Is this a free alternative to RISA-3D or SAP2000?

For linear and P-Delta analysis of frames made of prismatic beam-column members, yes: it solves the same 3D direct-stiffness problem (six degrees of freedom per joint, end releases, distributed and nodal loads, load combinations) and adds modal periods and mass participation. It does not include plates, shells or solids, member code checks, moving loads, response-spectrum or time-history analysis, or a section database. Use it to check a model, study a frame, teach, or run a quick independent verification of commercial software output.

What are the member local axes?

Local x runs from the start joint i to the end joint j. For a member that is not vertical, local y lies in the vertical plane containing the member and points upward, and local z completes the right-hand system, so a horizontal beam bends about local z (its strong axis, Iz) under gravity. For a vertical member, local y points along global +X. A rotation angle beta turns local y and z about local x. Mz and Vy are therefore the in-plane moment and shear of beams and of columns in an XY frame.

What does the P-Delta option do?

It adds the geometric stiffness of each member, N/L for the lateral translations at its ends, and re-solves until the displacements stop changing. Compression softens the frame and amplifies sway moments; tension stiffens it. This is the large P-Delta effect on member chords. The small P-delta effect along a member's length is not included. If the frame buckles under a combination, the solver reports it. AISC 360 direct analysis also needs notional loads and reduced stiffness (0.8τbEI), which you would apply in the inputs.

How are natural periods calculated?

Translational mass is lumped at the joints from member self-weight, and optionally from the dead-load case. The calculator then solves the generalized eigenproblem K φ = ω² M φ for the lowest modes by subspace iteration, and reports each period T = 2π/ω together with the effective modal mass ratios in X, Y and Z. ASCE 7 requires enough modes to reach 90% mass participation in each direction for modal response spectrum analysis.

How do I model a pinned connection or a truss member?

Set the member's end release to pin at the start, the end, or both. A pinned end releases both bending moments (My and Mz) at that end. A member pinned at both ends carries only axial force and torsion, like a brace or truss bar. If every member framing into a joint is pinned there, that joint has no rotational stiffness. The solver then restrains the rotation and lists it in the warnings, instead of failing as unstable.

Does shear deformation affect the results?

The members are Euler-Bernoulli beams, so shear deformation is neglected. That is accurate for slender steel and timber members. For deep beams or short, stocky members with span-to-depth ratios below about 5, shear deformation can add noticeably to deflection, and a Timoshenko formulation would be stiffer-correct.

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3D Frame Analysis

A lightweight structural analysis program in your browser, in the spirit of RISA-3D and SAP2000. Generate a beam, portal frame or multi-story building, or type joints and members into the tables. Assign sections, releases and loads, then read displacements, reactions and moment, shear and axial diagrams for every ASCE 7 combination. P-Δ and modal analysis (periods and mass participation) are one click away. Nothing is uploaded; the model stays on your computer unless you share a link.

Units Model 2D (XY plane only) Rigid floor diaphragms P-Δ Modes Mass from

Bays X Bays Z Stories Bay X ft Bay Z ft Story h ft Base Bracing Beam ends

Spans Span ft Ends Segments per span

Length ft Orientation Segments Tip P (L) kip Tip P_z (L) kip Axial P (D, comp.) kip Tip torque (L) kip-ft

Beam w_D kip/ft Beam w_L kip/ft Lateral W per level (+X) kip Self-weight in D

Changing a generator input rebuilds the joints, members and loads (sections, materials and combinations are kept). Choose "Custom" first to edit the tables freely.

Results for Show Mode Scale joint # member #

Drag to rotate · Shift-drag to pan · Wheel to zoom · Click a member for its diagrams

Status—

Max displacement— in

Max |Mz|— kip-ft

Max |My|— kip-ft

Max |V|— kip

Max tension— kip

Max compression— kip

Max torsion— kip-ft

ΣR_y / applied— kip

Max story drift—

Worst member L/Δ—

Period T₁— s

#	X	Y (up)	Z	Support

Coordinates in ft. Fixed = all 6 restrained; pinned = 3 translations; roller = Y only; "pin+Rx" also restrains rotation about X.

#	i	j	Section	End releases	β (deg)	L

A pinned end releases My and Mz at that end. β rotates the local y/z axes about the member axis.

