Cantilever Behavior 3D Simulator — Root Moment & Tip Deflection Interactive

Interactive 3D cantilever simulator with an Equipment laboratory workbench (wall-mounted arm, root anchor group, clamp/rotational-spring coupling, movable loading saddle and free-end displacement gauge), a Curves & measurements tab with live shear and hogging-moment charts and model equations, an Experiments tab with four guided fixtures and a model-verification bench, and a Learn & assess tab with lessons, a knowledge-check quiz and referenced scope notes.

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About the Cantilever Behavior 3D Simulator

This simulator inspects a wall-mounted cantilever test arm with root anchors, a movable loading saddle and a free-end displacement gauge, letting you compare an ideal rigid clamp against a translationally fixed but rotationally flexible root connection while tracing shear, hogging moment and tip deflection.

What the simulator shows

• A real-time 3D cutaway workbench with the cantilever arm and free tip, a reaction wall with base plate and anchor group, a clamp or rotational-spring root coupling, a movable point-load saddle with distributed-load hangers, a sliding inspection cut, and a free-end dial gauge with tension/compression fiber coloring, with home view, focus-selected-part, toggleable full enclosure, exploded view, auto-rotate, expand and show/hide labels controls. • Adjustable overhang length (1-6 m), downward point load (0-50 kN), uniform downward load (0-10 kN/m), point-load location (10-100% of length), inspection section position (0-100% of length), rectangular beam width (100-300 mm) and depth (150-500 mm), elastic modulus (70-210 GPa), root rotational condition (ideal fixed rotation or elastic rotational spring), and root rotational stiffness (1-100 MN·m/rad). • Loading actions: ramp loads from zero, apply full load, and release loads. • A Curves & measurements tab with shear-along-the-overhang and hogging-moment-along-the-overhang charts, the underlying model equations (root reaction, root moment, V(x), M(x), deflection formulas and root-spring rotation) and snapshot readouts (root reaction, support moment, section shear/moment/deflection, tip deflection, tip slope, root rotation, root-rotation tip contribution, root and section bending stress). • An Experiments tab with four guided fixtures (tip point load only, uniform load only, load moved to midlength, flexible root connection) and a model verification bench that runs independent deterministic checks against a fresh model without disturbing your live trial, plus a timestamped event log and a copyable trial report. • A Learn & assess tab with guided lessons on transferring load into the wall, tracing hogging moment, moving a point load inboard and distinguishing a clamp from a flexible connection, a knowledge-check quiz with reset, and a written model-scope statement with a technical reference link.

How the root carries shear and overturning moment

With one end restrained and the other free, the wall connection must supply both an upward reaction equal to the total applied load and a balancing support moment — the free tip itself carries no reaction. Downward loads create hogging bending: the internal moment is most negative at the root and eases toward zero at the free end, following M(x) = −P·max(a−x, 0) − w(L−x)²/2.

Moving the point load inboard changes the picture: the unloaded segment beyond the load has zero curvature contribution from that force, yet it still deflects because the section at the load carries nonzero displacement and slope that propagates outward.

Rigid clamp versus rotational spring, and model scope

The ideal-clamp option enforces zero root rotation. Switching to the elastic rotational spring keeps zero root translation but allows rotation θ₀ = Mroot/kθ, adding θ₀·x to the deflection at every section — importantly, this changes rotation and tip displacement without altering the statically determined root shear and reaction moment, since the structure remains statically determinate either way.

This is a static, prismatic Euler-Bernoulli beam model with small rotations and a linear root spring that retains zero translation. It excludes yielding, shear deformation, torsional instability, individual anchor-force distribution, concrete breakout capacity and any vibration model; large deflections are flagged rather than solved nonlinearly, and the connection hardware shown is representative, not a manufacturer detail.

Frequently asked questions

Does the free end of a cantilever provide a vertical reaction?

No. All support reactions in this model come from the wall connection at the fixed root — the free tip carries no reaction force at all.

Does a finite root rotational stiffness change the static root moment?

No. The cantilever remains statically determinate regardless of root stiffness, so equilibrium alone sets the support shear and moment. Root stiffness only controls how much the root rotates and how much extra tip displacement that rotation contributes.

What happens to the moment diagram if I move a point load inboard?

Moving the load inboard reduces the root moment (since it depends on the load's distance from the wall) and the unloaded outer segment carries zero curvature from that point force, though it still deflects due to the slope and displacement already present at the load location.

Can this simulator size a real cantilever connection?

No. It is a linear, small-rotation Euler-Bernoulli model that excludes yielding, shear deformation, individual anchor-bolt forces, concrete breakout and vibration effects. A qualified structural engineer must design any real cantilever connection.

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