Mechanics of Materials

This paper presents more convenient deflection function that properly substitutes slow converging series function by Naiver for simply supported quadrilateral thin plate. The formulation of the deflection function was conducted by using variational approach. During formulation, Rayleigh-Ritz procedures was used and coordinate function that satisfies kinematic boundary condition and the minimum potential energy principle was developed. In addition to coordinate function, modification factor was applied to the main function for curve fitting purpose. To validate the current study, comparisons were done with Navier's solution and finite element analysis. The results shown that the deviation for midpoint deflection of current study was very small, i.e. around 0.03%, from Navier's solution. Furthermore, it has been investigated that finite element analysis also resulted closer result with current study.

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This study was carried out on the mycoflora associated with seeds of different citrus species. Citrus seed material was collected from districts of Punjab, i.e. Multan, Sargodha and Khanpur. Standard methods were applied for the isolation and identification of fungi. A total of 11 fungi including Aspergillus fumigatus, Aspergillus flavus, Dreschslera tetramera, Alternaria alternata, Curvularia lunata, Macrophomina phaseolina, Aspergillus niger, Fusarium solani, Fusarium moniliforme, Rhizopus and Penicillium spp were isolated from the seeds of citrus. For control of isolated seed-born fungi, 3 recommended fungicides such as Ridomil Gold, Bavistin, Score and two chemical Salicylic acid and Boric acid, were used at 20, 30, 40 mg/10 mL and 5, 6, 7 µL/10 mL, respectively and chemical with 20, 30, 40 mg/10 mL. All these fungicide and chemicals significantly reuced with population of all fungi present in naturally infected seed samples. Ridomil Gold and Salicylic acid were found to be the best for the control of seed-born fungi of citrus seed at 40 mg/10 mL. The isolation and identification of different mycotoxins is essential to study health status of the citrus consumers and to safeguard the standards of WTO.

A constitutive model with microstructure, strength, work hardening submodels is developed for artificial ageing of AA2050. • The model has for the first time successfully predicted ageing behaviour covering under-ageing to over-ageing. • Yield strength and work hardening behaviour from under-aged to over-aged conditions has been characterised and modelled. • Shearing-to-bypassing strengthening transition does not occur immediately when reaching peak-ageing state.

The use of scrap rubber from waste motorcycle tire and asphalt materials is expected to improve the quality of the ballast structure. The objective of this paper is to analyze the characteristics of ballast mixture with additional scrap rubber (uniformed size 3/8” and graded size No.4, 3/8", 1/2", 3/4", 1") and asphalt materials through compressive strength test by Micro-Computer Universal Testing Machine (UTM). The samples are made in a ballast box with a size of 40 cm x 20 cm x 30 cm. The parameters of this research are the vertical deformation, the aggregate abrasion, and the elastic modulus of the ballast layer. It could be concluded that asphalt 2% able to improve the stiffness of the ballast layer so it could minimize the vertical deformation and increase the ability to retain the loads up to 28%. Moreover, the use of scrap rubber materials, especially with various sizes between No.4, 3/8", 1/2", 3/4", 1" combined with 2% asphalt could r...

