2D FRAME ANALYSIS

FIXED BASE — GRAVITY AND LATERAL LOADS

⬡ FRAME GEOMETRY

Number of bays

Bay widths

Egale Diferite

Number of storeys

Storey heights

Egale Diferite

⬡ SECTION

I column (cm⁴)

I beam (cm⁴)

Young's modulus E (N/mm²)

⬡ LOADING

Uniform load per storey (kN/m)

Egală Pe etaj

Lateral force per storey (kN, → to the right)

Egală Pe etaj

⬡ DISPLAY SCALES

Moment scale (M)

Shear scale (V)

Deflection scale

Tool information

What this page computes

The calculator solves a plane frame with multiple bays and storeys, with a fixed base, by the finite-element method (the FEALiTE2D engine). It returns the internal forces (moment, shear, axial) in the columns and beams, the deflected shape of the frame and the reactions at the fixed bases.

Why a frame is not calculated piece by piece

In a frame, the columns and beams are rigidly connected at the nodes, so they work together: the moment in a beam transfers into the columns, and a horizontal load (wind, earthquake) bends the columns and engages the whole structure. You cannot check a beam in isolation and a column in isolation — the behaviour is that of the assembly.

The frame is strongly statically indeterminate: the distribution of forces depends on the relative stiffnesses of all the members. The finite-element method assembles the stiffness of each member into a global system and solves it simultaneously for all the nodes.

The fixed base

This model assumes columns fixed at the base — the foundation node does not rotate. Fixity stiffens the frame laterally and attracts large moments to the column bases, but reduces horizontal displacements compared with a pinned base. (For an industrial-hall frame with inclined rafters, see the portal frame.)

What the analysis returns

The moment, shear and axial force diagrams on each member
The deflected shape of the frame under load
The reactions at the fixed bases — for designing the foundations

Input data

Geometry — the number of bays and storeys, the dimensions.
The sections of the columns and beams — the stiffness \(EI\) and the area (from profiles or entered).
The loads — vertical (permanent, imposed) and horizontal (wind, earthquake), on members or at nodes.

Assumptions and limitations

A linear-elastic first-order analysis; second-order effects (P-Δ), relevant for slender frames under horizontal load, are not included.
A plane (2D) model: the frame and the loads are in the same plane; spatial structures require a 3D analysis.
Rigid nodes and a fixed base; other conditions (pinned nodes, elastic base) change the result.
It gives the internal forces; the resistance and stability check of each member is done separately.

Continuous beam (finite element) — for beams without columns
Portal frame — a portal frame with inclined rafters
Bending and compression (steel) — checking the columns under N+M
Bending resistance (steel) — checking the beams