Strain Energy Stored In An Elastic Material
Strings (SiPjAjk) = S7P3A31 Base Sequence = 12735 String Sequence = 12735 - 3 - 31
A 15 in member is to be designed using a safety factor of 1.50, to withstand a tensile load of 6000 lb. The three choices of material available are:
(a) Aluminum Alloy, for which modulus of Elasticity, E = 10 x 106 psi and tensile stress σy = 52, 0000 psi
(b) Magnesium Alloy, for which modulus of Elasticity, E = 6.5 x 106 psi and tensile stress σy = 28,500 psi
(c) Molded Nylon, for which modulus of Elasticity, E = 410,000 psi and tensile stress σy = 8000 psi.
Calculate the total amount of strain energy stored by each member at the 6000 lb load.
S7P3A31 (Force - Pull).
Pj Problem of Interest is of type force (pull).
Formulas of interest:
Stress, σ = Load/Area; Strain, ε = δ/Length; where δ is total elongation
Stress = (modulus of elasticity)(strain)
Poisson's ratio, μ = lateral strain/longitudinal strain
Offset yield strength σy = (working stress σw)(safety factor)
Total strain energy, U = ∫0δ P(x) dx.
Where x is elongation and P(x) = kx is force as a function of elongation.
Strain energy per unit volume = σ2/(2E)
(a) yield strength, σy = [Load(safety factor)]/(Cross-section Area)
So, 52,000 = 6,000(1.50)/A
So, A = 6,000(1.5)/52,000 = 0.173 in2.
Total strain energy, U at Load can be calculated by integrating P(x) = kx from 0 to δ
Where k, (load/δ) is the slope of the graph relating load and elongation when material is elastic.
So, U = ∫0δ kx dx = (Load)(δ/2) = (Load)[(ε)(length]/2.
So, U = 6,000[(σy)/(1.5E)](length/2)
So, total strain energy, U = 6,000[(52,000/(1.5 x 10 x 106)](15/2)
= 156 lb-in.
(b) A = 6,000(1.5)/28,500 = 0.316 in2.
So, total strain energy, U = 6,000[(28,500/(1.5 x 6.5 x 106)](15/2)
= 132 lb-in.
(c) A = 6,000(1.5)/8000 = 1.125 in2
So, total strain energy, U = 6,000[(8,000/(1.5 x 410,000)](15/2)
= 586 lb-in.
Total strain energy can also be calculated by first calculatin strain energy per unit volume and then multiplying by total volume.
So, total strain energy = [σ2/(2E)]V.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Single Variable Functions
Ordinary Differential Equations (ODEs)
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
More Pj Problem Strings