Advanced Beam

Multi-span Euler-Bernoulli FEM with variable EI, internal hinges, spring supports, settlements, thermal gradients, and modal analysis. 126 unit tests against analytical solutions.

TERCERO TABLADA
Civil & Structural Engineering Inc.
ADVANCED BEAM ANALYSISMULTI-SPAN FEM · EULER-BERNOULLI

Model schematic · deformed

ABC10 kN/mL = 12.00 m
TypePosition / range (m)MagnitudeDirCase
UDL kN/m

Diagrams V · M · θ · δ

Shear VkN37-37Moment M (sagging +)kN·m25-45Slope θrad0.000.00Deflection δ (up +)mm-1.95x (m) · span 12.0 m

Reactions ↑ kN · kN·m

A · pin @ 0.0 m22.50 kN
B · roller @ 6.0 m75.00 kN
C · roller @ 12.0 m22.50 kN

Envelope max / location

Max +V37.50 kN@ 6.00 m
Min −V-37.50 kN@ 6.00 m
Max +M (sag)25.31 kN·m@ 2.25 m
Min −M (hog)-45.00 kN·m@ 6.00 m
Max |δ|-1.95 mm@ 2.52 m

First-order elastic direct-stiffness (FEM) Euler-Bernoulli analysis of a multi-span beam with variable EI, internal hinges, spring supports, prescribed settlements/rotations, thermal gradients and self-weight, plus natural-mode analysis. Sign convention: downward load positive, sagging moment positive, deflection reported in mm (up positive). Metric units. Verify the model independently; a licensed P.E. review remains required.