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# Leaf Springs Calculator

Input the required values and hit the calculate button to use Leaf Springs Calculator

## Leaf Springs Calculator

Leaf Springs Calculator is a mathematical tool that is used to find the stiffness of vehicles using the number of leaves, the width of leaves, and the thickness of the leaves.

## What is meant by leaf springs?

**Leaf springs** are a type of suspension system used in vehicles particularly models like **trucks **and long **vehicles**. They are a simple and effective way to absorb and distribute the weight and impact forces from the vehicle wheels.

Leaf springs consist of several **layers **or **leaves **of metal strips stacked on top of each other with the longest leaf at the bottom and progressively shorter leaves stacked on top.

Each leaf is slightly curved and made of **flexible **steel which allows the spring to **flex **and **absorb **shocks when the vehicle encounters bumps or uneven surfaces on the road.

The top end of the leaves is usually clamped to the vehicle frame while the bottom end is connected to the axle.

## Formula of Leaf Spring:

**k= (8****×E****×n****×b****×t ^{3})/(3l^{3})**

Where,

**E**= Young’s Modulus**n**= Number of Leaves**b**= Width of Leaf**t**= Thickness of Leaf**L**= Span of leave**k**= Stiffness of the leave

## How to solve the problems of leaf springs?

**Example 1:**

Find the stiffness of the leaves while the thickness of the leaf is **3**, the span of the leaf is **2**, the width of the leaf is **4**, and the young Modulus of metal is **6 **with the **15 **number of leaves.

**Solution:**

**Step 1:** Write the data from the question.

E = 6, n = 15, b = 4

t = 3, L = 2, k =?

**Step 2: **Write the formula of the leaf spring.

k= (8×E×n×b×t^{3})/(3l^{3})

**Step 3: **Put the all above values in the formula and simplify.

k = (8 × 6 × 15 × 4 × 3^{3})/(3(2)^{3})

k = (8 × 6 × 15 × 4 × 27)/(3 × 8)

k = (77760)/(24)

**k = 3240**

**Example 2:**

Find the stiffness of the leaves while the thickness of the leaf is 4, the span of the leaf is 3, the width of the leaf is 5, and the young Modulus of metal is 10 with the 20 number of leaves.

**Solution:**

**Step 1: **Write the data from the question.

E = 10, n = 20, b = 5, t = 4, L = 3, k =?

**Step 2: ****Write the formula of the leaf spring.**

`k= (8×E×n×b×t`

^{3})/(3l^{3})

**Step 3: **Put the all above values in the formula and simplify.

k = (8 × 10 × 20 × 5 × 4^{3})/(3(3)^{3})

k = (8 × 6 × 15 × 4 × 64)/(3 × 27)

k = (184320)/(81)

**k = 2275.5 **