Structural Engineering

Simple Stresses & Strains

Axial stress, Hooke's law, elongation and the elastic constants — the bedrock of solid mechanics.

PART 1

Topic Breakdown & Traps

Normal stress is internal force per unit area,

σ = P / A

. Within the elastic limit Hooke's law gives

σ = E ε

, so an axial member elongates by

δ = P L / A E

. The three elastic constants are linked by

E = 2 G (1 + ν) = 3 K (1 - 2 ν)

Axial stress:

σ = \frac{P}{A}

Strain & Hooke's law:

ε = \frac{δ}{L}, σ = E ε

Elongation:

δ = \frac{P L}{A E}

Elastic constants:

E = 2 G (1 + ν) = 3 K (1 - 2 ν)

Factor of safety:

FoS = \frac{yield (or ultimate) stress}{working stress}

⚠
Unit consistency. With $P$ in N and $A$ in mm², $σ$ is in MPa. Mixing kN and m introduces factors of $1 0^{3}$ .
⚠
** $ν$ range.** Poisson's ratio lies between $0$ and $0.5$ for common materials.
⚠
Series vs parallel bars. In series the load is common and elongations add; in parallel the elongation is common and loads share by stiffness.

PART 2

Q1BASIC1 Mark · NAT

A bar of area

500 mm^{2}

carries an axial tensile load of

100 kN

. The normal stress is _____ MPa.

Q2MEDIUM2 Marks · NAT

A steel bar (

E = 200 GPa

), area

400 mm^{2}

, length

2000 mm

, carries

80 kN

. Its elongation is _____ mm.

Q3HARD2 Marks · MCQ

For a material with

E = 200 GPa

and

G = 80 GPa

, Poisson's ratio is: