Free tool · Beam analyzer

One beam. Every diagram.

A single prismatic beam under any combination of point loads, moments and distributed loads — solved with the same FE engine that powers the StructArk app. Shear, bending, deflection, reactions and reference formulas, all live.

Figure Simply supported · L = 6.00 m
ABL = 6.00 m10.0 kN/mV30.00 kN @ 0.00 m-30.00 kN @ 6.00 mSHEAR V (KN)M45.07 kN·m @ 3.17 m-2.47 kN·m @ 0.08 mMOMENT M (KN·M)δ1.64 mm @ 3.00 mDEFLECTION Δ (MM, +DOWN)
Reactions
A Pin @ x = 0.00 m R = 30.00 kN
B Roller @ x = 6.00 m R = 30.00 kN
Extrema
|V| max
30.00 kN
M max (sag)
45.07 kN·m @ 3.17 m
M min (hog)
-2.47 kN·m @ 0.08 m
δ max (down)
1.64 mm
Span / δ
L / 3660
Equilibrium check

Σ Fy = 0 : Σ R = Σ P

Σ R = 60.00 kN · Σ P = 60.00 kN

Σ MA = 0 : Σ (R · x) + Σ Msupport + Σ Mapplied = Σ (P · x)

From loads about A : 180.00 kN·m · Reactions × arm + support moments : 180.00 kN·m

Sums above are taken from the FE solution. Mismatches greater than ~0.1% indicate an unstable model — usually missing supports.

Reference formulas — Simply supported

SS · UDL w over full span

R = wL/2

M_max = wL²/8 · (mid) | δ_max = 5wL⁴ / (384·EI)

SS · Point load P at mid-span

R = P/2

M_max = PL/4 | δ_max = PL³ / (48·EI)

SS · Point load P at distance a (b = L−a)

R_A = Pb/L · R_B = Pa/L

M_max = Pab/L (under load)

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