In engineering analysis, material’s physical and chemical properties in terms of are analysis based on its ability to withstand structural and chemical application. The testing focuses on determining the core properties and behaviour of materials under different conditions including failure geared towards usefulness structurally, chemically, and mechanically. Typically, during analysis the following material properties are examined; strength, toughness, hardness, brittleness, ductility, hardness, malleability, fatigue, and hardenability (Steele, 2001; Callister, and Rethwisch, 2007). In laboratory, mechanical testing involves subjecting a material to tension and deformation test determining its failure point, fatigue, and rate (Dowling, 2012). For instance, testing for material stress expressed as load per unit area enables designers and engineers to anticipate the amount of stress it can withstand before failure. Quantitatively and computational approach captures the point in values in which the specific material fails based on specified testing approach that include mechanical, chemical, electrical, or structural. In this report, test of various properties and characteristics of composite materials to determine deformation, fracture, and fatigue when subjected to force. Shortened from composition materials, composite materials are formed from combination of more than two materials with multiple chemicals and physical properties resulting in a material with distinct chemicals and physical characteristics from its constituents elements. Mechanical test of composite material involves determining its strength, toughness, and stiffness. Material strain, in this case composite, it measures its deformation during loading. It is expressed as 𝜀. Ability of a material to withstand tension is determined by its modulus of elasticity E and Poisson’s ratio (Lakes, and Wojciechowski, 2008).

When a material changes at 900 angle during loading the strain resulting to an angular deformation is referred to shear strain (γ). Like linear deformation measured by electricity modulus, in angular deformation (shear strain) is determined by shear modulus (G) (Wongpa et al., 2010; Gay, 2014). According to Gay (2014), composite toughness to withstand load (shear-strain) is measured through taking initial measurements before being exposure to load test, then values taken during loading and before yielding to fracture. Currently there are numerous testing are in use. Experimental stress analysis is the most common test used to analyse the behaviour of material under load (shear, tension, bending, torsion, and stress). In linear-elastic materials, Hooke’s law is used to determine elastic deformation

σ=ε. E

σ= Material stress (N/mm2)

ε= Strain (m/m)

E= modulus of elasticity, i.e Young’s modulus (N/mm2)

Hooke’s Law, as shown by the equation above, states that stress applied to a material is directly proportional to the strain exposed. The figure below show graphical representation of stress-strain relationship.

In the simplest form, any material when subjected to a load (tension) tends to behaviour elastically (point A to B) before exhibiting plastic behaviour then fracture when a load is gradually increased. However, unlike materials such as metals and plastics, as demonstrated by laboratory findings, composite goes through elasticity stage but fails after a certain amount of load has been add (depending on the structural composition of the material) without exhibiting plastic characteristics. The following is a stress-strain curve of composites demonstrating its behaviour when exposed to load.

Observably, different composite materials behave differently when exposed to tension (stress-strain) based on respective building blocks. Similarly, conductivity properties of the composite materials can be tested. Both thermal and electrical conductivity of such composite materials largely depends on the individual properties of building materials (Wang et al., 2009; Sato et al., 2010). In most case, though largely depends on specific composite material, such composite materials made from graphite and dielectric polymers have high thermal efficiency (Pincemin et al., 2008; Huang et al., 2011). However, as pointed by Molina et al. (2009), some composite materials have low thermal (W/mK) and electrical (Siemens/meter) conductivity. Increasing the electrical current or heat while maintaining the materials thickness will ultimately result in failure, as a poor conductors. Structurally, composite material enhances such properties as strength, weight, wear and tear, fatigue life, stiffness corrosion, resistance, and conductivity of the material form it (Shirshova et al., 2013; Lesovik et al., 2014). Notably, the characteristics of composite materials depend squarely on the components, morphology, crystallographic textures, composition, and structural elements of building elements. Lurie and Minhat (2015) highlighted that degradation of composite materials through damage-accumulation process occurs on two levels; macroscale and microscale. Mostly, kinetic energy is used to describe the failure progress and layered structure at macroscopic level evident by appearance of transverse cracks while microdefects show by breakdown in chemical and structure of an element. Subjecting a material to a load it experiences a strain becoming elastic but this goes on (adding load) to a point it cannot behaviour as such. Beyond this stage, adding load results in the material not returning to its original shape. This is described as elastic deformation occurring at microscopic level (Lagzdins, and Zilaucs, 2006).

For composite material, the modulus of elasticity is relative low through depend on physical properties and micro-structural characteristics of parent materials. Degradation in respect to magnetic hysteresis or property of a ferromagnetic material to be magnetised can occur when a material is exposed to huge magnetic field resulting to failure demagnetise (Drummond, 2008). Referred to as saturation remanence (Mrs) of a material, in this case composite material, is measured using B-H analyser measuring response to AC magnetic field.

A simply supported beam of length 6m supports a vertical point load of 45kN at a distance of 4m from one end

Determine the reaction forces at either end

Taking moments about point A

(4mx45kN)-(R2x6)=0

(180kNm)-(6R2)=0

R2=(180/6)=30kN

R2=30kN

Let the sum of vertical forces equal to 0

Summation Fy= 0 = ((R1+R2)-45kN)

But R2 = 30kN

Therefore:

((30kN+R1) - 45kN) = 0

R1 = (45-30) = 15kN

Recalculate the reaction forces at either end, taking into account the actual weight of the beam as a UDL. Assume that the mass of the beam is 39Kg/m and g= 9.81 m/s2

When the load type is UDL

The UDL = (39Kg/m x 9.81m/s2) = 382.59N/m

Sum of the vertical force (Fv) = (382.59N/m x 6m) = 2295.54N

Taking moments about point A and weight acting centrally

(R1x0) + (2295.54N x 3m) - (R2x6m) = 0

R2 = (6886.62/6) = 1147.77N

But since the load is UDL and acts centrally R1 = R2 = 1147.77N

Buoyancy is the ability of an object to float on fluid. This can be either on liquid such as water or gases. There are two main commonly applications of buoyancy which are: Submarine floating on water: This is enabled by buoyancy since the submarine displaces the amount of water equal to the weight of the ship therefore the pressure exerted on the water by the submarine is the same to the opposing pressure produced by the water.

Hot air balloon: The same principle applies to hot air balloon that displaces air of weight same to the weight of the balloon therefore creating equal and opposing pressures.

Discuss briefly the temperature effects on mechanical properties such as a dimensional change, elasto-plastic changes, due to thermal stresses

Metals such as steels are among the best elements reactive to changes in temperature such that the mechanical properties generally decrease with increase in temperature. When a metal has no thermal loads, they have the capacity of performing elastic behaviours under special situations. However, when thermal loads are applied to the metal they tend to change the behaviour of its structure as a result of temperature change or conduction. This stage when the thermal loads are removed the materials tend to retract to its initial structure but when the thermal loads or temperature is increased further the material goes to elastoplastic state which is a state in which the material cannot retract to its original structure.

Find the acceleration which will be produced in a body having a mass of 60 kg when a force of 150 N acts on this body by using d’ Alembert’s Principle

d’ Alembert’s Principle. = Force = Mass x Acceleration

150N = 60Kg x Acceleration

Acceleration = (150/60) = 2.5m/s2

Acceleration = 2.5m/s2

For a domestic hot water system, a copper pipe carries hot water at 70 0c and has an external diameter of 150 mm and is lagged to an overall diameter of 500 mm. If the surface temperature of the lagging is 20 0C determine the rate of heat loss per metre length of pipe if it can be assumed that the inner surface of the lagging is at the hot water temperature. The thermal conductivity of the lagging is 0.09 W/mK

Let the rate of heat loss per metre length of pipe be (h)

h = (2πKL(ø1 - ø2)) / (ln(R1/R2))

Where K is the thermal conductivity of the lagging, ø1 is the internal temperature of the copper pipe in degrees Celsius, ø2 is the surface temperature of the lagging, R1 is the radius of the Overall radius and R2 is the radius of the copper pipe carrying hot water.

