Structural Design and Drawing (RCC-II) (CE-702 (D)) - Unit 1 Short Notes

UNIT 1: Structural Design and Drawing (RCC-II) - Short Notes

(Based on CE-702(D) Nov 2023 Paper & Past Analysis)

1. Cantilever Retaining Wall Design

Earth Pressure Theories

Active Earth Pressure (when wall moves away from soil):

• Rankine’s Theory (for granular soil, wall friction δ = 0):

$$ \sigma_a = \gamma z K_a - 2c\sqrt{K_a} \quad \text{(with cohesion)} $$

$$ K_a = \tan^2\left(45^\circ - \frac{\phi}{2}\right) \quad \boxed{\text{for cohesionless soil}} $$

[!TIP] Rankine assumes vertical wall, horizontal backfill, and no wall friction.

• Coulomb’s Theory (accounts for wall friction δ and sloping backfill):

$$ K_a = \frac{\cos^2(\phi - \delta)}{\cos^2\delta \cos(\delta + \beta) \left[1 + \sqrt{\frac{\sin(\phi + \delta)\sin(\phi - \beta)}{\cos(\delta + \beta)\cos(\beta)}}\right]^2} $$

where β = backfill slope angle.

Stability Criteria

1. Overturning Stability:

   • Factor of Safety (F.S.) = $$\displaystyle \frac{\text{Resisting Moment}}{\text{Overturning Moment}} \geq 1.5 $$ (typical).

   • Check for resultant within middle-third of base.

2. Sliding Resistance:

   • F.S. = $$\displaystyle \frac{\mu \cdot \text{Vertical Load} + \text{Cohesion} \cdot \text{Base Area}}{\text{Horizontal Force}} \geq 1.5 $$.

   • μ = coefficient of friction (≈ 0.5 for concrete on soil).

3. Bearing Pressure:

   • $$\displaystyle q_{\text{max/min}} = \frac{W}{b}\left(1 \pm \frac{6M}{Wb}\right) $$ (for rectangular base).

   • Ensure $$\displaystyle q_{\text{max}} \leq \text{Allowable soil pressure} $$.

Design of Stem

• Bending Moment & Shear:

  • At base: $$\displaystyle M = \frac{1}{2} K_a \gamma H^2 \times \frac{H}{3} $$ (triangular pressure).

  • Shear at base: $$\displaystyle V = \frac{1}{2} K_a \gamma H^2 $$.

• Thickness:

  • Base thickness $$\displaystyle t_b \approx 0.05H $$ to $0.08H$ (H = height).

  • Top thickness ≥ 150 mm (practical).

• Reinforcement:

  • Vertical bars at tension face (stem front).

  • Distribution steel (0.12% of gross area).

Design of Base Slab

• Bending Moment:

  • Heel (back): $$\displaystyle M_{\text{heel}} = \frac{1}{2} \gamma H \cdot \frac{b_h^2}{2} \cdot \frac{b_h}{3} $$ (soil pressure on heel).

  • Toe (front): $$\displaystyle M_{\text{toe}} = \frac{1}{2} q_{\text{toe}} \cdot \frac{b_t^2}{2} \cdot \frac{b_t}{3} $$.

• Shear Check:

  • Critical at $d$ from face. F.S. ≥ 1.25 (IS 456).

• Reinforcement:

  • Bottom steel in heel & toe (tension from soil pressure).

Reinforcement Detailing

• Curtailment:

  • Stem bars curtailed at height where BM reduces to 50%.

  • Base slab bars curtailed beyond L/3 from toe/heel.

• Development Length: $$\displaystyle L_d = \frac{\phi \sigma_s}{4\tau_{bd}} $$ (IS 456).

• Key/Shear Key:

  • Provided at base-soil interface to increase sliding resistance.

2. Circular Water Tank (Rigid Base & Wall)

Hoop Tension in Walls

• Thin Cylinder Assumption ($t \ll r$):

$$ \sigma_h = \frac{p r}{t} \quad \boxed{\text{(hoop stress)}} $$

where $$\displaystyle p = \gamma_w h $$ (hydrostatic pressure at depth h).

• Partial vs Full Water Pressure:

  • Design for full water level + surcharge (if any).

• Temperature/Shrinkage:

  • Provide minimum reinforcement (0.3% of concrete area) for restraint stresses.

Vertical Reinforcement

• Bending due to Hydrostatic Pressure:

  • Wall acts as vertical cantilever (fixed at base).

  • $$\displaystyle M_{\text{max}} = \frac{p r^2}{2} $$ per unit height.

