In physics, the stress at a point in a material is the applied force per unit area. The stress unit is the Pascal (symbol Pa). To be exact, the stress at a point may be determined by taking the limit of the load being carried by a particular cross section, divided by that cross section, as the area of the cross section aproaches zero. In general the stress may vary from point to point, but for simple cases, such as circular cylinders with pure axial loading, the stress is constant and equal to the cross-sectional area divided by the applied load.
Stress is described by a symmetric tensor.
For instance, if we have a steel bolt with a diameter of 5 mm, it has a cross-sectional area of 2*10-5m2. Suppose that the load is 50 kN, the stress (force distributed across the cross-section) is about 2.5 MPa.
That means each m2 of bolt would support 2.5 MN of the total load.
In another bolt with half the diameter, and hence a quarter the cross-sectional area, carrying the same 50 kN load, the stress will be quadrupled (10 MPa).
The ultimate tensile strength of a material is the value of the tension stress causing the material's fracture. The compression strength is analogous for compression strain. The yield strength is the value of stress causing plastic deformation. These values are determined experimentally using the measurement procedure known as the tensile test.