Govt. Exams
Entrance Exams
Three-hinged arch has 4 reaction components (2 at each support) and 3 equilibrium equations plus 1 condition that moment at internal hinge = 0, making it statically determinate.
Shear force diagram shows a vertical jump equal to the magnitude of the concentrated load at its point of application.
Relative stiffness (I/L) is used in distribution factor calculations when moments of inertia vary across spans.
Distribution factor = (stiffness of member)/(sum of stiffness of all members at joint). DF ∝ stiffness (4EI/L).
Carry-over factor = 0.5 for both fixed and pinned end conditions in slope-deflection method.
Element stiffness matrix is derived by applying unit displacements at nodes and calculating corresponding forces (unit displacement method).
Influence line for reaction at A is triangular, varying from 1 at A to 0 at B, representing the reaction at A due to unit load.
Two-hinged arch has 2 supports (each with 2 reactions) = 4 unknowns total (horizontal and vertical at each hinge).
Virtual work principle applies universally to all structures, both determinate and indeterminate, and rigid/deformable bodies.
Fixed-end moment for fixed beam with UDL = wL²/12 at each end (opposite signs).
