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:

SymbolMeaningUnit
σ \sigma Normal stress (tensile positive, compressive negative)Pa=N/m2 \text{Pa} = \text{N}/\text{m}^2
F F Applied axial forceN \text{N}
A A Cross-sectional aream2 \text{m}^2

Normal Strain (Deformation per Length)

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

Where:

SymbolMeaningUnit
( \varepsilon )Normal straindimensionless
( \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:

SymbolMeaningUnit
( E )Young’s modulus (stiffness)( \text{Pa} )
( \sigma )Normal stress( \text{Pa} )
( \varepsilon )Normal straindimensionless

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

PropertyExplanation
DirectionalActs along the material’s axis
LinearProduces straight-line elongation or shortening
ReversibleElastic deformation returns to original shape
IrreversiblePlastic deformation causes permanent change
Material-dependent( E ) varies widely (steel ~200 GPa, rubber ~0.01 GPa)
Temperature-dependentHigher ( T ) → lower ( E ) (generally)
Scale-dependentDominant at structural scales

Stress–Strain Curve (Material Behavior)

RegionBehavior
ElasticLinear; Hooke’s Law applies
YieldOnset of plastic deformation
PlasticPermanent deformation
UltimateMaximum stress before failure
FractureMaterial 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

ExampleHow Tensile/Compression Works
1. Suspension bridge cablesTensile forces pull cables straight, supporting deck weight
2. Concrete pillarsCompressive forces push down, supporting building loads
3. Rubber bandTensile force stretches it; releases when force removed
4. Rebar in concreteSteel reinforcement handles tensile forces; concrete handles compression
5. Bicycle spokesSpokes are under tension, holding wheel rim in compression
6. Bone structureBones experience tension and compression during walking
7. Crane cablesTensile forces lift heavy loads
8. SpringCompression or tension stores elastic energy
9. Guitar stringsTensile forces tune pitch; tighter = higher pitch
10. Arch bridgesCompression flows through arch; tension in tie rods

Summary

QuestionAnswer
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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