Modeling of Compressive Strength Characteristics of Structural-sized Afara (Terminalia superba) and Babo (Isoberlinia doka) Timber Columns Using Constant Failure Rate (CFR) Model of Reliability

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This paper investigated the reliability of the Structural-sized Afara and Babo timber species as column materials. The work centers on the compressive strength characteristics of Nigerian Afara (Terminalia superba) and Babo (Isoberlinia doka) timber
  Journal of Soft Computing in Civil Engineering 2 - 2 (2018) 102 - 115    journal homepage:   Modeling of Compressive Strength Characteristics of Structural - sized Afara ( Terminalia superba ) and Babo (Isoberlinia  doka ) Timber Columns Using Constant Failure Rate (CFR) Model of Reliability   A. A. Jimoh 1 , R.O. Rahmon 1* , K.H. Ibrahim 1   1. Department of Civil Engineering, Faculty of Engineering and Technology, University of Ilorin, Ilorin, Nigeria. Corresponding author:   ARTICLE INFO   ABSTRACT   Article history: Received: 12 November 2017 Accepted: 05 February 2018 This paper investigated the reliability of the Structural-sized Afara and Babo timber species as column materials. The work centers on the compressive strength characteristics of Nigerian Afara ( Terminalia superba ) and Babo (  Isoberlinia doka ) timber column of nominal lengths 200, 400, 600 and 800 mm and a nominal width and thickness of 50 mm by 50 mm. The steps involved collection and conditioning of Afara and Babo timber species, preparation of test specimens, determination of physical properties such as moisture content and density, determination of compressive strengths using varying heights of 200, 400, 600 and 800 mm and derivation of continuous column design equations. Forty test samples were used in all the tests carried out. Afara and Babo have an average density of 509.80   and 849.67 kg/m 3 respectively. Moisture content of both species less than the maximum recommended value of 20 % and the average strength at yield of Afara and Babo are 19.99 and 30.96 N/mm 2 . The derived continuous equations for design of Afara column and Babo column are =. .  and =. −.  respectively. The results of the reliability analysis show that Afara and Babo timber species have reliability index of 0.63  and 0.64 respectively   for a service life of 50  years, assuming other serviceability conditions are met. This design procedure is distinct and more effective than the usual procedure of classification of compression members as short, intermediate and long.   The paper therefore recommends the adoption of these equations for the design of compression members from these timber species in Nigeria. Keywords: Afara, Babo, Compressive strength, Regression Analysis, Reliability.     A. A. Jimoh et al./ Journal of Soft Computing in Civil Engineering 2 - 2 (2018) 102 - 115   103   1.   Introduction Timber is a natural structural material from matured trees which serves various purposes in construction and furniture industry [1]. Timber is the oldest and widely used construction material. It is used in various structural forms such as railway sleepers, columns, beams, joists, trusses and so on. The strength of a timber depends on its species and the effects of certain growth characteristics [2]. It is one of the few natural and renewable construction materials that exists but has its limitations in general use for construction, carpentry and upholstery [3]. Also, timber is an organic material and thus is subject to deterioration with time [4]. Structural timbers are timbers used in framing and load -  bearing structures, where strength is the major factor in its selection and use [5]. Nigeria is a country with an abundant timber [6]. If this natural resource is properly utilized, it will of great benefit to the country in terms of reduction in the cost of construction [1]. The common names of Afara in Nigeria is Yoruba (Afara), Nupe (Eji), Igbo (Edo), Efik (Afia eto) and that of Babo is Yoruba (Babo), Nupe (Baborochi), Hausa (Doka), Tiv (Mkovol).   The main characteristic of these timber species under investigation is their buckling characteristics when subjected to compressive load. According to [7], buckling is a mode of failure that generally results from structurally unstable member due to compressive action on the said member and it depends on the geometric properties of the member. This study concerns about the current trends and integration of advanced technologies to suit the available climatic, human and natural resources to solve the problem of transportation, by making cheaper, better and more reliable structural system in highways [8]. Environment conditions as well as the soil affect the growth of trees and their strength  properties. Since most of the strength properties of the timber species recorded in International Standards were based on timber obtained from trees in those areas and the laboratory tests were conducted there as well. Therefore, there is need to determine the strength properties of the locally available timber species and verify their structural reliability in order to prove their degree of structural performances with time [6].   Reliability, R(t) of an item is defined as the ability of an item to perform a required function under stated conditions without failure for a stated period of time [9]. Ghasemi & Nowak [10] stated that, Reliability is often understood to equal the probability that a structure will not fail to perform its intended function. Reliability -  based designs are efficient because they make it to achieve either to design a more reliable structure for a given cost and to design a more economical structure for a given reliability. Reliability coefficients ranges from 0 to 1, with higher coefficients indicating higher levels of reliability. However, reliability specifically measures the consistency of an item. According to [11], reliability index using constant failure rate (CFR) model is as given in equation (1):    104    A. A. Jimoh et al./ Journal of Soft Computing in Civil Engineering 2 - 2 (2018) 102 - 115   R(t)= −  (1)  Where: R(t) = reliability index; λ = constant rate of failure; t = variable time and the failure rate (λ) is express as in equation (2):   λ= 1 (2)   Where: T is the time (years), expected life span of timber, and d: the average compressive strength rate.    