Govt. Exams
Entrance 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.
Flexibility coefficients for non-uniform beams require integration accounting for variable EI along the length.
Maximum bending moment occurs at the section where shear force is zero (point of contraflexure). For moving loads, position varies but this principle always applies.
For a parabolic arch under UDL, the horizontal thrust H = wL²/(8f), where f is rise. The thrust decreases with increase in rise-to-span ratio. Optimal ratio is 1/2 for many design considerations.
For SS beam with central load, maximum deflection occurs at x = L/√3 ≈ 0.577L from support, not at center due to boundary conditions.
Williot-Mohr diagram graphically represents the deflected shape showing displaced position of all joints in a truss.
Castigliano's first theorem: ∂U/∂P = δ, where U is strain energy and δ is deflection at point of load P.
For planar frames: DI = (m + r) - 2j, where 2j accounts for 2 equilibrium equations per joint in 2D.
