Solid Mechanics

1.What are the key assumptions made in Strength of Materials analysis, and why are they important for simplifying the study of material behavior under stress?

The key assumptions in Strength of Materials are:

1. Homogeneity – Material properties are uniform throughout.
2. Isotropy – Properties are the same in all directions.
3. Linear Elasticity – Stress is proportional to strain (Hooke’s Law).
4. Small Deformations – Deformations are minimal, ensuring linear behavior.
5. Plane Sections Remain Plane – Cross-sections remain flat during bending.

These assumptions simplify the analysis by allowing linear models and ignoring complexities like material nonlinearity or large deformations.

2.Engineering stress/strain and True stress/strain ?

Aspect	Engineering Stress/Strain	True Stress/Strain

Definition

Based on original dimensions (area/length).

Accounts for current dimensions during deformation.

Formula

Stress = Force / Original Area, Strain = ΔLength / Original Length

Stress = Force / Instantaneous Area, Strain = ln(1 + ΔLength / Original Length)

Accuracy

Less accurate for large deformations.

More accurate for large strains and plastic deformation.

Application Range

Valid in elastic region, small deformations.

More valid in plastic region, for large deformations.

Representation

Assumes constant original dimensions throughout the process.

Considers changing dimensions (area/length) during deformation.

Measurement Focus

Initial length and area.

Instantaneous length and area.

3.What are the different elastic constants in Strength of Materials?

Elastic Constant	Symbol	Definition
Young’s Modulus	E	Ratio of normal stress to normal strain. Measures stiffness of a material. Higher E → more rigid.
Shear Modulus / Modulus of Rigidity	G	Ratio of shear stress to shear strain. Indicates resistance to shear deformation.
Bulk Modulus	K	Ratio of volumetric stress to volumetric strain. Shows how incompressible a material is.
Poisson’s Ratio	ν	Ratio of lateral strain to longitudinal strain. Indicates how a material contracts laterally when stretched.

4. What are thermal stress and thermal strain?

Parameter	Definition	Formula
Thermal Strain	Change in length due to change in temperature. It occurs even without external load.	εₜ = α ΔT
Thermal Stress	Stress developed when thermal expansion or contraction is restricted. No restriction → no thermal stress.	σₜ = E α ΔT