Stress is the internal resistance offered by the body to the external load applied to it per unit cross sectional area. Stresses are normal or tangential to the plane to which they act and are tensile, compressive or shearing in nature.
When a member is subjected to loads it develops resisting forces. To find the resisting forces developed a section plane may be passed through the member and equilibrium of any one part may be considered. Each part is in equilibrium under the action of applied forces and internal resisting forces. The resisting forces may be conveniently split into normal and parallel to the section plane. The resisting force parallel to the plane is called Shearing resistance. The intensity of resisting force normal to the sectional plane is called Normal resistance.
Consider a rectangular rod subjected to axial pull P. Let us imagine that the same rectangular bar is assumed to be cut into two halves at section XX. The each portion of this rectangular bar is in equilibrium under the action of load P and the internal forces acting at the section XX has been shown in figure. The symbol ‘σ’ is used to represent stress.
Where A is the area of the X –X section
Here we are using an assumption that the total force or total load carried by the rectangular bar is uniformly distributed over its cross section. But the stress distributions may be far from uniform, with local regions of high stress known as stress concentrations. If the force carried by a component is not uniformly distributed over its cross sectional area, A, we must consider a small area, ‘δA’ which carries a small load ‘δP’, of the total force ‘P', Then definition of stress is
Unit of Stress
The basic units of stress in S.I units i.e. (International system) are N/m^2 (or Pa). When Newton is taken as unit of force and millimeter as unit of area, unit of stress will be N/mm^2. The other derived units used in practice are kN/mm^2, N/m^2 or kN/m^2. A stress of one N/m2 is known as Pascal and is represented by Pa.
Hence, 1 MPa = 1 MN/m^2 = 1 × 10^6 N/(1000 mm^2) = 1 N/mm^2.
Thus one Mega Pascal is equal to 1 N/mm^2.
Types of Stress
The two basic stresses exists are Normal stress and Shear stress. Other stresses either are similar to these basic stresses or as a combination of this.
Example : Bending stress is a combination tensile, compressive and shear stresses.
Torsional stress, as encountered in twisting of a shaft is a shearing stress.
1) Normal stress
If the stresses are normal to the areas concerned, then these are termed as normal stress. The normal stress is generally denoted by a Greek letter (σ). Stress is said to be normal stress when the direction of the deforming force is perpendicular to the cross-sectional area of the body. Normal stress can be further classified into three types based on the dimension of force. This is also known as uniaxial state of stress, because the stresses acts only in one direction however, such a state rarely exists, therefore we have biaxial and triaxial state of stresses where either the two mutually perpendicular normal stresses acts or three mutually perpendicular normal stresses acts as shown in the figures below.
a) Tensile Stress
Consider a bar subjected to force P as shown in figure. To maintain the equilibrium the end forces applied must be the same, say P. If the deforming force or applied force results in the increase in the object’s length then the resulting stress is termed as tensile stress.For example when a rod or wire is stretched by pulling it with equal and opposite forces (outwards) at both ends.
b) Compressive Stress
If the deforming force or applied force results in the decrease in the object’s length then the resulting stress is termed as compressive stress. For example: When a rod or wire is compressed/squeezed by pushing it with equal and opposite forces (inwards) at both ends.
Sign convections for Normal stress
Tensile stress is taken as +ve
Compressive stress is taken as –ve
2) Shear Stress
The cross sectional area of a block of material is subject to a distribution of forces which are parallel, rather than normal, to the area concerned. Such forces are associated with a shearing of the material and are referred to as shear forces. The resulting stress is known as shear stress.
Bearing Stress
When one object presses against another, it is referred to a bearing stress (They are in fact the compressive stress).
Bending Stress
Bending stress is the stress that results from the application of a bending moment to a material, causing it to deform. This results in the development of a combination of tensile and compressive stresses through the cross-section of the material and creates a stress gradient that causes the material to bend.
Torsional stress
Torsional shear stress or Torsional stress may be defined as that shear stress which acts on a transverse cross-section that is caused by the action of a twist.
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