KR20110094619A - Method for estimating deflections in reinforced concrete beams - Google Patents

Abstract

PURPOSE: A method for estimating the slack of concrete beam is provided to estimate the slack of a concrete beam by measuring cracking distribution on a beam in a safety inspection process. CONSTITUTION: A method for estimating the slack of concrete beam is as follows. The cracking distribution of the concrete beam is measured(S12). The slack is measured according to basic model based on correlation between the sum of a cracking width and slack(S15). The final slack is determined by selecting a correction factor and correcting the estimated slack(S18). A material characteristic is determined before the measurement of the cracking distribution.

Description

Method for Estimating Deflections in Reinforced Concrete Beams

The present invention relates to a method for estimating deflection of concrete beams, and more particularly, to a method for estimating deflection of concrete beams by measuring crack distribution and width generated in a beam.

All building structures must be designed to meet the required strength and at the same time ensure usability for their intended use. In general, the required strength of reinforced concrete structural members can be estimated by the ultimate strength design method, and the usability can be examined by whether or not factors such as deflection, crack width, and vibration that occur under working load are within limited tolerances. Can be ensured by limiting the occurrence of excessive cracking or deflection (Ref. 1-3). As the long span structure increases, the deflection and cracking problems of reinforced concrete flexural members have been recognized as a very important problem in terms of securing usability for use of the structure. If cracks occur in reinforced concrete flexural members, there is a close relationship between deflection and cracking because flexural stiffness is lowered and this causes an increase in deflection. However, it is difficult to estimate the exact bending stiffness of one reinforced concrete member because the degradation of flexural stiffness due to cracking is very complicated depending on the crack initiation section, crack height and crack width. Looking at a number of known studies (see references 3 to 7), including design criteria for determining the bending stiffness required for the deflection of flexural members, the concept of effective cross-sectional secondary moments is applied. However, it is known that the known effective cross-sectional secondary moments are applied in such a way that a number of influencing factors are limited to reflect them.

The present invention is to solve such problems in the known method, and proposes a new method in which the deflection of a member can be estimated through the correlation between crack width and deflection, rather than supplementing or modifying the effective cross-sectional secondary moment concept. do. Specifically, in the present invention, unlike the case where the deflection is calculated using the effective cross-sectional secondary moment, a method in which the deflection of the member can be directly calculated based on the correlation between the crack width and the deflection is proposed. In addition, experiments were carried out on a total of 17 simple supported reinforced concrete beams, and the ultimate crack width and deflection were measured at the loading stage, and the correlation was analyzed and compared with the experimental results. The accuracy of the method is verified. First, known studies are disclosed for comparison.

In general, the reinforced concrete member has a characteristic that the secondary moment of the cross section is not changed uniformly due to the crack generated due to the material properties of the concrete. Therefore, the effects of stiffness reduction due to cracking must be fully reflected in order for accurate deflection to be calculated. If cracks occur in the reinforced concrete flexural member, the flexural stiffness decreases as shown in FIG. 22A and the curvature rapidly increases despite a small increase in load compared to before cracking (Ref. 4). In general, the flexural stiffness of the beam can be expressed by the cross-sectional secondary moment (I), the concrete modulus of elasticity (E _c ) and the length of the member. Current standards assume that the stress state of the material is elastic and the modulus of elasticity is constant during the usability review. Secondary moments due to cracks are presented in shear, effective and crack sections according to the magnitude of the applied load. In other words, the cross-sectional secondary moment (I _g ) using the shear area before the crack is used as shown in FIG. 22B, and the crack cross-sectional secondary moment (I _cr ) when 3 or more times the load is applied after the crack is applied. If less than one, the effective cross-sectional secondary moment (I _e ) with a value between I _g and I _cr is applied. According to the Concrete Structural Design Criteria (Refs. 2 and 3), the effective cross-sectional secondary moment (I _e ) is calculated using the methods proposed by Branson (Refs. 5 and 6) and ACI Committee 435 (Ref. 7). And for simple beams under uniformly distributed loads, the effective section secondary moment (I _e ) is

----- 식(1)

----- Formula (1)

