Govt. Exams
Entrance Exams
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.
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).
∂U/∂P = Deflection at point of application of load P. ∂U/∂M = Slope at point of application of moment M.
Influence line for reaction is linear: value = 1 at support A and linearly decreases to 0 at support B, representing unit load position effect on reaction RA.
Plastic analysis assumes yielding at critical sections forms plastic hinges where full plastic moment capacity is achieved, leading to collapse mechanism.
Conjugate beam method applies M/EI diagram as load on conjugate structure. Deflection and slope are obtained as reactions and moments on conjugate beam.
For a frame to be stable and determinate: m + r = 2j. If m + r < 2j, the frame is unstable (insufficient members/supports). If m + r > 2j, frame is indeterminate.
