Fareed Mohmed · Engineering
Structural Frame Analysis
Nodes · Members · Loads · Stress
Define nodes in X, Y and Z, join them with members, choose sections, hold the structure and apply loads, and see how it deflects and how hard each member works. It handles beams, trusses and full 3D frames, and shows the deformed shape, the reactions, the forces and stresses in every member and the bending, shear and deflection diagrams.
This is a linear, small-displacement beam analysis for a first check on machine frames, platforms and supports. It does not do load combinations, buckling analysis, connection design or code checks, and the stresses ignore local effects at joints and holes. Confirm important structures with a full analysis and your design code.
Start Here: Analysing a Frame
A frame or truss is a set of members joined at nodes. To analyse it, you tell the tool where the nodes are, which pairs are joined by which sections, how the structure is held, and what loads it carries. The tool then works out how every node moves and how much force each member carries, and from that the stress. It is a 3D beam analysis, so a table frame, a machine base or a platform can be modelled, as well as simple beams and trusses.
Load an example or start blank
The examples have hand-calculated answers. Load one to see how a model is built, then change it.
Open the workspace →Define materials and sections
Pick a material and give each member a section: a tube, a pipe, a bar, an I-beam, or your own properties. Use the Sections tab.
Sections tab →Add nodes and members
Nodes are points in X, Y, Z (mm). Members join two nodes. Use truss bars for pin-jointed members and tick the pin boxes to release the end moments.
Nodes and Members tabs →Add supports and loads
Hold the nodes that sit on the ground or a wall. Then add forces and moments at nodes, uniform or point loads on members, and self-weight.
Supports and Loads tabs →Read the results
Switch the plot between stress, deflection, utilisation and axial force, and read the peak values marked on the model. The Results tab has the tables and diagrams.
Results tab →Check the answer
Look at the equilibrium check, the deformed shape, and whether the supports act the way the real ones do. Confirm important designs with a full analysis.
Common mistakes
Model and Analysis
Build the model in the panel beside the view and watch it update. Drag to rotate, hold Shift (or use the right button) and drag to pan, scroll or pinch to zoom, and click a node or a member to select it. Use Full screen for a bigger workspace. After the analysis the members are coloured by stress, deflection, utilisation or axial force and drawn deformed, and the peak values are marked on the model.
Reference
The formulas and conventions the tool uses.
Section properties (mm)
| Shape | Area and second moments | Torsion constant J |
|---|---|---|
| Rectangle b × h | A = bh; Iz = bh³/12; Iy = hb³/12 | ab³(1/3 − 0.21(b/a)(1 − b⁴/12a⁴)), a = longer side, b = shorter |
| Round bar d | A = πd²/4; I = πd⁴/64 | πd⁴/32 |
| Rectangular tube b × h × t | A = bh − (b−2t)(h−2t); I from outer minus inner rectangle | 4Am²t / perimeter of the mid-line (thin wall, closed) |
| Round tube D, t | A = π/4 (D² − di²); I = π/64 (D⁴ − di⁴) | 2I |
| I beam h, b, tf, tw | A = 2btf + (h − 2tf)tw; I from outer minus the two voids | (2btf³ + (h − 2tf)tw³)/3 (open section) |
Analysis
| Item | Formula |
|---|---|
| Element stiffness | 12 × 12 matrix per member, with EA/L, GJ/L, 12EI/L³, 6EI/L², 4EI/L and 2EI/L terms, in local axes |
| Global matrix | Kg = TT K T, assembled over all members. Solved for the free movements by Cholesky factorisation |
| Member end forces | f = K u − feq, where feq are the fixed-end forces from the member loads |
| Reactions | Sum of the member end forces at a supported node, minus any load applied there |
| Axial stress | σa = N / A |
| Bending stress | σb = |Mz| cy / Iz + |My| cz / Iy, at the corner of the section |
| Peak stress | σ = |σa| + σb; von Mises = √(σ² + 3τ²), with τ the torsion shear |
| Utilisation | von Mises ÷ (fy ÷ safety factor) |
| Euler load | Pcr = π² E Imin / (K L)² |
Sign convention
Member local axes: x runs from node 1 to node 2. For a member that is not vertical, local y is the global vertical direction made square to the member (so it points up for a horizontal member), and local z = x × y. For a vertical member, local y points along global X. The roll angle turns y and z about x. Axial force is positive in tension. Shear and moment diagrams follow these local axes, so read them with the axes in mind; the size of the values is what matters for the stress.
Explanatory Notes
What the model is
A three-dimensional frame of straight beam elements, each with six movements at each end (three translations and three rotations). The material is linear elastic and the movements are small. Each member is a straight Euler–Bernoulli beam, so it does not include shear deformation. That is accurate for slender members, and slightly under-estimates deflection in short, deep ones.
Units
Lengths and section sizes in millimetres, forces in newtons, stresses and moduli in MPa, moments entered and shown in newton-metres. A uniform load in N/mm is the same number as kN/m.
