Stress (mechanics)

Figure 1.1 Stress in a loaded deformable material body assumed as a continuum.

Figure 1.2 Axial stress in a prismatic bar axially loaded.

Figure 1.3 Normal stress in a prismatic (straight member of uniform cross-sectional area) bar. The stress or force distribution in the cross section of the bar is not necessarily uniform. However, an average normal stress$\sigma _{\mathrm {avg} }\,\!$can be used.

Figure 1.4 Shear stress in a prismatic bar. The stress or force distribution in the cross section of the bar is not necessarily uniform. Nevertheless, an average shear stress$\tau _{\mathrm {avg} }\,\!$is a reasonable approximation.

Stressis theforceper unitareaon a body that tends to cause it tochange shape.

Stress is a measure of the internal forces in a body between itsparticles.These internal forces are a reaction to the external forces applied on the body that cause it to separate,compressor slide.External forces are eithersurface forcesorbody forces.Stress is the average force per unit area that aparticleof a body exerts on an adjacent particle, across an imaginary surface that separates them.

The formula foruniaxialnormal stress is:

${\sigma }={\frac {F}{A}}$

where σ is the stress, F is the force and A is the surface area.

InSIunits, force is measured innewtonsand area insquare metres.This means stress is newtons per square meter, or N/m².However, stress has its own SI unit, called thepascal.1 pascal (symbol Pa) is equal to 1 N/m².InImperial units,stress is measured inpound-forceper squareinch,which is often shortened to "psi". The dimension of stress is the same as that ofpressure.

Incontinuum mechanics,the loaded deformable body behaves as acontinuum.So, these internal forces are distributed continually within the volume of the material body. (This means that the stress distribution in the body is expressed as apiecewisecontinuous functionof space and time.) The forces causedeformationof the body's shape. The deformation can lead to a permanent shape change or structural failure if thematerial is not strong enough.

Some models of continuum mechanics treat force as something that can change. Other models look at the deformation of matter and solid bodies, because the characteristics of matter and solids are three dimensional. Each approach can give different results. Classical models of continuum mechanics assume an average force and do not properly include "geometrical factors". (Thegeometryof the body can be important to how stress is shared out and how energy builds up during the application of the external force.)

Shear stress

Further information:Shear stress

Simple stresses

In some situations, the stress within an object can be described by a single number, or by a singlevector(a number and a direction). Three suchsimple stresssituations are theuniaxial normal stress,thesimple shear stress,and theisotropic normal stress.

Uniaxial normal stress

Tensile stress(ortension) is the stress state leading toexpansion;that is, the length of a material tends to increase in the tensile direction. The volume of the material stays constant. When equal and opposite forces are applied on a body, then the stress due to this force is called tensile stress.

Therefore in a uniaxial material the length increases in the tensile stress direction and the other two directions will decrease in size. In the uniaxial manner oftension,tensile stress is induced by pulling forces. Tensile stress is the opposite ofcompressive stress.

Structural members in direct tension areropes,soilanchorsandnails,bolts,etc.Beamssubjected to bendingmomentsmay include tensile stress as well as compressive stress and/orshear stress.

Tensile stress may be increased until the reach oftensile strength,namely thelimit stateof stress.

Stress in one-dimensional bodies

All real objects occupy three-dimensional space. However, if two dimensions are very large or very small compared to the others, the object may be modelled as one-dimensional. This simplifies themathematical modellingof the object. One-dimensional objects include a piece of wire loaded at the ends and viewed from the side, and a metal sheet loaded on the face and viewed up close and through the cross section.

Related pages

• Tension
• Bending
• Stress–strain curve

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Other websites

• Stress analysis, Wolfram ResearchArchived2006-09-03 at theWayback Machine
• ESDU Stress Analysis Methods
• True stress and true strainArchived2008-04-30 at theWayback Machine
• Stress-Strain Curve for Ductile MaterialArchived2008-05-01 at theWayback Machine
• Encyclopædia Britannica article