Govt. Exams
Entrance Exams
Abrams' Law states that compressive strength decreases exponentially with increase in water-cement ratio.
C3A reacts rapidly with water and is responsible for flash setting. Gypsum is added to control this reaction.
DSI = (r + 3m) - 2j = (4 + 3×3) - 2×4 = 13 - 8 = 3 for this portal frame configuration.
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.