Can be obtained as In Eq. (1), M _cr is the crack moment, M _a is the maximum moment, I _cr is the crack cross section secondary moment, I _g is the shear plane secondary moment, and Y _t is the distance from the center to the outermost side of the tension side, respectively. . Al-difference DE, etc. (see reference 8) it was carried out an experiment for the reinforced concrete beams that can have one point or two-point concentrated load and a uniform load and the effective moment of inertia (I _e)

----- 식(2)

----- Formula (2)

In the equation (2), L is the length of the member, L _cr is the length of the crack, m ^' is the coefficient considering the effect of the tensile reinforcement and the working load, βM _{cr /} M _a , and β is calculated as 0.8ρ. And ρ represents the tensile reinforcement ratio, respectively. Al-sayikeu etc. (Ref. 9) Al-difference corrected by the effect on the reinforcement ratio on the basis of previous studies, such as de the effective moment of inertia (I _e)

----- 식(3)

----- Formula (3)

In the formula (3), m represents 3-0.8ρ. (Reference 10), etc. On the other hand, blood Cri experiments and cracks moment of inertia of the experimental data the basis torn surface 2 The formula (I _cre) of the moment of inertia to the measuring less than the theoretical measurement through analysis of

----- 식(4)

----- Formula (4)

In Eq. (4), α and β are coefficients considering the effects of elastic modulus ratio (n) and tensile reinforcement ratio (ρ) of reinforcement and concrete, and are as shown in Table 1 below. From this the effective cross-section secondary moment (I _e )

----- 식(5)

----- Formula (5)

In the formula (5), φ is an experimentally determined coefficient, when ρ> 1%,-(M _a / M _cr ) (L _cr / L) / ρ and-(M) when ρ≥1%. _a / M _cr ) (L _cr / L)

Factor for the output of I _cre range for nρ ≤ 1.9% 0.003 β = 0.095 If 1.9% <nρ ≤ 5% 0.05 β = 0.07 5% <nρ ≤ 17% 0.16 β = 0.05 17% <nρ ≤ 32% 0.50 β = 0.03 for nρ> 32% 0.80 β = 0.02

Acmaludin and Thomas (Ref. 11) modify the I _cre and the coefficient φ of _Piccory and the like to approximate the effective cross-sectional secondary moment.

I _e = I _cre + (I _g -I _cre ) e ^φ ----- equation (6)

In equation (6), I _cre and the coefficient φ are respectively,

I _cre = (0.1618 + 0.0418nρ) (bd 3/12) ----- ( Equation 7)

----- 식(8)

----- Formula (8)

Becomes Lee Seung-bae et al. (12) proposed a method to calculate the effective cross-sectional secondary moments by modifying the equations proposed by Al-Chide and Al-Secich in consideration of the influence of moment distribution and effective tensile area of concrete. .

----- 식(9)

----- Formula (9)

In formula 9 m ^'is

----- 식(10)

----- Formula (10)

And A represents the effective tensile cross section of the concrete.

The known effective cross-sectional secondary moments presented above have the advantage that deflections can be predicted in a relatively simple manner, but differences may appear due to limited or major considerations of the major influence factors. In addition, since the magnitude of the working load is reflected using M _a , the exact working load is required for the calculation of the deflection. However, it is often difficult to accurately estimate the load that caused a crack when an existing building is diagnosed safely. On the other hand, the crack width can be measured relatively clearly through the crack situation and the crack width measuring device which can be directly identified with the naked eye.

The present invention has been made in order to solve the problems of the above known methods.

It is an object of the present invention to provide a method by which the deflection of a member can be inversely estimated using the measured crack width.

Another object of the present invention is to provide a method for estimating deflection of a concrete beam in which a deflection of a member can be calculated regardless of a load.

Still another object of the present invention is to provide a method for estimating deflection of a concrete beam in which a deflection of a member can be calculated in conjunction with a crack measuring device.

According to a preferred embodiment of the present invention, a method for estimating deflection of a concrete beam includes measuring a crack distribution of the concrete beam; Predicting deflection according to a basic model based on the correlation between the sum of crack widths and deflection from the crack distribution; And selecting the correction factor to correct the predicted deflection to determine the final deflection.

According to another suitable embodiment of the present invention, the crack distribution comprises a crack generation section length and a crack width.

According to another suitable embodiment of the present invention, the correction factor is determined by the value of (crack generation interval) / (beam member span).

