Govt Exams
Beam elements use cubic Hermite shape functions to ensure C¹ continuity (displacement and slope continuity).
Plastic collapse occurs when sufficient plastic hinges develop to convert the structure into a mechanism, allowing unbounded deformation.
Global stiffness matrix is assembled by superposition of element stiffness matrices after coordinate transformation.
I = bd³/12, A = bd, r = √(I/A) = √(d²/12) = d/(2√3) for axis parallel to base.
For symmetrical continuous beam with equal spans and loads, negative moments at all interior supports are equal.
Three-hinged arch has 4 reactions with 3 global + 1 local equilibrium equation at crown, making it statically determinate (DSI=0).
[K]{D} = {F}, where stiffness matrix K relates displacements D to forces F. K represents member/structure stiffness.
Flexibility coefficients for non-uniform beams require integration accounting for variable EI along the length.
Virtual work principle: Work done by actual loads through virtual displacements equals work by virtual loads through actual displacements.
For fixed beam with central point load, fixed end moment = PL/8 and maximum deflection = PL³/(192EI).