A method for analyzing the shear capacity of oblique section of a corroded reinforced concrete member subjected to bending

Abstract

This invention relates to a method for analyzing the shear capacity of the inclined section of a flexurally corroded reinforced concrete member, comprising the following steps: establishing a database of shear test data for the inclined section of flexurally corroded reinforced concrete members; verifying the corrosion reduction function based on different types of shear test data in the database; establishing a calculation model for the shear capacity of the inclined section based on the corrosion reduction function; and determining the final shear capacity of the inclined section of the flexurally corroded reinforced concrete member by comparing the shear capacity calculated from the calculation model with the maximum shear capacity of the inclined section when the flexural member fails under shear-compression conditions. Compared with existing technologies, this invention calibrates the reduction functions for the concrete, stirrup, and bent-up reinforcement terms based on the mean and lower limit values, and establishes a method for calculating the shear capacity of corroded reinforced concrete members composed of the corrosion-reduced concrete, stirrup, and bent-up reinforcement terms, which has the advantages of clear concept and simple calculation.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, and in particular to a method for analyzing the shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion. Background Technology

[0002] Under the long-term influence of corrosive media in the environment, the reinforcing steel in concrete structures will corrode. This corrosion leads to the degradation of concrete structural performance, causing premature failure and imposing a significant burden on national economic and social development. Therefore, understanding the evolutionary laws governing the performance of concrete structures has attracted widespread attention from academic and engineering communities both domestically and internationally.

[0003] To address this, numerous scholars both domestically and internationally have explored simplified calculation methods for the shear capacity of corroded reinforced concrete members. However, existing simplified calculation methods for the shear capacity of corroded reinforced concrete members suffer from several drawbacks. The shear mechanism of flexural members is highly complex, and the academic community has not reached a consensus on the shear failure mechanism of flexural members. Consequently, the forms of various calculation models differ, and most calculation formulas involve exponential operations, making them inconvenient for engineering applications. Further research is needed to determine the shear capacity of corroded reinforced concrete members that can account for the corrosion of longitudinal reinforcement, stirrups, and bent-up bars. Summary of the Invention

[0004] The purpose of this invention is to provide a simple and clear method for analyzing the shear capacity of the inclined section of a flexurally corroded reinforced concrete member, so as to facilitate those skilled in the art to quickly and accurately evaluate the shear capacity of the inclined section of the flexurally corroded reinforced concrete member.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for analyzing the shear capacity of a bent, corroded reinforced concrete member, comprising the following steps:

[0007] A database of shear tests on bent-corrosion reinforced concrete members with inclined sections was established. The database was divided into several categories according to the initial reinforcement and the location of corrosion.

[0008] The corrosion reduction function was verified based on different types of shear test data in the database.

[0009] A calculation model for the shear capacity of the inclined section of a flexural reinforced concrete member is established based on the corrosion reduction function;

[0010] The final shear capacity of the inclined section of the flexurally corroded reinforced concrete member is determined by the smaller value between the shear capacity calculated by the inclined section shear capacity calculation model and the maximum shear capacity of the inclined section when the flexural member fails under shear and compression.

[0011] The database is subdivided into 6 categories based on the initial reinforcement details and corrosion location, including:

[0012] 1) D1: Shear test data of beams without web reinforcement but with only longitudinal reinforcement corrosion;

[0013] 2) D2: Shear test data for beams with stirrups and web reinforcement but only longitudinal reinforcement corrosion;

[0014] 3) D3: Shear test data for stirrup-reinforced beams with web reinforcement but only rusted stirrups;

[0015] 4) D4: Shear test data of stirrup-reinforced beams with web reinforcement where both longitudinal reinforcement and stirrup corrosion occur simultaneously;

[0016] 5) D5: Shear test data for beams with both stirrups and bent-up bars, where only the stirrups are corroded;

[0017] 6) D6: A beam with both stirrups and bent-up bars that simultaneously experiences corrosion of longitudinal reinforcement, stirrups, and bent-up bars;

[0018] The above databases are divided into three main categories according to reinforcement type:

[0019] 1) Only longitudinal reinforcement is configured: D1;

[0020] 2) Configure longitudinal reinforcement and stirrups: D2+D3+D4;

[0021] 3) Configure longitudinal reinforcement, stirrups and bent-up bars: D5+D6.

[0022] The calculation model for the shear capacity of the inclined section of the flexural reinforced concrete member is as follows:

[0023]

[0024] In the formula, V u β represents the shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion; cc β vc β bc These are the corrosion reduction functions for the concrete, stirrups, and bent-up reinforcement components, respectively, which bear the shear force; V c0 V v0 V b0 These represent the shear forces borne by the concrete, stirrups, and bent-up reinforcement sections, respectively, when there is no corrosion; f t λ is the axial tensile strength of concrete; b and h0 are the initial section width and section height of the flexural member, respectively; s is the effective stirrup spacing; λ is the shear span ratio of the calculated section, taken as λ = a / h0, where a is the distance from the concentrated load application point to the support; f vy0 f by0 These are the initial yield strengths of the stirrups and bent-up bars, respectively; A v0 Ab0 These are the initial cross-sectional areas of the stirrups and bent-up bars, respectively; α is the angle between the bent-up bars and the axis of the member.

[0025] The corrosion reduction function for the shear force borne by the concrete component is verified based on shear test data in the database with only longitudinal reinforcement. Specifically, it calculates the relative value V of the shear force borne by the concrete component based on the shear test data of the reinforced concrete beam with longitudinal reinforcement after the longitudinal reinforcement has corroded, i.e., database D1. c,exp / V c0,exp The relative value V of the test value is determined according to actual needs. c,exp / V c0,exp Perform mean-value fitting or lower bound fitting to determine the corrosion reduction function β for the concrete term. cc , where V c,exp V c0,exp These are the test values ​​of the shear capacity of the unreinforced beam sections without stirrups, representing both rusted and unrusted sections.

