concrete beam to have a large cross-mid deflection under the normal service limit state, so it is necessary to design the reinforcement by limiting the cross-mid deflection. For the cross-mid deflection limit of flexural members under different conditions, GB 50608-2020 follows the relevant provisions in GB 50010-2010. In addition, for safety reasons, ACI 440.1R-15, CSA S806-12 and GB 50608-2020 all do not recommend using FRP rebar as compression reinforcement, so stainless steel bars are arranged in the compression zone.

[0004] In existing research, although some scholars have carried out relevant research on the cross-mid deflection of the FRP rebar concrete beam, there is still no systematic arrangement and implementation at the design method level, which brings certain difficulties to the design and application of the FRP rebar concrete beam in actual engineering. SUMMARY

[0005] Therefore, a design method of a FRP rebar seawater-sea sand concrete beam with cross-mid deflection control is proposed, which is expected to meet the relevant provisions of the specification while providing more reasonable safety reserves. The design method of the FRP rebar seawater-sea sand concrete beam with cross-mid deflection control effectively solves the problem of steel bar corrosion. Since the cross-mid deflection of the FRP rebar concrete beam is usually large at the time of failure, the normal service limit state is used as the design basis of the FRP rebar concrete beam, which not only ensures that the cross-mid deflection of the FRP rebar concrete beam under the normal service limit state meets the service performance, but also further ensures the safety and applicability of the FRP rebar concrete beam in engineering practice.

[0006] In order to achieve the above-mentioned application purposes and solve the problems existing in the prior art, the application provides the following scheme.

[0007] The application discloses a design method of a FRP bar seawater sea sand concrete beam with mid-span deflection control, the FRP bar seawater sea sand concrete beam comprises upper longitudinal bars and lower longitudinal bars, the upper longitudinal bars comprise compression zone stainless steel bars, the lower longitudinal bars comprise tensile zone FRP bars, FRP stirrups are arranged between the longitudinal bars, and the longitudinal bars and the stirrups are filled with seawater sea sand concrete.

[0008] The design method comprises the following steps: inputting a design bending moment and a mid-span deflection limit value ; selecting initial cross-section size and material properties; determining the concrete edge compressive strain under the condition of and calculating the equivalent rectangular stress diagram width coefficient of the concrete under the normal use limit state and the equivalent rectangular stress diagram height coefficient of the concrete ; determining the tensile zone FRP bar strain , so as to obtain the tensile zone FRP bar reinforcement ratio determined by ; judging whether the reinforcement meets the failure condition, that is, whether the reinforcement is greater than or equal to the balanced reinforcement ratio , if , the balanced reinforcement ratio is selected as , if , the minimum reinforcement ratio is judged, if the minimum reinforcement ratio is met, the result is unchanged, and if the minimum reinforcement ratio is not met, the design needs to be re-performed; determining the safety reserve coefficient according to the construction requirement; the final reinforcement result and the safety reserve coefficient result are output.

[0009] The design method specifically comprises the following steps:

[0010] S1 inputting a design bending moment and a mid-span deflection limit value ;

[0011] the design bending moment is the quasi-permanent combination of the dead load standard value and the live load standard value;

[0012] the mid-span deflection limit value is when , when , , when , or ;

[0013] wherein, For the calculation of span, the value after "or" is applicable to the flexural member with higher requirement on mid-span deflection;

[0014] S2 preliminary section size and material properties;

[0015] The section size is the section height and the section width ;

[0016] The material properties are the concrete strength grade, the yield strength of the stainless steel bar in the compression zone , the elastic modulus of the stainless steel bar in the compression zone , the standard value of the tensile strength of the FRP bar in the tension zone , the elastic modulus of the FRP bar in the tension zone , the standard value of the tensile strength of the FRP stirrup , and the elastic modulus of the FRP stirrup ;

[0017] wherein, the concrete strength grade ranges from less than or equal to C50;

[0018] S3 determining the concrete edge compression strain under the condition , and calculating the equivalent rectangular stress diagram width coefficient of the concrete and the equivalent rectangular stress diagram height coefficient of the concrete under the serviceability limit state;

[0019] The equivalent rectangular stress diagram width coefficient of the concrete and the equivalent rectangular stress diagram height coefficient of the concrete under the serviceability limit state are calculated by the following formula: ;

[0020] In the formula, is the peak compression strain of the concrete, and the value is 0.002; is the edge compression strain of the concrete, and the value is 0.001.

