Arche 2 Strength Of Materials Simulations

A collection of interactive 3D visualizations and simulations to help you master concepts in arche 2 strength of materials.

Module 1: Simple Stresses - Examples & Applications

Concept of internal forces, normal stress, shear stress, bearing stress, and allowable stress.

Normal Stress Visualizer

50 kN

←

50 kN

→

Area (

A

): 314.2 mm²

Calculated Stress (

\\sigma

)

159.15 MPa

Force (

P

): 50 kN

Radius (

r

): 10 mm

Adjust the force and the radius of the circular cross-section to see how they affect the normal stress. Notice that increasing the area (radius) decreases the stress, while increasing the force increases the stress.

Module 2: Simple Strain and Deformation - Theory & Concepts - Stress Strain States

Axial deformation, strain concepts, Stress-Strain Diagram, Hooke's Law, Poisson's Ratio, and thermal stresses.

Material Behavior States

Explore how different materials deform under stress

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Apply Strain (Pull Material)ε = 0.0000

Current Stress0.0 MPa

Current StateElastic Region

Ductile Steel (e.g., Low Carbon Steel)

Exhibits a distinct elastic region, yield point, a plastic plateau, strain hardening, and necking before fracture. Highly ductile and tough.

What is happening now?

Elastic Region

Material deforms reversibly. Stress is directly proportional to strain (Hooke's Law applies). If the load is removed, the material returns exactly to its original shape. The bonds between atoms are stretched but not broken.

Microscopic View

Atoms are stretched uniformly like springs.

Module 2: Simple Strain and Deformation - Theory & Concepts - Strain Deformation

Axial deformation, strain concepts, Stress-Strain Diagram, Hooke's Law, Poisson's Ratio, and thermal stresses.

Axial Deformation & Stress-Strain Curve

L = 2000mm + 0.00mm

Applied Tensile Load (

P

): 0 kN

0Yield (125 kN)Ultimate (200 kN)

Normal Stress (

\\sigma

)

0.0 MPa

Deformation (δ)

0.000 mm

Stress-Strain Diagram

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Module 6: Stresses in Beams - Theory & Concepts - Stresses Beams

Flexural (Bending) Stress formula, section modulus, horizontal/longitudinal shear stress, and shear flow.

Flexural Stress Distribution

Beam Cross-Section

200mm

100mm

Compression

Tension

Stress Profile (Depth vs Stress)

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Bending Moment (

M

): 15 kN·m

Width (

b

): 100 mm

Depth (

h

): 200 mm

Moment of Inertia (

I

)

66.67 × 10⁶ mm⁴

Section Modulus (

S

)

666.67 × 10³ mm³

Max Flexural Stress (

\sigma_{max}

)

22.50 MPa

Module 7: Deflection of Beams - Theory & Concepts

Concept of elastic curve, Double Integration Method, Area-Moment Method, and Superposition Method.

Beam Deflection (Elastic Curve)

Simply supported beam under a Uniformly Distributed Load (UDL).

Uniform Load (

w

): 10 kN/m

Span Length (

L

): 5 m

Modulus of Elasticity (

E

): 200 GPa

Moment of Inertia (

I

): 50 ×10⁶ mm⁴

Maximum Deflection (

\delta_{max}

)

8.14 mm

Typical Allowable (L/240): 20.8 mm

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Module 9: Combined Stresses - Theory & Concepts

Combined axial and flexural loads and eccentrically loaded members.

Eccentrically Loaded Column Visualizer

Combine uniform axial compression with bending stress caused by an eccentric load.

P = 150 kN

e=50

Cross-section: 300mm × 200mm

Compressive Load (

P

): 150 kN

Eccentricity (

e

): 50 mm

Left edge (-150)Centroid (0)Right edge (+150)

Stress Distribution across Width (MPa)

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Axial

Bending

Combined

Stress at Left Face (y = -150)

0.00 MPa

(Compression)

Stress at Right Face (y = +150)

-5.00 MPa

(Compression)

Module 9: Combined Stresses - Theory & Concepts - Middle Third Rule

Combined axial and flexural loads and eccentrically loaded members.

Middle-Third Rule Simulation

Load Eccentricity (e)

Status

All Compression

Base Width ( $b$ ) = 120 units
Kern Limit ( $b/6$ ) = $\\pm$ 20 units

When the load $P$ is applied within the green highlighted Kern (the middle third of the base), the entire cross-section remains in compression (blue distribution).

If the eccentricity $e$ exceeds $b/6$ , the bending stress ( $Mc/I$ ) becomes greater than the uniform axial stress ( $P/A$ ) on the opposite face, causing tension to develop (red distribution).

Module 10: Columns - Theory & Concepts

Definition and behavior of columns, Euler's formula, effective length factors, and intermediate columns.

Column Buckling Visualizer (Euler's Formula)

Analyze how length, cross-section, and support conditions affect a column's critical buckling load.

P_cr

↓

End Conditions

Length (

L

): 4 m

Width: 100

Depth: 200

Effective Length (

KL

)

4.00 m

Weak Axis

I_{min}

16.7 ×10⁶

Slenderness (

KL/r

)

138.6

Fails by Buckling

2056.2 kN

Column Strength Curve (Stress vs Slenderness)

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