Mechanics Of Deformable Bodies Simulations

A collection of interactive 3D visualizations and simulations to help you master concepts in mechanics of deformable bodies.

Simple Stress and Strain - Theory & Concepts

Interactive simulation.

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.

Axial Deformation - Theory & Concepts

Interactive simulation.

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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Torsion - Theory & Concepts

Interactive simulation.

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

Shear and Moment in Beams - Theory & Concepts

Interactive simulation.

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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Stresses in Beams - Theory & Concepts

Interactive simulation.

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

Beam Deflections - Theory & Concepts

Interactive simulation.

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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Combined Stresses - Theory & Concepts

Interactive simulation.

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)

Thin-Walled Pressure Vessels - Theory & Concepts

Interactive simulation.

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.

Buckling of Columns - Theory & Concepts

Interactive simulation.

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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Strain Energy and Impact Loading - Theory & Concepts

Interactive simulation.

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

Mechanics Of Deformable Bodies Simulations

Simple Stress and Strain - Theory & Concepts

Normal Stress Visualizer

Axial Deformation - Theory & Concepts

Axial Deformation & Stress-Strain Curve

Stress-Strain Diagram

Torsion - Theory & Concepts

Torsion of a Circular Shaft

Shear and Moment in Beams - Theory & Concepts

Shear & Moment Diagram Generator

Shear Force Diagram (VVV)

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

Stresses in Beams - Theory & Concepts

Flexural Stress Distribution

Beam Cross-Section

Stress Profile (Depth vs Stress)

Beam Deflections - Theory & Concepts

Beam Deflection (Elastic Curve)

Combined Stresses - Theory & Concepts

Eccentrically Loaded Column Visualizer

Stress Distribution across Width (MPa)

Thin-Walled Pressure Vessels - Theory & Concepts

Thin-Walled Pressure Vessel Analysis

Buckling of Columns - Theory & Concepts

Column Buckling Visualizer (Euler's Formula)

Column Strength Curve (Stress vs Slenderness)

Strain Energy and Impact Loading - 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