Structural Analysis Tool (3D)

What it solves

This is a 3D structural analysis calculator for space frames and space trusses. You build the model in three dimensions and the solver returns support reactions, member end forces - axial, two shears, torsion and two bending moments - nodal displacements and rotations, and the force diagrams along each member.

It runs in the browser with no install. Space trusses and 3D frames use the same solver with different member releases, so a model can mix pin-ended bracing with moment-resisting frame members, which is what most real structures are.

What actually changes from 2D

A 2D node has three degrees of freedom; a 3D node has six - three translations and three rotations. The member element grows from 6x6 to 12x12, and each member now carries torsion and biaxial bending in addition to axial force and single-axis shear and moment.

Two things follow that catch people moving up from 2D. Torsion becomes a real result rather than something that cannot exist, and it is often what governs an edge beam or a curved member. And member orientation about its own axis now matters: a beam rotated 90 degrees about its length is a completely different member, because its strong and weak axes have swapped. In 2D that ambiguity does not exist, so it is easy to forget to set it.

Restraint in three dimensions

A 3D model needs restraint against six rigid-body movements rather than three, and the extra three are the ones people forget. A frame that is perfectly stable in its own plane can be a mechanism out of plane, and the solver will refuse to solve rather than quietly returning a wrong answer.

The usual cause is a planar frame modelled in 3D with no out-of-plane restraint at all, or a space truss where a node has members meeting it that are all coplanar - that node can move perpendicular to their plane without any member resisting it. Adding bracing or an appropriate support fixes both.

Formula reference

Stiffness relation

$\mathbf{K}\,\mathbf{u} = \mathbf{F}$

Degrees of freedom, 3D node

$u_{x,}\;u_{y,}\;u_{z,}\;\theta_{x,}\;\theta_{y,}\;\theta_z$

Axial stiffness

$k_a = \dfrac{EA}{L}$

Torsional stiffness

$k_t = \dfrac{GJ}{L}$

Shear modulus

$G = \dfrac{E}{2(1+\nu)}$

Flexural stiffness, each axis

$k_b = \dfrac{EI}{L}$

Static determinacy, space truss

$m + r = 3j$

Assumptions and limits

Linear-elastic first-order analysis: small displacements, equilibrium on the undeformed geometry, no P-delta. Members are prismatic with constant section properties, and the torsion constant J is the St Venant value - warping torsion, which dominates for open sections such as an I-beam under significant torque, is not modelled.

That torsion limitation deserves emphasis in 3D specifically, because torsion is a result you now get and might act on. For an open section the true torsional behaviour is mostly warping rather than St Venant, so a large reported torsion on an I-section should prompt a proper torsion assessment rather than a direct comparison against GJ.

The solver returns forces and displacements; it does not check members against any design code. Buckling, dynamics, second-order effects, connection flexibility and construction sequence are all outside the scope.

FAQ