About Structural Analyzer
The structural analyzer is a finite element solver that uses the direct stiffness method to analyse 2D and 3D trusses, beams, and frames. It is used by structural engineers to find nodal displacements, support reactions, and member forces under point, moment, and distributed loads, with a 3D view of the model and result diagrams.
Define nodes with their coordinates and supports, connect them with elements that reference a material (E, G) and a section (A, Iy, Iz, J), and apply loads grouped into load cases and combinations. The tool assembles the global stiffness matrix, solves K*u = F, and reports displacements, reactions, and element forces.
How It Works
- Build each element stiffness matrix in local coordinates (axial EA/L, bending 12EI/L^3, 6EI/L^2, 4EI/L, torsion GJ/L) and rotate it to global axes with K_global = T^T * K_local * T.
- Assemble the element matrices into the global stiffness matrix K and the load vector F using the node degree-of-freedom map.
- Apply the support boundary conditions and solve the reduced system K*u = F for the unknown nodal displacements u.
- Recover the support reactions as R = K*u - F and the member end forces from f_local = K_local * T * u_global.
Worked Example
A 5 m steel cantilever beam (E = 210 GPa, Iz = 2.835e-5 m^4) fixed at one end with a 10 kN transverse tip load. The analytical tip deflection is delta = P*L^3/(3*E*Iz) = 10000*5^3/(3*210e9*2.835e-5) = 0.0700 m, and the tip rotation is theta = P*L^2/(2*E*Iz) = 10000*5^2/(2*210e9*2.835e-5) = 0.0210 rad. The direct stiffness solver reproduces these values, with a vertical reaction of 10 kN at the fixed support.
Formulas
- Global equilibrium
K * u = F- Axial member stiffness
k_axial = E * A / L- Bending stiffness terms (Euler-Bernoulli)
b12 = 12*E*I/L^3 ; b6 = 6*E*I/L^2 ; b4 = 4*E*I/L- Element transformation and reactions
K_global = T^T * K_local * T ; R = K*u - F
Standards & References
- EN 1993
- AISC 360
- AS 4100
Frequently Asked Questions
What analysis method does the structural analyzer use?
It uses the direct stiffness method (matrix structural analysis). Each element stiffness matrix is formed in local coordinates, transformed to global axes, and assembled into the global matrix K, after which the system K*u = F is solved for the nodal displacements.
What element types are supported?
Truss elements (axial only), and beam and frame elements using a 2-node Euler-Bernoulli formulation with 6 degrees of freedom per node (three translations and three rotations), so the tool can model 2D and 3D structures.
What results does it produce?
For each node it reports the six displacement components and the support reactions, and for each element the axial force, shears, bending moments, and torsion at both ends, together with 3D diagrams.
How are loads and load cases handled?
Loads are point forces, moments, and distributed (trapezoidal) loads assigned to load cases categorised as permanent, variable, or accidental. Load combinations apply factors to each case, for example 1.35*permanent + 1.5*variable.