Fundamentals of Stress & Strain

It is helpful to understand some fundamental concepts related to stress and strain prior to making any calculations or referencing torque tables in order to orient ourselves to a basic understanding of what torque is and what we are trying to accomplish by using it.

Below is a visual introduction to the diagram:

What is Stress?

Stress refers to the internal resistance a material offers per unit area to an external force trying to deform it.

Formula:  σ = F/A where:

•  σ = stress (psi, ksi, or MPa)
• F = force (lbf or N)
• A = area (in² or mm²)

Note: Pound-force (lbf) is a measure of force and is distinct from mass or weight.

What is Strain?

Strain represents the geometric deformation of a material in response to applied stress. Essentially, it pictorially shows how materials behaves under loading.

Formula: ε = ∆L / Lο where:

• ε is strain (unitless)
• ∆L is change in length (in or mm)
• Lο is the original length (in or mm)

Elongation Curve

Elongation Curve is a graphical representation of how a material stretches in response to applied stress. It includes both elastic and plastic deformation phases.

Elastic Range

Elastic Range is the portion of a material’s stress-strain curve in which the material behave elastically meaning that it returns to its original shape when an applied load is removed. This represents reversible deformation.

Plastic Deformation

Plastic Deformation is the permanent change in shape or size of a material when subjected to a stress beyond its elastic limit. Plastic deformation causes irreversible changes in the material’s structure.

Yield Point

Yield Point is the exact point at which material begins to deform plastically. This is often impossible to determine without testing. And even with testing, it changes slightly depending on test samples.

Yield Strength

Yield Strength is the maximum stress level at which a material will begin to deform permanently.

Ultimate Tensile Strength (UTS)

Ultimate Tensile Strength refers to the maximum stress a material can withstand before breaking.

Fastener Mechanics: Key Definitions

Proof Load

Proof Load is the maximum force a fastener can withstand without experiencing permanent deformation. Because the exact point fluctuates slightly, it is typical for the value to be multiplied by 92% to ensure that the yield point is not exceeded.

Proof Load = σ_y * A * 0.90 Where:

• σ_y = Minimum yield strength (psi, ksi, or MPa)
• A = stress area (in² or mm²)

Clamp Load

Clamp Load is the axial force applied to a fastener (i.e. bolt or screw) to hold components together in an assembly. Typically clamp load is multiplied by a factor of safety of 75% of the proof load.  (This is a general factor of safety. Different industries and specific structural designs have different factor of safety values. Consult with a professional engineer for your specific application.)

Importance of Fastener Torque

Fastener torque is important because there needs to be enough load applied to the bolt and nut to prevent it from loosening. This can lead to a loss in structural integrity of the unit. However, too much fastener torque moving beyond the elastic range will lead to permanent deformation of the bolt and nut. This can lead to damage and failure of the structural components as well.

Calculating Fastener Torque

Here are the steps for calculating fastener torque:

• Determine the Yield Strength (σ_y).
• Identify or calculate the Cross-sectional Stress Area. Use ASME B01.01 or Cross Sectional Stress Area A = π/4 * ( D – 0.9743/n)² Where n = # of threads per inch & D = diameter  (Note: Threads are excluded from the stress area. Differentiate between coarse and fine threads.)
• Calculate Proof Load. Proof Load = σ_y * A * 92%
• Calculate Clamping Load. Clamping Load = Proof Load * 75%
• Identify Friction Coefficient (k). This is a unitless factor typically between 0.15 to 0.3 based on material, lubrication, and thread type.
• Calculate your fastener torque. Fastener Torque = k * D * Clamp Load ÷ 12 (If D is in inches, divide by 12 to convert to ft-lb)

Get our NSI Torque Tables below