[0021] S4 determining the strain of the FRP bar in the tension zone based on , so as to obtain the reinforcement ratio of the FRP bar in the tension zone determined by ;

[0022] The strain of the FRP bar in the tension zone is calculated by the following formula: ;

[0023] In the formula, is the effective height of the cross section; is a coefficient related to the applied load and boundary conditions; is the calculated span;

[0024] The reinforcement ratio of the tensile zone FRP bar is calculated using the following formula: ;

[0025] In the formula, is the prismatic compressive strength of the concrete;

[0026] S5 determines whether the reinforcement meets the failure, that is, whether it is greater than or equal to the balanced reinforcement ratio , if , then , if , then ;

[0027] The balanced reinforcement ratio is calculated using the following formula: ;

[0028] In the formula, and are the equivalent rectangular stress diagram width coefficient and the equivalent rectangular stress diagram height coefficient of the concrete under the bearing capacity limit state, respectively, and when the concrete strength grade is less than or equal to C50, the values are , ; is the ultimate compressive strain of the concrete, and when the concrete strength grade is less than or equal to C50, the value is ; is the tensile strength design value of the tensile zone FRP bar; is the partial coefficient of FRP bar, and the value is 1.25; is the environmental impact coefficient of FRP bar, which is taken from Table 4.2.13 of GB 50608-2020;

[0029] If , it means that the reinforcement result obtained by the mid-span deflection limit satisfies the reinforcement failure, so the reinforcement is carried out according to ;

[0030] If , it means that the reinforcement result obtained by the mid-span deflection limit does not satisfy the reinforcement failure, so the reinforcement is carried out according to ;

[0031] S6 judge whether the minimum reinforcement ratio is satisfied If satisfied, the result is unchanged, if not satisfied, the design needs to be redesigned;

[0032] The minimum reinforcement ratio , calculated by the following formula: ;

[0033] In the formula, is the tensile strength of concrete;

[0034] If satisfied, it means that the minimum reinforcement ratio of the construction requirements is satisfied, so the original result is reinforced;

[0035] If not satisfied, it means that the current design is unreasonable, so it should be redesigned;

[0036] S7 According to the construction requirements, the stainless steel bars and FRP stirrups in the compression zone are configured;

[0037] The construction requirements configure the stainless steel bars in the compression zone, which follow the relevant provisions in GB 50010-2010 for reinforcement, that is, when , the diameter 8mm, when , the diameter 10mm, when , the diameter 12mm;

[0038] The construction requirements configure the FRP stirrups, which meet the minimum stirrup ratio in GB 50608-2020;

[0039] S8 Determine the safety reserve coefficient ;

[0040] The safety reserve coefficient is the ratio of the ultimate bending moment to the design bending moment , calculated by the following formula: ;

[0041] The ultimate bending moment , calculated by the following formula: ;

[0042] In the formula, is the area of the FRP bars in the tension zone; is the stress of the FRP bars in the tension zone; is the actual compression zone height under the ultimate bending moment; This represents the area of ​​the stainless steel reinforcement in the pressure zone; The strain of the stainless steel reinforcement in the compression zone; This is the distance from the stainless steel reinforcement in the pressure zone to the edge of the pressure zone; The yield strain of the stainless steel reinforcement in the compression zone;

[0043] S9 outputs the final reinforcement result and safety reserve factor result.

[0044] The design bending moment described in step S1 It should be a quasi-permanent combination of the standard values ​​of dead load and live load; mid-span deflection limit. It should be based on the calculated span Sure.

[0045] The cross-sectional height mentioned in step S2 for ; cross-sectional width for .

[0046] The state described in step S3 Concrete edge compressive strain under certain conditions Based on the test results of FRP reinforced concrete beams, a value of 0.001 was set, meaning that when the concrete strength grade is less than or equal to C50, the beam's corresponding state is that the mid-span deflection reaches the limit value. It reached 0.001.

[0047] In step S5, determining whether the condition for adequate reinforcement failure is met requires ensuring that the selected reinforcement ratio is greater than or equal to the equilibrium reinforcement ratio. .

[0048] In step S6, determining whether the structural requirements are met should ensure that the selected reinforcement ratio is greater than or equal to the minimum reinforcement ratio. .

[0049] The specific configuration of the FRP stirrups in step S7 is set to a diameter of 12mm and a spacing of 80mm, based on the test results of FRP reinforced concrete beams.

