GATE Exam Questions

The modulus of elasticity (E) is a measure of the stiffness of a material. It is important in civil engineering because:

• It indicates the ability of a material to deform elastically (i.e., return to its original shape after the removal of a load).
• It helps in determining the deflection of structural elements under load, ensuring that they remain within permissible limits.
• It is used in the design and analysis of structures to ensure they can withstand applied loads without excessive deformation, ensuring stability and integrity.

Shear force and bending moment are internal forces in a beam that result from external loads:

• Shear Force: The force that causes a sliding failure along a plane parallel to the force direction. It is a measure of the internal forces acting along the cross-section of the beam.
• Bending Moment: The moment that causes the beam to bend. It is a measure of the internal moments acting along the length of the beam, resulting in bending. Understanding shear force and bending moment is crucial for designing safe and efficient structural elements, ensuring they can carry applied loads without failing.

The safe bearing capacity of soil is determined through various methods, including:

1. Field Tests: Standard Penetration Test (SPT), Plate Load Test, Cone Penetration Test (CPT).
2. Empirical Formulas: Using empirical relationships based on soil type and conditions.
3. Laboratory Tests: Conducting tests on soil samples to determine properties like cohesion, angle of internal friction, and density.
4. Terzaghi’s Bearing Capacity Theory: Calculating bearing capacity using Terzaghi's equations, which account for soil properties and load conditions.
5. Geotechnical Reports: Using data from geotechnical investigations and past experiences in similar conditions.

• WSD (Working Stress Design): This method ensures that the stresses in materials do not exceed their permissible limits under service loads. It uses a factor of safety applied to the material strengths and focuses on elastic behavior.
• LSD (Limit State Design): This modern method considers both ultimate limit states (safety against collapse) and serviceability limit states (comfort and usability). It applies partial safety factors to loads and material strengths, ensuring a more reliable and optimized design. LSD accounts for the actual behavior of materials under loads and provides a balance between safety and economy.

Concrete mix design involves determining the proportions of cement, water, aggregates, and admixtures to achieve the desired strength and workability. The process includes:

1. Define Requirements: Specify the desired properties, such as strength, workability, durability, and exposure conditions.
2. Select Materials: Choose suitable materials, including type of cement, aggregates, water, and admixtures.
3. Determine Mix Proportions: Use guidelines or standards (e.g., IS 10262 in India, ACI in the USA) to calculate the mix proportions. Adjust for water-cement ratio, aggregate size, and workability.
4. Trial Mixes: Prepare trial batches and test them for workability (slump test) and strength (compressive strength test).
5. Adjust and Finalize: Adjust the mix based on test results to meet the desired specifications and finalize the mix design.

The Darcy-Weisbach equation is used to calculate the pressure drop or head loss due to friction in a pipe. It is given by:

hf=fLDV22gh_f = f \frac{L}{D} \frac{V^2}{2g}hf​=fDL​2gV2​

Where:

• hfh_fhf​ = head loss due to friction (m)
• $f$ = Darcy-Weisbach friction factor (dimensionless)
• $L$ = length of the pipe (m)
• $D$ = diameter of the pipe (m)
• $V$ = velocity of the fluid (m/s)
• $g$ = acceleration due to gravity (m/s²)

Application: It is used in the design and analysis of pipe systems in water supply, irrigation, sewage systems, and other fluid transportation systems to ensure proper sizing and energy efficiency.

Types of foundations include:

1. Shallow Foundations: Used when the soil has sufficient bearing capacity near the surface.
   • Strip Footing: For load-bearing walls.
   • Spread Footing: For individual columns.
   • Raft or Mat Foundation: For heavy loads or poor soil conditions.
2. Deep Foundations: Used when the soil near the surface is not suitable to support the loads.
   • Piles: Driven or drilled deep into the ground to transfer loads to deeper, more stable soil or rock layers.
   • Caissons: Large-diameter, cast-in-place piles for bridges and large structures.
   • Piers: Similar to piles but larger and used in different conditions.

Permeability is a measure of the ability of soil to allow water to flow through its pores. It is an important property in soil mechanics because it affects:

• Drainage and Seepage: How quickly water drains or seeps through soil, impacting the stability of slopes and the design of drainage systems.
• Consolidation: The rate at which soil compresses under load, affecting settlement calculations.
• Aquifer Performance: The capacity of soil layers to transmit groundwater, impacting well design and groundwater management

Structural analysis of a multi-story building involves:

1. Load Calculation: Determine loads (dead, live, wind, seismic) acting on the structure.
2. Modeling: Create a mathematical model of the structure using software (e.g., ETABS, SAP2000).
3. Load Distribution: Distribute loads among structural elements (beams, columns, slabs) based on their stiffness and connectivity.
4. Analysis: Perform analysis to determine internal forces (bending moments, shear forces, axial forces) and displacements.
5. Design Checks: Ensure elements are designed to resist calculated forces, and check for stability, serviceability, and compliance with codes.
6. Iterative Process: Refine the design based on analysis results, adjusting member sizes, and reinforcements.

Tests for fresh concrete include:

• Slump Test: Measures workability.
• Compaction Factor Test: Measures workability for low-slump concrete.
• Vee-Bee Consistometer Test: Measures workability and consistency.
• Flow Table Test: Measures flowability for high-slump concrete.

Tests for hardened concrete include:

• Compressive Strength Test: Measures the ability to withstand loads.
• Flexural Strength Test: Measures the ability to resist bending.
• Split Tensile Strength Test: Measures the ability to resist tension.
• Rebound Hammer Test: Measures surface hardness and indirectly indicates strength.
• Ultrasonic Pulse Velocity Test: Measures the quality and uniformity of concrete.
• Water Permeability Test: Measures the resistance to water penetration.