يشتمل هذا الكتاب على تسع فصول. يتناول الفصل الأول أساليب طاقة الإنفعال مشفوعاً ببعض الأمثلة المحلولة والمسائل.
أما الفصل الثاني فيتضمن الإنهيار اللدن في العارضات والهياكل البسيطة (الجزء الأول) من وجهة نظر طريقة مخطط عزم الإنحناء وطريقة الشغل الإفتراضي. يحتوي هذا الفصل على نماذج من الأمثلة المحلولة وبعض التدريبات.
يواصل الفصل الثالث في دراسة الإنهيار اللدن في العارضات والهياكل البسيطة (الجزء الثاني) ويستعرض العديد من الأمثلة المحلولة والمسائل.
يتناول الفصل الرابع نظرية المرونة (1) (الإجهادات المستوية – الإحداثيات الكارتيزية) حيث يناقش معادلات الإتزان، معادلات الإنفعال – الإزاحة، معادلات التوافق، معادلات الإجهاد –
الإنفعال، والحالات الحدودية أو الطرفية متضمناً العديد من الأمثلة والمسائل.
يستعرض الفصل الخامس نظرية المرونة (2) (نظام الإجهادات الثلاثية – الإحداثيات الكارتيزية) من وجهة نظر معادلة الإتزان، معادلات الإنفعال – الإزاحة، معادلات الإجهاد – الإنفعال، ومعادلات التوافق.
أما الفصل السادس فيتناول نظرية المرونة لحالة الإجهادات الثلاثية – الكارتيزية لتحليل لوح مستطيل مسلَّط عليه حمل عرضي ويشتمل هذا الفصل على العديد من الأمثلة النموذجية والمسائل.
يواصل الفصل السابع في دراسة نظرية المرونة (3) (الإجهادات المستوية – الإحداثيات القطبية) من وجهة نظر معادلة الإتزان، معادلات الإنفعال – الإزاحة، معادلات الإجهاد – الإنفعال، ومعادلة البايهارمونيك إضافة للعديد من الأمثلة والمسائل.
أما الفصل الثامن فيستعرض نظرية المرونة (4) (الإجهادات الثلاثية – الإحداثيات الأسطوانية) من وجهات نظر معادلة الإتزان، معادلات الإنفعال – الإزاحة، معادلات الإجهاد – الإنفعال.
يشتمل الفصل التاسع والأخير على دراسة الألواح الدائرية من وجهات نظر معادلات الإتزان، معادلات الإنفعال – الإزاحة بالإضافة للعديد من الأمثلة المحلولة والمسائل الإضافية.
إنَّ الكاتب يأمل أن يساهم هذا الكتاب في إثراء المكتبة الجامعية داخل السودان وخارجه في هذا المجال من المعرفة ويأمل من القارئ ضرورة إرسال تغذية راجعة إن كانت هنالك ثَمَّة أخطاء حتى يستطيع الكاتب تصويبها في الطبعة التالية للكتاب.

A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo grain level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.

The differential method is used to calculate the elastic moduli of a solid that contains a random distribution of spherical inclusions. Closed-form solutions are obtained for the two limiting cases of rigid inclusions and vacuous pores. These solutions obey the Hashin-Shtrikman bounds, and reduce to the correct values as the inclusion concentration approaches 0 or 1. The predictions are compared with data from the literature, and are shown to be very accurate over wide ranges of the inclusion concentration.

A micromechanics framework for the development of continuum-level constitutive models for the large-strain deformation of porous hyperelastic materials is presented. A kinematically admissible deformation field is assumed which enables the derivation of a strain energy density function for the porous material. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. Differentiation of the strain energy density function, with respect to deformation, provides an expression for the stress–strain behavior of the porous hyperelastic material. Example calculations are carried out for porous hyperelastic materials with a Neo–Hookean matrix. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. Predictions of the dependence of the small-strain elastic response on porosity are compared to various estimates of effective elastic moduli for porous materials found in the literature. Constitutive model predictions of the small to large-strain deformation behavior compare well with results from numerical three-dimensional micromechanical multi-void cell models.

In the Upper Peninsula of Michigan, over 500 million tons of copper rich rock were removed from mines and treated in chemical baths to extract copper. Toxic substances have been seeping into the watersheds from the resultant waste stamp sands. Recent work on developing a circular economy using recycled plastic for distributed manufacturing technologies has proven promising, and this study investigates the potential to use this approach to form stamp sand and acrylonitrile styrene acrylate (ASA) composites. Specifically, this study found the maximum amount of stamp sand that was able to be added to waste ASA by mass with a single auger recyclebot system for compounding was below 40%. The mechanical properties of the composite were evaluated up to 40%, and the addition of stamp sand reduced the material's ultimate tensile strength by about half compared to the strength of raw recycled ASA, regardless of the percent stamp sand in the composite. However, this strength reduction plateaus and the tensile strength of the ASA and stamp sand composites can be compared favorably with acrylonitrile butadiene styrene (ABS) at any level. This makes waste ASA-stamp sand composites potential replacements for outdoor applications of ABS as well as some current ASA applications. These results are promising and call for future work to evaluate the technical, economic and environmental potential for waste ASA-stamp sand composites.

A procedure for determining the stress-strain curve including post-necking strain is proposed. Hourglass type specimens were used for tensile tests, and the stress-strain curves were identified through an iteration process using finite element analysis. The strain at the position of minimum diameter was measured by digital image correlation. This procedure was applied to carbon steel of various degrees of cold work. The radius of the minimum section of the hourglass type specimen was changed in order to investigate the effect of stress triaxiality on the failure strain. The procedure could derive the stress-strain curve including the post-necking strain. From the obtained curve, it was shown that the stress-strain curves for different degrees of cold work were almost identical when the plastic strain by the cold working was added to the strain. Furthermore, it was revealed that the true stress-strain curve could be approximated well by the power law equation and the curve could be estimated by using the stress-strain relation for before-necking strain.

