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Statics Of Rigid Bodies Simulations

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

Introduction to Statics - Theory & Concepts

A comprehensive overview of Introduction to Statics explaining core principles.

Vector Addition Simulation

Vector A Magnitude: 10.0 N
Vector A Angle: 30.0°
Vector B Magnitude: 8.0 N
Vector B Angle: 120.0°

Resultant Vector R

Magnitude: 12.81 N

Angle: 68.66°

R=A2+B2+2ABcos⁡(θA−B)R = \sqrt{A^2 + B^2 + 2AB \cos(\theta_{A-B})}
ABR

Force Systems - Theory & Concepts

A comprehensive overview of Force Systems explaining core principles.

Rectangular Components of a Force

FxFyF

Results

Magnitude (F):

100.0 N

Angle (θ):

45.0°

x-component (Fx):

70.7 N

y-component (Fy):

70.7 N

F_x = F cos(θ)
F_y = F sin(θ)

Equilibrium of Particles - Theory & Concepts

A comprehensive overview of Equilibrium of Particles explaining core principles.

2D Particle Equilibrium (Concurrent Forces)

WT1T2

Calculated Tensions

Tension 1 (T1):

89.7 N

Tension 2 (T2):

73.2 N

ΣF_x = 0 => T2 cos(θ2) - T1 cos(θ1) = 0

ΣF_y = 0 => T1 sin(θ1) + T2 sin(θ2) - W = 0

Equilibrium of Rigid Bodies - Theory & Concepts

A comprehensive overview of Equilibrium of Rigid Bodies explaining core principles.

Beam Equilibrium Simulation

Load Position (x)4 m
Load Magnitude (P)500 N
Reactions:
Ay:300.0 N
By:200.0 N
Notice how the reactions change proportionally as the load moves closer to or further from a support.
Σ M_A = 0 ⇒ B_y = P(x) / L

Analysis of Structures - Theory & Concepts

A comprehensive overview of Analysis of Structures explaining core principles.

Truss Analysis Simulator

METHOD OF JOINTS

Member Forces Results:

  • AB:0 N
  • BC:0 N
  • AC:0 N

Support Reactions:

  • Ay = 0.0 N (Up)
  • Cy = 0.0 N (Up)
  • Ax = 0.0 N

Tension (T) members are shown in blue and pull away from joints. Compression (C) members are shown in red and push into joints. Zero-force members are gray.

ABC600 N

Internal Forces in Structural Members - Theory & Concepts

A comprehensive overview of Internal Forces in Structural Members explaining core principles.

Shear & Moment Diagram Visualizer

5 m
10 kN

Reactions:

Left Support ($R_1$): 5.00 kN

Right Support ($R_2$): 5.00 kN

Maximum Moment: 25 kN·m (at x = 5m)

Shear Diagram (V)

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Moment Diagram (M)

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Dry Friction - Theory & Concepts

A comprehensive overview of Dry Friction explaining core principles.

Friction on an Inclined Plane

NWxWyW = 100Nθ=0°
Static

Forces & Status

Normal (N):100.0 N
Weight (Wx):0.0 N
Max Static (μs N):50.0 N
Friction (f):0.0 N

Wx ≤ Max Static Friction (0.0 ≤ 50.0)

The block is at rest. Static friction matches the parallel force component: f_s = Wx = 0.0 N

Distributed Forces, Centroids, and Centers of Gravity - Theory & Concepts

A comprehensive overview of Distributed Forces, Centroids, and Centers of Gravity explaining core principles.

Composite Centroid Simulation

Flange Height ($h_1$)40 mm
Web Width ($w_2$)40 mm
Area 1 (Flange):8000 mm²
Area 2 (Web):6400 mm²
Total Area:14400 mm²
Notice how the centroid (Ȳ, red dot) shifts towards the part with the larger area.
Ȳ = (Σ y_i * A_i) / Σ A_i

Moments of Inertia - Theory & Concepts

A comprehensive overview of Moments of Inertia explaining core principles.

Parallel-Axis Theorem

Adjust the dimensions and distance of the rectangle to see how the moment of inertia changes relative to the reference axis.

I_bar (bh³/12):6666.7 cm⁴
Area (bh):200.0 cm²
Ad² term:45000.0 cm⁴
Total I:51666.7 cm⁴
Ref Xx'd

Cables and Arches - Theory & Concepts

A comprehensive overview of Cables and Arches explaining core principles.

Cable Forces Simulation

Analysis Results

Min Tension ($T_0$ at center):100.0 kN

Max Tension ($T_max$ at supports):141.4 kN

Three-Hinged Arches - Theory & Concepts

A comprehensive overview of Three-Hinged Arches explaining core principles.

Three-Hinged Arch Analysis

Real-time Reactions:

A_y: 75.0 kN

B_y: 25.0 kN

Thrust (H): 50.0 kN