Govt. Exams
Entrance Exams
IS 800:2007 uses nonlinear interaction equations for combined bending and compression, typically: (P/Pc) + (M/Mc) ≤ 1.0, where Pc and Mc are critical values.
Stiffness coefficient k_ij represents the force/moment at DOF i due to unit displacement at DOF j. k₁₂ means effect at location 1 from displacement at location 2.
For continuous beams with equal spans and uniform loading, the middle span typically experiences larger negative moments at supports and larger positive moments due to symmetry considerations.
Fixed-end moment for a fixed-fixed beam with central point load = ±WL/8. This is a standard formula used in slope-deflection equations.
DKI = 3n - r, where n = number of joints = 8, r = reaction components = 9 (3 fixed supports × 3). DKI = 3(8) - 9 = 24 - 9 = 15.
For a simply supported beam with UDL, maximum deflection occurs at 0.577L from either support, not at midspan. This is approximately √(1/3) × L.
Portal frames under lateral load experience combined bending and axial forces in columns and beams, not simple bending.
For fixed-fixed beam with UDL, FEM = wL²/12 at both ends (opposite in direction for equilibrium).
Release means removing redundant constraints/reactions to convert indeterminate structure into determinate one for analysis.
Three-hinged arch has 4 reaction components (2 at each support). Three hinges provide 3 moment equations. Total 4 independent equations.