According to another suitable embodiment of the present invention, the method further includes measuring the crack distribution and calculating the host rebar ratio and the reinforcing bar and concrete elastic modulus.

According to another suitable embodiment of the present invention, the correction coefficient comprises a simple correction coefficient determined experimentally and a detailed correction coefficient determined by regression analysis of the simple correction coefficient.

According to another suitable embodiment of the invention, further comprising the step of determining the material properties before the measurement of the crack distribution is made.

According to another suitable embodiment of the present invention, the basic model is represented by the following equation.

Where l ₀ , l _cr , ε _ave , h, k, d and ω _cr are the beam span length, crack section length, average strain, beam height, effective depth and neutral axis distance ratio, beam member effective depth and crack width, respectively. Indicates.)

According to another suitable embodiment of the present invention, the correction coefficient is in the form of an exponential function.

According to another suitable embodiment of the present invention, the final deflection is represented by the following equation.

(C ₁ , l ₀ , l _cr , h, k and Σ _cr are the exponential functions, respectively, the beam span length, crack section length, beam height, effective depth and neutral axis distance ratio and crack width, respectively, and δ _cr is The deflection of the basic model.)

According to still another preferred embodiment of the present invention, the determination criterion is 0.3 by the value of (crack generation interval) / (beam member span).

According to another suitable embodiment of the present invention, the crack distribution is measured in the form of being scanned by the measuring equipment.

According to another suitable embodiment of the invention, the final deflection is calculated in the measuring equipment.

The present invention has the advantage that the deflection can be calculated relatively easily without a separate deflection measurement when the load calculation is uncertain. In addition, the method according to the invention has the following advantages.

end. The deflection calculation model proposed in the present invention allows the deflection to be accurately calculated under the working load.

I. Deflection calculation method according to the present invention can be applied in conjunction with the crack measurement equipment in a way to estimate the deflection using the crack width inevitably measured in the safety diagnosis process.

All. The deflection calculation method according to the present invention allows the deflection to be easily calculated as compared with the method of estimating deflection using the existing effective cross-sectional secondary moment.

la. The deflection calculation method according to the present invention allows the deflection to be calculated only by the crack width regardless of the load when the exact load is difficult to be estimated.

1 illustrates an embodiment of a process to which the method for measuring the deflection of a concrete beam of the present invention is applied.
FIG. 2 illustrates a process of de-bonding longitudinal bars.
Figure 3 shows the cross-sectional details of the test body (a) and (b) shows the X chain (series) and Y chain, respectively.
Figure 4 shows the reinforcing details of the test body.
Figure 5 shows an embodiment of the configuration for the experiment.
6 shows examples of support and load conditions.
7 shows an example of the strain measurement position.
FIG. 8 shows the load-center deflection curve of each specimen.
Figure 9 shows the relationship between the sum of the crack width and the deflection up to the step before the yield load of the test specimens. In FIG. 9, (a) shows 40 mm cover specimens having different compressive strengths, and (b) shows 60 mm cover specimens having different compressive strengths, respectively.
10 shows the sum of crack width and deformation.
11 illustrates a typical configuration of flexural cracks.
12 shows curvature deformation and ideal shape.
13 shows the length tension in the crack area.
14 shows the average curvature in the crack area.
15 illustrates the moment-area theory.
Fig. 16 shows the prediction result of equation (15).
17 shows the effect of M _α / M _cr on l _cr / l ₀ .
FIG. 18 shows comparative values of the strains calculated by the simplified method and test results by equations (16) and (17).
Fig. 19 shows the comparison values of the strains calculated by the detailed method and test results by the formulas (16), (18) and (19).
20 illustrates an embodiment in which a crack in a concrete beam is scanned by a measuring device.
FIG. 21 shows the parameters or associated equations used in each step shown in FIG. 1.
22A illustrates the change in moment-curvature correlation and flexural stiffness.
22B shows the change in moment of inertia.

Hereinafter, the present invention will be described in detail with reference to the presented embodiments, but the embodiments are illustrative for clarity of understanding and should not be construed as limiting the present invention.

Deflection estimation method of a concrete beam according to the present invention comprises the steps of measuring the crack distribution; Predicting deflection according to a basic model based on the correlation between the sum of crack widths and deflection from the crack distribution; And selecting the correction factor to correct the predicted deflection to determine the final deflection.

