STRUCTURAL ENGINEERING · VERSION 2
More spans.
A clearer picture.
Continuous beams and 2D frames. One connected structural model.
Results ready
InsureCalc · Beam & frame analysis
CONTINUOUS BEAM
03
Inspect a member
Axial force
N · kNShear force
V · kNBending moment
M · kN·mTransverse displacement
local v · mmSection position from end i
At an internal force/couple, left/right values show discontinuities. N is positive in tension; M is positive in sagging. Local +y is 90° counterclockwise from i → j.
Support reactions & node displacements
| Node | Support | Rx (kN) | Ry (kN) | M (kN·m) | Ux (mm) | Uy (mm) | θ (mrad) |
|---|
Member end actions in local coordinates
These are member end-action vectors [Fx, Fy, M] at i and j. They are not the same sign convention as the internal N/V/M diagrams.
| Member | Fx,i | Fy,i | M,i | Fx,j | Fy,j | M,j |
|---|
Equilibrium & numerical checks
Models are calculated in your browser. Save locally or export a backup.
THE MODEL BEHIND THE DIAGRAMConnected members.
Connected members.
Compatible movements.
Version 2.0.0 · Direct stiffness method
Open the classic single-beam tool ↗Continuous beams and plane frames
Each node has horizontal displacement, vertical displacement and in-plane rotation. Members share these movements at a common node, so bending continuity is maintained across adjacent beam spans and rigid frame joints. Each member has its own E, cross-sectional area A, and second moment of area I. Axial deformation and bending deformation are included.
Build spans, bays and storeys
Use Add span for a continuous beam. The frame generator accepts comma-separated bay widths and storey heights, such as 6, 5 for two bays and 4, 3.5 for two storeys. Nodes, connectivity, supports and member properties remain editable. A roller Y restrains vertical movement; a roller X restrains horizontal movement. A pin restrains both translations; a fixed support also restrains rotation.
Loads and coordinate directions
All input load components use global X to the right and global Y upward. Enter negative Fy or qy for downward gravity loads. Applied moments are counterclockwise positive. Member load positions and UDL intervals are measured from end i along the actual member length; line-load intensities are per metre of actual member length. Loads are transformed to each member’s local axes before analysis.
K u = F · EA = E[GPa] × A[mm²] · EI = E[GPa] × I[10⁶ mm⁴]
With these input units, EA is in kN and EI in kN·m². The solver assembles the global stiffness matrix, enforces the support restraints and solves the remaining equations using diagonal scaling and Cholesky factorisation. Member response between nodes is reconstructed by integrating the actual applied load functions, including the particular displacement caused by distributed loads.
A two-span check you can reproduce
For two equal 6 m spans, constant EI, three simple vertical supports and 10 kN/m downward on both spans: the end reactions are 22.5 kN each, the middle reaction is 75 kN, and the hogging moment over the middle support is −45 kN·m. The total upward reaction is 120 kN, equal to the total applied downward load.
Analysis scope
This version performs first-order linear elastic 2D analysis with Euler–Bernoulli members and rigid joints. It excludes P–Δ effects, shear deformation, member-end hinge releases, support settlements, plasticity, buckling, cracking and creep. Self-weight is included only when entered as a load. Strength checks, code load combinations and design-compliance decisions are outside this tool. Crossed members connect only when they share a node ID.