[0050] The beneficial effects of this invention are as follows:

[0051] (1) FRP bars are used in the tension zone and stainless steel bars are used in the compression zone. This effectively solves the problem of steel corrosion and avoids the use of FRP bars as compression bars.

[0052] (2) The reinforcement design is carried out by the mid-span deflection limit to ensure that the mid-span deflection under the normal service limit state meets the service performance.

[0053] (3) The formula for calculating the ultimate bending moment considering the contribution of stainless steel reinforcement in the compression zone was re-derived, and the prediction effect was significantly improved.

[0054] The present application aims at solving the double pain points of corrosion and deflection in seawater and sea sand environment, and forms a simple, high-adaptation and full-performance guarantee FRP bar seawater and sea sand concrete beam design scheme through the design of deflection leading reinforcement, minimum reinforcement ratio checking and quantitative safety reserve, thereby providing key technical support for the application of FRP bar concrete structure in marine engineering. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 is a structural schematic diagram of the FRP bar seawater and sea sand concrete beam.

[0056] Figure 2 is a sectional schematic diagram of the FRP bar seawater and sea sand concrete beam.

[0057] Figure 3 is a design flowchart of the FRP bar seawater and sea sand concrete beam.

[0058] Among them, 1 is a compression zone stainless steel bar, 2 is a tensile zone FRP bar, and 3 is a FRP stirrup. DETAILED DESCRIPTION

[0059] The present application will be further described below in combination with the drawings of the present application and by introducing a FRP bar seawater and sea sand concrete beam design example.

[0060] Example 1

[0061] A design method of a FRP bar seawater and sea sand concrete beam for controlling mid-span deflection, as shown in Figure 1 and Figure 2 , the FRP bar seawater and sea sand concrete beam comprises upper longitudinal bars and lower longitudinal bars, the upper longitudinal bars comprise compression zone stainless steel bars 1, the lower longitudinal bars comprise tensile zone FRP bars 2, FRP stirrups 3 are arranged between the longitudinal bars, and the longitudinal bars and the stirrups are filled with seawater and sea sand concrete around.

[0062] Figure 3 is a design flowchart of the FRP bar seawater and sea sand concrete beam, and a FRP bar seawater and sea sand concrete beam design example can be introduced for further description.

[0063] In the FRP bar seawater and sea sand concrete beam design example, a certain frame beam is taken as an example and can be approximately regarded as a simply supported beam. The calculated span of the beam is known ,the design moment obtained by the quasi-permanent combination of the dead load standard value and the live load standard value is ;

[0064] The design method comprises the following steps:

[0065] ​S1 input design bending moment with mid-span deflection limit ;

[0066] When , , input with ;

[0067] S2 initial selection of cross-sectional size and material properties

[0068] When , , then , , then ;

[0069] When the concrete strength grade is C40, the elastic modulus of concrete , the prism compressive strength of concrete , the standard value of tensile strength of concrete , the tensile strength of concrete ;

[0070] When stainless steel is arranged in the compression zone, the yield strength of stainless steel in the compression zone , the elastic modulus of stainless steel in the compression zone ;

[0071] When GFRP is arranged in the tension zone, the standard value of tensile strength of FRP in the tension zone , the elastic modulus of FRP in the tension zone ;

[0072] When GFRP is arranged in the compression zone, the standard value of tensile strength of FRP in the compression zone , the elastic modulus of FRP in the compression zone ;

[0073] S3 determine (determine the edge compressive strain of concrete in case ), calculate and ;

[0074] When the concrete strength grade is C40, the mid-span deflection limit reaches at the same time ;

[0075] ;

[0076] ;

[0077] wherein, 0.002 for the peak compressive strain of concrete; 0.001 for the edge compressive strain of concrete;

[0078] S4 determining (based on determining the strain of the tensile zone FRP bar ), calculating the reinforcement ratio of the tensile zone FRP bar ;

[0079] When regarded as a simply supported beam and subjected to uniform load, the coefficient related to the applied load and boundary conditions ;

[0080] ;

[0081] ;

[0082] S5 determining (determining whether it meets the reinforcement failure, that is, whether it is greater than or equal to the balanced reinforcement ratio , if , select , if , select );

[0083] ;

[0084] ;