Each step will be described in detail below.

1 illustrates an embodiment of a process to which a deflection estimation method of a concrete beam of the present invention is applied.

The basic model for calculating the deflection can be determined from member material properties and crack distribution of reinforced concrete beams. Once the base model is determined, the deflection of the reinforced concrete beam can be calculated accordingly. However, since the deflection is different depending on the length ratio of the crack section to the span length, the base model must be modified according to the crack distribution. Once the correction factor is determined according to the crack distribution, the base model can be modified to determine the final model and thus the final deflection can be calculated. This process is described according to the embodiment shown in FIG. 1. Crack distribution herein means a measurable crack state shown in a concrete beam and includes, but is not limited to, for example, crack location, length of crack section and crack width. As such, crack distribution includes any condition or situation related to a crack that can be measured and quantified by the crack equipment.

Referring to Figure 1, the final deflection value is the step of inputting the member material properties of the reinforced concrete beam (S11); A crack generation section length and a crack width are measured by using a measurement device (S12); Owner reinforcement ratio and the ratio of the reinforcement and concrete elastic modulus is calculated (S13); A neutral axis is calculated (S14); Predicting sag based on the basic model (S15); A step (S16) of examining the validity of the anticipated deflection according to the size of the (cracking period) / (beam member span); Selecting a simple correction factor and a detailed correction factor according to the value of (cracking period) / (beam member span) (S171 or S172); And the final deflection is calculated by supplementing the deflection value according to the selected correction factor (S18).

The above process is described in detail below.

Experiments were made to create a basic model from the correlation between the crack width and deflection of reinforced concrete beams. The experiment was carried out through a total of 17 specimen rolls as shown in Table 2 below. The main variables were selected as the concrete compressive strength, the cover thickness of the host rebar, and the rebar quantity. The diameter of the reinforcing bar and the non-attachment of the main bar were selected as additional variables.

Details of the test object Experiment Display f _ck
(MPa) Concrete cover at the center of the bar (mm) Number and diameter of bars A _s
(mm ² ) Presence and absence of exfoliation bars G X A0 G-X-13-A0 24 40 4-D13 508 0.0066 0 A0 G-X-16-A0 5-D16 995 0.0128 0 A0 G-X-19-A0 3-D19 861 0.0111 0 A3 G-X-19-A3 3-D19 861 0.0111 3 EA A0 G-X-25-A0 2-D25 1014 0.0131 0 Y A0 G-Y-13-A0 60 4-D13 508 0.0070 0 A0 G-Y-19-A0 3-D19 861 0.0119 0 A3 G-Y-19-A3 3-D19 861 0.0119 3 EA A0 G-Y-25-A0 2-D25 1014 0.0140 0 H X A0 H-X-13-A0 70 40 4-D13 508 0.0066 0 A0 H-X-16-A0 5-D16 995 0.0028 0 A0 H-X-19-A0 3-D19 861 0.0111 0 A3 H-X-19-A3 3-D19 861 0.0111 3 EA A0 H-X-25-A0 2-D25 1014 0.0131 0 Y A0 H-Y-13-A0 60 4-D13 508 0.0070 0 A0 H-Y-19-A0 3-D19 861 0.0119 0 A0 H-Y-25-A0 2-D25 1014 0.0014 0

The compressive strength of concrete was 24MPa general strength and 70MPa high strength. For the host reinforcement, 4-D13, 5-D16, 3-D19 and 2-D25 made of SD40 were used. Was used. The effective dance of the beams is 290mm and 310mm, and the A3 series specimens are artificially attached to the center 1600mm section of the member as shown in FIG. 2 in order to consider the effect of the non-bonding section on the crack width and deflection. This was placed. The distance between the test points was 4400 mm, and the cross section was 250 mm wide and 350 mm high. Specifications and reinforcement details of each specimen are as shown in Table 2 and FIGS. 3 and 4, except that the host reinforcing bars represented by 3-D19 in FIGS. 3 and 4 are merely examples of one specimen, and each specimen as shown in Table 2 It's different. As a result of the compressive strength test of concrete, the average compressive strength of the general strength test specimen was 28.0MPa and the high strength specimen was 76.4MPa.

The specimens were forged by a two-point concentrated load on top of the specimens at an acceleration rate of 5 kN per minute as shown in FIGS. 5 and 6. In order to measure the displacement of the test object, a displacement sensor (Linear Varialbe Differential Transformer (LVDT)) was installed at a point, a center of gravity, and a point 700 mm away from the point and the point of tension as shown in FIG. 7. Loads per second and displacement of members were collected via data loggers and crack generation and propagation were directly marked on the specimens at each load stage. For each specimen, a crack measuring device that can image the crack width and shape was used, and the crack widths of all cracks occurring in the range of 0-50mm from the bottom of the specimen were measured in 10kN units and the data was stored.

The collected data was analyzed to establish a basic model.

FIG. 8 shows the load-center deflection curve of each specimen.

Referring to FIG. 8, both the normal strength and the high-strength test specimens undergo full elastic modulus until the crack load, but the rigid decline occurs after the crack, resulting in nonlinear behavior, and after the yield strength is reached, the displacement is continuously increased with little increase in the load. It can be seen that typical bending behavior is shown. The higher the reinforcement ratio and the higher compressive strength after cracking, the greater the flexural strength, and the greater the coating thickness, the smaller the effective depth of the rebar and the smaller the flexural strength.

Figure 9 shows the relationship between the sum of the crack width and the deflection up to the step before the yield load of the test specimens.

10 shows the sum of crack width and deformation.

Referring to FIG. 9, in the case of the relationship between the sum of the crack widths (∑w _cr ) and the deflection up to the step before the yield load of the test specimens, the sum and the deflection of the crack widths under the use loads are almost proportional to each other. . 10, the correlation between the sum of the crack width and the deflection according to the compressive strength of the concrete and the coating thickness, which are the main variables of the experiment, can be seen. (A) and (b) of FIG. 10 show the sum-sag relationship of the crack width according to the concrete compressive strength when the coating thickness is 40 mm and 60 mm, respectively. The experimental results show that the larger the compressive strength of concrete at the same coating thickness, the smaller the deflection, and the linear trend line shows that the sum of the crack widths and the deflection are in a proportional relation.

Based on the analysis results of the collected data, a basic deflection model can be created.

It is described in detail below.

11 illustrates a typical configuration of flexural cracks.

12 shows curvature deformation and ideal shape.

13 shows the length tension in the crack area.

14 shows the average curvature in the crack area.

15 illustrates the moment-area theory.

In general, the deflection of reinforced concrete flexural members is mainly due to the bending deformation, and the deflection due to the shear force can be almost ignored (Ref. 13). In addition, the initial bending cracks tend to occur and gradually spread near the maximum moment zone as shown in FIG. 11. Therefore, as shown in FIG. 12, the distribution of curvature in the longitudinal direction of the member is greatly increased in the portion where the crack is generated, and the curvature other than the crack section will be very small compared to the curvature in the crack section (Refs. 14 to 16). Based on this assumption, in the case of the present invention, it is assumed that all deformations are concentrated in the crack section indicated by l _cr as shown in FIGS. 11 and 12, and through this assumption, the idealized curvature distribution of FIG. 12 can be obtained. Based on the idealized curvature distribution shown in FIG. 12, it can be assumed that the strain distributions of the cross sections within the crack length are all the same. Thus, as shown in FIGS. 13 and 14, the sum of the crack widths measured at the outermost side of the tension (∑w _cr ) Is divided by the length of the cracked section (l _cr ) and the average strain in the cracked section (ε _ave ) is

----- 식(11)

----- Formula (11)

And the curvature in the cracking section (φ _ave )

----- 식(12)

----- Formula (12)

Can be calculated as In formulas (11) and (12), h represents the depth of the member, kd represents the depth of the neutral axis,

----- 식(13)

----- Formula (13)

Where p represents the tensile reinforcement ratio.

Using the average curvature within the crack length thus determined and applying the moment area method (reference 13) shown in FIG. 15, the deflection of the member (δ _cr ) is

----- 식(14)

----- Formula (14)

이다(도 14 참조). 따라서,

및 식(12)에 나타낸 φ_ave를 식(14)에 대입하여 정리하면 부재의 처짐(δ_cr)은And in equation (14)

(See FIG. 14). therefore,

And substituting φ _ave shown in equation (12) into equation (14), the deflection of the member (δ _cr ) is

----- 식(15)

----- Formula (15)

Becomes

The basic deflection model created above needs to be corrected according to the crack distribution.

