Simple Stress and Strain in Strength of Materials

Simple Stress and Strain

• Stress can be either tensile or compressive, depending on the direction of the force applied to a metal bar
• Tensile stresses are positive, while compressive stresses are negative
• Direct or normal stresses are stresses that act perpendicular to the cut surface
• The stress equation gives the average normal stress acting on the cross-sectional area
• The maximum stress will depend on the bar's geometry and the type of discontinuity, and can be calculated using a stress concentration factor K

Tensile-Test

• A tensile test is used to determine the properties of a material under tension
• The test involves stretching a metal bar until it fractures
• The percentage elongation and percentage reduction of area can be calculated from the test results
• A material is classified as brittle if the percentage elongation is less than 5 in a gauge length of 50 mm

Factor of Safety

• A factor of safety is used to ensure that the working stresses in a structure remain within safe limits
• The factor of safety is defined as the ratio between the failure stress and the working stress
• To avoid failure, the allowable stress must be less than or equal to the failure stress divided by the factor of safety

Hooke's Law

• Within the elastic region, there is a linear relationship between stress and strain
• Hooke's Law is represented by the equation σ = Eε, where σ is the stress, E is the modulus of elasticity, and ε is the strain

Axially Loaded Spring/Bars

• The stiffness of an axially loaded bar is defined as the force required to produce a unit deflection
• The flexibility of an axially loaded bar is defined as the deflection given to a unit load
• The strain energy of an axially loaded bar can be calculated using the equation U = (1/2)Pδ

Strain Energy

• Strain energy is the energy stored in a deformed material
• The strain energy of an axially loaded bar can be calculated using the equation U = (1/2)Pδ
• The strain energy of a non-prismatic bar with continuously varying axial force can be calculated using the equation U = ∫(P^2/2EA)dx

Temperature Stress and Shear Stress

• Temperature changes can cause stresses and strains in a structure
• Temperature stresses occur when the expansion or contraction of a material is restricted
• Shear stresses occur when there is a change in the right angle at the corners of a face
• Shear strain is defined as the change in the right angle at the corners of a face

Shear Stress and Shear Strain

• The relationship between shear stress and shear strain is similar to that between normal stress and normal strain
• Within the linear elastic region, the shear stress and shear strain are directly proportional, and can be represented by the equation τ = Gγ
• The shearing modulus of elasticity (modulus of rigidity) is defined as the ratio of the shear stress to the shear strain

Quiz on simple stress and strain, including tension and compression, Poisson ratio, and strain energy. Important concepts in strength of materials.