(2xπx0.09W/mK(70- 20)) / (ln(0.25/0.075))

28.274334/1.2039728

h = 23.48 J/sec

Norton's theorem is a DC-related theory which states that any linear electrical circuit with current and voltage sources however much complex they might seem to be can be simplified or replaced by an equivalent current source with an equivalent resistance connected on the circuit load (Bird, 2017). Norton theory is also applicable for the AC mainly on the reactive impedances and resistances as well as solving cases of parallel generators with unequal EMFs and unequal internal impedances.

Thévenin's theorem states that a linear electrical circuit comprising of only current source, voltage source and resistance source can be replaced by an equivalent of combined voltage sources that will be placed in series connection with the resistance hence allowing a one-port network to be reduced to a single impedance and also a single voltage source (Hongyang, 2011). The theory is also applicable to frequency domain AC circuits and also when conducting an analysis of the power systems or circuits where a resistor in the circuit is subject to change (Volk et al., 2014).

Superposition theorem holds that the voltage or current responses in any branch of a bilateral linear circuit in a linear system containing two or more independent sources is equivalent to the algebraic sum of the voltage or current that results from each independent source acting alone and other sources replaced by their specified internal impedances (Bird, 2017). The theory is also applied to time-varying networks with independent sources, linear transformers, linear passive elements, and linear dependent sources.

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Callister, W.D. and Rethwisch, D.G., 2007. Materials science and engineering: an introduction (Vol. 7, pp. 665-715). New York: John wiley & sons.

Dell'Isola, F., Sciarra, G. and Vidoli, S., 2009. Generalized Hooke's law for isotropic second gradient materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465(2107), pp.2177-2196.

Dowling, N.E., 2012. Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Pearson.

Hongyang, Z., 2011, August. Discussion on the Thevenin's theorem and Norton's theorem. In Proceedings of 2011 International Conference on Electronic & Mechanical Engineering and Information Technology (Vol. 1, pp. 520-522). IEEE.

Huang, X., Jiang, P. and Tanaka, T., 2011. A review of dielectric polymer composites with high thermal conductivity. IEEE Electrical Insulation Magazine, 27(4), pp.8-16.

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Lesovik, V.S., Zagorodnuk, L.H., Tolmacheva, M.M., Smolikov, A.A., Shekina, A.Y. and Shakarna, M.H.I., 2014. Structure-formation of contact layers of composite materials. Life Science Journal, 11(12), pp.948-953.

Molina, J.M., Prieto, R., Narciso, J. and Louis, E., 2009. The effect of porosity on the thermal conductivity of Al–12 wt.% Si/SiC composites. Scripta Materialia, 60(7), pp.582-585.

Pincemin, S., Olives, R., Py, X. and Christ, M., 2008. Highly conductive composites made of phase change materials and graphite for thermal storage. Solar Energy Materials and Solar Cells, 92(6), pp.603-613.

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Shirshova, N., Qian, H., Shaffer, M.S., Steinke, J.H., Greenhalgh, E.S., Curtis, P.T., Kucernak, A. and Bismarck, A., 2013. Structural composite supercapacitors. Composites Part A: Applied Science and Manufacturing, 46, pp.96-107.

Steele, B.C., 2001. Material science and engineering: the enabling technology for the commercialisation of fuel cell systems. Journal of Materials Science, 36(5), pp.1053-1068.

Volk, T., Bhattacharyya, M., Grünwald, W., Reindl, L. and Jansen, D., 2014. Formal description of inductive air interfaces using thévenin's theorem and numerical analysis. IEEE transactions on magnetics, 50(6), pp.1-9.

Wang, W., Yang, X., Fang, Y., Ding, J. and Yan, J., 2009. Enhanced thermal conductivity and thermal performance of form-stable composite phase change materials by using β-Aluminum nitride. Applied Energy, 86(7-8), pp.1196-1200.

Wongpa, J., Kiattikomol, K., Jaturapitakkul, C. and Chindaprasirt, P., 2010. Compressive strength, modulus of elasticity, and water permeability of inorganic polymer concrete. Materials & Design, 31(10), pp.4748-4754.

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