Elastic Strain - Plastic Strain

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{31} Base Sequence = 12735 String Sequence = 12735 - 3 - 31 **

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The proportional limit of a member made of a type of steel is 30,000 psi. Modulus of elasticity of member is 30 x 10^{6} psi. When this member is subjected to a tensile load of 45,000 psi, the strain is 0.0615 in./in. When this member is subjected to a tensile load of 60,000 psi, the strain is 0.2020 in./in.

What is the ratio of elastic strain to plastic strain?

**The strings**:
S_{7}P_{3}A_{31} (Force - Pull).
**The math**:

Pj Problem of Interest is of type *force* (pull).

Formula of interest:

Stress = (modulus of elasticity)(strain)

Strain = Stress/Modulus of Elasticity

The plastic range in a stress-strain relationship is the region in which yielding and strain-hardening takes place. The strain from this yielding is permanent.

Load = 30,000 psi:

Elastic strain, ε_{e} = 30,000/(30 x 10^{6}) = 0.0010 in./in.

No plastic strain since this is the proportional limit stress.

Load = 45,000 psi:

Elastic strain, ε_{e} = 45,000/(30 x 10^{6}) = 0.0015 in./in

plastic strain, ε_{p} = 0.0615 - 0.0015 = 0.0600 in./in.

So, ε_{e}/ε_{p} = 1/40

So, ε_{e} = 2.5% of ε_{p}

Load = 60,000 psi:

Elastic strain, ε_{e} = 60,000/(30 x 10^{6}) = 0.0020 in./in

plastic strain, ε_{p} = 0.2020 - 0.0020 = 0.2000 in./in.

So, ε_{e}/ε_{p} = 1/100

So, ε_{e} = 1% of ε_{p}

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.

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