Nowak [12] defines structural reliability as the probability that a structural system will satisfy the  purpose for which it was designed and efficiently serve the period for which it was designed to without attaining a given limit state. Structural reliability and probabilistic methods have gradually grown to be important in modern structural engineering practice, especially when it involves naturally occurring materials like timber. Structural reliability could currently be used in the formulation of new generation design codes, evaluation of existing structures and probability risk assessment. Ghasemi & Nowak [13] established an optimization procedure to determine the target reliability for structures with consideration of the construction cost, failure cost, maintenance cost, structural life - time, discount rate, time - dependency of the load and resistance, and structural important factor. The contour concept approach was adopted to establish the above relationship. Part of the Objectives for structural design is to fulfill certain performance criteria related to safety and serviceability. One of such performance criteria is usually formulated as a limit state, that is, a mathematical description of the limit between performance and non -  performance [14]. Parameters used to describe limit states are loads, strength and stiffness parameters, dimensions and geometrical imperfections; since the  parameters are random variables, the outcome of a design in relation to limit state is associated with uncertainty [15]. A significant element of uncertainty is also introduced through lack of information about the actual physical variability. The aim of this study is to evaluate the compressive strength characteristics of structural - sized  Nigerian grown Afara and Babo timber species columns using constant failure rate reliability method. The objectives are: to conduct experiments on the Nigerian Afara and Babo timber species; to derive continuous column design equations for the Nigerian Afara and Babo timber species as column structural material; to estimate the reliability of the Nigerian Afara and Babo timber species; and to  promote our locally available and affordable structural material.  2.   MATERIALS AND METHOD    Material procurement    –    Terminalia superba  (Afara) and  Isoberlinia doka   (Babo)   timber species were bought from Tanke, Odo-Okun and Saboline sawmills in Ilorin, Kwara State, Nigeria. These were     A. A. Jimoh et al./ Journal of Soft Computing in Civil Engineering 2 - 2 (2018) 102 - 115   105  naturally seasoned for seven months in order to reach moisture content equilibrium environmentally. The natural seasoning were adopted. The timber samples were prepared and tested in accordance with [16]. Test for physical and mechanical properties of structural timbers at the Wood section of the Civil Engineering Department, University of Ilorin, Nigeria. Timber lengths of 50 mm x 50 mm section obtained from each sawmill was cut into lengths 200, 400, 600 and 800 mm. A maximum height of 800 mm was used due to the limited height of the testing machine. The physical property tests of the timber species was carried out at the structural laboratory of Civil Engineering Department, University of Ilorin, while the mechanical strength test was carried out using a Universal Testing Machine (UTM) of capacity 300 kN at the Agricultural and Biosystems Engineering Laboratory at University of Ilorin, Kwara State, Nigeria.  Physical property tests Moisture Content - In Accordance with [17] immediately after each mechanical test has been conducted, a small sample for determination of moisture content was cut from each test piece. The sample size was 50 x 50 x 50 mm and consists of a transverse section from near the point of fracture. The sample was weighed and then dried in an oven at a temperature of 103 ± 2 °C (217 ± 4 °F) until the weight is constant. The loss in weight expressed as a percentage of the final oven-dry weight is taken as the moisture content of the test piece. Percentage Moisture content, (m.c) is given as: ..%=   −       100% (3)  Where: W a  = Air-dried weight of sample at test in grams, W 0  = Oven-dried weight of sample in grams. Density - Density of a material is the ratio of the mass to the volume. In the 50mm x 50mm standard given by [17], all test pieces weight and dimensions were determined before test. The density is given as: =     =    (4)   Where: ρ = density in kg/m 3 , B = Breadth in cm, D = Depth in cm, H = height in cm, W a  = Air-dry weight of sample at test in grams (g), V a  = Air-dry volume of sample at test in cubic meters (m 3 ).  Mechanical property test   Compressive Strength - Compressive strength test was carried out using a Testometric Universal Testing Machine. The following procedures were carried out: i. The timber was cut into various sizes (200, 400, 600 and 800mm); twenty samples for each of the sizes and then labeled.  106    A. A. Jimoh et al./ Journal of Soft Computing in Civil Engineering 2 - 2 (2018) 102 - 115   ii. The machine height was now adjusted to the sizes of the specimen. Then the timber was fixed for loading.   iii. The speed of the test was calculated according to [17] standard as 13.020, 26.040, 39.060 and 52.075mm/min for the length 200, 400, 600 and 800 mm respectively. iv. The nominal length, the test speed, weight, breadth, width of the samples was inputted into the computer. v. The machine was started and load deflection curve can be seen on the computer, the machine was stopped when the sample fails or when the curve starts to deflect downward. vi. The buckling was measured, and the sample taken out of the machine. vii. The steps were repeated for the remaining samples. viii. From the load deflection curve obtained after the test, the stress and strain is calculated Stress, σ (N/mm  ) =   (5)   Strain, ε (%) = ΔH  (6)      Member slenderness was calculated as follows: Slenderness ratio, = Ler  (7)  Where: Le = 1.0L, =√   , =    , A = B*D and λ = Slenderness Ratio, Le = effective length, r = radius of gyration, I = moment of inertia, A = cross -sectional area, L = Length, B = Breadth, D = Depth. 3.   RESULTS AND DISCUSSIONS Density  - The density of an air-dried timber has a direct relationship with the strength of the timber. Hence, the higher the density the higher the strength of the timber and vice versa. The average density of Terminalia superba  (Afara) and  Isoberlinia doka   (Babo) are 509.80 and 849.67 kg/m³ respectively as presented in Table 1. When compared with Afzelia bipindensis (Apa) and Lannea schimperi (Opon) obtained by [18] the values of 652.74 and 472.60 kg/m 3 , this show that Afara is more denser than Opon but less densed to Apa. However, Babo is denser than both Apa and Opon. Also, comparing the result with those of [19], Afara has a lesser density when compared with Albizia, Ekhimi, Ekki and Opepe with density values of 690, 912, 997 and 776 kg/m 3 , respectively, whereas Babo was denser than Albizia. This implies that Babo has higher yield strength than Afara. According to [20], Afara can be classified as medium wood whereas Babo is hardwood.
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