#	Name	Shape	d1	d2	d3	d4	Material	A	I_z (strong)	I_y	J

#	Name	E	G	Unit weight

Joint	Case	F_x	F_y	F_z	M_x	M_y	M_z

Forces in kip, moments in kip-ft, global axes (Y up, so gravity is −F_y).

Member	Case	Direction	w

Uniform load over the full member length, in kip/ft of member length. Global directions are signed (gravity = GY with a negative w); local y / z follow the member axes.

Name	D	L	W

Factors on the three load cases. Without P-Δ the results superpose; with P-Δ each combination is solved separately, as it must be.

Joint	R_x	R_y	R_z	M_x	M_y	M_z

Mem	N i	N j	max \|V_y\|	max \|V_z\|	max \|T\|	M_z i	M_z max +	M_z j	max \|M_y\|	L/Δ

Tension positive. M_z positive = tension on the −y face (sagging for beams). Values in kip and kip-ft. L/Δ is the deflection relative to the member chord.

Joint	Δx	Δy	Δz	θx	θy	θz

Translations in in, rotations in radians.

Mode	Period T (s)	Frequency (Hz)	Mass X	Mass Y	Mass Z	Σ X	Σ Y	Σ Z

Open model (.json)

The share link stores the whole model in the URL fragment, which is never sent to the server.

$$ \mathbf{k}_e^{(xy)} = \frac{EI_z}{L^3}\begin{bmatrix} 12 & 6L & -12 & 6L\\ 6L & 4L^2 & -6L & 2L^2\\ -12 & -6L & 12 & -6L\\ 6L & 2L^2 & -6L & 4L^2\end{bmatrix},\quad \mathbf{k}_G = \frac{N}{L}\begin{bmatrix}1&-1\\-1&1\end{bmatrix},\quad \mathbf K\boldsymbol\phi = \omega^2\mathbf M\boldsymbol\phi $$

k^(xy) bending block for v_i, θz_i, v_j, θz_j (the xz block uses I_y) · k_G P-Δ geometric stiffness on lateral translations, N tension positive · M lumped translational mass · end releases by static condensation of the released rotations.

How the solver works

Every member is a straight, prismatic, Euler-Bernoulli beam-column with six degrees of freedom at each end: three translations and three rotations. The page forms each 12 × 12 member stiffness matrix in local axes, condenses out any released end moments, rotates it to global axes, and assembles the global stiffness matrix. It renumbers the joints by reverse Cuthill–McKee to keep the matrix banded, then factors it as LDLᵀ. A 10-story, 5 × 5-bay building (2,000+ equations) solves in well under a second.

Uniform member loads become fixed-end forces. After the solve, each member's end forces are recovered and the internal forces are computed at 40 stations from statics, using the end forces plus the distributed load. Deflections along each member come from integrating the curvature M/EI twice between the computed end displacements, so they include the effect of end releases exactly. The page checks equilibrium of every combination by comparing the sum of the vertical reactions with the total applied load.

Instability. If a translational pivot vanishes during factorization, the structure is a mechanism, and the page names the joint and direction. If a rotational pivot vanishes, for example at a joint where every member is pinned, that rotation has no stiffness and does not affect the answer. The page restrains it and lists it as a warning.

Rigid floor diaphragms. With the option on, the joints at each floor level (the same Y, not restrained against X, Z or rotation about Y) are tied to a master point at the level's mass centroid: u_x = u_xm + θ_y·Δz, u_z = u_zm − θ_y·Δx, θ_y = θ_ym. The floor then translates and twists as a rigid body in plan while each joint keeps its own vertical displacement and bending rotations, which is how a concrete slab or a composite deck is normally idealized. Because the master sits at the mass centroid, the floor mass and its polar moment of inertia stay uncoupled, and torsional modes come out correctly. Without diaphragms, each frame line moves on its own, and an unbraced interior frame can dominate the first mode.

P-Δ. With P-Δ on, each combination is solved, the member axial forces are taken from that solution, and the geometric stiffness N/L is added to both lateral translations of every member. This repeats until the largest displacement changes by less than 0.01%. A negative pivot means the frame has buckled under that combination. Only the chord (P-Δ) effect is modelled, not member curvature (P-δ).

