Structural Analysis Simulations

A collection of interactive 3D visualizations and simulations to help you master concepts in structural analysis.

Introduction to Structural Analysis - Theory & Concepts

Interactive simulation.

Tributary Area Interactive Lab

Adjust the grid spacing and area load to see how the tributary area and total axial load change for different column types.

Column Type:

Grid Spacing X: 6 m

Grid Spacing Y: 8 m

Area Load (DL + LL): 5 kPa

Floor Plan View

Tributary Width ($W_x$):6.00 m

Tributary Length ($W_y$):8.00 m

Tributary Area ($A_T$):48.00 m²

Total Axial Load ($P$):240.00 kN

Analysis of Statically Determinate Structures - Theory & Concepts

Interactive simulation.

Analysis of Statically Determinate Trusses - Theory & Concepts

Interactive simulation.

Truss Analysis Simulator

METHOD OF JOINTS

Downward Load Magnitude: 600 N

Apply Load At Node:

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.

Cables and Arches - Theory & Concepts

Interactive simulation.

Cable Loading Simulation

Load Position (horizontal)

Load Magnitude (affects sag)

Notice how the perfectly flexible cable forms a funicular shape of two straight segments under a single point load.

Influence Lines for Statically Determinate Structures - Theory & Concepts

Interactive simulation.

Influence Line Generator

Beam Configuration

Beam Length: 10 m

Target Section (POI) at x = 5.0 m

Add Elements

Manage Supports

pin0.0m

roller10.0m

Manage Hinges

No hinges added.

Deflection of Structures - Theory & Concepts

Interactive simulation.

Adjust the load position to see how the M/EI diagram becomes the load for the Conjugate Beam.

Real Beam (Point Load)

Conjugate Beam (M/EI Load)

Analysis of Statically Indeterminate Structures - Theory & Concepts

Interactive simulation.

Force Method: Propped Cantilever Simulation

Observe how the method of consistent deformations solves for the redundant reaction $R_B$. The primary structure (a simple cantilever) deflects downwards due to the uniform load. The redundant force $R_B$ must push upwards exactly enough to bring the net deflection at support B back to zero.

Uniform Load ($w$): 10 kN/m

Calculations

Length ($L$): 10 m
Flexural Rigidity ($EI$): 10000 kN·m²
Primary Deflection at B ( $\\Delta_{B0}$ ): 1250.00 mm (down)
Flexibility Coefficient ( $f_{BB}$ ): 33.33 mm/kN
Redundant Reaction ($R_B$): 37.50 kN (up)

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Three-Moment Equation - Theory & Concepts

Interactive simulation.

Three-Moment Equation Interactive Lab

Adjust the span lengths and uniform loads for a two-span continuous beam. Exterior supports are simple pins/rollers ($M_A=0, M_C=0$). Observe how the internal moment at the middle support ($M_B$) changes.

Span 1 ($L_1$): 5 m

Load 1 ($w_1$): 10 kN/m

Span 2 ($L_2$): 5 m

Load 2 ($w_2$): 10 kN/m

Calculation

$M_A L_1 + 2M_B(L_1 + L_2) + M_C L_2 = dots$

$dots -rac{w_1 L_1^3}{4} - rac{w_2 L_2^3}{4}$

$0(5) + 2M_B(5 + 5) + 0(5) = dots$

$dots -rac{(10)(5)^3}{4} - rac{(10)(5)^3}{4}$

$20 M_B = -625.00$

Internal Moment $M_B$-31.25 kNm

Slope-Deflection Method - Theory & Concepts

Interactive simulation.

Slope-Deflection Method: Propped Cantilever

Span Length (L): 10 m

Uniform Load (w): 10 kN/m

Support A Settlement (Δ): 0 mm

Results

Rotation at A (θ_A): 0.000 x 10^-3 rad
Rotation at B (θ_B): 0.000 rad (Fixed)
Moment at A (M_AB): 0.00 kNm (Pinned)
Moment at B (M_BA): 0.00 kNm

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Moment Distribution Method - Theory & Concepts

Interactive simulation.

Moment Distribution Interactive Lab

Adjust the initial Fixed End Moments (FEM) and the Distribution Factor at Joint B for a two-span continuous beam (fixed at A and C). Watch how the unbalanced moment at B is iteratively distributed and carried over.

Distribution Factor DF_BA: 0.50(DF_BC = 0.50)

FEM_AB

FEM_BA

FEM_BC

FEM_CB

Joint	A	B		C
Member	AB	BA	BC	CB
DF	0	0.50	0.50	0

* Check Equilibrium at B: + = NaN

Approximate Analysis of Frames - Theory & Concepts

Interactive simulation.

Matrix Analysis of Structures - Theory & Concepts

Interactive simulation.

Direct Stiffness Assembly Simulation

Walk through the core concept of matrix structural analysis: assembling local stiffness matrices into a global matrix.

1. Define the Structure

Consider a 1D axial structure with two spring members (Member 1 and Member 2) connected in series at three nodes (Node 1, Node 2, Node 3).