Strength of Materials 

Axial deformation is calculated using Hooke’s Law, which relates stress (σ) to strain (ε) for elastic deformation. The formula for axial deformation is given by: ​ where: δaxial​ = Axial deformation (in meters, m) F = Applied axial force or load (in newtons, N) L = Original length of the structural member (in meters, m) […]

The cross-sectional area (A) represents the area enclosed by the shape of the structural member, typically perpendicular to the axis of bending or rotation. The SI units for the radius of gyration formula are meters (m) for length measurements (both r and any dimensions involved in calculating I and A). It’s essential to ensure that

The radius of gyration (r) is a measure of how the mass or area of a structural member is distributed relative to its centroid or axis of rotation. It is commonly used in structural engineering to characterize the bending behavior of columns and beams For structural purposes, the radius of gyration is calculated based on

The slenderness ratio (λ) is a dimensionless parameter used in structural engineering to evaluate the stability of slender columns under compressive loads. It is calculated based on the column’s effective length (Le​) and its radius of gyration (r). ​​ where: λ = Slenderness ratio (dimensionless) Le​ = Effective length of the column (in meters, m)

Thermal strain refers to the deformation or change in dimensions of a material due to a change in temperature. It is calculated based on the material’s coefficient of thermal expansion (α) and the change in temperature (ΔT). Thermal strain is calculated using the formula: where: εthermal​ = Thermal strain (dimensionless) α = Coefficient of thermal

Thermal stress refers to the stress that develops in a material due to a change in temperature. When a material is subjected to non-uniform temperature changes, different parts of the material expand or contract at different rates, leading to internal stresses. Thermal stress is calculated using the formula: where: σthermal​ = Thermal stress (in pascals,

The percent reduction in area measures the decrease in cross-sectional area of a tensile specimen at the point of fracture compared to its original cross-sectional area. It is calculated using the formula:  where: Ai​ is the initial cross-sectional area of the specimen (in square meters, m²). Af​ is the final cross-sectional area of the specimen

Flexural strength, also known as bending strength, is a measure of a material’s ability to resist deformation under bending loads. It is an important property in structural engineering, particularly for beams and other components subjected to bending stresses. Flexural strength is calculated using the formula: ​​ where: σ_flexural​ = Flexural strength (in pascals, Pa or

The percent elongation measures how much a material elongates before fracture during a tensile test. It is calculated using the formula: Percent Elongation where: L_f​ is the final length of the specimen after elongation (in meters, m). L_i​ is the initial gauge length of the specimen (in meters, m).

Stiffness (K) is a measure of the force required to produce a unit deflection in a structure or material. It indicates how rigid or flexible a structure is when subjected to an external force. Formula for Stiffness (K): The formula for stiffness in the context of a spring or an elastic element is given by: