# How to Calculate and Solve for Critical Wall Stress of Spherical Body | Fracture

**Last Updated on December 15, 2022**

The image of critical wall stress of spherical body is represented below.

To compute for critical wall stress of spherical body, three essential parameters are needed and these parameters are **Wall Pressure (p), Radius of Sphere (r) **and **Wall Thickness (t).**

The formula for calculating critical wall stress of spherical body:

σ_{y} = ^{pr}/_{2t}

Where:

σ_{y} = Critical Wall Stress of Spherical Body

p = Wall Pressure

r = Radius of Sphere

t = Wall Thickness

Let’s solve an example;

Find the critical wall stress of spherical body when the wall pressure is 17, the radius of sphere is 13 and the wall thickness is 5.

This implies that;

p = Wall Pressure = 17

r = Radius of Sphere = 13

t = Wall Thickness = 5

σ_{y} = ^{pr}/_{2t}

σ_{y} = ^{(17)(13)}/_{2(5)}

σ_{y} = ^{(221)}/_{(10)}

σ_{y} = 22.1

Therefore, the **critical wall stress of spherical body **is **22.1 Pa.**

**Calculating the Wall Pressure when the Critical Wall Stress of Spherical Body, the Radius of Sphere and the Wall Thickness is Given.**

p = ^{σy x 2t} / _{r}

Where:

p = Wall Pressure

σ_{y} = Critical Wall Stress of Spherical Body

r = Radius of Sphere

t = Wall Thickness

Let’s solve an example;

Find the wall pressure when the critical wall stress of spherical body is 8, the radius of sphere is 4 and the wall thickness is 2.

This implies that;

σ_{y} = Critical Wall Stress of Spherical Body = 8

r = Radius of Sphere = 4

t = Wall Thickness = 2

p = ^{σy x 2t} / _{r}

p = ^{8 x 2(2)} / _{4}

p = ^{8 x 4} / _{4}

p = ^{32} / _{4}

p = 8

Therefore, the **wall pressure **is **8.**

**Calculating the Radius of Sphere when the Critical Wall Stress of Spherical Body, the Wall Thickness is Given.**

r = ^{σy x 2t} / _{p}

Where:

r = Radius of Sphere

σ_{y} = Critical Wall Stress of Spherical Body

p = Wall Pressure

t = Wall Thickness

Let’s solve an example;

Find the radius of sphere when the critical wall stress of spherical body is 10, the wall pressure is 6 and the wall thickness is 3.

This implies that;

σ_{y} = Critical Wall Stress of Spherical Body = 10

p = Wall Pressure = 6

t = Wall Thickness = 3

r = ^{σy x 2t} / _{p}

r = ^{10 x 2(3)} / _{6}

r = ^{10 x 6} / _{6}

r = ^{60} / _{6}

r = 10

Therefore, the **radius of sphere **is **10 m.**

**Calculating the Wall Thickness when the Critical Wall Stress of Spherical Body, the Wall Pressure and the Radius of Sphere is Given.**

t = ^{pr} / _{2σy}

Where:

t = Wall Thickness

σ_{y} = Critical Wall Stress of Spherical Body

p = Wall Pressure

r = Radius of Sphere

Let’s solve an example;

Given that the critical wall stress of spherical body is 6, the wall pressure is 14 and the radius of sphere is 2.

This implies that;

σ_{y} = Critical Wall Stress of Spherical Body = 6

p = Wall Pressure = 14

r = Radius of Sphere = 2

t = ^{pr} / _{2σy}

t = ^{14(2)} / _{2(6)}

t = ^{28} / _{12}

t = 2.3

Therefore, the **wall thickness **is **2.3 m.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the critical wall stress of spherical body.

To get the answer and workings of the critical wall stress of spherical body 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 **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

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

**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 **Materials and Metallurgical **under **Engineering****.**

Now, Click on **Fracture**** **under **Materials and Metallurgical**

Now, Click on **Critical Wall Stress of Spherical Body**** **under **Fracture**

The screenshot below displays the page or activity to enter your values, to get the answer for the critical wall stress of spherical body according to the respective parameter which is the **Wall Pressure (p), Radius of Sphere (r) **and **Wall Thickness (t).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Wall Pressure (p)** is **17**,** Radius of Sphere (r)** is **13 **and **Wall Thickness (t)** is **5**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the critical wall stress of spherical body and presents the formula, workings and steps too.