Stress Strain Equations Formulas Calculator

Mechanics of Materials - Solid Formulas

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Solve for Young's modulus

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	stress
	force
	area

	strain
	change in length
	original length

	Young's modulus
	stress
	strain

References - Books

Tipler, Paul A.. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.

Background

Young's modulus, te modulus of elasticity, measures how stiff a solid material is. It shows the relationship between stress (force per unit area) and strain, which is the proportional deformation of the object. It is a fundamental concept in engineering and materials science.

Equation

The formula to calculate Young's modulus ( E ) is given by:

E = σ / ε

Where:

E is Young's modulus in pascals (Pa)
σ is the stress in pascals (Pa)
ε is the strain (dimensionless)

How to Solve

To solve for Young's modulus, follow these steps:

Determine the stress (σ): This is calculated by dividing the force applied (F) by the area (A) over which the force is distributed. ( σ = F / A ).
Determine the strain (ε): Strain is calculated as the change in length (ΔL) divided by the original length (L). ( ε = ΔL / L ).
Apply the Formula: Substitute the values of stress and strain into Young's modulus equation ( E = σ / ε ).

Example

Consider a metallic rod subjected to a tensile force of 1000 N. Assume the original length of the rod is 2 meters, and under the load, it stretches by 1 mm. The cross-sectional area of the rod is 0.01 square meters.

Calculate the stress:

σ = 1000 N / 0.01 m² = 100000 Pa

Calculate the strain:

ε = 0.001 m / 2 m = 0.0005

Calculate Young's modulus:

E = 100000 Pa / 0.0005 = 200 x 10⁶ Pa

Therefore, Young's modulus for the material of the rod is 200 x 10⁶ Pa.

Fields/Degrees

Mechanical Engineering
Civil Engineering
Aerospace Engineering
Materials Science
Biomechanics

Real Life Applications

Construction: Determining suitable materials for beams, columns, and slabs.
Automotive: Designing components such as springs, chassis, and engine parts.
Aerospace: Material selection for aircraft frames and other structural elements.
Consumer Electronics: In designing thin, robust cases and frames for smartphones and laptops.
Medical Devices: Design of prosthetics and other supportive equipment.

Common Mistakes

Mixing units (e.g., using mm versus meters for length).
Not accounting for uniform cross-sectional area along the length of the material.
Neglecting the effect of temperature and environment on material properties.
Overlooking existing microscopic stress while measuring applied stress.
Applying the modulus of elasticity beyond the elastic limit of the material.

Frequently Asked Questions

Is Young's modulus the same for all materials?
No, Young's modulus varies from material to material, reflecting different stiffness levels.
Can Young's modulus be negative?
No, Young's modulus is a measure of stiffness and cannot be negative.
Does temperature affect Young's modulus?
Yes, with most materials, the increasing temperature tends to lower Young's modulus.
How does Young's modulus relate to strength?
Young's modulus measures stiffness, not strength. High Young's modulus means a material is stiff but not necessarily strong.
Is it applicable only under tensile stress?
Young's modulus is generally considered under both tensile and compressive stress as long as the material remains within the elastic limit.

Stress Strain Equations Calculator

Problem:

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References - Books

Background

Equation

How to Solve

Example

Fields/Degrees

Real Life Applications

Common Mistakes

Frequently Asked Questions