Tensile and Compression Forces

Unit 2 Displacement

Tensile and Compression Forces

Juan Juan
13 min read
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Tensile and Compression Forces are the directed, linear forces that either pull a material apart (tension) or push it together (compression) along its axis. They are the Mid Displacement force in Superphysics’ Solid Relationalities — the linear, translational action at the intermediate scale where the aetherspace and space interact through bulk material deformation.

Unlike shear (rotational/cohesive), tensile and compressive forces are directional and linear — they act along the material’s axis, stretching or shortening it in a straight line.

The Equation: Stress and Strain Fundamentals

Normal Stress (Force per Area)

σ=FA \sigma = \frac{F}{A}

Where:

Symbol Meaning Unit
σ \sigma Normal stress (tensile positive, compressive negative) Pa=N/m2 \text{Pa} = \text{N}/\text{m}^2
F F Applied axial force N \text{N}
A A Cross-sectional area m2 \text{m}^2

Normal Strain (Deformation per Length)

ε=ΔLL0 \varepsilon = \frac{\Delta L}{L_0}

Where:

Symbol Meaning Unit
( \varepsilon ) Normal strain dimensionless
( \Delta L ) Change in length ( \text{m} )
( L_0 ) Original length ( \text{m} )

Hooke’s Law (Linear Elastic Regime)

σ=Eε \sigma = E \varepsilon

Where:

Symbol Meaning Unit
( E ) Young’s modulus (stiffness) ( \text{Pa} )
( \sigma ) Normal stress ( \text{Pa} )
( \varepsilon ) Normal strain dimensionless

Axial Deformation (Displacement Formula)

ΔL=FL0AE \Delta L = \frac{F L_0}{A E}

This is the direct displacement equation — force stretches or compresses a material along its axis.

Poisson’s Ratio (Lateral Contraction)

ν=−εlatεaxial \nu = -\frac{\varepsilon_{\text{lat}}}{\varepsilon_{\text{axial}}}

Where ( \nu ) is Poisson’s ratio, ( \varepsilon_{\text{lat}} ) is lateral strain, and ( \varepsilon_{\text{axial}} ) is axial strain. Materials thin when stretched and thicken when compressed.

Key Properties of Tensile and Compression Forces

Property Explanation
Directional Acts along the material’s axis
Linear Produces straight-line elongation or shortening
Reversible Elastic deformation returns to original shape
Irreversible Plastic deformation causes permanent change
Material-dependent ( E ) varies widely (steel ~200 GPa, rubber ~0.01 GPa)
Temperature-dependent Higher ( T ) → lower ( E ) (generally)
Scale-dependent Dominant at structural scales

Stress–Strain Curve (Material Behavior)

Region Behavior
Elastic Linear; Hooke’s Law applies
Yield Onset of plastic deformation
Plastic Permanent deformation
Ultimate Maximum stress before failure
Fracture Material breaks

Thermal Stress (Temperature-Induced Displacement)

σthermal=−EαΔT \sigma_{\text{thermal}} = -E \alpha \Delta T

Where ( \alpha ) is the coefficient of thermal expansion and ( \Delta T ) is temperature change. Constrained materials develop stress when heated or cooled.

Buckling (Compression Instability)

Fcr=π2EI(KL)2 F_{\text{cr}} = \frac{\pi^2 E I}{(K L)^2}

Where ( F_{\text{cr}} ) is critical buckling load, ( I ) is moment of inertia, and ( K ) is effective length factor. Compression can cause sudden lateral displacement.

Real-Life Examples

Example How Tensile/Compression Works
1. Suspension bridge cables Tensile forces pull cables straight, supporting deck weight
2. Concrete pillars Compressive forces push down, supporting building loads
3. Rubber band Tensile force stretches it; releases when force removed
4. Rebar in concrete Steel reinforcement handles tensile forces; concrete handles compression
5. Bicycle spokes Spokes are under tension, holding wheel rim in compression
6. Bone structure Bones experience tension and compression during walking
7. Crane cables Tensile forces lift heavy loads
8. Spring Compression or tension stores elastic energy
9. Guitar strings Tensile forces tune pitch; tighter = higher pitch
10. Arch bridges Compression flows through arch; tension in tie rods

Summary

Question Answer
What are tensile/compression forces? Linear axial forces pulling apart or pushing together
What law describes them? Hooke’s Law: ( \sigma = E \varepsilon ); Axial Deformation: ( \Delta L = \frac{F L_0}{A E} )
What type of force? Mid Displacement (linear, Rule 1 + 3)
What drives them? Applied axial loads, thermal expansion, structural weight
Real examples? Bridge cables, concrete pillars, rubber bands, bicycle spokes
What’s its rotational counterpart? Shear (Mid Cohesion)

Bottom line: Tensile and compression forces are the linear, axial push-pull of materials — the Mid Displacement force that pairs with shear’s rotational sliding cohesion in Superphysics’ Solid Relationalities.

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