CM 3502 Exam Notes

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Louisiana State University *

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3502

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Mechanical Engineering

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Dec 6, 2023

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CM 3502 Cheat Sheet

CM 3502 Cheat Sheet How many lives were lost in the Teton Dam Failure? 14

CM 3502 Cheat Sheet When considered over long periods of time, operations and maintenance costs, ____________ the initial cost of construction of a typical building. Exceed A material that experiences large deformation before failure is called Ductile A material that fails with very little deformation is called Brittle Precision refers to the variability of repeat measurements under carefully controlled conditions. Accuracy is the conformity of results to the true value or the absence of bias. The ________________ rating system is used to evaluate the sustainability of a project. LEED The _________________ is a measure of the dispersion or spread of the results. Standard deviation Stress and Strain Strain is a physical change in the size or shape of the material. Total strain refers to the total change in size due to a load, its units are any dimensional units, inches, feet, meters, millimeters. Unit strain is the change per unit length, this variable is unitless, it is a ratio but is often represented as inches per inch for clarity. Axial strain is a strain in the direction along a linear member or perpendicular to the cross-section. Tensile strain results in a lengthening of the member, compressive strain, such as in a column, is a shortening or contraction of the member. Shear Stress is stress across a linear member or parallel to the cross-section. Shear strain can be visualized in the previous bolt example or by thinking of the opposing forces at the edge of the support of a beam, with the support acting upward and the beam acting downward.

CM 3502 Cheat Sheet Bending strain is strain due to bending forces, this strain results in the vertical deflection of a horizontal beam. Horizontal shearing strain is due to shear stress from beam loads, it also contributes to beam deflection. Axial Strain Example A linear member 33.3 feet long elongates by 2 inches due to a tensile load. Determine the unit strain. Total change equals unit strain times the original length, or unit strain equals total change divided by the original length. Unit strain equals 2 inches divided by 33.3 feet, however, we must have matching units, so we will multiply by 12 inches per 1 foot. Unit strain equals .005. Example A linear member 33.3 ft long elongates by 2 inches due to a tensile load Determine the unit strain, ε δ = εL O → ε = δ/L O δ = Total Strain, Lengthening or Shortening, in, ft, m ε = Unit Strain in/in, ft/ft, m/m, unitless L O = Original Length, in, ft, m ε = δ/L O = 2in/(33.3ft x (12in/1ft)) ε = .005 in/in → ε = .005 Stress-Strain diagram The following graph shows a typical stress strain diagram for mild steel in tension. Stress strain diagrams exist for multiple materials and all types of stress. The first part of the diagram is the elastic range. A material stressed within this range will return to its original size and shape when the load is removed. The stress at the end

CM 3502 Cheat Sheet of the elastic range is called the yield stress, a material stressed beyond this point will deform or yield. When we go beyond the elastic range into the plastic range a material will experience permanent deformation. Next is the strain hardening range where material becomes stronger, up to the point of Fu, the ultimate stress. The final section is the failure range, in this range, the material weakens until the failure point, with x denoting the failure point. Modulus of Elasticity(Young’s Modulus) The measure of the stiffness of the material is the modulus of elasticity or Young’s modulus. It is represented by E and has units similar to stress, pounds per inch square, kips per inch square, kilopascals, megapascals. The modulus of elasticity defines the relationship between stress and strain, it is the material factor in deformation and deflection calculations. It defines the stiffness of the material, not

CM 3502 Cheat Sheet the strength. The modulus of elasticity is the change in stress divided by the change in unit strain within the elastic range of material. Modulus of Elasticity(Young’s Modulus), E, lbs/in 2 , k/in 2 , kPa, MPa Modulus of Elasticity defines the relationship between stress and strain Material Factor in deformation and deflection calculations Defines the Stiffness, not the strength of a material E = Δf/Δε Valid within a materials elastic range Some materials have nonlinear behavior, we can however estimate a modulus of elasticity within the working range of that material. E = Δf/Δε Below is an example problem using test data to determine the modulus of elasticity. Test data from within the elastic range of an unknown material is given. Data point 1, stress equals 7400 pounds per inch square, unit strain equals .00025. Data point 2, stress equals 22,200 pounds per inch square, unit strain equals .00075. Determine the modulus of elasticity. The modulus of elasticity equals the change in stress divided by the change in unit strain, the modulus of elasticity equals 22,200 pounds per inch square -7400 pounds per inch square divided by .00075-.00025. Modulus of elasticity equals 29.6×10 to the 6th pounds per inch square. Referring to appendix E we see that this material may be steel. The typical value for the modulus of elasticity of steel that we will use in all our calculations is 29×10 to the 6th pounds per inch square or 29×10 to the third, kips per inch square. Example Test data from within the elastic range of an unknown material is given. Data point 1: f = 7400 lbs/in 2 , ε = .00025 Data point 2: f = 22,200 lbs/in 2 , ε = .00075 Determine the Modulus of Elasticity E = Δf/Δε E = (22,200 lbs/in 2 - 7400 lbs/in 2 )/(.00075 - .00025) E = 29.6(10) 6 lbs/in 2 Refer to Appendix E to determine what material this may be E STEEL = 29(10) 6 lbs/in 2 or 29(10) 3 k/in 2

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