Portal Method Frame Analyser

Approximate lateral-load analysis for multi-storey, multi-bay rigid frames with selectable classical, tributary-width, or custom column-shear distribution. Calculates storey shear, column shear, column end moments, beam end moments, beam shear and approximate column axial force.

2. Geometry, loads and stiffness

Storey 1 is the lowest storey. Floor load is the horizontal point load applied at that floor level. Bay 1 is the leftmost bay.

Analysis summary

Build the input tables and run the analysis.

Member-force results

Annotated diagrams

To keep the results readable, the calculator produces separate diagrams for applied loads, shear, moment and axial force. All values are written directly on the diagrams.

FrameApplied lateral loadShear valuesMoment valuesAxial values

Calculation method

For floor lateral loads \(P_i\), the storey shear in storey \(s\) is:

V_s = Σ P_i for all floors i ≥ s

Column shear is distributed using the selected weights \(w_j\):

V_c(s,j) = V_s × w_j / Σw

Classical portal method: exterior weights are 1 and interior weights are 2.

w = [1, 2, 2, …, 2, 1]

Tributary-width modification: each column receives one-half of each adjacent bay width.

w₁ = L₁/2; wⱼ = (Lⱼ₋₁ + Lⱼ)/2; wₙ₊₁ = Lₙ/2

User-defined weights: positive relative values entered by the user are normalised automatically.

With a column contraflexure point at mid-height, the end-moment magnitude for a column in storey \(s\) is:

M_c(s,j) = V_c(s,j) × h_s / 2

At each floor joint, the beam moment demand is taken as the sum of the adjoining column end-moment magnitudes. It is distributed to the beam on the left and/or right using relative \(EI/L\), or equally when that option is disabled.

M_beam,end = M_joint × (EI/L)_beam / Σ(EI/L)_connected beams

The approximate beam shear magnitude is:

V_beam = (|M_left| + |M_right|) / L

Approximate column axial forces are obtained by accumulating the vertical beam shears from the roof downwards using joint vertical equilibrium. Signs are reported using tension positive and compression negative.

Important limitation: For irregular geometry or stiffness, the beam moment distribution introduced here is a practical extension of the basic portal method. It does not replace a rigorous displacement-method analysis.
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