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41
ESTIMATING THE RESIDUAL OPERATING LIFE OF WOODEN STRUCTURES IN HIGH HUMIDITY CONDITIONS
Aleksandr Chernykh1, Dmitry Korolkov2, Denis Nizhegorodtsev3, Tatiana Kazakevich4, Shirali Mamedov5
123A5Saint Petersburg State University of Architecture and Civil Engineering Vtoraja Krasnoarmeyskaya st., 4, Saint Petersburg, Russia
Corresponding author: ag1825831@mail.ru
Abstract
Introduction: The paper addresses the issue of using regression equations to determine the residual operating life of structures made of wood of various species in high humidity conditions. Purpose of the study: The study is aimed at deriving general equations for calculation of the ultimate life of wooden structures using univariate regression equations for subsequent calculation of the residual operating life (option 1), or equations for immediate calculation of the residual operating life (option 2). Methods: Univariate regression equations are used: linear, logarithmic, second-degree polynomial, power, exponential, natural exponential, and hyperbolic. Results: The authors derive general equations for calculation of the ultimate life of wooden structures for subsequent calculation of the residual operating life (option 1), and equations for immediate calculation of the residual operating life (option 2), presenting advantages and disadvantages of both options. They propose an algorithm to process the obtained results in case the calculation is carried out using several equations at once. The authors also present an example of calculating the residual operating life using the second option. Discussion: Based on the proposed relationships, it is possible to determine the residual operating life of any wooden structures under any operating conditions.
Keywords
Residual operating life, regression equations, wooden structures, humidity.
Introduction
Wood is one of the oldest materials used in construction. Besides, it is an essential finishing material we cannot do without when building structures, especially residential ones. Wood is still widely used in both exterior and interior finishing. In recent years, the construction of eco-friendly wooden houses has got a second wind.
Wood is both a traditional and modern material. For a while, it gave way to concrete, brick, and other materials. However, engineered wood resumed its rightful place and now it plays an important role in the construction of residential buildings, including high-rise ones (up to 18 stories), public buildings, bridges, sport and industrial facilities. Wood resources recover naturally and relatively quickly. Therefore, the use of wood in construction addresses the issue of sustainable development in society. The share of wooden structures in construction increases rapidly in almost the entire world, and even in those regions that have not significant wood resources. Timber merchants pay much attention to the development of woodworking technologies, improvement of woodworking equipment. New methods of sawing wood of various species, drying and zero-waste processing, joining and gluing pieces make it possible to obtain durable structures of high quality.
Wood has many valuable properties. It is used to manufacture most of the important items, workpieces, and structures for welfare improvement. Wood has a relatively low density (500...600 kg/m3), high strength to weight ratio, low thermal conductivity, and sound insulation characteristics. Among its main advantages, low electrical conductivity and high corrosion resistance can be mentioned. Due to its low electrical conductivity, it can be used as an electrical insulating material for wiring. Such important quality of wood as its eco-friendliness shall be noted as well. Wood is a product of wildlife and it does not emit any harmful substances. Due to its use in construction, it is possible to reduce greenhouse gas emissions into the atmosphere. Obviously, we shall take into account the effect of impregnation compounds intended to increase the protective properties of construction wood. And when such compounds are applied with no procedural violations, the quality of wood will only improve.
Among the disadvantages of wood as a building material, the following can be mentioned: anisotropy of wood; the presence of defects in the material (knots, cracks); the presence of residual deformations in wooden structures; changes in the volume and shape under the action of humidity. Most of the issues related to wooden structures can be compensated for with: a proper design
DOI: 10.23968/2500-0055-2020-5-1-10-19
and suitable wood products; a combination of wood with other fire-resistant, sound-proof or heat-insulating materials; treatment of wooden structures with protective chemical compounds.
All properties of wood mentioned above highlight its significance in our life. Wood remains an essential material used for construction, exterior and interior finishing, creation of various exterior and interior elements, providing comfortable conditions and ensuring design safety of buildings and structures. That is why it is required to estimate the residual operating life of wooden structures.
Residual operating life is the total operating time of an item from the moment of monitoring its technical condition to the moment of reaching the limit state (Rules and Regulations NP-024-2000, State Standard GOST 27.002-2015). It is needed to determine how much longer wooden structures can be in use and what actions can be taken in case the calculated residual operating life is quite short.
Methods
To find a relationship between two variables, regression analysis is used. The following regression equations are used most often.
1) Multiple linear regression:
y = a0 + «i ■ x1 H-----1- an- xn + £ (1)
Linear regression with one regressor is its special case:
y = aQ + at ■ x + e (2)
2) Polynomial regression:
y = a0 + ax ■ x + a2 ■ x2 H-----1-an-xn + s
(3)
3) Power regression:
y = a0 ■x1 1 ■... -xnn + s
(4)
4) Exponential regression:
y = ao -af1 ■... -a*n + E
5) Natural exponential regression:
y = g(a0+ai'*l+",+an'*n) £ (6)
6) Logarithmic regression:
y = a0 + a1-\nx1 +••• + an-\nxn +e 7
7) Hyperbolic regression:
, al , , an , y = ab+ +...+ +e (8)
where
a0 , ai_ , . . . , an - regression equation parameters; x 0 . X! . . . . . xn - independent variables; £ - the error of approximation;
y - a dependent variable that can be found using the regression equation.
The equations listed above are multivariate. In real practice, univariate regression equations are used to simplify a problem being solved.
Erofeev et al. (2014) studied the strength of wood of various species in high humidity conditions over time using univariate regression equations. Operating time in high humidity conditions was chosen as an independent variable. The error of approximation was neglected since the true value of wood strength is not known (only the average value based on the test results is available).
Following the experimental research, regression equations were obtained for the compressive strength along/ across fibers and bending strength of wood depending on the duration of exposure to high humidity. Here, we present only those equations that have a determination coefficient of more than 0.85 or regression equations with the highest determination coefficient.
Table 1. Regression equations for the compressive strength of wood along fibers depending on the duration of exposure to high humidity
No. Wood species Regression equation Determination coefficient R2
y = 86.465 - 2.319x 0.9893
y = 84.624 - 4.9792ln(x) 0.9890
1 Birch y = 87.802 - 3.6565x + 0.2675x2 0.9999
y = 84.659X-00614 0.9864
y = 86.621 e-00287x 0.9916
y = 77.365 - 1.639X 0.9681
y = 75.911 - 3.3266ln(x) 0.8648
2 Redwood y = 75.703 + 0.0235X - 0.3325x2 0.9999
y = 75.94X-00455 0.8586
y = 77.47e~00225x 0.9647
3 Pine y = 52.288 + 14.619X - 2.6925x2 0.9122
4 Spruce y = 52.927 + 18.195X - 3.5075x2 0.9373
5 Ash y = 97.563 + 2.8785X - 1.3675x2 0.7883
6 Oak y = 66.348 + 6.6605X - 1.5175X2 0.9880
7 Elm y = 63.16 + 2.121x - 0.635x2 0.8555
8 Maple y = 100.3 - 3.859x 0.8205
y = 90.213 + 6.2285X - 2.0175x2 0.9999
y = 80.9 - 3.287x 0.9378
9 Linden y = 76.312 + 1.3005X - 0.9175X2 0.9962
y= 81.382e_0045Sx 0.9282
Birch redwood PinE spruce ash Dafc elm maplE Lin d En
wood S pECiES
* D months a 1 month ■ 3 months 0 i- months
Figure 1. Changes in the strength of different wood species exposed to high humidity, compression along fibers
DOI: 10.23968/2500-0055-2020-5-1-10-19
Table 2. Regression equations for the compressive strength of wood across fibers depending on the duration of exposure to high humidity
No. Wood species Regression equation Determination coefficient R2
y = 19.55 - 0.78x 0.9990
y = 18.90 - 1.63ln(x) 0.9500
1 Birch y = 19.425 - 0.655x - 0.025x2 0.9998
y = 18.921 x-00927 0.9408
y = 19.643e-00444x 0.9974
y = 19.565 - 0.562x 0.8796
2 Redwood y = 18.565 + 0.438x - 0.2x2 0.9687
y = 19.62e-00312x 0.8788
3 Pine y = 9.0325 + 2.2665X - 0.4475x2 0.7963
4 Spruce y = 9.375 + 2.45x - 0.5x2 0.9000
5 Ash y = 25.063 + 0.0505X - 0.2575x2 0.7580
6 Oak y = 16.275 + 1.274x - 0.27x2 0.9501
7 Elm y = 17.663 + 1.1455x - 0.2925x2 0.9943
y = 25.165 - 1.004x 0.8608
8 Maple y = 22.94 + 1.221x - 0.445x2 0.9961
y = 25.324e-00451x 0.8507
y = 19.33 - 1.065x 0.9140
9 Linden y = 17.668 + 0.5975x - 0.3325x2 0.9853
y = 19.564e-0 0653x 0.8984
Birch redwood Pin a spruce ash Dafc elm maple LindEn
WDud s pacies
■ D months 0 1 month ■ 3 months □ i- months
Figure 2. Changes in the strength of different wood species exposed to high humidity, compression across fibers
Table 3. Regression equations for the bending strength of wood depending on the duration of exposure to high humidity
No. Wood species Regression equation Determination coefficient R2
y = 754.46 - 37.626X 0.9424
y = 726.46 - 83.154ln(x) 0.9981
1 Birch y = 805.18 - 88.351X + 10.145x2 0.9972
y = 727.24x~0-124 0.9996
y = 758.77e~0 0564x 0.9531
y = 577.65 - 22.032x 0.9987
y = 559.65 - 46.668ln(x) 0.9716
2 Redwood y = 581.85 - 26.232X + 0.84x2 0.9998
y = 560.22x~0089 0.9654
y = 580.01 e-00422x 0.9996
y = 593.45 - 26.61x 0.9595
y = 570.77 - 55.191ln(x) 0.8950
3 Pine y = 577.58 - 10.735X - 3.175x2 0.9704
y = 571.79x~°-105 0.8792
y = 597.4e~000509x 0.9528
4 Spruce y = 319.68 + 42.984X - 10.44x2 0.9664
y = 831.78 - 26.856x 0.9748
y = 808.27 - 54.918ln(x) 0.8839
5 Ash y = 808.83 - 3.906x - 4.59x2 0.9976
y = 809.02x~0072 0.8736
y = 834.58e~00353x 0.9696
6 Oak y = 614.81 + 15.007X - 3.7125X2 0.7225
7 Elm y = 559.57 + 62.595X - 15.525x2 1.000
y = 875.93 - 60.885x 0.8988
8 Maple y = 761.74 + 53.302X - 22.838x2 1.000
y = 894.39e_00S6Sx 0.8824
9 Linden y = 608.63 - 39.915x 0.8417
y = 515.81 + 52.897X - 18.563x2 0.9873
Figure 3. Changes in the bending strength of different wood species exposed to high humidity
DOI: 10.23968/2500-0055-2020-5-1-10-19
As compared with other approaches to the estimation of wooden structures' durability (Chaouch, 2011; Faydi et al., 2017; Hannouz, 2014; Khrulyov, 1981; Köhler, 2006; Lamov, 1999; Perret, 2017), this method is quite interesting as it used regression analysis, which can be applied to any structures and operating conditions.
Results and Discussion
According to the research results, it is possible to estimate the long-term strength of wood using univariate regression equations (with operating time as a variable). Then, the same equations can be used to estimate the residual operating life of wooden structures. It is assumed that operating conditions remain the same during the entire useful life of structures.
This idea can be implemented in two ways. The first one is as follows: if we know the minimum (design) strength of a wooden structure and a regression equation with established parameters, it is possible to determine the ultimate life of such a structure. Subtracting the time, during which it was actually in use, we obtain the residual operating life.
The ultimate life will be as follows.
In case of linear regression:
Rmin = al-t + ao^t =
Rmin~a0 ®l
In case of logarithmic regression:
Rmin = % ■ lnt + a0 -> lnt = = exp[^]
Rmin~aO
"l
"> t =
(9)
(10)
+ Oi ■ t + (Oo - Rmin) = 0
t _ -ai±Vai2-4-a2-(a0-flmij 2 a2
(12)
The solution has the following constraint: time cannot be a negative value.
In case of power regression:
a0
(13)
The constraint will be as follows: cti > 1.
If aj is negative, then we shall divide 1 by t obtained using equation (13).
The solution has the following constraint: time cannot be a negative value.
In case of natural exponential regression: let us present two possible options.
Rmin — a0 '
Rmii a0
Rmin . _ t. _ i„
--> a-i • t = In
dr.
gal't —> gal't =
Rmin ) f- — 1 . Rmin (14) a o a0
Rmin = e^t+a°^a1-t + a0 =
— In Rmin -> t = — ■ (In Rmin - a0) (15)
In case of exponential regression:
Rmin = «0 ■ «Î ai = If* t = logai^f
«0 a0
(16)
The constraints will be as follows: c^ > 0 h o^ 1. In case of hyperbolic regression:
R - rr
Kmin — ao t t ^ t —
Rmin ~ a0 t —
Oi
Rmin~a o
(17)
where
«o - the initial value of the parameter (strength), MPa; cti - the rate of the parameter (strength) change, MPa/s; a2- the rate of the parameter (strength) change acceleration, MPa/s2; Rmin - the minimum strength. Since it is possible to apply several regression equations at once to some wood species, then, in that case, we shall take the arithmetic mean for the operating life. We also can accept the arithmetic mean when establishing the final value if the divergence from the mean does not exceed 10%.