Corrosion induced failure of buried ferrous pipelines causes significant economic losses to the world. Many of the existing buried water pipelines are made of ductile iron in most of the developed countries. Literature shows that the research on the corrosion-induced degradation assessments of ductile iron pipelines is limited and mostly deals with the physical deterioration i. e., loss of wall thickness determined by short-term research. This paper addresses this gap and presents a comparatively long-term study on the corrosion and its subsequent effect on the composition and nanomechanical properties of buried ductile iron pipelines in the accelerated corrosive environment. For experimentation, ductile iron specimens were immersed in the acidic simulated soil solution for 365 days. Physical deterioration assessment over the time was carried out in terms of corrosion rates measured at intervals of 180 and 365 days. A significant change in the percentage composition of key elements and phases were quantified. Furthermore, the mechanical properties of the grains were found to be considerably reduced after 365 days of immersion in the acidic environment by the nanoindentation technique. The results revealed an alarming increase of structural degradation at nano scale for some of the grains due to chloride induced localised corrosion. The significance of the current research is its in-depth analysis of the corrosion-induced degradation of ductile iron pipes which enhances the knowledge related to the failure of these pipelines.

The current study assesses the residual stresses and remnant damage caused by a spherical projectile impacting upon a¯at surface. The immediate application of this information is to the problem of foreign object damage (FOD) associated with the ingestion of debris into an aircraft turbine engine and the subsequent reduction in component lifetime. The work is focused on two primary features: (i) the development of numerical models for the evaluation of the deformation and stresses associated with the impact process and (ii) the use of spatially resolved residual stress measurements to verify experimentally the numerical analysis. As a ®rst approximation, a quasi-static numerical model was developed by ignoring time-dependent eects (i.e., strain-rate sensitivity, wave and inertia eects, etc.), where the eects of velocity were approximated by adjusting the depth and diameter of the resulting impact crater to match that of actual impact craters at the corresponding velocity. The computed residual stresses and associated elastic strain gradients were compared to experimentally measured values, obtained using synchrotron X-ray diraction (XRD) methods. This comparison indicated that the quasi-static numerical analysis was adequate for moderate impact conditions (velocity 200 m/s, energy 2.7 J); however, under more aggressive conditions (velocity 300 m/s, energy 6.1 J), there was signi®cant discrepancy between the numerical predictions and experimental measurements. Such discrepancy may be attributed to several factors that can occur at higher impact velocities, including strain-rate sensitivity, microcrack formation, and shear-band formation. A dynamic simulation, where the time-dependent eects of strain-rate sensitivity and elastic-wave interactions were approximated, provided results in closer agreement with the experimental diraction observations. Ó

The structural insulated panel is an engineered composite product composed of an insulating foam core sandwiched to provide the insulation and rigidity, and two face-skin materials to provide durability and strength. SIPs can also be used as permanent wood foundation (PWF) for basements in low-rise residential construction to save in the energy cost. The maximum deflection equation specified in the Canadian Standard for Engineering Design of Wood, CAN/CSA-O86.09 specifies expressions for the effects of short-term bending deflection on the PWF timber stud walls. Information on the long-term creep behavior of SIPs under sustained triangular loading, simulating soil pressure, including effect of the change in ambient temperature and relative humidity is as yet unavailable. The long-term creep deflection for permanent wood foundation panels that is characterized as viscoelastic materials is highly affected by the change in ambient temperature and relative humidity. This paper reported the results from flexural creep experiments performed on two sets of different sizes of PWF made of structural-insulated foam-timber panels. In these tests, deflection, temperature and relative humidity were tracked for an eight-month period. The experimental findings were examined against existing creep models in the literature. Then, a creep model incorporating the effects of temperature and relative humidity on creep deflection was developed. Correlation between the proposed model and the experimental findings provides confidence of using the proposed model in the determination of the capacity of the PWF under combined gravity loading and sustained soil pressure.