[0026] The corrosion reduction function for the shear force borne by the stirrups is verified based on the shear test data of reinforced concrete beams with longitudinal reinforcement and stirrups configured in the database, after the longitudinal reinforcement is not corroded and the stirrups are corroded. Specifically, it calculates the relative value of the shear force borne by the stirrups (V) based on the test data in database D3. cv,exp -V c0,exp ) / (V cv0,exp -V c0,exp The relative value (V) of the test value is determined according to actual needs. cv,exp -V c0,exp ) / (V cv0,exp -V c0,exp The mean or lower bound fitting of the stirrup term is used to determine the corrosion reduction function β. vc , where V cv,exp V cv0,exp These are the test values ​​of the shear capacity of the inclined section of the reinforced concrete beam with and without longitudinal reinforcement and stirrups, respectively. c0,exp These are test values ​​for the shear capacity of uncorroded beams without web reinforcement; since database D3 does not contain the same group of V values... c0,exp Relevant experimental data, therefore V is adopted. c0,cal Replace V c0,exp V c0,cal This is the calculated value of the shear force borne by the concrete when it is not corroded.

[0027] The corrosion reduction function for the shear force borne by the bent-up reinforcement is verified based on the shear test data of reinforced concrete beams with both longitudinal and bent-up reinforcement, after the longitudinal reinforcement is free of corrosion and the bent-up reinforcement is corroded. Specifically, it is based on the relative value of the shear force borne by the bent-up reinforcement (V... cb,exp -V c0,exp ) / (Vcb0,exp -V c0,exp The relative value (V) of the test value is determined according to actual needs. cb,exp -V c0,exp ) / (V cb0,exp -V c0,exp The mean or lower bound fitting of the mean value is used to determine the corrosion reduction function β for the bent-up rebar term. bc , where V cb,exp V cb0,exp These are the test values ​​of the shear capacity of the inclined section of the reinforced concrete beam with and without longitudinal reinforcement and bent-up bars, respectively. c0,exp The test value of the shear capacity of the uncorroded beam without web reinforcement;

[0028] Since there is no database in the database that verifies the corrosion reduction function for bent-up rebar items bearing shear force, the corrosion reduction function for bent-up rebar items bearing shear force is determined according to the following steps:

[0029] S231: Determine the shear force and corrosion reduction function β of the concrete term in the mean sense based on databases D1 and D3. cc,a and the corrosion reduction function β of the stirrups vc,a Calculate the shear force V borne by the concrete and stirrups after corrosion and before corrosion. cv,cal V cv0,cal , where V cv,cal =β cc,a V c0 +β vc,a V v0 V cv0,cal =V c0 +V v0 ;

[0030] S232: Test values ​​V of the shear capacity of the inclined section of reinforced concrete beams with and without rusted longitudinal stirrups and bent-up bars in database D6. cvb,exp V cvb0,exp Subtract the calculated shear force V borne by the concrete and stirrups, as determined in step S231, for both the rusted and unrusted sections. cv,cal V cv0,cal Calculate the relative shear force (V) borne by the bent-up reinforcement. cvb,exp -V cv,cal ) / (V cvb0,exp -V cv0,cal ), thus obtaining the corrected database D6;

[0031] S233: Verification analysis is performed on database D6 modified based on S232, and the relative values ​​(V) of the experimental data in the modified database D6 are analyzed. cvb,exp -V cv,cal ) / (V cvb0,exp -Vcv0,cal The mean or lower limit of the fitting is used to determine the corrosion reduction function of the bent-up reinforcement bearing the shear force.

[0032] Under concentrated loads, when flexural reinforced concrete members corrode, if the longitudinal reinforcement, stirrups, or bent-up bars cannot provide sufficient tensile force to form a shear-resistant mechanism with the concrete, the corroded flexural members will prematurely fail under shear stress. Therefore, parameters are introduced: critical corrosion rate of longitudinal reinforcement, critical corrosion rate of stirrups, and critical corrosion rate of bent-up bars, to quantitatively assess whether the longitudinal reinforcement, stirrups, and bent-up bars can effectively provide the necessary tensile force. If the corrosion rate of a certain component is greater than or equal to the corresponding critical corrosion rate, it is considered that the component cannot effectively resist shear, and the corresponding corrosion reduction function is set to 0.

[0033] The critical corrosion rate η of the longitudinal reinforcement s,c Calculated by the following formula:

[0034]

[0035] The longitudinal rib corrosion reduction function β in the sense of mean and lower limit value. cc,a β cc,l Substitute β into each cc The critical corrosion rate η of the corresponding longitudinal ribs was calculated respectively. s,ca With η s,cl , where η s f represents the corrosion rate of the longitudinal reinforcement. y0 Let A be the initial yield strength of the longitudinal reinforcement. s0 This represents the initial cross-sectional area of ​​the longitudinal reinforcement.

[0036] The critical corrosion rate η of the stirrup v,c Calculated by the following formula:

[0037]

[0038] The stirrup corrosion reduction function β in the sense of mean and lower limit values. vc,a β vc,l Substitute β into each vc The critical corrosion rate η of the stirrups was calculated respectively. v,ca With η v,cl ;

[0039] The critical corrosion rate η of the bent-up reinforcing bar b,c Calculated by the following formula:

[0040]

[0041] The corrosion reduction function β of bent-up steel bars in the sense of mean and lower limit values. bc,a β bc,l Substitute β into each bcThe critical corrosion rate η of the bent-up steel bars was calculated respectively. b,ca With η b,cl .

[0042] The method for determining the maximum shear capacity of the inclined section when the bending member fails under shear-compression is as follows:

[0043] When h 0c / b c When ≤4, V u,max =0.25β c f c b c h 0c ;

[0044] When h 0c / b c When ≥6, V u,max =0.20β c f c b c h 0c ;

[0045] In the formula, V u,max β represents the maximum shear capacity of the inclined section of the corroded bending member; c b is the influence coefficient on concrete strength. c h 0c These are the cross-sectional width and effective height after corrosion damage, respectively.

[0046] When 4 < h 0c / b c When the value is less than 6, based on the maximum shear capacity obtained above, the corresponding V is calculated using the linear interpolation method. u,max .