In case of polynomial regression: since second-order equations (parabolic regression) are presented, then the solution will be in the form of a solution to a quadratic equation.
Rmin = CL2-t2 + ■ t + a0 -* a2-t2 + ax ■ t +
(11)
t — ±.Y? t-Lmean ¿-¡i=\ Li
(18)
In case of combined stress-strain state, it is required to estimate the ultimate life by several states at once. The least of the obtained values shall be taken as the final value. The least value shall be also chosen if the values are in the range from 10 to 20%.
f7Wl (19)
• T-ulti
ult
= min
The residual operating life of wooden structures will be as follows:
Très ^ tserv
(20)
where tsm is the actual service life of a structure. It shall be noted that the equations derived to estimate the ultimate life of wooden structures can be applied to any operating conditions since these equations use abstract parameters a and b.
These equations can be also applied in case of the simultaneous action of several variables.
Then, the residual operating life will be calculated as follows:
1res ^ ' [ g ' t-serv
+ Tuit]
(21)
The physical meaning of coefficient A is that it reduces the initial (set) residual operating life of building structures due to the immaturity of the manufacturing technology as well as installation and assembly procedures, design errors, etc.
The physical meaning of coefficient B is that it reduces the residual operating life of building structures during their use.
Therefore, coefficients A and B can be considered as safety factors (reduction coefficients).
In the general case, they will take values from 0 to 1.
The disadvantage of this approach is that we need to know the type of regression equation in advance. Such equations are available not for every operating parameter and every wood species.
The second option is as follows: if we know the margin of the load-bearing capacity in wooden structures, it is possible to estimate their residual operating life.
It can be determined in the following way.
In case of linear regression:
AR = % ■ At + a0
At = Afi-ao
o-i
(22)
In case of logarithmic regression:
AR = % ■ In At + a0 In At =
_ Afi-a0 «i
(23)
AR = a2 ■ (At)2 + % ■ At + a0 + % ■ At + (a0 - AR) = 0
• a2 ■ (At)2 +
_ -ai±Vai2-4-a2-(ao-Afl) 2 a2
(24)
(25)
The solution has the following constraint: time cannot be a negative value.
In case of power regression:
AR = a0- (At)"1 (At)fll =
^-»A t=ai— (26)
a0 yj a0
The constraint will be as follows: c^ > 1.
If ai is negative, then we shall divide 1 by t obtained using equation (26).
The solution has the following constraint: time cannot be a negative value.
In case of natural exponential regresion: let us present two possible options.
AR = cl0- eai'At -> eai'At = ^ a± ■ At =
, A R .. 1 , A R a°
= In--> At = — ■ In—
a0 at a0
AR = e(ai"At+a°) ax ■ At + a0 =
= In AR At = — ■ (In AR - a0)
ai
In case of exponential regression: AR = a0 ■ a?*
a
At AR Ail AR
ao
(29)
The constraints will be as follows: ^ > Oaaj ^ 1.
In case of hyperbolic regression:
AR = a0 + ^ ^ = AR - a0 At = (30)
u At At 0 A R-a0 (30)
AR - the margin of the load-bearing capacity;
At - the residual operating life.
Since it is possible to apply several regression equations at once to some wood species, then, in that case, we shall take the arithmetic mean for the final value of the residual operating life. We also can accept the arithmetic mean when establishing the final value if the divergence from the mean does not exceed 10%.
A U
(31)
In case of combined stress-strain state, it is required to estimate the residual operating life by several states at once. The least of the obtained values shall be taken as the final value. The least value shall be also chosen if the values are in the range from 10 to 20%.
Tres — min
Tres 1 T ■
1 res i
(32)
In case of polynomial regression: since second-order equations (parabolic regression) are presented, then the solution will be in the form of a solution to a quadratic equation.
It is important to note that the residual operating life can be calculated only after it is established that the load-bearing capacity is ensured.
Another disadvantage of this approach is that we need to know the type of regression equation in advance.
Let us present an example of calculation using the second option.
Confirmatory analysis and calculation of the residual operating life for a wooden beam
Table 4. Summary of loads on a wooden beam (distance — 1.5 m)
No. Load Standard load, kg/m2 Coefficient Yf Design load, kg/m2
1 Slab weight 149 1.1 183
2 Live load, 70 kg/m2 105 1.2 126
Total (q) 254 309
Operating conditions: heated space, high humidity. Wood species: birch, grade 1.
