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For Hobbyists & Makers · Multi-Story Frame

Multi-Story Frame for a stair stringer

Built for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker. Simulate a stair stringer live below — adjust the inputs and watch it respond, right in your browser.

Base Shear

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Seismic Base ShearLive

equivalent lateral force

Controls

Presets

Number of stories

Weight per floor (kN)

Design accel. SDS (g)

Response factor R

Importance factor I

The equivalent lateral force method estimates the total earthquake base shear as V = Cs·W, where the seismic coefficient Cs scales the design acceleration by the structure's ductility (R) and importance (I). The base shear is distributed up the building, concentrating force at the top. Educational tool, not a code design.

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Data Inspector

Seismic coeff. Cs0.150

Total weight W9,000 kN

Base shear V1350 kN

Roof force386 kN

Governing equation

V = C_{s} W = min (\frac{S _{D S} I}{R}, 0.15) W = 0.150 \times 9, 000 = 1350 kN

Reading this result: Cs would be 0.167 but is capped at 0.15, so base shear is code-floored here — cutting R further will not add demand.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Column Buckling

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Column Buckling (Euler)Live

critical load & slenderness

Controls

Presets

Young's modulus E (GPa)

Moment of inertia I (10⁶ mm⁴)

Length L (m)

Cross-section area (mm²)

A slender column fails not by crushing but by buckling sideways at the Euler critical load Pcr = π²EI/(KL)². The effective-length factor K depends on the end restraints — fixing both ends quadruples the capacity versus pinned. Educational tool, not a substitute for code-based design.

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Data Inspector

Critical load Pcr2193 kN

Effective length3.00 m

Slenderness KL/r52

Critical stress731 MPa

Governing equation

P_{cr} = \frac{π ^{2} E I}{( K L ) ^{2}} = \frac{π ^{2} ( 200 GPa ) ( 10 \times 1 0 ^{6} mm ^{4} )}{( 1 \times 3 m ) ^{2}} = 2193 kN

Reading this result: Intermediate slenderness (KL/r = 52): buckling and yielding compete, so design codes blend the two rather than trusting Euler alone.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Beam Deflection

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Beam Deflection & BendingLive

Euler-Bernoulli beam theory

Controls

Presets

Span L (m)

Load P (kN)

Flexural rigidity EI (kN·m²)

Euler-Bernoulli theory relates a beam's deflection and internal moment to its load, span, and flexural rigidity EI. Deflection grows with the cube or fourth power of span, which is why doubling a span is far worse than doubling the load. Educational tool — not a substitute for a stamped structural design.

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Data Inspector

Max deflection1.30 mm

Max moment12.5 kN·m

Span/deflectionL/3840

Governing equation

δ = \frac{P L ^{3}}{48 E I} = \frac{10 \cdot 5 ^{3}}{48 \cdot 20000} = 1.30 mm

Reading this result: At L/3840 this beam clears the usual L/360 serviceability limit, so strength (not deflection) is likely to govern the design.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Mohrs Circle

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Mohr's CircleLive

2D stress transformation

Controls

Presets

σx (MPa)

σy (MPa)

τxy (MPa)

Mohr's circle is a graphical way to transform a 2D stress state to any rotated axis. The circle's center is the average normal stress and its radius is the maximum shear. Where it crosses the horizontal axis gives the principal stresses — the orientation with zero shear. Educational tool.

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Data Inspector

σ₁ (max principal)92.4 MPa

σ₂ (min principal)7.6 MPa

τmax42.4 MPa

Principal angle22.5°

Governing equation

σ_{1, 2} = \frac{80 + 20}{2} \pm (\frac{80 - 20}{2})^{2} + 3 0^{2} = 92.4, 7.6 MPa

Reading this result: The circle radius sets τmax = 42.4 MPa on planes 45° from the principals; rotate the element by 22.5° to reach the shear-free principal orientation.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

Is this good for hobbyists & makers?: Yes — this version of "Multi-Story Frame for a stair stringer" is framed for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.