Area of Member given Strain Energy Stored by Member Calculator

Formula Used:

\[ A = \frac{2 \times E \times U_{member}}{L \times \sigma^2} \]

Young's Modulus (E):

Strain Energy stored by Member (U_member):

Length of Member (L):

Direct Stress (σ):

Area of Cross-Section (A):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Area of Member given Strain Energy Stored by Member?

The Area of Member given Strain Energy Stored by Member formula calculates the cross-sectional area of a structural member based on the strain energy stored, Young's modulus, length of the member, and direct stress applied. This is important in structural engineering for determining member dimensions that can safely store specific amounts of strain energy.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{2 \times E \times U_{member}}{L \times \sigma^2} \]

Where:

\( A \) — Area of Cross-Section (m²)
\( E \) — Young's Modulus (Pa)
\( U_{member} \) — Strain Energy stored by Member (J)
\( L \) — Length of Member (m)
\( \sigma \) — Direct Stress (Pa)

Explanation: The formula relates the cross-sectional area to the strain energy stored in a member under direct stress, considering the material's elastic properties and member dimensions.

3. Importance of Area Calculation

Details: Accurate area calculation is crucial for designing structural members that can safely withstand specific loads while storing acceptable amounts of strain energy without permanent deformation or failure.

4. Using the Calculator

Tips: Enter Young's Modulus in Pascals, Strain Energy in Joules, Length in meters, and Direct Stress in Pascals. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Young's Modulus?
A: Young's Modulus is a measure of the stiffness of a material, defined as the ratio of stress to strain in the elastic deformation region.

Q2: What is strain energy?
A: Strain energy is the energy stored in a material when it is deformed elastically. It represents the work done on the material to cause the deformation.

Q3: Why is direct stress squared in the formula?
A: The stress is squared because strain energy is proportional to the square of stress for elastic materials, following Hooke's law.

Q4: What are typical units for these calculations?
A: SI units are typically used: Pascals for stress and modulus, Joules for energy, meters for length, and square meters for area.

Q5: When is this formula applicable?
A: This formula applies to members experiencing uniform direct stress and undergoing elastic deformation only.