[0047] The width and effective height of the cross-section after corrosion damage are calculated and determined according to the following method:

[0048] For the concrete cover on both sides in the width direction, if actual observation shows that the corrosion of the stirrups along the height direction has caused the concrete cover to peel off, then the width of the section after corrosion damage is taken as b. c =bc b -c′ b Where b is the initial cross-sectional width, c b c′ b These represent the initial concrete cover thicknesses for the stirrups on both sides in the width direction; if no spalling of the stirrup cover is observed along the height direction, then approximately take b. c =b, meaning that the weakening effect of stirrup corrosion on the width direction of the cross section is not considered;

[0049] For the top concrete cover in the height direction, introduce the parameter η′ s,sp η′v,sp w′ cr w′ vcr This is used to determine whether the concrete cover at the top of a flexural member has peeled off.

[0050]

[0051]

[0052] In the formula, η′ s,sp η′ v,sp w′ represents the critical corrosion rate for rust expansion and spalling of the concrete cover caused by corrosion of the longitudinal reinforcement and the top stirrups, respectively. cr w′ vcr These are the critical rust expansion crack widths (d′0 and d) caused by corrosion of the longitudinal reinforcement and top stirrups, respectively, leading to spalling of the concrete cover. v0 c and c′ represent the initial diameters of the compression longitudinal reinforcement and stirrups, respectively, and c′ represents the thickness of the concrete cover in the compression zone.

[0053] If one of the following conditions is met: η′ s ≥η′ s,sp η′ v ≥η′ v,sp w′≥w′ cr w′ v ≥w′ vcr If the top concrete protective layer peels off, take a′ sc =0,h 0c =ha s -a′ s Otherwise, approximate a′. sc =a′ s h 0c =ha s , where a′ sc a is the distance from the edge of the cross-section after corrosion damage to the point of resultant force of the compression longitudinal reinforcement. s 、a′ s These are the distances from the edge of the initial section to the resultant force point of the tension and compression longitudinal reinforcement, respectively.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] (1) This invention conducts verification analysis using test data of a single corrosion variable in the test database, and calibrates the reduction functions of concrete, stirrup, and bent-up steel reinforcement items based on the mean and lower limit values ​​respectively, and establishes a calculation model for the shear bearing capacity of corroded reinforced concrete members composed of the corroded concrete, stirrup, and bent-up steel reinforcement items after corrosion reduction.

[0056] (2) This invention uses the mean value β of the concrete term reduction function. cc,aFor the corrosion reduction function of stirrups and bent-up bars, a lower limit value β is taken for safety. vc,l β bc,l The established practical calculation method for the shear capacity of corroded reinforced concrete members under concentrated loads can safely assess the shear capacity of corroded flexural members.

[0057] (3) This invention has the advantages of clear concept and simple calculation, and can help those skilled in the art to quickly and accurately evaluate the shear bearing capacity of the inclined section of the flexurally corroded reinforced concrete member, providing support for the safety assessment of in-service reinforced concrete structures, and is highly practical. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method of the present invention;

[0059] Figure 2 This is a graph showing the fitting result of the corrosion reduction function in one embodiment of the present invention, where (2a) is the corrosion reduction function β of the concrete component bearing the shear force. cc The fitted graph (2b) shows the corrosion reduction function β of the stirrups bearing the shear force. vc The fitted graph (2c) shows the corrosion reduction function β for the bent-up rebar bearing the shear force. bc Fitted plot. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0061] This embodiment provides a method for analyzing the shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion, such as... Figure 1 As shown, it includes the following steps:

[0062] S1: Establish a database of shear resistance tests on the inclined sections of flexurally corroded reinforced concrete members.

[0063] This embodiment collects shear test data of bent-corrosion reinforced concrete members from domestic and international literature, and subdivides the database into 6 categories based on initial reinforcement and corrosion location, including:

[0064] 1) D1: Shear test data of beams without web reinforcement with longitudinal reinforcement corrosion rate in the range of 0 to 0.125;

[0065] 2) D2: Shear test data of stirrup-reinforced beams with web reinforcement and longitudinal reinforcement corrosion only, with a longitudinal reinforcement corrosion rate in the range of 0 to 0.17;

[0066] 3) D3: Shear test data for stirrup-reinforced beams with stirrups only, with a stirrup corrosion rate in the range of 0 to 0.5415;

[0067] 4) D4: Shear test data of stirrup-reinforced beams with web reinforcement where the longitudinal reinforcement corrosion rate is 0-0.262 and the stirrup corrosion rate is 0-0.601;

[0068] 5) D5: Shear test data for beams with both stirrups and bent-up bars, where only stirrup corrosion is present and the stirrup corrosion rate is within the range of 0 to 0.3633.

[0069] 6) D6: Beams with both stirrups and bent-up bars that have a longitudinal reinforcement corrosion rate of 0 to 0.1742, a stirrup corrosion rate of 0 to 0.6835, and a bent-up bar corrosion rate of 0 to 0.299.

[0070] The above databases can be divided into three main categories according to reinforcement type:

[0071] 1) Only longitudinal reinforcement is configured: D1;

[0072] 2) Configure longitudinal reinforcement and stirrups: D2+D3+D4;

[0073] 3) Configure longitudinal reinforcement, stirrups and bent-up bars: D5+D6.

[0074] In this embodiment, the database contains a total of 326 corroded beams and 93 non-corroded beams, as shown in Table 1.

[0075] Table 1. Database of Shear Tests for Corroded Reinforced Concrete Members

[0076]

[0077] S2: Verify the corrosion reduction function based on different types of shear test data in the database.

[0078] In practical engineering, reinforced concrete beams with longitudinal reinforcement, stirrups, and bent-up bars may all corrode. The reduction in the concrete, stirrup, and bent-up bar components due to corrosion is actually coupled and difficult to distinguish. To facilitate the determination of the corrosion reduction function for each component, it is necessary to perform verification analysis based on shear test data for each single variable, and take the corrosion reduction function for each single variable as the mean or lower limit of the corresponding test data.

[0079] This invention introduces the following parameters: corrosion reduction function β for concrete, stirrups, and bent-up bars bearing shear force. cc β vc β bcA calculation model for the shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion is established. The specific form of the model is detailed in step S3. This step explains β in detail. cc β vc β bc The verification process.

