The image above represents resiliency.

To compute for resiliency, two essential parameters are needed and these parameters are **Maximum Stress (σ _{max})** and

**Young’s Modulus of Elasticity (E).**

The formula for calculating resiliency:

R = ^{σmax²} / _{2E}

Where:

R = Resiliency

σ_{max} = Maximum Stress

E = Young’s Modulus of Elasticity

Let’s solve an example;

Find the resiliency when the maximum stress is 32 and the young’s modulud of elasticity is 12.

This implies that;

σ_{max} = Maximum Stress = 32

E = Young’s Modulus of Elasticity = 12

R = ^{σmax²} / _{2E}

R = ^{32²} / _{2(12)}

R = ^{1024} / _{24}

R = 42.67

Therefore, the **resiliency **is **42.67 Pa.**

**Calculating the Maximum Stress when the Resiliency and the Young’s Modulus of Elasticity is Given.**

σ_{max} = **√**R x 2E

Where;

σ_{max} = Maximum Stress

R = Resiliency

E = Young’s Modulus of Elasticity

Let’s solve an example;

Find the maximum stress when the resiliency is 15 and the young’s modulus of elasticity is 3.

This implies that;

R = Resiliency = 15

E = Young’s Modulus of Elasticity = 3

σ_{max} = **√**R x 2E

σ_{max} = **√**15 x 2 x 3

σ_{max} = **√**90

σ_{max} = 9.48

Therefore, the **maximum stress **is **9.48.**

Continue reading How to Calculate and Solve for Resiliency | Fracture Mechanics