The image above represents vertical strain.

To compute for vertical strain, five essential parameters are needed and these parameters are **Vertical Stress (σ _{v}), Poisson’s Ratio (v), Principal Horizontal Stress Component 1 (σ_{H1}), Principal Horizontal Stress Component 2 (σ_{H2})** and

**Young’s Modulus (E).**

The formula for calculating the vertical strain:

ε_{v} = ^{(σv – vσH1 – vσH2)} / _{E}

Where:

ε_{v} = Vertical Strain

σ_{v} = Vertical Stress

v = Poisson’s Ratio

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

E = Young’s Modulus

Let’s solve an example;

Find the vertical strain with a vertical stress of 44, Poisson’s ratio of 5, principal horizontal stress component 1 of 6, principal horizontal stress component 2 of 4 and young’s modulus of 12.

This implies that;

σ_{v} = Vertical Stress = 44

v = Poisson’s Ratio = 5

σ_{H1} = Principal Horizontal Stress Component 1 = 6

σ_{H2} = Principal Horizontal Stress Component 2 = 4

E = Young’s Modulus = 12

ε_{v} = ^{(σv – vσH1 – vσH2)} / _{E}

ε_{v} = ^{(44 – 5(6) – 5(4))} / _{12}

ε_{v} = ^{(44 – 30 – 20)} / _{12}

ε_{v} = ^{-6} / _{12}

ε_{v} = -0.5

Therefore, the **vertical strain **is **-0.5.**

**Calculating the Vertical Stress when the Vertical Strain, Poisson’s Ratio, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2 and Young Modulus is Given.**

σ_{v} = (ε_{v} x E) + vσ_{H1} + vσ_{H2}

Where:

σ_{v} = Vertical Stress

ε_{v} = Vertical Strain

v = Poisson’s Ratio

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

E = Young’s Modulus

Let’s solve an example;

Find the vertical stress with a vertical strain of 52, Poisson’s ratio of 12, principal horizontal stress component 1 of 15, principal horizontal stress component 2 of 10 and young’s modulus of 13.

This implies that;

ε_{v} = Vertical Strain = 52

v = Poisson’s Ratio = 12

σ_{H1} = Principal Horizontal Stress Component 1 = 15

σ_{H2} = Principal Horizontal Stress Component 2 = 10

E = Young’s Modulus = 13

σ_{v} = (ε_{v} x E) + vσ_{H1} + vσ_{H2}

σ_{v} = (52 x 13) + 12(15) + 15(10)

σ_{v} = 676 + 180 + 150

σ_{v} = 1006

Therefore, the **vertical stress **is **1006.**

**Calculating the Poisson’s Ratio when the Vertical Strain, Vertical Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2 and Young Modulus is Given.**

v = ^{σv – (εv x E)} / _{σH1 + σH2}

Where:

v = Poisson’s Ratio

ε_{v} = Vertical Strain

σ_{v} = Vertical Stress

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

E = Young’s Modulus

Let’s solve an example;

Find the Poisson’s ratio with a vertical strain of 16, vertical stress of 110, principal horizontal stress component 1 of 7, principal horizontal stress component 2 of 13 and young’s modulus of 6.

This implies that;

ε_{v} = Vertical Strain = 16

σ_{v} = Vertical Stress = 110

σ_{H1} = Principal Horizontal Stress Component 1 = 7

σ_{H2} = Principal Horizontal Stress Component 2 = 13

E = Young’s Modulus = 6

v = ^{σv – (εv x E)} / _{σH1 + σH2}

v = ^{110 – (16 x 6)} / _{7 + 13}

v = ^{110 – 96} / _{20}

v = ^{14} / _{20}

v = 0.7

Therefore, the **P****oisson’s ratio **is **0.7.**

**Calculating the Principal Horizontal Stress Component 1 when the Vertical Strain, Vertical Stress, Poisson’s Ratio, Principal Horizontal Stress Component 2 and Young Modulus is Given.**

σ_{H1} = -(^{(Ev x E) – σv + vσH2} / _{v})

Where;

σ_{H1} = Principal Horizontal Stress Component 1

ε_{v} = Vertical Strain

σ_{v} = Vertical Stress

v = Poisson’s Ratio

σ_{H2} = Principal Horizontal Stress Component 2

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 1 with a vertical strain of 15, Poisson’s ratio of 10, vertical stress of 11, principal horizontal stress component 2 of 8 and young’s modulus of 14.