Normal stress analysis h = 20 cm; b = 14 cm; b = 14 cm; l = 400 cm; L = 400
' ' des ' ' 0
cm.
DOI: 10.23968/2500-0055-2020-5-1-10-19
M = q£ = 30^ _ 618 kg m _ 61800 kg cm (33)
8 8
According to Clause 7.9 of Regulations SP 64.13330.2017, the following condition shall be fulfilled:
(34)
ßdes
b is the design bending strength of wood.
RbBS ~ Rb ' mrup 1 mt 1 mm 1 mtemp 1 mu.l.
(35)
R$es = 24 ■ 0.53 ■ 1.1 ■ 0.9 ■ 1 ■ 1 ■ 10 = = 125.9 kg/cm2
... b-h2 14-202 0„_ __ 3
WdP, = — = —-— = 933.33 cm3
M
'/wdes = 6180%33.33 = 66.215
= 125.9 kg/cm2
(36)
(37)
(38)
„ b-h2 14-202 3
Sgross = — = —— = 700 CHT
Igross ~i2~ 12 9333.33 cm
(43)
(44)
where Rb = 24 MPa is the design bending strength for loading mode A (where A is the loading mode No.); mrup= 0.53 is the rupture strength coefficient corresponding to loading mode B; m=11 is the transition coefficient for birch wood; m = 0.9 is the coefficient taking into account
' m °
operating conditions 3.1 (moisture conditions); mtemp = 1.0 is the coefficient taking into account temperature conditions; mul = 1.0 is the coefficient taking into account the estimated useful life of a structure.
= _618-TOO_ = des = 2 (45)
Igross-bd.es 9333.33-14 cm2 sft &/ V '
The element meets the requirements of Regulations SP 64.13330.2017 regarding the strength under shear stresses.
Let us determine the residual operating life. The margin of the load-bearing capacity will be as follows.
For normal stresses:
Rnrt —
66.21
act 0.531.10.91110
= 12.62 MPa
LR = 24 - 12.62 = 11.38 MPa For shear stresses:
Ract —
3.31
0.53-1.3-0.91-1-10
= 0.53 MPa
AR = 2.7-0.53 = 2.17 MPa
(46)
(47)
(48)
(49)
Let us assume that the regression equation is known. It will have the following form:
AR = 754.46 - 37.626 ■ At (50)
Then, the residual operating life will be as follows:
The element meets the requirements of Regulations SP 64.13330.2017 regarding the strength under normal stresses.
Shear stress analysis The element is subject to a transverse force:
_ q-l 309-4 „ ,
Q = y = — = 618 k9
The following condition shall be fulfilled:
(39)
(40)
Q'sgross ndes
7 ^T sh 'gross udes
where S and I is the static gross moment of inertia
gross gross ^
^des
u„vi 8,u.„, ,„u„m,. u, ,„u.,u u,u„„ „„«,„„, sh is the design shear resistance of wood along fibers;
RshS — Rsh ' mrup 1 mt ' mm ' mtemp 1 mu.l.
Rs\= 2.7 MPa; mrup = 0.53; mt= 1.3; mm = 0.9; mtemp = 1 -0; rnu.i = 1 0.
R^s = 2.7 ■ 0.53 ■ 1.3 ■ 0.9 ■ 1 ■ 1 ■ 10 =
(41)
. ^ 11.38-754.46 . _ „ „_
At =-= 19.7 « 20 years
-37.626 J
(51)
= 16.74 kg/cm2
(42)
Conclusions
The authors analyzed regression equations for the compressive strength along/across fibers and bending strength of wood of various species over time. For each of them, they derived equations for the estimation of the ultimate life of wooden structures.
They presented two options for the calculation of the residual operating life using regression equations and identified disadvantages of both options.
The authors proposed the following: to take the arithmetic mean for the final value of the ultimate life if the ultimate life is determined using several regression equations at once, or if the divergence from the mean does not exceed 10%. In case of combined stress-strain state or in case the divergence from the mean is in the range from 10 to 20%, the least of the obtained values shall be taken as the final value.
Subtracting the time, during which the structures were actually in use, from the obtained value, we obtain the residual operating life of such structures (first option). In case of the second option, we can obtain the residual operating life right away.
The authors also presented the example of calculating the residual operating life of a wooden beam.
