Stress & Strain Calculator

Stress & Strain is evaluated from Axial Force, Cross-Section Area and Original Length. The calculation reports Normal Stress, Normal Stress and Axial Strain.

Results

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About the Stress & Strain Calculator

Stress & Strain is treated here as a quantitative relation between Axial Force, Cross-Section Area, Original Length and Change in Length and Normal Stress, Normal Stress, Axial Strain and Elongation.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
sigma = F / A (normal stress, psi or ksi)
ε = ΔL / L₀ (axial strain, dimensionless)
E = sigma / ε (Young's modulus, psi)
ΔL = FL₀ / (AE) (elongation, inches)
SF = Fᵧ / sigma (safety factor vs yield)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

sigma = F / A (normal stress, psi or ksi)
ε = ΔL / L₀ (axial strain, dimensionless)
E = sigma / ε (Young's modulus, psi)
ΔL = FL₀ / (AE) (elongation, inches)
SF = Fᵧ / sigma (safety factor vs yield)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Steel Hanger Rod Under Tension

Inputs

F: 25000 A_in2: 0.785 L0_in: 120 E_psi: 29000000 Fy_psi: 36000
Normal Stress: 31,847.1 psi. Normal Stress: 31.847 ksi. Axial Strain: 0.001098 in/in. Elongation: 0.1318 in. Young's Modulus: 29,000,000 psi. Safety Factor: 1.13

With Axial Force = 25,000, Cross-Section Area = 0.785, Original Length = 120 and Young's Modulus = 29,000,000 as the stated inputs, the result is Normal Stress = 31,847.1 psi, Normal Stress = 31.847 ksi and Axial Strain = 0.001098 in/in. Each value corresponds to the declared output fields.

Example 2: Bridge Cable Elongation Check

Inputs

F: 500000 A_in2: 12.5 L0_in: 2400 E_psi: 27000000 Fy_psi: 215000
Normal Stress: 40,000 psi. Normal Stress: 40 ksi. Axial Strain: 0.001481 in/in. Elongation: 3.5556 in. Young's Modulus: 27,000,000 psi. Safety Factor: 5.38

With Axial Force = 500,000, Cross-Section Area = 12.5, Original Length = 2,400 and Young's Modulus = 27,000,000 as the stated inputs, the result is Normal Stress = 40,000 psi, Normal Stress = 40 ksi and Axial Strain = 0.001481 in/in. Each value corresponds to the declared output fields.

Example 3: Concrete Column Compression

Inputs

F: -200000 A_in2: 100 L0_in: 144 E_psi: 3600000 Fy_psi: 4000
Normal Stress: -2,000 psi. Normal Stress: -2 ksi. Axial Strain: -0.000556 in/in. Elongation: -0.08 in. Young's Modulus: 3,600,000 psi. Safety Factor: -2

With Axial Force = -200,000, Cross-Section Area = 100, Original Length = 144 and Young's Modulus = 3,600,000 as the stated inputs, the result is Normal Stress = -2,000 psi, Normal Stress = -2 ksi and Axial Strain = -0.000556 in/in. Each value corresponds to the declared output fields.

Example 4: Measuring Young's Modulus — Tensile Test

Inputs

F: 10000 A_in2: 0.196 L0_in: 8 dL_in: 0.00138
Normal Stress: 51,020.4 psi. Normal Stress: 51.02 ksi. Axial Strain: 0.000173 in/in. Elongation: 0.0014 in. Young's Modulus: 295,770,482 psi

With Axial Force = 10,000, Cross-Section Area = 0.196, Original Length = 8 and Change in Length = 0.00138 as the stated inputs, the result is Normal Stress = 51,020.4 psi, Normal Stress = 51.02 ksi and Axial Strain = 0.000173 in/in. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate stress in a tension rod under axial load
  • Find elongation of a steel cable under load
  • Determine required cross-section area for a given stress limit