STRESS-STRAIN DIAGRAMS

Stress – Strain Relationships :

One basic ingredient in the study of the mechanics of deformable bodies is the resistive 

properties of materials. These properties relate the stresses to the strains and can only 

be determined by experiment. 

One of the simplest tests for determining mechanical properties of a material is the 

tensile test. In this test, a load is applied along the longitudinal axis of a circular test 

specimen. The applied load and the resulting elongation of the member are measured. 

In many cases, the process is repeated with increased load until the desired load levels 

are reached or the specimen breaks. 

Load-deformation data obtained from tensile and/or compressive tests do not give a 

direct indication of the material behavior, because they depend on the specimen 

geometry. 

However, using the relationships we previously discussed, loads and deformations may 

be converted to stresses and strains. 

σ = normal stress on a plane perpendicular to the longitudinal axis of the specimen 

P = applied load 

A = original cross sectional area 

ε = normal strain in the longitudinal direction 

δ = change in the specimen’s gage length 

L = original gage length 

The resulting stress-strain curve or diagram gives a direct indication of the material 

properties. 

Note: Stress-strain diagrams are typically based upon the original cross sectional area 

and the initial gage length, even though these quantities change continuously during the 

test. These changes have a negligible effect except during the final stages of the test.