[0085] wherein, and are the equivalent rectangular stress diagram width coefficient and the equivalent rectangular stress diagram height coefficient of concrete under the bearing capacity limit state, respectively, and when the concrete strength grade is less than or equal to C50, the values are , ; is the ultimate compressive strain of concrete, and when the concrete strength grade is less than or equal to C50, the value is ; is the tensile strength design value of the tensile zone FRP bar; is the partial coefficient of FRP bar, and the value is 1.25; is the environmental influence coefficient of FRP bar, and the value is 1.6 according to Table 4.2.13 of GB 50608-2020;

[0086] , it indicates that the reinforcement result obtained by does not meet the reinforcement failure, so the reinforcement can be carried out according to ;

[0087] S6 Determine (determine whether the minimum reinforcement ratio is met, if met, the result is unchanged, if not met, the design needs to be redone);

[0088] ;

[0089] meet the construction requirements, so the original result can be used for reinforcement;

[0090] S7 Configure stainless steel bars and FRP stirrups in the compression zone according to the construction requirements;

[0091] If stainless steel bars are configured in the compression zone, configure 2 stainless steel bars with a diameter of 12 mm;

[0092] If the stirrup is a GFRP stirrup, the stirrup is set to a diameter of 12 mm and a spacing of 80 mm;

[0093] S8 Determine the safety reserve coefficient ;

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] , then ;

[0102] ;

[0103] ;

[0104] ;

[0105] where, is the area of the FRP bar in the tension zone; is the stress of the FRP bar in the tension zone; is the actual compression zone height under the ultimate moment; is the area of the stainless steel bar in the compression zone; is the strain of the stainless steel bar in the compression zone; Distance of compressive zone stainless steel bar to compressive zone edge; Yield strain of compressive zone stainless steel bar;

[0106] S9 Output final reinforcement result and safety reserve coefficient result;

[0107] Final reinforcement result is that 4 GFRP bars with diameter of 25 mm are arranged in tensile zone, 2 stainless steel bars with diameter of 12 mm are arranged in compressive zone, and GFRP stirrups with diameter of 12 mm and spacing of 80 mm are used as stirrups;

[0108] Final safety reserve coefficient result is 2.12.

Claims

1. A design method for FRP-reinforced seawater-sand concrete beams with mid-span deflection control, characterized in that: The FRP bar seawater sea sand concrete beam comprises upper longitudinal reinforcement and lower longitudinal reinforcement, the upper longitudinal reinforcement comprises a compression zone stainless steel bar, the lower longitudinal reinforcement comprises a tension zone FRP bar, FRP stirrups are arranged between the longitudinal reinforcement, and the longitudinal reinforcement and the stirrups are filled with seawater sea sand concrete around the longitudinal reinforcement and the stirrups; The design method includes inputting a design bending moment and a midspan deflection limit value ; Primary section dimensions and material properties; determine the Concrete edge compressive strain in the case of And calculate the width factor of the equivalent rectangular stress diagram of concrete under the serviceability limit state And the height factor of the equivalent rectangular stress diagram of concrete ; Based on determining the strain of the tensile zone FRP tendon , so as to obtain the reinforcement ratio of the tensile zone FRP tendon determined by ; it is judged whether the reinforcement failure is met, that is, whether it is greater than or equal to the balanced reinforcement ratio , if , the selected is , if , the selected is ; it is judged whether the minimum reinforcement ratio is met , if met, the result is unchanged, if not met, it needs to be redesigned; the compressive zone stainless steel bar and FRP stirrup are configured according to the construction requirements;​ Determination of safety reserve coefficient ; output final reinforcement result and safety reserve coefficient result.