It will be described in detail below.

Fig. 16 shows the prediction result of equation (15).

17 shows the effect of M _α / M _cr on l _cr / l ₀ .

FIG. 18 shows comparative values of the strains calculated by the simplified method and test results by equations (16) and (17).

Fig. 19 shows the comparison values of the strains calculated by the detailed method and test results by the formulas (16), (18) and (19).

Fig. 16 shows the ratio of the deflection value δ _Exp measured in the experiment and the deflection value δ _{Ep. (15)} calculated by Equation (15) to the ratio of the length of the crack section and the span length (l _cr / l ₀ ). It is shown. The deflection ratio (δ _Exp / δ _{Eq. (15)} ) has almost constant value when the crack length is about 30% or more of the total span length, whereas when it is about 30% or less, the deflection ratio varies greatly. Shows. In the low load state in which a small number of cracks have a small crack width, the difference in the deflection value and the experimental value calculated by Eq. (15) is large because the contribution of the deflection due to the elastic deformation is greater than the contribution of the crack to the deflection. It is. Therefore, the deflection equation of Eq. (15) needs to be modified to reflect this. By introducing the correction factor (C ₁ ), the modified deflection (δ _modified )

----- 식(16)

----- Formula (16)

Becomes Since the trend line shown in FIG. 16 shows the shape of an exponential curve, the correction coefficient C ₁ can be assumed to be an exponential function, and the ratio of the length of the crack section to the length of the span (l _cr / l ₀ ) is considered as the main influence factor. It can be seen that. In addition, as shown in FIG. 17, when the ratio of crack length to span length (l _cr / l ₀ ) is about 0.3 or more, the length of crack section (l _cr ) increases proportionally as the working bending moment increases beyond the crack moment. On the other hand, when about 0.3 or less it can be seen that there is no such proportionality. Therefore, it is reasonable to apply different correction factors based on the boundary point where the ratio of the length of the pre-cracks to the length of the span (l _cr / l ₀ ) is 0.3. Therefore, according to the present invention, the correction coefficient C ₁ based on the experimental results

-----식(17)

----- Equation (17)

In equation (17), η is 0.55 when l _cr / l ₀ is less than 0.3, 0.65 is used when l _cr / l ₀ is _greater than 0.3, and the proposed correction factor C ₁ is shown in FIG. It is indicated by the trend line shown. The deflection (δ _modified ) calculated by applying equations (16) and (17) is shown in FIG. 18 in comparison with the experimental values. The deflection ratio (δ _Exp / δ _{Eq. (16)} ) by the proposed model shows a mean of 0.917 and a coefficient of variation (cov) of 0.287, suggesting that the proposed equation (16) provides very close to the experimental results. Able to know.

As mentioned earlier, the concrete compressive strength and cover thickness were found to affect the relationship between the deflection-crack width summation, which can be reflected in the proposed equation. Therefore, the regression analysis based on the experimental results, considering the effective tensile cross-sectional area (A), which can take into account the concrete compressive strength (f _ck ) and the cover thickness, results in a correction factor C ₁

----- 식(18)

----- Formula (18)

----- 식(19)

----- Formula (19)

Can be finally derived. As a result of comparing the deflection value calculated by substituting the correction coefficients of Eqs. (18) and (19) into Eq. (16) and the actual deflection value, as shown in FIG. 19, the analysis result was 0.951 on average and the coefficient of variation (COV) 0.219. Higher predictive accuracy.

Summarizing the above experiments, it can be seen that the sag can be calculated if only the crack width is scanned through the following process. Cracking can be made according to the method shown in FIG. 20 using crack measuring equipment.

Referring to FIG. 20, the measurement of the crack L generated in the reinforced concrete beam 20 by the measurement equipment 21 may be measured. The measuring equipment 21 scans the crack L while moving along the crack measurement reference line B in the direction indicated by M. FIG. The scanned crack-related data may be applied to a process of calculating the deflection method below to calculate deflection of the reinforced concrete beam 20.

FIG. 21 shows the parameters or associated equations used in each step shown in FIG. 1.

