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STEMORIA scientific instrument
Explore planar beam theory and solve connected three-dimensional frame-element models with linked loads, deformations, reactions, and spatial member-result diagrams.
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Manipulate
02
Measure
03
Interpret
Scientific viewport
Spatial reasoning engine
Explore beam bending and connected 3D frame mechanics from one synchronized finite-element workspace.
16 beam elements · Structural steel · Timoshenko field · spatial theory comparison
WebGL finite-element scene · orbit · zoom · probe · drag load
The rendered volume, section orientation and result contour all come from the active solved beam field.
Transition regime
Shear flexibility is becoming relevant · shear estimate 11.6%
Same load, section and mesh. Only beam-theory kinematics differ.
active field
8.589 MPa peak stress
probe Δ|v| = 0.05 mm
Station
2m
Deflection
-0.4317mm
Moment
-10kN·m
Shear
5kN
Theory difference at probe
Timoshenko − Euler–Bernoulli · |v|
0.05 mm
Direct manipulation: drag the violet load handle along the beam. Orbit with drag, zoom with wheel/pinch-equivalent browser gesture, click the beam to move the section probe.
The x′/y′/z′ triad follows the active deformed section. Display deformation ×28; numerical displacement remains physical.
Timoshenko FE solution summary
Maximum deflection
Magnitude from the active solved displacement field.
Maximum |M|
Maximum |σx|
Linear elastic bending stress at the extreme fiber.
Second moment I
Strain energy
Boundary equilibrium
Left vertical
Left moment
Right vertical
Right moment
Timoshenko displacement along x
Probe the curve to read approximate model values at any x-position.
Internal force result
Probe the curve to read approximate model values at any x-position.
Internal force result
Probe the curve to read approximate model values at any x-position.
Section mechanics
Probe the curve to read approximate model values at any x-position.
Single member · 6 DOF/node · axial + biaxial bending + torsion
Spatial frame member · 6 DOF per node · 12×12 element
Axial deformation, biaxial bending and Saint-Venant torsion are solved together. This is a real 3D frame-element model, not a planar beam merely extruded into 3D.
Tip load vector
WebGL 3D response · orbit · zoom · twist-aware sections
tip resultant
|u⊥| 24.732 mm
twist 3.6739°
uₓ tip
Axial deformation
uᵧ tip
Bending in local x–y plane
u_z tip
Out-of-plane bending
θₓ tip
Saint-Venant twist
|u⊥|
Transverse resultant
Strain energy
Root N
Root Vy / Vz
Root T
Root My / Mz
Iy / Iz
J
Thin-wall Saint-Venant approximation; warping torsion is not modeled.
Free-form multi-member network · arbitrary orientation · local UDL
Shared structural workspace
This editor publishes the exact active frame, loads, section orientation, ideal member-end releases and selected member to the result inspector. The WebGL members follow the solved Euler–Bernoulli Hermite deformation field.
Target-node load vector
Forces use global X/Y/Z; Mx is the applied torque about global X.
Selected member · orientation & results
Member BC orientation
Roll rotates the section principal axes about local +x′. Positive values follow the right-hand rule.
Ideal member-end releases
Release My (local ry) and/or Mz (local rz) independently at either member end. A released component is forced to zero member-end moment while the joint may still connect to other members.
General 3D frame network · Hermite-deformed members
Click a member in the guided frame to send the same selection to Member Forces. The active cross-section, member roll and amplified Hermite deformation are the exact model state consumed by the result inspector below.
Selected/focus |u|
Node C
Maximum translation
Across all solved nodes.
Strain energy
0.5 uᵀKu for this exact network.
Support resultant
ΣR = (-4, 18, -3) kN
Solver validation
Checks the exact assembled load case against restrained support reactions. Force and moment residuals are evaluated in global axes; moments are taken about O = (0, 0, 0) m.
Applied resultant
Support resultant
Closure residual
This is a numerical equilibrium check, not a structural safety check. A balanced result confirms global force/moment closure for the assembled linear frame equations; it does not validate section capacity, buckling, connection design, model idealization or code compliance.
N · Vy · Vz · T · My · Mz in member local axes
Live source · Portal
This panel consumes the exact builder model. The displayed member shape uses recovered member-side Euler–Bernoulli DOFs, so an ideal released end can rotate independently of the shared joint while the force diagram uses the same released end actions.
Member from active builder
Shared solved frame · curved spatial result overlay
The N/Vy/Vz/T/My/Mz diagram follows the same amplified Hermite member centerline shown by the WebGL frame and respects the active ideal end-release state.
Selected station
BC · Mz · x/L 0.50
-4.9802 kN·m
Peak sampled magnitude
5.4326 kN·m
Probe station
50% of member BC
Selected resultant
Mz
Member length
local x′ from B to C
Peak diagram magnitude
Maximum absolute sampled value on this member.
| Station | N | Vy | Vz | T | My | Mz |
|---|---|---|---|---|---|---|
| BC · 2.5 m | -1.4552 kN | -1.3488 kN | -0.0029741 kN | -0.011657 kN·m | -1.137e-16 kN·m | -4.9802 kN·m |
Does shear deformation change the answer?
Euler–Bernoulli δmax
Bending deformation only.
Timoshenko δmax
Bending plus transverse shear flexibility.
Deflection increase
Shear flexibility materially changes the displacement prediction.
Probe the curve to read approximate model values at any x-position.
G = E / [2(1 + ν)], with ν = 0.30. The active diagnostics use the same ν, κ and effective shear area as the Timoshenko solve. For I-sections this remains an educational clear-web shear-area approximation, not a code-level shear-design check.
Can you trust this solve?
Model adequacy
Transition regime
Euler–Bernoulli remains useful for learning and first-pass analysis, but shear flexibility is becoming noticeable.
Slenderness L/h
13.3
Estimated shear share
11.6%
Effective shear area is supplied explicitly by the active shear-deformation model. G = E/[2(1+ν)] uses the active ν = 0.30. The shear-energy fraction and the Euler–Bernoulli/Timoshenko displacement difference are different measures of shear importance and are not expected to be numerically equal.
Mesh convergence
Difference from the finest 40-element solution
Probe the curve to read approximate model values at any x-position.
A result that barely changes as the mesh is refined is numerically converged. A converged answer can still be physically inappropriate if the underlying beam theory assumptions are violated.
Finite-element method
K u = F
The planar modes use two-node beam elements with transverse displacement v and section rotation θ. Euler–Bernoulli suppresses transverse shear deformation. Timoshenko adds shear flexibility through G Aₛ.
The Spatial 3D Frame panel uses a 12×12 space-frame element with six degrees of freedom per node: u, v, w, θx, θy, θz, with internal resultants N, Vy, Vz, T, My, Mz.
The 3D Frame Builder assembles those elements across arbitrary node coordinates using local-to-global transformation matrices, applies per-DOF restraints in the solver, and transforms nodal plus consistent distributed member loads into the global system. Optional ideal local My/Mz end releases are enforced by static condensation of both member stiffness and consistent member-load vectors; released member-side rotations are recovered after the global solve before end actions and Hermite deformation are evaluated. The 3D Member Result panel reconstructs the continuous section-resultant field from those solved end actions plus uniform local member loads. It is frame-element FEM, not continuum solid FEA.