2. A method of designing a FRP tendon seawater sea sand concrete beam according to claim 1, wherein: Specifically comprising the following steps: S1 input design bending moment With midspan deflection limit ; The design bending moment is the quasi-permanent combination of the characteristic value of the dead load and the characteristic value of the live load; the mid-span deflection limit when , or when , or when , or ; S2 initial selection of section size and material properties; The cross-sectional dimension is a cross-sectional height The cross-sectional dimension is a cross-sectional width ; the material properties are concrete strength class, yield strength of stainless steel in compression zone , elastic modulus of stainless steel in compression zone , standard value of tensile strength of FRP in tension zone , elastic modulus of FRP in tension zone , standard value of tensile strength of FRP stirrup , and elastic modulus of FRP stirrup ; Wherein, the concrete strength grade is less than or equal to C50; S3 determines to be in the concrete edge compressive strain in the case and calculates the equivalent rectangular stress diagram width factor of the concrete in the normal use limit state and the equivalent rectangular stress diagram height factor of the concrete ; the width factor of the equivalent rectangular stress diagram of the concrete in the normal use limit state the height factor of the equivalent rectangular stress diagram of the concrete is calculated using the following equation: ； In the formula, is the peak compressive strain of the concrete, and is 0.002; is the edge compressive strain of the concrete, and is 0.001; S4 based on determining the strain of the tensile zone FRP tendon , thereby obtaining the reinforcement ratio of the tensile zone FRP tendon determined determining the reinforcement ratio of the tensile zone FRP tendon ; Strain of the tensile region FRP tendon is calculated using the following equation: ； In the formula, is the effective height of the cross section; is a coefficient related to the applied load and boundary conditions; is the calculated span; The reinforcement ratio of the tensile region FRP tendon is calculated using the following equation: ； In the formula, is the compressive strength of the concrete prism; S5 judge whether the reinforcement failure is satisfied, that is, whether the balanced reinforcement ratio is greater than or equal to , if , then select , if , then select ; The balanced reinforcement ratio is calculated using the following equation: ； In the formula, and are the equivalent rectangular stress diagram width coefficient and the equivalent rectangular stress diagram height coefficient of concrete under the bearing capacity limit state, and when the concrete strength grade range is less than or equal to C50, the values are , ; is the ultimate compressive strain of concrete, and when the concrete strength grade range is less than or equal to C50, the value is ; is the tensile strength design value of the tensile zone FRP bar; is the partial coefficient of FRP bar, and the value is 1.25; is the environmental influence coefficient of FRP bar, which is taken according to GB 50608-2020; If , it is indicated that the cross mid-span deflection limit is met by the reinforcement result, so the reinforcement is carried out according to ; If , it is indicated that the cross mid-span deflection limit is not met by the reinforcement result, so the reinforcement is carried out according to ; S6 judge whether the minimum reinforcement ratio is satisfied If satisfied, the result is unchanged, if not satisfied, the design needs to be redone; said minimum reinforcement ratio is calculated using the following formula: ； In the formula, ft is the tensile strength of the concrete; If satisfied, it shows that the minimum reinforcement ratio is met The construction requirements, so according to the original results reinforcement; If not, it means that the current design is unreasonable, so the design should be re-performed; S7 configuring compression zone stainless steel bars and FRP stirrups according to the construction requirements; The construction requires that the pressure zone stainless steel bars are arranged according to the relevant provisions in GB 50010-2010, that is, when the diameter is 8 mm, when the diameter is 10 mm, and when the diameter is 12 mm. ​​​ The construction requirements configure the FRP stirrups, and the minimum stirrup ratio in GB 50608-2020 can be met; S8 determining a safety reserve factor ; The safety reserve factor The limit moment The ratio of the design moment The ratio of the design moment ； said limit bending moment is calculated using the following formula: ； In the formula, A is the area of the FRP tendon in tension zone; σ is the stress of the FRP tendon in tension zone; h is the actual height of the compression zone under the ultimate moment; A is the area of the stainless steel tendon in compression zone; ε is the strain of the stainless steel tendon in compression zone; d is the distance from the stainless steel tendon in compression zone to the edge of the compression zone; εy is the yield strain of the stainless steel tendon in compression zone; S9 outputting the final reinforcement result and the safety reserve coefficient result.

3. A method of designing a FRP tendon seawater sea sand concrete beam according to claim 2, wherein: the cross-sectional height in step S2 to ; Cross-sectional width To .

4. A method of designing a FRP tendon seawater sea sand concrete beam according to claim 2, wherein: The concrete edge compressive strain in step S3 is The concrete edge compressive strain in step S3 is According to the test results of the FRP bar concrete beam, the value is set to 0.001, i.e. when the concrete strength grade range is less than or equal to C50, the state corresponding to the beam is that the mid-span deflection reaches the limit value at the same time, 0.

001.

5. A method of designing a FRP tendon seawater sea sand concrete beam according to claim 2, wherein: The judgment in step S5 whether the reinforcement failure is satisfied should ensure that the selected reinforcement ratio is greater than or equal to the balanced reinforcement ratio .

6. A method of designing a FRP tendon seawater sea sand concrete beam according to claim 2, wherein: The judgment whether the construction requirement is satisfied in step S6 should ensure that the selected reinforcement ratio is greater than or equal to the minimum reinforcement ratio .

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