Types of Stresses

In engineering mechanics, a body may experience two primary types of stresses: normal stress or shear stress. Normal stress is the stress that acts perpendicular to the surface area. It is commonly represented by the symbol σ (sigma). Normal stress is further divided into tensile and compressive stresses.

Tensile Stress

Tensile stress develops in a material when it is pulled by two equal and opposite forces. As shown in Fig. 1.1(a), when a bar is stretched, its length increases. This induced stress is known as tensile stress. The relative increase in length compared to the original length is termed as tensile strain.

Tensile stress acts perpendicular to the area and tends to pull the section apart.

Let:

P = Applied pull (force)
A = Cross-sectional area
L = Initial length
dL = Increment in length
σ = Tensile stress
ε = Tensile strain

When a section x–x divides the bar, the internal resisting force balances the applied load, as shown in Fig. 1.1 (b) and Fig. 1.1 (c). This resistance per unit area is known as stress.

Therefore,

Tensile Stress:

σ = P / A ...(1.1)

Tensile Strain:

ε = dL / L ...(1.2)

Compressive Stress

Compressive stress is the opposite of tensile stress. When a body is pushed from both ends with equal and opposite forces, its length reduces. This behavior is illustrated in Fig. 1.2(a). The stress induced due to this shortening is called compressive stress.

The ratio of decrease in length to the original length is called compressive strain. Compressive stress also acts normal to the surface area but pushes the material inward.

Compressive Stress:

σ = P / A

Compressive Strain:

ε = dL / L

Shear Stress

Shear stress is produced when a pair of equal and opposite forces act tangentially on the surface, trying to slide one layer of the material over the other. This situation is shown in Fig. 1.3.

As these forces attempt to shear the body along the resisting plane, the developed stress is called shear stress. The corresponding angular deformation is termed as shear strain.

Shear stress acts parallel to the area on which it is applied.

Shear Stress Formula:

τ = P / A ...(1.3)

Illustration of Shear Stress

Consider a rectangular block of height h and length L. If a tangential force P is applied at the top surface (Fig. 1.4a), the bottom is fixed while the top tends to slide. The lower surface offers resistance to this motion.

When the section x–x divides the block, the upper portion remains in balance due to an internal resisting force R, as depicted in Fig. 1.4(b) and 1.4(c).

Thus,

τ = R / A = P / (L × 1)

Since shear deformation causes the top surface to shift horizontally, the angular distortion is known as shear strain (φ).

Shear Strain:

φ = (Transverse displacement) / (Original height) = dD / h ...(1.4)

Types of Stresses