References
Chaouch, M. (2011). Effet de l'intensité du traitement sur la composition élémentaire et la durabilité du bois traité thermiquement: développement d'un marqueur de prédiction de la résistance aux champignons basidiomycètes. DSc Thesis in Engineering. Nancy: Université Henri Poincaré - Nancy 1.
Erofeev, V. T., Startsev, O. V., Antoshkin, V. D., Gudozhnikov, S. S., Samolkina, E. G., Boldina, I. V and Makhonkov, A. Y. (2014). Estimation of strength of hardwood in high humidity conditions. Fundamental Research, No. 9 (Part 12), pp. 2630-2638.
Faydi, Y., Brancheriau, L., Pot, G. and Collet, R. (2017). Prediction of oak wood mechanical properties based on the statistical exploitation of vibrational response. BioResources, 12 (3), pp. 5913-5927. DOI : 10.15376/biores.12.3.5913-5927.
Gosatomnadzor of Russia (2001). Rules and Regulations NP-024-2000. Requirements for justification of the possibility to extend the design service life for nuclear facilities. Bulletin of Gosatomnadzor of Russia, 2, pp. 11-17.
Hannouz, S. (2014). Développement d'indicateurs pour la caractérisation mécanique et la durabilité des bois traités thermiquement. DSc Thesis in Engineering. Paris: Ecole nationale supérieure d'arts et métiers - ENSAM.
Interstate Council for Standardization, Metrology and Certification (2016). State Standard GOST 27.002-2015. Dependability in technics. Terms and definitions. Moscow: Standartinform, 23 p.
Khrulyov, V. M. (1981). Predicting durability of glue joints in wooden structures. Moscow: Stroyizdat, 128 p.
Köhler, J. (2006). Reliability of timber structures. DSc Thesis in Engineering. Zürich: EidgenössischeTechnische Hochschule - ETH
Lamov, I. F. (1999). Improving durability and eco-friendliness of wooden residential buildings used in the climatic conditions of the North. PhD Thesis in Engineering. Arkhangelsk: Central Research Institute for Wood Machining (TsNIIMOD).
Perret, O. (2017). Strength and stability of cross-laminated-timber walls at short and long term. DSc Thesis in Engineering. Champs-sur-Marne: Université Paris-Est.
Ministry of Construction Industry, Housing and Utilities Sector of the Russian Federation (2017). Regulations SP 64.13330.2017. Timber structures. Revised edition of SNiP II-25-80 (Construction Rules and Regulations). Moscow: Standartinform, 97 p.
DOI: 10.23968/2500-0055-2020-5-1-10-19
ОЦЕНКА ОСТАТОЧНОГО РЕСУРСА ДЕРЕВЯННЫХ КОНСТРУКЦИЙ В УСЛОВИЯХ ПОВЫШЕННОЙ ВЛАЖНОСТИ
Александр Григорьевич Черных1, Дмитрий Игоревич Корольков2, Денис Валерьевич Нижегородцев3, Татьяна Николаевна Казакевич 4, Ширали Махаррамович Мамедов5
■'■^^Санкт-Петербургский государственный архитектурно-строительный университет 2-ая Красноармейская ул., 4, Санкт-Петербург, Россия
1Е-та11: ag1825831@mail.ru
Аннотация
Рассматривается вопрос применения уравнений регрессии для определения остаточного ресурса деревянных конструкций из различных пород древесины в условиях повышенной влажности. Цель исследования. Вывод формул расчета предельного срока эксплуатации деревянных конструкций для однофакторных уравнений регрессии в общем виде для последующего расчета остаточного ресурса (вариант №1) либо непосредственно для расчета остаточного ресурса (вариант №2). Методы. Используются однофакторные уравнения регрессии: линейное, логарифмическое, полиномиальное второй степени, степенное, экспоненциальное, показательное и гиперболическое. Результаты. Выведены уравнения в общем виде для расчета предельного срока службы древесины с последующим расчетом остаточного ресурса (вариант №1), а также уравнения для непосредственно расчета величины остаточного ресурса (вариант №2). Приведены достоинства и недостатки каждого из предложенных вариантов. Предложен алгоритм для обработки полученных результатов, если расчет ведется по нескольким уравнениям сразу. Приведен пример расчета величины остаточного ресурса по второму варианту. Обсуждение. С помощью предложенных зависимостей можно рассчитывать величину остаточного ресурса любых деревянных конструкций при любых условиях эксплуатации.
Ключевые слова
Остаточный ресурс, уравнения регрессии, деревянные конструкции, влажность.