The open source introduction of fused filament fabrication (FFF) enables distributed manufacturing of consumer products. However, with a wide range of low-cost FFF 3-D printers and settings possible, there is a lack of information on the variability in printed mechanical properties. This paper utilizes a large pool of 47 user-assembled 3-D printers to quantify the mechanical property variations of ultimate tensile strength (UTS) and yield strength of FFF printed components using ASTM D638-14 horizontally-oriented Type I and IV geometries for poly lactic acid (PLA). The results indicate that utilizing Type IV tensile test piece geometry may overestimate the UTS relative to the Type I. Furthermore, anisotropic mechanical property variances were quantified for Type IV specimens (vertical and horizontal orientations). Vertical tensile specimens had an ultimate tensile strength 47.9% less than horizontal. Finally, the abundant supply of PLA 3-D prints suggest open-source printers assembled by individual operators can produce quality plastic components although the mechanical performance of the given part can vary dramatically based on the operator selection of printing parameters that provide a visually acceptable part.

An algebraic relationship between the fourth rank elasticity tensor of a porous, anisotropic, linear elastic material and the fabric tensor of the material is considered. The fabric tensor is a symmetric second rank tensor which characterizes the geometric arrangement of the porous material microstructure. In developing this result it is assumed that the matrix material of the porous elastic solid is isotropic and, thus, that the anisotropy of the porous elastic solid is determined by the fabric tensor. It is then shown that the material symmetries of orthotropy, transverse isotropy and isotropy correspond to the cases of three, two and one distinct eigenvalues of the fabric tensor, respectively. 0167-6636/85/$3.30 © 1985, Elsevier Science Publishers B.V.

A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.

يشتمل هذا الكتاب على اربعة عشر فصول. يتناول الفصل الأول تعريفاً لبعض المصطلحات الأساسية في ميكانيكا المواد.
أما الفصل الثاني عشر فيتضمن دراسة تفصيلية لقوة القص وعزم الإنحناء في العارضات مشمولاً ببعض الأمثلة المحلولة والمسائل الإضافية.
يناقش الفصل الثالث عشر دراسة لعزم المساحة من وجهة نظر العزم الأول للمساحة، والعزم الثاني للمساحة نظرية المحاور المتوازنة ونظرية المحاور المتعامدة بالإضافة لبعض الأمثلة المحلولة والمسائل الإضافية.
يتناول الفصل الرابع عشر دراسة إجهاد الإنحناء من حيث تعريفه، فرضياته واشتقاق معادلاته إضافة لبعض الأمثلة المحلولة والمسائل الإضافية.
يستعرض الفصل الخامس عشر إجهاد القص في العارضات ذات المقطع المستطيل ويدرس كيفية تحديد مركز القص في العارضات. في نهاية هذا الفصل يوجد العديد من الأمثلة والمسائل.
أما الفصل السادس عشر فيتناول دراسة الإلتواء في الأعمدة الدوَّارة من خلال الأمثلة المحلولة والمسائل.
يناقش الفصل السابع تحليل الإجهادات والإنفعالات المركَّبة من خلال العديد من الأمثلة المحلولة والمسائل.
يستعرض الفصل الثامن القضبان أو الأنابيب المركبة من خلال مجموعة من الأمثلة والمسائل.
يتناول الفصل التاسع دراسة لنظريات الإنهيار أو الفشل من وجهة نظر الإجهاد الرئيس الأقصى ، إجهاد القص الأقصى ، طاقة الإنفعال ، طاقة إنفعال القص ، والإنفعال الرئيس الأقصى . هنالك أمثلة محلولة ومسائل إضافية في نهاية هذا الفصل.
يناقش الفصل العاشر إنحراف العارضات من خلال العديد من المسائل والأمثلة.
يتناول الفصل الحادي عشر دراسة للعارضات الغير محدّدة إستاتيكياً التي يزيد فيها عدد ردود الأفعال المجهولة عن عدد معادلات الإتزان ويتضمن الفصل العديد من الأمثلة المحلولة والمسائل الإضافية المتنوعة.
أما الفصل الثاني عشر فيدرس الإنحناء في المقاطع غير المتماثلة مشفوعاً بعديد الأمثلة النموذجية المحلولة وبعض التدريبات.
يتناول الفصل الثالث عشر الإنبعاج في الأعمدة الذي يحدث نتيجة لتعرض الأعمدة الطويلة لأحمال إنضغاط محورية تؤدي إلى تقوسها وإنهيارها نتيجة لعدم الإتزان. يستعرض هذا الفصل نظرية أويلر لتحليل عدد من الأعمدة بحالات طرفية مختلفة: عمود مسماري من الطرفين، عمود مبني من الطرفين، عمود مبني من طرف وحر من الطرف الآخر، عمود مبني من طرف ومسماري من الطرف الآخر، وعمود مسلَّط عليه حمل لا تمركزي. أيضاً يوضّح هذا الفصل مناحي القصور في نظرية أويلر بالإضافة للعديد من الأمثلة المحلولة والمسائل الإضافية. 
أما الفصل الرابع عشر والأخير فيتناول بالدراسة الإسطوانات الرفيعة والسميكة مشفوعاً بالعديد من الأمثلة والتدريبات.
إنَّ الكاتب يأمل أن يساهم هذا الكتاب في إثراء المكتبة الجامعية داخل السودان وخارجه في هذا المجال من المعرفة ويأمل من القارئ ضرورة إرسال تغذية راجعة إن كانت هنالك ثَمَّة أخطاء حتى يستطيع الكاتب تصويبها في الطبعة التالية للكتاب.

