Mechanical stress is a fundamental concept in physics and engineering that quantifies the intensity of internal forces acting within a deformable body. It represents how a material resists an external load, whether that load is tensile (pulling), compressive (pushing), or shear (sliding). Understanding stress is necessary for designing structures and mechanical components, ensuring they can withstand applied forces without failing.
Stress as Force per Unit Area
Mechanical stress ($\sigma$) is mathematically defined as the ratio of an applied force ($F$) to the cross-sectional area ($A$) over which that force is distributed, represented by the formula $\sigma = F/A$. This calculation normalizes the internal reaction of a material, allowing engineers to compare how different sizes of the same material behave under varying loads. The resulting measure is independent of the object’s size.
This definition applies to the three basic types of stress: tensile stress, which is a pulling action that stretches the material; compressive stress, which is a pushing action that shortens it; and shear stress, which involves forces acting parallel to the surface. By calculating the stress, engineers determine if the internal forces generated within the material exceed its inherent strength limit.
Standard International Units: The Pascal
The standard unit for measuring stress in the International System of Units (SI) is the Pascal (Pa), a unit also used to quantify pressure. The Pascal is formally defined as one Newton of force applied perpendicularly over one square meter of area, giving it the dimensional equivalent of $1 \text{ Pa} = 1 \text{ N/m}^2$.
Because the Pascal represents a relatively small amount of stress, engineers typically use multiples for practical measurements. The most common multiples are the kilopascal (kPa), which is 1,000 Pa, and the megapascal (MPa), which is one million Pa. The megapascal is the preferred unit in materials science and structural engineering because real-world stresses are often in the millions of Pascals. For example, high-strength structural steel can have a tensile strength of $500 \text{ MPa}$ or more, making MPa a conveniently sized unit.
Imperial and Alternative Units
While the Pascal is the international standard, engineers in the United States and other regions using the imperial system frequently use Pounds per Square Inch (psi) for stress. This unit aligns directly with the force-per-area concept, where one psi is defined as one pound-force applied over an area of one square inch ($1 \text{ psi} = 1 \text{ lbf/in}^2$).
For materials that withstand extremely high stress, a common multiple is the kilopound per square inch (ksi), which is $1,000$ psi. Converting between psi and SI units is necessary in international projects, as $1 \text{ MPa}$ is equivalent to approximately $145.038 \text{ psi}$. Understanding these alternative units is important for interpreting specifications for items like tires, hydraulic systems, and structural materials, which are often rated in psi.
Understanding the Stress-Strain Relationship
Stress is often discussed alongside strain, which measures the amount of deformation a material experiences when subjected to stress. Strain is defined as the change in a material’s dimension divided by its original dimension. Because this is a ratio of two lengths, strain is typically a dimensionless quantity. Stress and strain are connected through Young’s Modulus, a material property that defines its stiffness.
Young’s Modulus is mathematically calculated as the ratio of stress to strain. Since strain is dimensionless, the units of Young’s Modulus are the same as the units of stress, most commonly expressed in megapascals (MPa) or gigapascals (GPa). Engineers use this modulus to predict material behavior, ensuring the designed component maintains its required shape and function under operational loads.