Modal analysis. Mass is lumped at the joints in all three translations: half of each member's self-weight at each end, plus, optionally, the dead-load joint and member loads converted to mass. Rotational inertia is neglected. The lowest modes come from subspace iteration (Bathe), with Jacobi rotations for the reduced eigenproblem. Each mode is reported with its period, frequency and effective modal mass ratio in X, Y and Z.

Verification problems

Closed-form checks (all reproduced by the automated test suite)
Problem	Exact	How to set it up
Cantilever, tip load P	Δ = PL³/3EI, M = PL	Cantilever, any segments
Simple beam, uniform w	M = wL²/8, Δ = 5wL⁴/384EI	Continuous beam, 1 span, pinned
Fixed–fixed beam, uniform w	M_end = wL²/12, M_mid = wL²/24	Continuous beam, 1 span, fixed
Two equal spans, uniform w	M_B = −wL²/8, R_B = 1.25wL	Continuous beam, 2 spans
Cantilever, tip torque T	θ = TL/GJ	Cantilever, tip torque
Column, axial P + lateral H, P-Δ, 1 element	Δ = H / (3EI/L³ − P/L)	Vertical cantilever, 1 segment, P-Δ on
Simple beam, first mode	f₁ = (π/2)√(EI/(m̄L⁴))	1 span, pinned, many segments

Worked example — fixed-base portal frame under lateral load

One bay, 20 ft wide, 12 ft tall, rigid beam, H = 10 kip at the roof

Given: fixed bases, columns with EI_c, and a beam so stiff that the joints do not rotate.

Each fixed–fixed column with no end rotation has lateral stiffness k = 12EI_c/h³; two columns share H equally, so each takes a 5 kip shear.

Column end moments: M = V h / 2 = 5 × 12 / 2 = 30 kip-ft at the top and bottom of each column (inflection at mid-height).

Sway: Δ = H h³ / (24 EI_c). With EI_c = 29,000 ksi × 500 in⁴ and h = 144 in: Δ = 10 × 144³ / (24 × 29,000 × 500) = 0.0858 in.

To reproduce it, set the beam section's I_z about 1000 times the column's. The page then gives 30.0 kip-ft and 0.086 in. With a real beam, the joints rotate, the moments shift toward the base and the drift grows, which is why a frame analysis is needed.

Limits

Frame members only: no plates, shells, solids, cables, springs, semi-rigid diaphragms, or rigid end offsets. Members are straight and prismatic; shear deformation is neglected.
Uniform member loads cover the whole member. Split a member at a new joint to place a point or partial load.
No member design checks (AISC, ACI, NDS), no moving loads, and no response spectrum or time history. The modal results are periods, mode shapes and mass participation only.
P-Δ includes the large-Δ effect only. The AISC 360 direct analysis method also needs notional loads and the 0.8 τ_b stiffness reduction, which you would apply in the inputs.
The I-shape and box properties are computed from plate dimensions without fillets or corner radii. They are close to, but not identical to, tabulated AISC values. Enter tabulated A, I and J with the "Custom" shape when it matters.

References: McGuire, W., Gallagher, R.H. and Ziemian, R.D., Matrix Structural Analysis, 2nd ed. (2000), Ch. 4–5 (3D frame element, transformation, condensation of releases) and Ch. 9 (geometric stiffness). Przemieniecki, J.S., Theory of Matrix Structural Analysis (1968). Bathe, K.-J., Finite Element Procedures, §11.6 (subspace iteration). Gibbs, N.E., Poole, W.G. and Stockmeyer, P.K., "An algorithm for reducing the bandwidth and profile of a sparse matrix," SIAM J. Numer. Anal. 13(2), 1976. ASCE/SEI 7-22 §2.3 and §2.4 (combinations) and §12.9.1.1 (90% modal mass participation). ANSI/AISC 360-22 Chapter C and Appendix 7.

Related tools

Truss calculator — roof and bridge trusses with NDS and AISC member checks
Continuous beam — pattern live load envelopes and HL-93 for girders
Beam deflection — closed-form single-span cases
Section properties — A, I, S, r, Z for common shapes
AISC LRFD steel design — check the members for the forces found here

Worked examples and guides

Portal frame under lateral load — slope-deflection vs this tool, fixed vs pinned bases
P-Δ column — exact second-order vs AISC B₂ vs element count
3-story building period — modal analysis vs ASCE 7 T_a, rigid diaphragms
How to model a 3D frame — local axes, releases, diaphragms, model checks
All structural analysis tools and examples