deflection-conjugate-beam - eboraonlinetutorialservices.com

Conjugate Beam Deflection Solver — Ebora

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The conjugate-beam solver works best in landscape — turn your phone sideways.

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📐 Solve = 10 EP · 📷 Scan (beam + load input only) = 10 EP — review, then Solve. Balance … EP

Units

📏 Units switching converts your values

Supports & Conditions

Support / Hinge

Pick each entry's type. Internal hinge (M = 0) builds overhang / Gerber / compound beams — each hinge needs one extra support reaction to stay determinate.

Concentrated Loads

Point Loads

Moment Loads

Applied Moments

Distributed / Varying Loads

Varying Loads

Section Properties

Flexural Rigidity (EI)

Input Method

Normalized keeps answers as value / EI (board form). The other two also report the real deflection (length units).

Two EI segments (section changes once)

Output

Deflection & slope at x (m)

Beam length L (m) — blank = auto-fit to the supports & loads

Set L past the last support to add a free overhang/cantilever tip. The maximum deflection over the whole beam is always reported.

Solution & diagrams

① 🪵 Beam — as given (updates as you type)

📐

Set your supports and loads on the left — the beam above updates live. Tap Solve by conjugate beam for the full solution: real reactions → bending-moment diagram → that diagram loaded on the conjugate beam (area above = up, below = down) → conjugate shear = slope, conjugate moment = deflection.

Answers

📐 Moment diagram by parts — reference point tap to switch ▾

↻ Switch the reference — the by-parts diagram & deflection recompute live (no re-charge). Default = the deflection point, so spandrels stay whole.

② 🔧 Adjusted beam (loads extended & balanced to the reference)

③ 🪞 Conjugate beam (M diagram by parts — ↑ where M>0, ↓ where M<0)

Areas & centroids (the M/EI loads carried onto the conjugate beam)

Conjugate beam — reactions by statics

↔️Some equations are wide — drag / swipe them sideways (left and right) to read the full line.

📝 Want the full slope & deflection solution at your point?

The app solves the conjugate-beam reactions in full (above) and gives the final slope & deflection at your point. The step-by-step working for that point needs a section cut on the conjugate beam — that's hard to turn into a clean closed-form, so the app doesn't auto-derive it. You can request the complete hand solution from Marvin, made for your exact beam & point:

Marvin personally solves it for your beam and emails it to you (the video discusses his solution). ⏰ He teaches all day and prepares these at night — expect your solution by around 12 midnight.

✂️ Crop — draw a box around just the beam

Drag to select; resize with the corner handles. No other figures needed.