Developing new energy efficient building materials to reduce the carbon footprint is now the core of sustainability in construction and an essential factor of life cycle assessment (LCA). The extensive and increasing usage of conventional concrete, mortar, plasters and various cement based materials is only one of the many factors contributing towards urban thermal discomfort caused by urban heat island phenomena and the poor thermal insulation of ordinary cement mortar. Not only this, the wide use of concrete and mortar in construction increases the consumption of their primary components mainly -Portland cement- requiring a large consumption of energy and causing a significant rise in CO2 emissions. Embedding natural and artificial cementitious/pozzolana materials in today`s cement-based building materials has become a common practice. Cementitious and Pozzolanic materials are known to provide an added value to mortar/concrete not only in terms of mechanical and durability properties but also in energy efficiency and enhancing sustainability. Sarooj is a local term describing an artificial cementitious and pozzolana material obtained by traditional calcining of the raw clayey soil. Although its usage is nowadays very limited, Sarooj has been used in Oman and other neighboring countries for centuries, in various buildings and defense into an engineered binding material and hence investigating its physico-mechanical and thermal properties. The raw soil used to produce the traditional Sarooj was employed to engineer a modern “Sarooj” under controlled energy processing (grinding and calcination) conditions. The raw clay minded from specific location was ground first to a fine powdered material and then subjected to full characterization. The physical and chemical characterization indicated that the raw soil is suitable for producing a cementitious/pozzolanic calcined clay. The thermogravimetric and differential thermal analysis of the clay used reveal that only a moderate temperature of around 800 °C is required for its calcination which preserves energy and reduces CO2 emissions compared to 1600 °C to produce clinker cement. The strength development showed a slow early-age reactivity but an appreciable enhancement in long-term which demonstrates a remarkable latent hydraulic potential of the clay used. It was also found that adding an optimum amount of the calcined clay enhances the thermal properties. The annual energy performance of a typical housing in the hot climate of Muscat, Oman, was evaluated using DesignBuilder software, a whole-building simulation tool. The simulation results showed insignificant savings in annual energy consumption when the developed mixes are used as plastering materials. The clay alkali-activated with NaOH has, however, showed great potential to enhance the mortar`s long-term strength. Using locally engineered cementitious material in a partial replacement of Portland cement can further enhance durability and sustainability by reducing the manufacturing energy of the produced building material such mortars and plasters

Moment-Curvature Relationship: s = c r E = a 0.005 10 b C200A10 9 B D = 100 MPa 1 r = 1 c s EI 1 r = M EI however, M = I c s •12-1. An A-36 steel strap having a thickness of 10 mm and a width of 20 mm is bent into a circular arc of radius 10 m. Determine the maximum bending stress in the strap. r = Ans. s = c r E = a 0.02 4.5 b C131A10 9 B D = 582 MPa 1 r = I c s EI 1 r = M EI however, M = I c s 12-2. A picture is taken of a man performing a pole vault, and the minimum radius of curvature of the pole is estimated by measurement to be 4.5 m. If the pole is 40 mm in diameter and it is made of a glass-reinforced plastic for which GPa, determine the maximum bending stress in the pole. E g = 131 r ϭ 4.5 m 12 Solutions 46060 6/11/10 11:52 AM Page 883

Strength of materials, also called mechanics of materials, deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko. The study of strength of materials often refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio; in addition the mechanical element's macroscopic properties (geometric properties), such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.