According to Abrams' Law, the relationship between w/c ratio and compressive strength is:
A
Linear positive relationship
B
Inverse/Negative exponential relationship
C
No relationship
D
Directly proportional
Correct Answer:
B. Inverse/Negative exponential relationship
Abrams' Law states that compressive strength decreases exponentially with increase in water-cement ratio.
Which chemical compound in cement causes flash setting when exposed to water?
A
C3S (Tricalcium Silicate)
B
C2S (Dicalcium Silicate)
C
C3A (Tricalcium Aluminate)
D
C4AF (Tetracalcium Aluminoferrite)
Correct Answer:
C. C3A (Tricalcium Aluminate)
C3A reacts rapidly with water and is responsible for flash setting. Gypsum is added to control this reaction.
For a portal frame with fixed bases and pinned roof, subjected to horizontal load, the degree of indeterminacy is:
DSI = (r + 3m) - 2j = (4 + 3×3) - 2×4 = 13 - 8 = 3 for this portal frame configuration.
For a beam element in finite element analysis, the shape functions are typically:
A
Linear functions
B
Cubic Hermite polynomials
C
Quadratic functions
D
Trigonometric functions
Correct Answer:
B. Cubic Hermite polynomials
Beam elements use cubic Hermite shape functions to ensure C¹ continuity (displacement and slope continuity).
In plastic hinge formation, the condition for plastic collapse is:
A
Bending moment equals yield moment
B
Deflection becomes zero
C
Sufficient plastic hinges form to create mechanism
D
Shear force equals yield shear
Correct Answer:
C. Sufficient plastic hinges form to create mechanism
Plastic collapse occurs when sufficient plastic hinges develop to convert the structure into a mechanism, allowing unbounded deformation.
In the direct stiffness method, the global stiffness matrix is formed by:
A
Assembly of element stiffness matrices
B
Averaging element stiffness matrices
C
Selection of largest element stiffness
D
Transformation of local to global coordinates only
Correct Answer:
A. Assembly of element stiffness matrices
Global stiffness matrix is assembled by superposition of element stiffness matrices after coordinate transformation.
For a beam with varying moment of inertia, the flexibility coefficient method requires:
A
Constant EI throughout
B
Integration with variable EI
C
Average value of EI
D
Maximum value of EI
Correct Answer:
B. Integration with variable EI
Flexibility coefficients for non-uniform beams require integration accounting for variable EI along the length.
In a moving load problem on a simply supported beam, the maximum bending moment under a point load occurs when the load is positioned:
A
At the midspan
B
At 0.577L from nearest support
C
At any position for symmetry
D
When the shear force equals zero
Correct Answer:
D. When the shear force equals zero
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.
A parabolic arch carries a uniformly distributed load. At the crown (center) of the arch, the horizontal thrust is minimum when the rise-to-span ratio is:
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.
A simply supported beam with central point load shows maximum deflection at:
A
At the point of load
B
At distance L/√3 from either support
C
At distance 0.577L from either support
D
Exactly at center for symmetric loading
Correct Answer:
C. At distance 0.577L from either support
For SS beam with central load, maximum deflection occurs at x = L/√3 ≈ 0.577L from support, not at center due to boundary conditions.
