7.1 Concept of stress and its types

Stress is the internal force per unit area in a material when subjected to external loads. It's crucial for designing strong, stable structures. Engineers use stress analysis to select materials and ensure components can withstand various loads without failing.

Normal stress acts perpendicular to a material's surface, causing compression or tension. Shear stress acts parallel, making adjacent planes slide. Materials often experience both types. Understanding these helps engineers design safer, more reliable structures and components.

Stress in Engineering Materials

Definition and Significance

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• Stress is the internal force per unit area that a material experiences when subjected to external loads or forces
• Stress is a crucial concept in engineering that determines the strength, stability, and durability of materials and structures
• Understanding stress helps engineers design components and structures that can withstand applied loads without failure or excessive deformation
• The units of stress are typically expressed in pascals (Pa), megapascals (MPa), or gigapascals (GPa) in the SI system, and pounds per square inch (psi) in the US customary system
• Stress analysis is essential for selecting appropriate materials and designing components with adequate factors of safety to ensure reliable performance under various loading conditions

Normal vs Shear Stress

Normal Stress

• Normal stress acts perpendicular to the surface of a material, causing either compression (pushing together) or tension (pulling apart)
• Normal stress is denoted by the Greek letter sigma (σ)
• The formula for normal stress is [σ = F/A](https://www.fiveableKeyTerm:σ_=_f/a), where F is the normal force and A is the cross-sectional area
• Examples of normal stress include the stress in a rope supporting a weight (tension) or the stress in a column supporting a building (compression)

Shear Stress

• Shear stress acts parallel to the surface of a material, causing adjacent planes to slide relative to each other
• Shear stress is denoted by the Greek letter tau (τ)
• The formula for shear stress is $τ = F/A$, where F is the shear force and A is the area over which the force is applied
• Examples of shear stress include the stress in a bolt subjected to a shearing force or the stress in the adhesive layer of a bonded joint
• In many loading scenarios, materials experience a combination of normal and shear stresses, which can be analyzed using Mohr's circle or other stress transformation techniques

Types of Stress

Compressive and Tensile Stress

• Compressive stress occurs when a material is subjected to forces that push its particles closer together, causing a decrease in length or volume
• Tensile stress occurs when a material is subjected to forces that pull its particles apart, causing an increase in length or volume
• Examples of compressive stress include the stress in a concrete foundation supporting a building or the stress in a gear tooth during meshing
• Examples of tensile stress include the stress in a stretched rubber band or the stress in a metal wire under tension

Torsional and Bending Stress

• Torsional stress (or shear stress due to torsion) occurs when a material is subjected to a twisting force, causing angular deformation
• Bending stress is a combination of compressive and tensile stresses that occurs when a material is subjected to a bending moment, causing it to curve
• Examples of torsional stress include the stress in a shaft transmitting power or the stress in a torsion spring
• Examples of bending stress include the stress in a beam supporting a load or the stress in a cantilever subjected to a concentrated force at its free end

Thermal and Residual Stress

• Thermal stress is induced in a material due to changes in temperature, which cause expansion or contraction of the material
• Residual stress is the stress that remains in a material after the external loads have been removed, often due to manufacturing processes such as welding or heat treatment
• Examples of thermal stress include the stress in a heated pressure vessel or the stress in a bi-metallic strip used in a thermostat
• Examples of residual stress include the stress in a welded joint after cooling or the stress in a heat-treated gear after quenching

Stress Distribution Analysis

Stress Distribution and Equilibrium

• Stress distribution refers to the variation of stress magnitude and direction throughout a structural element
• To analyze stress distribution, engineers use free-body diagrams to identify the external forces and moments acting on the element
• The stress distribution can be determined by applying equilibrium equations, constitutive relationships (such as Hooke's law), and compatibility conditions
• For simple loading cases, such as uniaxial tension or compression, the stress distribution is uniform throughout the cross-section of the element

Stress Concentration and Finite Element Analysis

• For more complex loading scenarios, such as bending or torsion, the stress distribution varies across the cross-section, with maximum stresses occurring at specific locations (the outer fibers in bending)
• Stress concentration factors are used to account for the increased stress levels at geometric discontinuities, such as holes, notches, or sharp corners, which can lead to localized failure
• Examples of stress concentration include the stress around a hole in a plate subjected to tension or the stress at the root of a gear tooth
• Finite element analysis (FEA) is a powerful numerical method for analyzing stress distribution in complex geometries and loading conditions, providing detailed insights into the stress state of a component or structure