How the stress is found
At each of 25 points along a member the tool takes the axial force and the two bending moments and finds the stress at the extreme corner of the section, adding the axial and bending parts as absolute values, which is safe. The torsion shear comes from the section shape. The two are combined as the von Mises stress. The shear stress from transverse shear is not added, because it is at its largest near the neutral axis where bending stress is small.
Pins and truss bars
A pin releases the two bending moments at that end of a member. A truss bar carries axial force only and has no bending stiffness. A node that only truss bars reach is held against rotation automatically, and in a planar truss the out-of-plane movement is held with a note. If you need the real support condition, add the supports yourself.
Self-weight and loads
Self-weight is the density times the section area, as a uniform load down the vertical axis. Member loads given in global axes are converted to the member’s local axes, and a load per mm is per mm of the member’s length, not of its projection.
Euler buckling check
For a member in compression the tool compares the force with π²EImin / (KL)². This is only a first look. It does not account for imperfections, local buckling, or the real end restraints, and it is not a design-code check. If the ratio is above about 50 %, check the member to your code.
Checks you can do
The examples in section 01 have hand-calculated answers: the cantilever deflection PL³ ÷ 3EI, the simply supported beam deflection 5wL&sup4; ÷ 384EI and stress, and the force in each bar of a three-bar truss. The equilibrium check compares the applied loads and the reactions, in force and in moment about the origin, for every model.
What it does not do
Load combinations or several load cases, support springs or settlement, thermal loads, P-Δ and second-order effects, buckling modes, tapered, curved or cable members, connection and weld design, local stress concentrations, fatigue, dynamic or seismic analysis, and design-code checks. For critical structures use a full structural or finite element package.
Catalogue sections
Sections added from the Tata Structura list carry the catalogue area, second moments, torsion constant and torsional modulus, which include the rounded outer and inner corners. A tube typed in by hand uses sharp-corner formulas and shows about 5 to 10 percent more area and stiffness for the same size. If you change a dimension of a catalogue section, the catalogue values are dropped and the formulas take over. Sizes marked under development are in the brochure but not yet rolled, so confirm availability before you design with them.
Size
The tool solves models of up to about 400 nodes in the browser. A larger model needs desktop software.
Sources
The method is the standard direct stiffness method for three-dimensional frames. Material values are typical values and the section examples are common sizes: confirm them against your material and tube supplier’s data.
Method
The direct stiffness method for space frames, as given in textbooks on matrix structural analysis, for example McGuire, Gallagher and Ziemian, Matrix Structural Analysis, and Kassimali, Matrix Analysis of Structures. Fixed-end forces for uniform and point loads are the standard beam results.
Torsion and section data
Torsion constants follow the usual closed-form results for round, rectangular, thin-walled closed and open sections (for example Roark’s Formulas for Stress and Strain). They are approximate for thick walls.
Tata Structura sections
Tata Steel, Tata Structura: Rectangular, Square and Circular Steel Hollow Sections (brochure). Square and rectangular sections to IS 4923 and circular sections to IS 1161, grade YST 310 (yield 310 MPa, tensile 450 MPa). The size, thickness, area, mass, moment of inertia, torsion constant and torsional modulus come from its section property tables. The rolled and under-development flags come from its product range tables.
Plate checks
Base plate: a rigid plate on concrete that takes compression only, with anchors that take tension only, solved for the axial load and both bending moments at once (the same idea as a reinforced-concrete section, with concrete modulus 5000 √f′c and anchor modulus 200 GPa). The plate is then checked for bearing pressure, anchor tension and shear, their interaction (V/Vcap)² + (T/Tcap)² ≤ 1, and bending as a cantilever from the column face. Gusset: Whitmore width (30° spread over the connection length), plate yield and net-section rupture in tension, a column curve in compression (AISC 360 E3, K = 0.65), then bolt shear and bearing or fillet weld strength, in the manner of IS 800 and AISC 360. Not checked: block shear, concrete breakout and pull-out of anchors, grout, prying, plate flexibility in the stiffness model, weld or bolt eccentricity, and end moments on gusset joints. Anchor shear ignores friction. Treat the result as a first sizing check, not a code design.
Alstrut aluminium profiles
Alstrut, Aluminium Profile System Product Catalog, profile pages for the 6, 8 and 10 mm groove series (20 profiles). Area, mass and the two second moments are the catalogue values; alloy 6063-T6 to DIN 17615 with E = 70,000 MPa and yield (Rp0.2) 195 MPa from its technical data page. Poisson ratio 0.33 is assumed. The catalogue gives no torsion constant, so the tool assumes J = 0.4 (Ix + Iy), a rough figure that only matters for twisting members. For 30x30, 30x30-3N, 40x40 and 40x80 the printed area disagrees with the printed weight by 14 to 26 percent; the tool uses the lower of the two. Check these four against the drawing. Bending stress uses half the larger outside dimension as the fibre distance.
Material values
Steel 200 GPa; grade yield strengths 250 MPa (E250, IS 2062) and 355 MPa; 304 stainless 193 GPa and about 215 MPa; aluminium 6061-T6 and 6063-T5 at 68.9 GPa and 276 and 145 MPa. They are typical figures, not certified values.