[0080] S21: Check the corrosion reduction function β of the concrete term bearing shear force. cc

[0081] The corrosion reduction function for the shear force borne by the concrete component is verified based on shear test data from the database containing only longitudinal reinforcement (without web reinforcement). Specifically, it calculates the relative value V of the shear force borne by the concrete component based on the shear test data of reinforced concrete beams with longitudinal reinforcement after the longitudinal reinforcement has corroded, i.e., database D1. c,exp / V c0,exp The relative value V of the test value is determined according to actual needs. c,exp / V c0,exp Perform mean fitting (β) cc,a ) or lower limit fitting (β) cc,l Determine the corrosion reduction function β for the concrete term. cc , where V c,exp V c0,exp These are the test values ​​of the shear capacity of the unreinforced beam sections without stirrups, representing both rusted and unrusted sections.

[0082] In this embodiment, relative values ​​are used as the vertical axis and corrosion rate is used as the horizontal axis for function fitting. The corrosion reduction function fitting based on the mean is obtained by least squares verification. The corrosion reduction function fitting based on the lower limit value ensures that more than 95% of the data points (relative values) are above the reduction function. The fitting in steps S22 and S23 below also adopts this principle.

[0083] The corrosion reduction function β obtained by fitting the concrete term bearing shear force in this embodiment is... cc As shown in Figure (2a).

[0084] S22: Check the corrosion reduction function β of the stirrups bearing shear force. vc

[0085] The corrosion reduction function for shear force borne by stirrups is verified based on shear test data of reinforced concrete beams with longitudinal reinforcement and stirrups configured in the database, after the longitudinal reinforcement is not corroded and the stirrups are corroded. Specifically, based on the test data in database D3, the relative value of the shear force borne by stirrups (V) is calculated. cv,exp -V c0,exp ) / (V cv0,exp -V c0,exp The relative value (V) of the test value is determined according to actual needs. cv,exp -V c0,exp) / (V cv0,exp -V c0,exp Mean fit (β) vc,a ) or lower limit fitting (β) vc,l Determine the corrosion reduction function β for the stirrup term. vc , where V cv,exp V cv0,exp These are the test values ​​of the shear capacity of the inclined section of the reinforced concrete beam with and without longitudinal reinforcement and stirrups, respectively. c0,exp These are test values ​​for the shear capacity of uncorroded beams without web reinforcement. Since database D3 does not contain the same group of V values... c0,exp Relevant experimental data, therefore V is adopted. c0,cal Replace V c0,exp V c0,cal This is the calculated value of the shear force borne by the concrete when it is not corroded.

[0086] The corrosion reduction function β obtained by fitting the stirrup term in this embodiment bears the shear force. vc As shown in Figure (2b).

[0087] S23: Check the corrosion reduction function β of the bent-up reinforcement bearing shear force. bc

[0088] The corrosion reduction function for shear force borne by bent-up reinforcement is verified based on shear test data (database D*, no relevant data) of reinforced concrete beams with both longitudinal and bent-up reinforcement, after the longitudinal reinforcement is not corroded and the bent-up reinforcement is corroded. Specifically, it is based on the relative value of the shear force borne by the bent-up reinforcement test value (V... cb,exp -V c0,exp ) / (V cb0,exp -V c0,exp The relative value (V) of the test value is determined according to actual needs. cb,exp -V c0,exp ) / (V cb0,exp -V c0,exp Mean fit (β) bc,a ) or lower limit fitting (β) bc,l Determine the corrosion reduction function β for the bent-up rebar term. bc , where V cb,exp V cb0,exp These are the test values ​​of the shear capacity of the inclined section of the reinforced concrete beam with and without longitudinal reinforcement and bent-up bars, respectively. c0,exp The test value of the shear capacity of the uncorroded beam without web reinforcement;

[0089] Since database D* is not available in the database, the corrosion reduction function for the bent-up rebar items bearing shear force is determined by following these steps:

[0090] S231: Determine the shear force and corrosion reduction function β of the concrete term in the mean sense based on databases D1 and D3. cc,a and the corrosion reduction function β of the stirrups vc,a Calculate the shear force V borne by the concrete and stirrups after corrosion and before corrosion. cv,cal V cv0,cal , where V cv,cal =β cc,a V c0 +β vc,a V v0 V cv0,cal =V c0 +V v0 .

[0091] S232: Test values ​​V of the shear capacity of the inclined section of reinforced concrete beams with and without rusted longitudinal stirrups and bent-up bars in database D6. cvb,exp V cvb0,exp Subtract the calculated shear force V borne by the concrete and stirrups, as determined in step S231, for both the rusted and unrusted sections. cv,cal V cv0,cal Calculate the relative shear force (V) borne by the bent-up reinforcement. cvb,exp -V cv,cal ) / (V cvb0,exp -V cv0,cal ), thus obtaining the corrected database D6.

[0092] S233: Verification analysis is performed on database D6 modified based on S232, and the relative values ​​(V) of the experimental data in the modified database D6 are analyzed. cvb,exp -V cv,cal ) / (V cvb0,exp -V cv0,cal Mean fit (β) bc,a ) or lower limit fitting (β) bc,l Determine the corrosion reduction function for the bent-up reinforcement that bears the shear force.

[0093] The corrosion reduction function β for the bent-up rebar bearing shear force obtained in this embodiment is... bc As shown in Figure (2c).

[0094] Under concentrated loads, if the longitudinal reinforcement, stirrups, or bent-up bars cannot provide sufficient tensile force to form a shear-resistant mechanism with the concrete after corrosion of the flexural reinforced concrete member, the corroded flexural member will prematurely fail under shear stress. Therefore, this invention introduces the parameter: critical corrosion rate of longitudinal reinforcement (η). s,c ), Critical corrosion rate of stirrups (η) v,c ), Critical corrosion rate of bent-up steel bars (η) b,c), to quantitatively assess whether longitudinal reinforcement, stirrups, and bent-up bars can effectively provide the necessary tensile force; if the corrosion rate of a certain component (η) s / η v / η b )≥Critical corrosion rate (η) s,c / η v,c / η b,c If the value is 0, then the component is considered to be ineffective in resisting shear, and the corresponding corrosion reduction function is set to 0.

