Civil Engineering Quizzes

Determinate structures are those where all support reactions and internal forces can be determined using only the equations of static equilibrium (ΣFx=0, ΣFy=0, ΣM=0). Examples include simply supported beams, cantilever beams, and trusses with proper bracing.

Indeterminate structures have more unknown forces than available equilibrium equations, requiring additional compatibility conditions to solve. Examples include fixed beams, continuous beams, and rigid frames. The degree of indeterminacy is calculated as:

Degree of static indeterminacy = Number of unknown reactions - Number of equilibrium equations

For example, a propped cantilever has 3 unknowns (2 at fixed end, 1 at prop) and 2 equilibrium equations, making it 1st degree indeterminate.

The moment distribution method involves these steps:

1. Calculate stiffness factors (K): K = 4EI/L for far end fixed, 3EI/L for far end pinned
2. Determine distribution factors (DF): DF = K/ΣK at each joint
3. Compute fixed-end moments (FEM) for each member under applied loads
4. Lock all joints and apply FEMs
5. Release one joint at a time and distribute unbalanced moment to connected members
6. Carry over half of distributed moments to far ends (for fixed supports)
7. Repeat process until moments become negligible (typically 3-4 cycles)
8. Sum all moments at each end to get final moments

This method is particularly useful for analyzing continuous beams and rigid frames without solving complex equations.

The grain size distribution curve (also called sieve analysis curve) plots percentage finer (ordinate) against particle size (abscissa, logarithmic scale). Key features:

Significance:

• Determines effective size (D10): Particle size where 10% of soil is finer - affects permeability
• Calculates uniformity coefficient (Cu = D60/D10): Indicates particle size range
• Determines coefficient of curvature (Cc = (D30)²/(D10×D60)): Indicates shape of curve
• Identifies well-graded vs poorly-graded soils

Classification uses:

• USCS classification: Uses D10, D30, D60 to classify soils as GW, GP, SW, SP, etc.
• AASHTO classification: Uses % passing specific sieves (No. 10, 40, 200)
• Predicts engineering properties: Permeability, compressibility, shear strength
• Helps select appropriate construction methods and materials

Parameter	CPM (Critical Path Method)	PERT (Program Evaluation Review Technique)
Origin	Developed by DuPont for chemical plants (1957)	Developed by US Navy for Polaris missile (1958)
Time Estimation	Single deterministic time estimate	Three time estimates (optimistic, most likely, pessimistic)
Focus	Time-cost trade-off analysis	Probabilistic time analysis
Best For	Repetitive, predictable projects	R&D projects with uncertainty
Calculation	Forward/backward pass to find critical path	Uses expected time = (O+4M+P)/6 and variance

Similarities: Both use network diagrams, identify critical path, and help in resource allocation. Modern software often combines both approaches.

The California Bearing Ratio (CBR) method involves these steps:

1. Traffic Assessment:

• Calculate cumulative standard axle load (msa) for design period
• Determine traffic category (light, medium, heavy, very heavy)

2. CBR Testing:

• Conduct CBR test on subgrade soil (soaked for 96 hours)
• Take CBR value at 2.5mm or 5.0mm penetration (whichever is higher)

3. Thickness Determination:

• Use IRC charts (IRC:37) correlating CBR, traffic, and total thickness
• For CBR 5% and 10msa: Total thickness ≈ 700mm
• Layer thicknesses: Wearing course (25-50mm), Binder course (50-100mm), Base (100-300mm), Sub-base (150-300mm)

4. Material Specifications:

• Wearing course: Bituminous concrete (BC)
• Binder course: Dense bituminous macadam (DBM)
• Base: Wet mix macadam (WMM) or granular sub-base (GSB)
• Sub-base: GSB or selected subgrade material

5. Quality Control: Field density tests, CBR checks on compacted layers, and bitumen content verification.

The discharge (Q) through a rectangular notch can be derived as follows:

Assumptions:

1. Steady flow conditions
2. Velocity approach is negligible
3. No energy losses
4. Pressure distribution is hydrostatic

Derivation:

1. Consider a rectangular notch of width L and head H
2. At depth h below the free surface, consider an elementary strip of thickness dh
3. Area of strip (dA) = L × dh
4. Theoretical velocity through strip (v) = √(2gh) [from Torricelli's theorem]
5. Discharge through strip (dQ) = Cd × dA × v = Cd × L × dh × √(2gh)
6. Total discharge (Q) = ∫dQ from 0 to H = Cd × L × √(2g) ∫h^1/2dh from 0 to H
7. Q = Cd × L × √(2g) × [2/3 H^3/2]
8. Final expression: Q = (2/3) Cd × L × √(2g) × H^3/2

Where:
Cd = Coefficient of discharge (typically 0.60-0.65 for sharp-crested notches)
L = Length of notch
H = Head over the notch
g = Acceleration due to gravity