VisuApps
Grasp statics, strength of materials and dynamics interactively
Apps
Bending beam under moment M: linear bending stress σ=M·y/I across the section (tension/compression zones), neutral axis; switchable section (rectangle, I-beam) with live moment of inertia I.
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Schub als Impulsstrom, Widerstand quadratisch: m·dv/dt = ṁ·v_e − ṁ_a·v − k·v². Vier Presets (Übungsaufgabe, Kampfjet, Verkehrsflugzeug, Business-Jet), alle Größen als Slider; Kurven v(t) und a(t) mit v_max-Linie und Zeit bis 99 %, dazu die geschlossene Lösung Schritt für Schritt.
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Spring-mass oscillator: harmonic motion x(t)=A·cos(ωt) with ω=√(k/m), period T=2π·√(m/k); an energy bar shows the conversion kinetic ↔ potential (sum constant).
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Planar truss with an adjustable load: method of joints with force balance per joint, tension members red / compression members blue, zero-force members marked, member forces computed.
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Beam on pin and roller supports with movable loads: support reactions computed from ΣF=0 and ΣM=0 and shown as arrows, with a free-body diagram.
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Motion of a point with coupled diagrams s(t), v(t), a(t); uniform vs. uniformly accelerated, sliders v₀ and a, a time playhead runs in sync across all three.
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Newton's second law F=m·a: a body under a resultant force (optionally with friction) accelerates; sliders mass and force, a/v(t)/s(t) live, presets free fall and projectile with trajectory.
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Several forces act at one point: magnitude and direction by drag, the resultant as the vector sum (parallelogram or polygon), equilibrium when the resultant is zero.
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Decompose a force F into components — along the x/y axes (F_x=F·cosα, F_y=F·sinα) or two arbitrary lines of action via parallelogram; magnitude, angle and directions via slider/drag.
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Moment of a force M=F·r about a pivot with the perpendicular lever arm shown; the lever law on a seesaw with moment equilibrium ΣM=0 and the sense of rotation in colour.
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Block on an inclined plane: angle α, static friction coefficient μ and mass via slider, forces (weight, normal, downslope, friction) as vectors; slides when tanα>μ (angle of repose ρ=arctan μ).
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A robot arm with three joints: in forward mode you set the angles and the hand follows; in inverse mode you drag a target and the IK computes the angles — with two, one or no solution at all. Compare PTP and LIN motion on a glue seam, an overhead path and a stretch: the straight line in space turns curved in joint space, and near singularities the joint speed shoots up.
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Beam with loads and a section slider: axial force N, shear V and bending moment M at the cut plus the axis-aligned diagrams N(x), V(x), M(x) (dV/dx=−q, dM/dx=V).
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Composite area of rectangles, triangles and circles: the area centroid (x_s, y_s) as the area-weighted mean of the part centroids, computed and marked.
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Tensile bar under load plus the stress-strain diagram σ-ε with the Hooke line (Young's modulus), proportionality/yield limits, plastic region and fracture; the operating point moves along the curve.
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Twisted shaft in 3D: shear stress τ=T·r/I_p (linear over the radius) and twist angle φ=T·L/(G·I_p); sliders for torque T, length L and shear modulus G, the surface lines twist.
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Bar under tension/compression: normal stress σ=F/A, strain ε=σ/E and elongation ΔL=F·L/(E·A); sliders for F, A, L and E, the bar deforms visibly.
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