[0095] Critical corrosion rate η of longitudinal reinforcement s,c Calculated by the following formula:

[0096]

[0097] The longitudinal rib corrosion reduction function β in the sense of mean and lower limit value. cc,a β cc,l Substitute β into each cc The critical corrosion rate η of the corresponding longitudinal ribs was calculated respectively. s,ca With η s,cl , where η s f represents the corrosion rate of the longitudinal reinforcement. y0 Let A be the initial yield strength of the longitudinal reinforcement. s0 This represents the initial cross-sectional area of ​​the longitudinal reinforcement.

[0098] Critical corrosion rate η of stirrups v,c Calculated by the following formula:

[0099]

[0100] The stirrup corrosion reduction function β in the sense of mean and lower limit values. vc,a β vc,l Substitute β into each vc The critical corrosion rate η of the stirrups was calculated respectively. v,ca With η v,cl .

[0101] Critical corrosion rate η of bent steel bars b,c Calculated by the following formula:

[0102]

[0103] The corrosion reduction function β of bent-up steel bars in the sense of mean and lower limit values. bc,a β bc,l Substitute β into each bc The critical corrosion rate η of the bent-up steel bars was calculated respectively. b,ca With η b,cl .

[0104] In summary, this embodiment yields the corrosion reduction function shown in Table 2.

[0105] Table 2 Corrosion Reduction Function

[0106]

[0107] Since the formula for calculating the shear force borne by the concrete item when it is not corroded is itself a lower limit value, and the relative value of the shear force borne by the concrete item V c,exp / V c0,exp As determined by experiments, this method can effectively reflect the decreasing trend of shear force borne by the concrete term as the corrosion rate of longitudinal reinforcement increases. Therefore, in this embodiment, the mean value β of the reduction function for the concrete term is taken. cc,a However, the corrosion reduction function for stirrups and bent-up bars is conservatively set to a lower limit β. vc,l β bc,l Therefore, the corrosion reduction function was finally determined, and a calculation model for the shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion was established.

[0108] S3: Establish a calculation model for the shear capacity of the inclined section of a flexural reinforced concrete member based on the corrosion reduction function.

[0109] For a reinforced concrete member subjected to flexural stress with both stirrups and bent-up bars, GB50010-2010 "Code for Design of Concrete Structures" specifies its shear capacity under concentrated load as follows:

[0110]

[0111] In the formula, V u0 V represents the shear capacity of the inclined section of a non-corroded reinforced concrete member subjected to bending. c0 V v0 V b0 These represent the shear forces borne by the concrete, stirrups, and bent-up reinforcement sections, respectively, when there is no corrosion; f t λ is the axial tensile strength of concrete; b and h0 are the initial section width and section height of the flexural member, respectively; s is the effective stirrup spacing; λ is the shear span ratio of the calculated section, which can be taken as λ = a / h0, where a is the distance from the concentrated load point to the support; f vy0 f by0 These are the initial yield strengths of the stirrups and bent-up bars, respectively; A v0 A b0 These are the initial cross-sectional areas of the stirrups and bent-up bars, respectively; α is the angle between the bent-up bars and the axis of the member.

[0112] Corrosion of reinforcing steel in flexural members can lead to damage to the concrete and reinforcing steel sections, as well as a decrease in the yield strength of the reinforcing steel, both of which can reduce the shear capacity of the member's inclined section. Based on the formulas given in GB50010-2010 "Code for Design of Concrete Structures," this invention introduces the parameter β, which represents the corrosion reduction function β for the concrete, stirrups, and bent-up reinforcement components bearing shear force.cc β vc β bc A calculation model for the shear capacity of the inclined section of a flexural reinforced concrete member is established:

[0113]

[0114] In the formula, V u The shear bearing capacity of the inclined section of a reinforced concrete member subjected to bending corrosion.

[0115] S4: The final shear capacity of the inclined section of the flexurally corroded reinforced concrete member is determined by the smaller value between the shear capacity calculated by the inclined section shear capacity calculation model and the maximum shear capacity of the inclined section when the flexural member fails under shear and compression.

[0116] GB50010-2010 "Code for Design of Concrete Structures" specifies the maximum shear capacity of the inclined section when a flexural member with a rectangular cross-section experiences shear-compression failure. Substituting the section parameters after corrosion, we have:

[0117] When h 0c / b c When ≤4, V u,max =0.25β c f c b c h 0c ;

[0118] When h 0c / b c When ≥6, V u,max =0.20β c f c b c h 0c ;

[0119] In the formula, V u,max β represents the maximum shear capacity of the inclined section of the corroded bending member; c b is the influence coefficient on concrete strength. c h 0c These represent the cross-sectional width and effective height after corrosion damage, respectively.

[0120] When 4 < h 0c / b c When the value is less than 6, based on the maximum shear capacity obtained above, the corresponding V is calculated using the linear interpolation method. u,max .

[0121] The cross-sectional width b after corrosion damage c and effective height of cross section h 0c Calculated and determined using the following method:

[0122] In the calculation method of the shear capacity of the inclined section of a single-reinforced rectangular section flexural member, the parameter that may be damaged by corrosion of the tensile longitudinal reinforcement is the distance 'a' from the resultant point of the tensile longitudinal reinforcement to the edge of the concrete. s For safety considerations, this factor is not involved in the calculation of the shear capacity of the inclined section; therefore, there is no need to consider the reduction in concrete section capacity due to corrosion, and a can be considered as... sc =a s However, in the calculation method of the shear capacity of the inclined section of the double-reinforced rectangular section bending member, the corrosion of the compression longitudinal reinforcement and the top corrosion of the stirrups may cause the top concrete cover of the bending member to peel off, and the corrosion of the stirrups on both sides may cause the concrete cover on their respective outer sides to peel off, thus causing a reduction in the height and width of the concrete section, respectively.

[0123] For the concrete cover on both sides in the width direction, if actual observation shows that the corrosion of the stirrups along the height direction has caused the concrete cover to peel off, then the cross-sectional width after corrosion damage can be taken as b. c =bc b -c′ b Where b is the initial cross-sectional width, c b c′ b These represent the initial concrete cover thicknesses for the stirrups on both sides of the width direction. If no spalling of the stirrup cover is observed along the height direction, then b can be approximated. c =b, meaning that the weakening effect of stirrup corrosion on the width direction of the cross section is not considered.