Each step in FIG. 21 corresponds to each step in FIG. 1 and the parameters or equations shown are exemplary and the present invention is not limited by the parameters or equations shown.

The parameters used in each step are as follows.

f _ck : Concrete compressive strength f _y : Reinforcement yield strength A _s : Tensile rebar cross section b: Beam member width

d: Effective depth of beam member h: Beam height E _s : Reinforced elastic modulus E _c : Concrete modulus of elasticity

l _cr : crack length section l ₀ : beam span length ∑cr: sum of crack width ρ: host steel ratio

n: ratio of elastic modulus of reinforcing steel and concrete k: ratio of effective depth (d) to neutral axis distance

δ _basic : deflection basic model C ₁ : correction factor δ _proposed : modified deflection model

In general, the crack situation and the crack width of the member can be observed or measured very accurately, and due to the development of the crack width measuring equipment, various equipments capable of high-speed scanning have been developed, and each step applied to FIG. 1 or 21 is measured. It can be done directly on the equipment. Therefore, the present invention has the advantage that the problems of the existing method in which sag and crack are advanced by independent methods, respectively, can be solved. Another problem with known methods is that the deflections are calculated only by design criteria and can only be used if the loads on the structure are known, even if the loads are predicted, a significant range of errors can occur and many Branch investigation must be preceded. In addition, there is a problem that the measured deflection may not be accurate when the building or reinforced concrete beam is tilted.

According to the present invention such a problem can be easily solved and further has the following advantages.

end. The deflection calculation model proposed in the present invention allows the deflection to be accurately calculated under the working load.

I. Deflection calculation method according to the present invention can be applied in conjunction with the crack measurement equipment in a way to estimate the deflection using the crack width inevitably measured in the safety diagnosis process.

All. The deflection calculation method according to the present invention allows the deflection to be easily calculated as compared with the method of estimating deflection using the existing effective cross-sectional secondary moment.

la. The deflection calculation method according to the present invention allows the deflection to be calculated only by the crack width regardless of the load when the exact load is difficult to be estimated.

Although the present invention has been described in detail above with reference to the presented embodiments, one of ordinary skill in the art may make various changes and modifications to the disclosed embodiments without departing from the technical spirit of the present invention. It is apparent that the present invention is not limited by such modifications and variations.

references

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20: reinforced concrete beam
L: crack
21: measuring equipment
B: crack measurement baseline
M: direction of movement of measuring equipment

Claims (12)

Measuring the crack distribution of the concrete beam; Predicting deflection according to a basic model based on the correlation between the sum of crack widths and deflection from the crack distribution; And selecting the correction factor to correct the predicted deflection to determine the final deflection. The method of claim 1, wherein the crack distribution comprises a crack generation section length and a crack width. The method for estimating deflection of a concrete beam according to claim 1, wherein the correction factor is determined by a value of (crack generation interval) / (beam member span). The method for estimating deflection of a concrete beam according to claim 1, further comprising the step of measuring the crack distribution and calculating the reinforcement ratio of the reinforcement and the reinforcement coefficient of the reinforcing steel and the concrete. The method for estimating deflection of a concrete beam according to claim 1, wherein the correction coefficient comprises a simple correction coefficient determined experimentally and a detailed correction coefficient determined by regression analysis of the simple correction coefficient. The method of claim 1, further comprising determining material properties before the measurement of the crack distribution is made. The method of claim 1, wherein the basic model is represented by the following equation.

Where l ₀ , l _cr , ε _ave , h, k, d and ω _cr are the beam span length, crack section length, average strain, beam height, effective depth and neutral axis distance ratio, beam member effective depth and crack width, respectively. Indicates.) The method of claim 1, wherein the correction factor is in the form of an exponential function. The method of claim 1, wherein the final deflection is represented by the following equation.

(C ₁ , l ₀ , l _cr , h, k and Σ _cr are the exponential functions, respectively, the beam span length, crack section length, beam height, effective depth and neutral axis distance ratio and crack width, respectively, and δ _cr is The deflection of the basic model.) The method for estimating deflection of a concrete beam according to claim 3, wherein the determination criterion is 0.3 based on the value of (crack generation interval) / (beam member span). The method of claim 1, wherein the crack distribution is measured in the form of being scanned by a measuring device. The method of claim 10, wherein the final deflection is calculated by measuring equipment.

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