Design project report for Engineering Mechanics (Research Paper Sample)

Student Tutor Course Date Design project report for Engineering Mechanics Introduction Understanding materials in mechanics is critical in the application of the materials in the in mechanics. This fact has led to the investigation of a truss bridge to establish why it is permanently deflected under a load that is higher than the allowable specification CITATION Ash99 \l 1033 (Ashby). The test majorly entails establishing the causes of failure of a truss bridge due to loading. The test will majorly entail loading of the truss bridge and collect data relevant for the compilation of the Young's modulus, yield stress and ultimate tensile stress. These tests will be done severally so as to increase the accuracy of the data obtained. This document presents the raw data obtained, the failure report and the material testing discussion. The experiments aim at familiarizing with the relationship between load and deflection of the various beams that make up the truss bridge. It also aims at exploring the theory of young's modulus of the materials that comprise the beams. The experiments that will be undertaken are the bend testing rig, the deflection of a cantilever and deflection of a simply supported beam. The bending test will involve loading of masses on a shaft supported between clamps of a rig and measuring the load-deflection relations. The deflection of a cantilever experiment will involve deflection of a cantilevered beam for steel and aluminum. Finally, the deflection of a simply supported beam experiment entails investigating the deflection of a simply supported beam for steel and aluminum. Executive Summary The tests endeavor to explain the failure of the truss bridge using engineering principles. The bridge experienced permanent deflection under a load that is higher than the allowable specification. The test methods involved testing of the tension of metallic materials. The test was done at room temperature with the metals forged into beams. The test mainly was aimed at establishing the Young's modulus, yield stress and ultimate tensile stress of the beams making the truss bridge. The members of the truss were made from annealed stainless steel grade 405 (Modulus of Elasticity = 200 GPa, Yield Strength = 170 MPa, Ultimate Tensile Strength = 415 MPa). The length of the truss was found to be approximately 80 meters, and the height to be approximately 6 meters. Each truss bay is equal in size CITATION AST15 \l 1033 (International). The bottom chord members consist of 40x40 mm square sections, and all other truss members are 80x80 mm square sections. The exceptions to this tests were made for the individual members where it was imperative to conclude that the members would operate with their allowable stress and strain zones. The members were also assumed to be non-elastic hence they could experience fracture when their elastic limits are exceeded. Room temperature was considered to be 10 to 38°C. The values were all converted to the SI units. The labs mainly aimed at testing the two members of the bridge; the tensile and the compression members. The two different beams (cantilever and the simply supported) were tested under different loads obtaining the load deflection hence establishing that the bridge permanently deflects under load is higher than the allowable specification. The results from the test calculation of young's modulus accurately. This test proved useful in determining Young's modulus of the material of the beams and hence offer superior results as compared to the tensile test. The stress both in the (90x90) tension members and the (80x80) compression is higher than the one allowed by the material properties. A higher compression higher than the yield point caused deformation of the diameter hence distorting cross-sectional area of the member while the tension reduced the diameter of the member. The calculations for Young's modulus to establish the yield point of the material was able to establish that the bridge would succumb to masses introduced at the center of the bridge. The finding was because yield point would easily be exceeded when compression force was introduced. Materials Testing Discussion To test the behavior of the materials of the member of the truss bridge, we do a compression test and tensile test CITATION Pei12 \l 1033 (Peixoto, Sousa and Restivo). The main elements to be tested were the Young's modulus, yield stress and ultimate tensile stress of potential materials to be used to construct a new bridge. The bending experiment was effective in obtaining accurate values for the calculation of the Young's modulus. The simply supported was a little bit undesirable. Young's modulus The following are the dimensions of the beams used in the experiment material Material Nominal Thickness (T) mm Gauge Length (G) mm Width (W) mm MS Blackform 1.6 80 12 SS 304 1.5 80 12 Al 5005 1.6 80 12 Al 5052 1.6 80 12 The beams were deflected in agreement with the Euler-Bernoulli beam theory. The principles would be considered for both the set ups of the experiment. The cantilever beam had the maximum deflection occurs at the free end of the beam, and in the simply supported beam it occurs at the center of the beam. To calculate the maximum deflection of the cantilever and the simply supported beam the below equations can be used. L is the length of the beam (mm) E is Young's modulus (GPa or N/mm2) P is the load (Newtons) I is the 2nd moment of inertia (mm4) The figure below represent the deflection experienced in the two experiments. Young's modulus represents the slope of the line in a stress-strain curve. To determine the young modulus from the tests we plot the relationship between the load and the resulting deflection and hence obtain the slope of the graph. Treating the plot a linear relationship y = bx + c we obtain the following equations. From the experiment, we first calculate the second moment of inertia so as to be able to obtain the deflection Beam Width(mm) Height(mm) Length(mm) Cross-sectional area(mm2) I (mm4) Aluminium 19.2 3.1 150 2880 47.67 Steel 19.2 3.1 200 3840 47.67 19.2 x (3.1)3/ 12 47.6656mm4 From the above readings we can calculate the second moment of inertia = (0.02) (0.003)3/ 12 =4.5 x 10-11 m4 To obtain the maximum deflections = (2.5) (0.2)3/3(207 x 109) (4.5 x 10-11m4) = 0.000716 m = 0.716mm The deflection obtained can be used to determine the Young's modulus of the material of the beams. Property Your value Unit Young's modulus 46.025 GPa 0.2 % proof stress 283.07 MPa Ultimate tensile stress 348.54 MPa Engineering strain at the point of necking 22.26 % ductility 33.4599 % To design the beams we plot the respective extensions of the beams against the loads. MS Blackform SS 304 Al 5005 Al 5052 Yield stress and ultimate tensile stress The tensile test is used to measure the mechanical properties of the beams. It relates the effects of a tensile load on the elongation (change in length) of the bridge beams. To fully analyze the material of the beams we monitor their behavior under tension and compression CITATION GTo03 \l 1033 (G, Totten and MacKenzi ). The assumption for the tension and compression worked for the value of the material constant. The stress and deformation formula developed are applied to the members of the bridge in tension and compression hence establishing the effect of loading on the beams. The compressive strength of the materials is different from their tensile strength. From the stress-strain plots, the modulus of the elasticity is the same for tension and compression. But from the results, the compressive strength of aluminum was two times that of steel. Compression test was conducted without unloading hence the beams behavior was almost the same in the compression and the tension. The modulus of elasticity, yield stress and the ultimate stress become equal. From the strain and stress on the original length of the beam length of the sample obtained from the truss and equaled the elongation of the beam (the change in length of the beam) divided by the original length of the beam. Since both strain and stress have units of length, the strain has dimensionless units and is expressed mainly in meters and millimeter. Commonly strain can be expressed as engineering strain as a percent strain or percent elongation CITATION Rad04 \l 1033 (M). Engineering strain = engineering strain x 100% The plot of the stress vs. strain diagram results in a curve that is usually linear and follows the relationship. This linear relationship is based on Hooke's Law and has a yield point represents elastic deformation. Removal of the load in the region of the beam, the member will regain its original shape without permanent deformation. The gradient of the curve is the modulus of elasticity or Young's Modulus, which is similar to a spring constant. Materials differ in the young modulus due to the difference in the bonds, a material's Young's modulus is not affected by microstructure but is entirely affected by the bond strength holding the atoms in the structure. When the load increases the stress level is increased to the point beyond t...