[0124] For the top concrete cover in the vertical direction, considering that in actual engineering projects, the top of many flexural members is usually cast integrally with the floor slab, making it difficult to observe whether the top concrete cover has spalled off. However, at the same time, due to the presence of the floor slab, the top concrete cover is not easily spalled off due to corrosion of the longitudinal reinforcement and stirrups. After comprehensive consideration, and to simplify the calculation, the parameter η′ is introduced. s,sp η′ v,sp w′ cr w′ vcr It is used to determine whether the concrete cover at the top of a bending member has peeled off.

[0125]

[0126]

[0127] In the formula, η′ s,sp η′ v,sp These represent the critical corrosion rates for rust expansion and spalling of the concrete cover caused by corrosion of the longitudinal reinforcement and top stirrups, respectively; w′ cr w′ vcr These represent the critical rust expansion crack widths caused by corrosion of the longitudinal reinforcement and top stirrups leading to spalling of the concrete cover; d′0, d v0c' represents the initial diameter of the compression longitudinal reinforcement and stirrups, respectively; c' is the thickness of the concrete cover in the compression zone. For deformed reinforcement, take w'. cr w′ vcr The value is 3.5mm; for plain round steel bars, take w′. cr w′ vcr It is 2.5mm.

[0128] If one of the following conditions is met: η′ s ≥η′ s,sp η′ v ≥η′ v,sp w′≥w′ cr w′ v ≥w′ vcr If the top concrete protective layer peels off, then take a′ sc =0,h 0c =ha s -a′ s Otherwise, approximate a′. sc =a′ s h 0c =ha s That is, ignoring the reduction in the concrete cover at the top of the bending member due to the corrosion of the longitudinal stirrups. sc 、a′ sc These are the distances from the edge of the cross-section after corrosion damage to the resultant force point of the tensile and compressive longitudinal reinforcements, respectively, a s 、a′ s These are the distances from the edge of the initial section to the resultant force point of the tension and compression longitudinal reinforcement, respectively.

[0129] In this embodiment, min(V) is taken. u,max V u This serves as the final shear bearing capacity.

[0130] Specifically, this embodiment provides the following examples to verify the method described in this invention.

[0131] A laboratory in Shanghai obtained 10 reinforced concrete members with different degrees of corrosion using an electro-induced accelerated corrosion method. The members had cross-sectional dimensions b = 130 mm, h = 260 mm, h0 = 225 mm, and bottom reinforcement of 2B18 (A) s0 =508.94mm 2 ) or 2B22(A s0 =760.27mm 2 ), with A8@150 (A) v0 =100.53mm 2 The material's mechanical properties, corrosion degree, and shear span are shown in Table 3. Due to the lack of the f required in this invention, the experiment... t The parameter data is uniformly taken as 1 / 10f cFind the shear capacity of the inclined section of these 10 bent and corroded reinforced concrete members.

[0132] Table 3 Specimen Information Table

[0133]

[0134] In Table 3, the longitudinal reinforcement and stirrups of specimen L3LS-C1 were corroded. The example uses this specimen to calculate its shear capacity of the inclined section.

[0135] Calculate the critical corrosion rate (η) of longitudinal reinforcement s,c ):

[0136]

[0137] β in Table 2 cc,a Substituting the expression into the above formula for β cc ,have:

[0138]

[0139] Substituting the relevant data, we have:

[0140]

[0141] The following can be obtained by organizing the information about η. s The quadratic equation of :

[0142]

[0143] Solving the above equation, we can obtain η. s = -0.05456 (discarded) or 0.8303. Take the critical corrosion rate η of the longitudinal reinforcement. s,c =0.8303, in Table 3, η of specimen L3LS-C1 s =0.05<η s,c =0.8303, therefore the longitudinal reinforcement can effectively resist shear.

[0144] η s Substituting 0.05 into β cc,a The expression for β can be obtained cc =0.73684.

[0145] Calculate the critical corrosion rate (η) of stirrups v,c ):

[0146]

[0147] β in Table 2 vc,l Substituting the expression into the above formula for β vc ,have:

[0148]

[0149] Substituting the relevant data, we have:

[0150]

[0151] The following can be obtained by organizing the information about η. s The linear equation of one variable:

[0152] η s +0.1 = 0.1115

[0153] Solving the above equation, we can obtain η. s =0.0115. The critical corrosion rate η of the stirrups is taken as... v,c =0.0115, in Table 3, η of specimen L3LS-C1 v =0.16>η v,c =0.0115, therefore it is considered that the stirrups cannot effectively resist shear, and β is taken. vc =0.

[0154] Since specimen L3LS-C1 was not equipped with bent-up bars, no calculation is required.

[0155] The obtained β cc and β vc Substituting the bearing capacity calculation formula provided in S3 and the data, the shear capacity of the oblique section of specimen L3LS-C1 can be obtained as follows:

[0156]

[0157] Solve for the maximum shear capacity of the inclined section:

[0158] Since the experiment did not observe a reduction in cross-sectional width due to corrosion, b was chosen. c =b=130mm.

[0159] Meanwhile, the top longitudinal reinforcement was not corroded, so it is only necessary to confirm whether the corrosion of the stirrups will cause the concrete cover in the compression zone to peel off to obtain h. 0c .

[0160] Based on the cross-sectional dimensions and reinforcement information, the concrete cover thickness in the compression zone (defaulting to be the same as the concrete cover thickness c in the tension zone) is easily obtained as c′ = 18mm. The stirrups are plain round steel bars, and w′ is taken as... vcr =2.5mm. Substituting the data into the formula for calculating the critical corrosion rate of stirrups, we get:

[0161]

[0162] Because η v =0.16<η′ v,sp=0.8792, and the test did not provide the width of the corrosion crack, so it was assumed to be 0 mm. Therefore, the section height was not reduced, and h was taken as h. 0c =h0=225mm. At this time, h 0c / b c =1.73≤4, the maximum shear capacity of the inclined section is:

[0163] V u,max =0.25β c f c b c h 0c = 0.25 × 1 × 31.15 × 130 × 225

[0164] =227.78kN

[0165] V u =36.83kN < V u,max =227.78kN, therefore the final shear capacity of the oblique section of specimen L3LS-C1 is 36.83kN.

