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

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 3: Thin-Walled Pressure Vessels - Theory & Concepts

Analysis of tangential (hoop) stress and longitudinal stress in cylindrical and spherical pressure vessels.

Thin-Walled Pressure Vessel Analysis

Internal Pressure (

p

): 2 MPa

Inner Diameter (

D

): 1000 mm

Wall Thickness (

t

): 10 mm

Ratio (

r/t

) = 50.0(Thin-Walled)

Tangential (Hoop) Stress (

\sigma_h

)

100.0 MPa

Maximum Stress

Longitudinal Stress (

\sigma_L

)

50.0 MPa

For a cylinder, the hoop stress is always twice the longitudinal stress. A cylinder will tend to burst along its length before it pulls apart at the ends.

Module 4: Torsion - Theory & Concepts

Torsional deformation of circular shafts, shear stress formula, angle of twist, and power transmission.

Torsion of a Circular Shaft

T = 1.5 kN·m

The red dashed line represents a longitudinal line on the surface of the shaft before twisting. When torque is applied, the line twists, demonstrating angular deformation.

Max Shear Stress (

\tau_{max}

)

61.1 MPa

Angle of Twist (

\theta

)

3.50°

(0.0611 rad)

Torque (

T

): 1.5 kN·m

Diameter (

d

): 50 mm

Length (

L

): 2 m

Module 5: Shear and Moment in Beams - Examples & Applications

Types of beams, types of loads, internal shear, bending moment, and Shear and Moment Diagrams.

Shear & Moment Diagram Generator

Simply supported beam with a single concentrated point load.

10 kN

R_A

= 5.0

R_B

= 5.0

10 m

Point Load Magnitude (

P

): 10 kN

Load Position (

x

from left): 5 m

Shear Force Diagram ( $V$ )

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Bending Moment Diagram ( $M$ )Max: 25.0 kN·m

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Module 6: Stresses in Beams - Theory & Concepts

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 8: Principal Stresses and Mohr's Circle - Theory & Concepts

Understanding stress transformation, plane stress, principal stresses, maximum shear stress, and Mohr's Circle.

Mohr's Circle for Plane Stress

Input Stresses (MPa)

Normal Stress X (

\sigma_x

): +80

Normal Stress Y (

\sigma_y

): +20

Shear Stress (

\tau_{xy}

): +40

Principal Results

Center (C)

50.0

Radius (R)

50.0

Max Principal (

\sigma_1

)

100.0

Min Principal (

\sigma_2

)

0.0

Max In-Plane Shear (

\tau_{max}

)

50.0

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Red dots indicate principal stresses, max shear stresses, the center, and the original state of stress faces (X and Y).

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 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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Module 11: Strain Energy - Theory & Concepts

Understanding elastic strain energy, modulus of resilience, modulus of toughness, and impact loading.

Elastic Strain Energy Simulation

Axial Load ($P$): 100 kN

Original Length ($L$): 2 m

Cross-Sectional Area ($A$): 500 mm²

Modulus of Elasticity ($E$): 200 GPa

Calculations

Total Deformation ($\delta$): 2.000 mm

Total Strain Energy ($U$): 100.00 Joules

Strain Energy Density ($u$): 100000.00 J/m³

Load-Deformation Curve (Area = Strain Energy)

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The total Strain Energy ($U$) is the physical work done by the axial load as it deforms the member. In the linear elastic region, this is represented by the triangular area under the load-deformation curve:

U = \frac{1}{2} P \delta

Arche 2 Strength Of Materials Simulations

Module 1: Simple Stresses - Examples & Applications

Normal Stress Visualizer

Module 2: Simple Strain and Deformation - Theory & Concepts

Material Behavior States

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

What is happening now?

Elastic Region

Microscopic View

Module 3: Thin-Walled Pressure Vessels - Theory & Concepts

Thin-Walled Pressure Vessel Analysis

Module 4: Torsion - Theory & Concepts

Torsion of a Circular Shaft

Module 5: Shear and Moment in Beams - Examples & Applications

Shear & Moment Diagram Generator

Shear Force Diagram (VVV)

Bending Moment Diagram (MMM)Max: 25.0 kN·m

Module 6: Stresses in Beams - Theory & Concepts

Flexural Stress Distribution

Beam Cross-Section

Stress Profile (Depth vs Stress)

Module 7: Deflection of Beams - Theory & Concepts

Beam Deflection (Elastic Curve)

Module 8: Principal Stresses and Mohr's Circle - Theory & Concepts

Mohr's Circle for Plane Stress

Input Stresses (MPa)

Principal Results

Module 9: Combined Stresses - Theory & Concepts

Eccentrically Loaded Column Visualizer

Stress Distribution across Width (MPa)

Module 10: Columns - Theory & Concepts

Column Buckling Visualizer (Euler's Formula)

Column Strength Curve (Stress vs Slenderness)

Module 11: Strain Energy - Theory & Concepts

Elastic Strain Energy Simulation

Calculations

Load-Deformation Curve (Area = Strain Energy)

Shear Force Diagram ( $V$ )

Bending Moment Diagram ( $M$ )Max: 25.0 kN·m