Mechanics of Materials: Stress

Stress is a measure of internal forces within a material. Stress is generally expressed as force divided by area, but at we will see below there are a few different types. It has the SI units of N/m², which are also referred to as Pascals (Pa). In field of Mechanics of Materials, we often utilize the prefixes of kilo Pascal (kPa), mega Pascal (MPa), and giga Pascal (GPa).  Stress helps engineers determine if a material can safely support certain loads, or it the material will fail. 

Normal Stress

Normal stress is the kind of stress that acts perpendicular to a surface. It occurs when an axial force is applied along the length of a structural member. We often refer to these members as either being in tension or compression.  We express normal stress with the greek letter sigma, and write the expression as σ = P/A, where

• σ = normal stress
• P = internal axial force
• A = cross sectional area

Normal Stress in Members with Varying Cross-Section

If a member has various cross sections, like the example below, each section will carry the same internal load, but different normal stresses. This is because normal stress, σ = P/A depends on the cross sectional area. If the internal load is constant, but the area is different, the normal stress will be different in each section. The video explains this in detail. 

Shear Stress

Shear stress occurs when forces are acting parallel to the surface of a material. Where normal stress (for example, tension) would have the tenancy for a material to a material to rip apart across a plane, shear stress tends to cause one layer of the material to slide over an adjacent layer.  We express shear stress with the greek letter tau, and write the expression as τ = V/A, where

• τ = shear stress
• V = internal shear force
• A = area over which the force acts

When there is a single shearing plane, as highlighted in the video below, we refer to this as single shear.

Double Shear

Double shear occurs when a load is split between two shearing planes instead of one. Because the load is distributed over two areas instead of one, the shearing stress in the pin will be halved. Double shear can be achieved in a pin connection by using two plates, as described in the following video.

Bearing Stress

Bearing stress is the contact pressure between two bodies. Bearing stress helps determine how materials will resist localized crushing. A common example is a bolt or pin that is pressing against the side of a hole. We express bearing stress with the geek letter sigma, underscore b, and write the expression as σ_b = F/A, where

• σ_b = bearing stress
• F = force transmitted by the bolt/pin
• A = projected bearing area, ie, the area over which the force acts

In reality bearing stress is not distributed uniformly over the hole, but for basic calculations we will assume it is.

Factor of Safety

Factor of safety, abbreviated to FS or FoS, is the ratio of ultimate load over allowable load, or ultimate stress over allowable stress. This is a useful ratio that will enable us to design/select structural members that are stronger than they need to be for an intended load. Increasing the factor of safety means more reliability but may increase weight, size, or cost. Watch the video below for a discussion and example on this very important topic.

Further Study

This is chapter 1 of the Mechanics of Materials Course. Other chapters include Stress, Strain, Torsion, Pure Bending, Beam Deflection, Energy Methods, and Columns. For 50+ video tutorials and 50+ fully annotated practice problems, head over to the main course page.

Mechanics of Materials Course