[0166] Following the steps outlined above, the shear capacity of the remaining specimens at the oblique section can be calculated, as shown in Table 4.

[0167] Table 4 Comparison of test and calculated values ​​of specimen bearing capacity

[0168]

[0169] As shown in Table 4, the shear capacity of the flexural members obtained using the method provided by this invention is lower than the experimental values. The calculation method provided by this invention allows for a rapid, simple, and safe assessment of the shear capacity of corroded reinforced concrete members subjected to bending.

[0170] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for analyzing the shear capacity of a bent-corrosion reinforced concrete member, characterized in that, Includes the following steps: A database of shear tests on bent-corrosion reinforced concrete members with inclined sections was established. The database was divided into several categories according to the initial reinforcement and the location of corrosion. The corrosion reduction function was verified based on different types of shear test data in the database. A calculation model for the shear capacity of the inclined section of a flexural reinforced concrete member is established based on the corrosion reduction function; The final shear capacity of the inclined section of the flexurally corroded reinforced concrete member is determined by the smaller value between the shear capacity calculated by the inclined section shear capacity calculation model and the maximum shear capacity of the inclined section when the flexural member fails under shear and compression. The calculation model for the shear capacity of the inclined section of the flexural reinforced concrete member is as follows: In the formula, V u The shear capacity of the inclined section of a reinforced concrete member subjected to bending corrosion; β cc , β vc , β bc These are the corrosion reduction functions for the concrete, stirrups, and bent-up bars, respectively, which bear the shear force. V c0 , V v0 , V b0 These represent the shear forces borne by the concrete, stirrups, and bent-up steel reinforcement sections when they are not corroded. f t This refers to the axial tensile strength of concrete. b , h 0 represents the initial cross-sectional width and height of the bending member, respectively; s Effective stirrup spacing; λ To calculate the shear span ratio of the cross section, take... λ = a / h 0, a This is the distance from the point of application of the concentrated load to the support; f vy0 , f by0 These are the initial yield strengths of the stirrups and bent-up bars, respectively. A v0 , A b0 These are the initial cross-sectional areas of the stirrups and bent-up bars, respectively. α The angle between the bent reinforcing bar and the axis of the component.

2. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 1, characterized in that, The database is subdivided into 6 categories based on the initial reinforcement details and corrosion location, including: 1) D1: Shear test data of beams without web reinforcement but with only longitudinal reinforcement corrosion; 2) D2: Shear test data for beams with stirrups and web reinforcement but only longitudinal reinforcement corrosion; 3) D3: Shear test data for stirrup-reinforced beams with web reinforcement but only rusted stirrups; 4) D4: Shear test data of stirrup-reinforced beams with web reinforcement where both longitudinal reinforcement and stirrup corrosion occur simultaneously; 5) D5: Shear test data of a beam with both stirrups and bent-up bars, where only the stirrups are corroded; 6) D6: A beam with both stirrups and bent-up bars that simultaneously experiences corrosion of longitudinal reinforcement, stirrups, and bent-up bars; The above databases are divided into three main categories according to reinforcement type: 1) Only longitudinal reinforcement is configured: D1; 2) Configure longitudinal reinforcement and stirrups: D2+D3+D4; 3) Configure longitudinal reinforcement, stirrups and bent-up bars: D5+D6.

3. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 2, characterized in that, The corrosion reduction function for the shear force borne by the concrete component is verified based on shear test data in the database with only longitudinal reinforcement. Specifically, it calculates the relative value of the shear force borne by the concrete component based on the shear test data of the reinforced concrete beam with longitudinal reinforcement after corrosion, i.e., database D1. V c,exp / V c0,exp The relative values ​​of the test values ​​are determined according to actual needs. V c,exp / V c0,exp Perform mean-value fitting or lower bound fitting to determine the corrosion reduction function for the concrete term. β cc ,in, V c,exp , V c0,exp These are the test values ​​of the shear capacity of the unreinforced beam sections without stirrups, representing both rusted and unrusted sections.

4. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 2, characterized in that, The corrosion reduction function for the shear force borne by the stirrups is verified based on the shear test data of reinforced concrete beams with longitudinal reinforcement and stirrups configured in the database, after the longitudinal reinforcement is not corroded and the stirrups are corroded. Specifically, it calculates the relative value of the shear force borne by the stirrups based on the test data in database D3. V cv,exp - V c0,exp ) / ( V cv0,exp - V c0,exp ), and the relative values ​​of the test values ​​are determined according to actual needs. V cv,exp - V c0,exp ) / ( V cv0,exp - V c0,exp The mean or lower bound fitting of the stirrup term is used to determine the corrosion reduction function. β vc ,in, V cv,exp , V cv0,exp The figures represent the test values ​​of the shear capacity of the inclined section of reinforced concrete beams with and without longitudinal reinforcement and stirrups, respectively. V c0,exp These are test values ​​for the shear capacity of uncorroded beams without stirrups; since there are no similar values ​​in database D3. V c0,exp Relevant experimental data, therefore adopted V c0,cal Alternative V c0,exp , V c0,cal This is the calculated value of the shear force borne by the concrete when it is not corroded. .

5. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 2, characterized in that, The corrosion reduction function for the shear force borne by the bent-up reinforcement is verified based on the shear test data of the reinforced concrete beam with longitudinal reinforcement and bent-up reinforcement, after the longitudinal reinforcement is not corroded and the bent-up reinforcement is corroded. Specifically, it is based on the relative value of the shear force borne by the bent-up reinforcement test value. V cb,exp - V c0,exp ) / ( V cb0,exp - V c0,exp ), and the relative values ​​of the test values ​​are determined according to actual needs. V cb,exp - V c0,exp ) / ( V cb0,exp - V c0,exp The mean or lower bound fitting of the mean value is used to determine the corrosion reduction function for the bent-up rebar term. β bc ,in, V cb,exp , V cb0,exp The figures represent the test values ​​of the shear capacity of the inclined sections of reinforced concrete beams with and without longitudinal reinforcement and bent-up bars, respectively. V c0,exp The test value of the shear capacity of the uncorroded beam without web reinforcement; Since there is no database in the database that verifies the corrosion reduction function for bent-up rebar items bearing shear force, the corrosion reduction function for bent-up rebar items bearing shear force is determined according to the following steps: S231: Determine the shear force and corrosion reduction function of the concrete term in the mean sense based on databases D1 and D3. β cc,a Corrosion reduction function of stirrups β vc,a Calculate the shear force borne by the concrete and stirrups after corrosion and before corrosion. V cv,cal , V cv0,cal ,in, V cv,cal = β cc,a V c0 + β vc,a V v0 , V cv0,cal = V c0 + V v0 ; S232: Test values ​​of shear capacity of reinforced concrete beams with and without rusted longitudinal stirrups and bent-up bars in database D6. V cvb,exp , V cvb0,exp Subtract the calculated shear force borne by the concrete and stirrups, as determined in step S231, for both the rusted and unrusted sections. V cv,cal , V cv0,cal Calculate the relative value of shear force borne by the bent-up reinforcement ( V cvb,exp - V cv,cal ) / ( V cvb0,exp - V cv0,cal ), thus obtaining the corrected database D6; S233: Verification analysis is performed on database D6 modified based on S232, and the relative values ​​of experimental data in the modified database D6 are analyzed. V cvb,exp - V cv,cal ) / ( V cvb0,exp - V cv0,cal The mean or lower limit of the fitting is used to determine the corrosion reduction function of the bent-up reinforcement bearing the shear force.

6. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 2, characterized in that, Under concentrated loads, if the longitudinal reinforcement, stirrups, or bent-up bars cannot provide sufficient tensile force to form a shear resistance mechanism with the concrete after corrosion of the flexural reinforced concrete member, the corroded flexural member will experience premature shear failure at the oblique section. Therefore, parameters are introduced: critical corrosion rate of longitudinal reinforcement, critical corrosion rate of stirrups, and critical corrosion rate of bent-up bars, to quantitatively assess whether the longitudinal reinforcement, stirrups, and bent-up bars can effectively provide the necessary tensile force. If the corrosion rate of a certain component is greater than or equal to the corresponding critical corrosion rate, it is considered that the component cannot effectively resist shear, and the corresponding corrosion reduction function is set to 0.

7. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 6, characterized in that, The critical corrosion rate of the longitudinal ribs η s,c Calculated by the following formula: The longitudinal rib corrosion reduction function in the sense of mean and lower limit value. β cc,a , β cc,l Substitute them separately β cc The critical corrosion rate of the corresponding longitudinal ribs was calculated respectively. η s,ca and η s,cl ,in, η s The corrosion rate of the longitudinal reinforcement. The initial yield strength of the longitudinal reinforcement is denoted as . This represents the initial cross-sectional area of ​​the longitudinal reinforcement. The critical corrosion rate of the stirrups η v,c Calculated by the following formula: The stirrup corrosion reduction function in the sense of mean and lower limit value. β vc,a , β vc,l Substitute them separately β vc The critical corrosion rate of the corresponding stirrups was calculated respectively. η v,ca and η v,cl ; The critical corrosion rate of the bent-up steel bars η b,c Calculated by the following formula: The function for reducing the corrosion of bent-up steel bars in terms of mean and lower limit values. β bc,a , β bc,l Substitute them separately β bc The critical corrosion rate of the bent-up steel bars was calculated respectively. η b,ca and η b,cl .

8. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 1, characterized in that, The method for determining the maximum shear capacity of the inclined section when the bending member fails under shear-compression is as follows: when h 0c / b c When ≤4, ; when h 0c / b c When ≥6, ; In the formula, V u,max This represents the maximum shear capacity of the inclined section of the corroded bending member. β c This is the coefficient affecting concrete strength. b c , h 0c These are the cross-sectional width and effective height after corrosion damage, respectively. When 4 < h 0c / b c When the value is less than 6, based on the maximum shear capacity obtained above, the corresponding value is calculated using the linear interpolation method. V u,max .

9. The method for analyzing the shear capacity of a bent-corrosion reinforced concrete member with oblique section according to claim 8, characterized in that, The width and effective height of the cross-section after corrosion damage are calculated and determined according to the following method: For the concrete cover on both sides in the width direction, if actual observation shows that the corrosion of the stirrups along the height direction has caused the concrete cover to peel off, then the cross-sectional width after corrosion damage is taken as... b c = b - c b - c′ b ,in, b The initial cross-sectional width, c b , c′ b These represent the initial concrete cover thicknesses for the stirrups on both sides in the width direction; if no spalling of the stirrup cover is observed along the height direction, then approximately take... b c = b That is, the weakening effect of stirrup corrosion on the width direction of the cross section is not considered; For the top concrete cover in the height direction, introduce parameters. η′ s,sp , η′ v,sp , w′ cr , w′ vcr This is used to determine whether the concrete cover at the top of a flexural member has peeled off. In the formula, η′ s,sp , η′ v,sp These are the critical corrosion rates for rust expansion and spalling of the concrete cover caused by corrosion of the longitudinal reinforcement and top stirrups, respectively. w′ cr , w′ vcr These represent the critical rust expansion crack widths caused by corrosion of the longitudinal reinforcing bars and top stirrups, leading to spalling of the concrete cover. d ′ 0、 d v0 These are the initial diameters of the compression longitudinal bars and stirrups, respectively. c ′ represents the thickness of the concrete cover in the compression zone; If one of the following conditions is met: η′ s ≥ η′ s,sp , η′ v ≥ η′ v,sp , w′ ≥ w′ cr , w′ v ≥ w′ vcr Then the top concrete protective layer will peel off, and the top concrete protective layer will be removed. a′ sc =0, h 0c = h - a s - a′ s Otherwise, take an approximate value. a′ sc = a′ s , h 0c = h - a s ,in, a′ sc This is the distance from the edge of the cross-section after corrosion damage to the point of resultant force of the compression longitudinal reinforcement. a s , a′ s These are the distances from the edge of the initial section to the resultant force point of the tension and compression longitudinal reinforcement, respectively.

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