This implies that;

ε_{v} = Vertical Strain = 15

σ_{v} = Vertical Stress = 11

v = Poisson’s Ratio = 10

σ_{H2} = Principal Horizontal Stress Component 2 = 8

E = Young’s Modulus = 14

σ_{H1} = -(^{(Ev x E) – σv + vσH2} / _{v})

σ_{H1} = -(^{(15 x 14) – 11 + 10(8)} / _{10})

σ_{H1} = -(^{210 – 11 + 80} / _{10})

σ_{H1} = -(^{199 + 80} / _{10})

σ_{H1} = -(^{279} / _{10})

σ_{H1} = -(27.9)

σ_{H1} = -27.9

Therefore, the **principal horizontal stress component 1 **is **-27.9.**

**Calculating the Principal Horizontal Stress Component 2 when the Vertical Strain, Vertical Stress, Poisson’s Ratio, Principal Horizontal Stress Component 1 and Young Modulus is Given.**

σ_{H2} = -(^{(Ev x E) – σv + vσH1} / _{v})

Where;

σ_{H2} = Principal Horizontal Stress Component 2

ε_{v} = Vertical Strain

σ_{v} = Vertical Stress

v = Poisson’s Ratio

σ_{H1} = Principal Horizontal Stress Component 1

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 2 with a vertical strain of 30, Poisson’s ratio of 18, vertical stress of 17, principal horizontal stress component 1 of 11 and young’s modulus of 19.

This implies that;

ε_{v} = Vertical Strain = 30

σ_{v} = Vertical Stress = 17

v = Poisson’s Ratio = 18

σ_{H1} = Principal Horizontal Stress Component 1 = 11

E = Young’s Modulus = 19

σ_{H2} = -(^{(Ev x E) – σv + vσH1} / _{v})

σ_{H2} = -(^{(30 x 19) – 17 + 18(11)} / _{18})

σ_{H2} = -(^{570 – 17 + 198} / _{18})

σ_{H2} = -(^{533 + 198} / _{18})

σ_{H2} = -(^{751} / _{18})

σ_{H2} = -(41.72)

σ_{H2} = -41.72

Therefore, the **principal horizontal stress component 2 **is **-41.72.**

**Calculating the Young Modulus when the Vertical Strain, Vertical Stress, Poisson’s Ratio, Principal Horizontal Stress Component 1 and Principal Horizontal Stress Component 2 is Given.**

E = ^{(σv – vσH1 – vσH2)} / _{εv}

Where;

E = Young’s Modulus

ε_{v} = Vertical Strain

σ_{v} = Vertical Stress

v = Poisson’s Ratio

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

Let’s solve an example;

Find the young’s modulus with a vertical strain of 20, vertical stress of 60, Poisson’s ratio of 2, principal horizontal stress component 1 of 7, principal horizontal stress component 2 of 9.

This implies that;

ε_{v} = Vertical Strain = 20

σ_{v} = Vertical Stress = 60

v = Poisson’s Ratio = 2

σ_{H1} = Principal Horizontal Stress Component 1 = 7

σ_{H2} = Principal Horizontal Stress Component 2 = 9

E = ^{(σv – v(σH1) – v(σH2))} / _{εv}

E = ^{(60 – 2(7) – 2(9))} / _{20}

E = ^{(60 – 14 – 18)} / _{20}

E = ^{(28)} / _{20}

E = 1.4

Therefore, the **young’s modulus **is **1.4.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the vertical strain.

To get the answer and workings of the vertical strain using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

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**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Geology**** **under **Add-on.**

Now, Click on **Rock Mechanics**** **under **Geology**

Now, Click on **Vertical**** ****Strain **under **Rock Mechanics**

The screenshot below displays the page or activity to enter your values, to get the answer for the vertical strain according to the respective parameters which are the **Vertical Stress (σ _{v}), Poisson’s Ratio (v), Principal Horizontal Stress Component 1 (σ_{H1}), Principal Horizontal Stress Component 2 (σ_{H2})** and

**Young’s Modulus (E).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Vertical Stress (σ _{v})** is

**44**,

**Poisson’s Ratio (v)**is

**5**,

**Principal Horizontal Stress Component 1 (σ**is

_{H1})**6**,

**Principal Horizontal Stress Component 2 (σ**is

_{H2})**4**and

**Young’s Modulus (E)**is

**12**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the vertical strain and presents the formula, workings and steps too.