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sci.Timoshenko-beam-shear-defl Calculator
Calculates total beam deflection including shear deformation using the Timoshenko beam theory: δ_total = δ_bending + δ_shear = ML²/(2EI) + VL/(κAG). Shear deformation matters when L/h < 10 — it can exceed 10% of bending deflection for short, deep beams and composite structures.
Inputs
P N
Applied force or weight (N or kN). Divide into dead load (permanent) and live load (variable — people, wind, etc.).
L M
Distance between supports (m). Longer spans experience larger bending moments — structural adequacy must be rechecked.
E Gpa
Reference formula or conversion factor shown for context.
I Cm4
Reference formula or conversion factor shown for context.
G Gpa
Reference formula or conversion factor shown for context.
A Cm2
Two-dimensional surface extent (m²). For complex shapes, break into simpler sub-shapes and sum.
Kappa
A multiplier applied in the calculation.
Results
total midspan deflection (mm)
Maximum lateral displacement of the beam under load. Codes typically limit to L/360 for floors (to avoid cracking finishes) or L/240 for roofs. Excessive deflection signals the beam is undersized.
bending deflection (mm)
Maximum lateral displacement of the beam under load. Codes typically limit to L/360 for floors (to avoid cracking finishes) or L/240 for roofs. Excessive deflection signals the beam is undersized.
shear deflection (mm)
Maximum lateral displacement of the beam under load. Codes typically limit to L/360 for floors (to avoid cracking finishes) or L/240 for roofs. Excessive deflection signals the beam is undersized.
shear contribution (%)
Sample size or count used in the calculation.
Timoshenko 1921: δ_total = PL³/48EI + PL/(4κGA)
The combined total across all inputs and components.