• Distribution:

  • Vertical bars on outer face (tension).

  • Horizontal bars (0.2–0.4% of vertical section) for temperature/shrinkage.

Design of Components

• Wall Thickness:

  • $$\displaystyle t \geq \frac{p r}{0.2 f_{ck}} $$ (to limit hoop stress < 0.2 f_ck).

  • Minimum 150 mm (practical).

• Base Slab:

  • Circular slab with ring beam (if diameter > 10 m).

  • Design for soil pressure + water load.

• Roof Slab:

  • Flat (supported on walls) or dome (for large tanks).

Joints & Water Tightness

• Construction Joints:

  • Keyed, with water stops (copper/PVC).

• Expansion Joints:

  • Flexible water stops + compressible filler.

• Waterproofing:

  • Cement plaster + waterproofing admixture or membrane.

3. Intze Tank (Prestressed/Reinforced RC)

Top Dome Design

• Spherical Shell Theory:

  • Meridional stress: $$\displaystyle \sigma_m = \frac{p r}{2t} $$

  • Hoop stress: $$\displaystyle \sigma_h = \frac{p r}{4t} $$ (at crown, $$\displaystyle \sigma_h = \sigma_m $$).

• Thickness: Based on max compressive stress in concrete.

Ring Beam at Dome Base

• Load from Dome:

  • Hoop thrust $$\displaystyle H = p r $$ (transferred to ring beam).

• Design as Circular Beam:

  • Subject to bending + torsion from non-uniform thrust.

Cylindrical Wall Design

• Hoop Reinforcement:

  • Due to water pressure: $$\displaystyle A_{st} = \frac{p r t}{0.85 f_y} $$ (working stress).

• Vertical Reinforcement:

  • For bending from hydrostatic load + self-weight.

Material Specifications

• Concrete: M30 (f_ck = 30 MPa).

• Steel: Fe 415 (f_y = 415 MPa).

• Prestressing (if used):

  • High tensile wires/strands (f_pu = 1860 MPa).

4. Silo Design (Coal Storage)

Binning Pressure Calculation

• Janssen’s Equation (for vertical pressure):

$$ \sigma_v = \frac{\gamma R}{\mu K} \left(1 - e^{-\mu K z / R}\right) $$

where:

• R = silo radius,

• μ = coefficient of friction (wall-material),

• K = lateral pressure ratio (≈ 0.4–0.5 for coal).

• Horizontal Pressure: $$\displaystyle \sigma_h = K \sigma_v $$.

Wall Design for Horizontal Pressure

• Bending Moment:

  • Wall as vertical cantilever: $$\displaystyle M = \sigma_h \cdot R \cdot z^2 / 2 $$ (approx).

• Eccentric Discharge Effect:

  • Increases lateral pressure on discharge side (use Janssen with eccentricity factor).

Wall Design for Vertical Pressure

• Compression & Buckling:

  • Check $$\displaystyle \sigma_v < \text{permissible compressive stress} $$.

  • Slenderness ratio for buckling (if wall thin).

• Vertical Reinforcement:

  • For tensile stresses from bending + direct tension.

Base Design

• Hopper Bottom (if conical):

  • Design for mass flow, slope > angle of repose.

• Load Distribution:

  • Transfer to foundation via ring beam or slab.

5. Prestressed Concrete (Basics)

Definition & Principle

• Pre-compression applied to counter tensile stresses under service loads.

Systems of Prestressing

Advantages & Disadvantages

Stress Concept

• Equivalent Load: Prestress force as external load.

• Load Balancing: Tendon profile shaped to counteract applied loads.

Types

• Pre-tensioning: Tendon tensioned before casting, released after hardening.

• Post-tensioning: Tendon tensioned after concrete gains strength.

Losses of Prestress

1. Immediate:

   • Elastic shortening, friction, wedge slip.

2. Time-dependent:

   • Creep, shrinkage, steel relaxation.

   • Total loss ≈ 15–25% (design with loss ratio 0.8).

6. Solid Slab Bridge Design

IRC Loading

• Class AA Tracked Vehicle:

  • 70R (wheel load 70R = 70 × 9.81 = 686 kN) or 70T (70 × 10 = 700 kN).

  • Load distribution to slab via wheel contact area.

Effective Span & Geometry

• Effective Span (simply supported):

  • $$\displaystyle L_e = \text{clear span} + \text{width of bearing} $$ (IRC 6).

• Carriageway Width: As per road classification.

Slab Thickness

• Empirical Formula (IRC 6):

$$ D = \frac{L}{20} + 0.6 \text{ m (min)} $$

for simply supported slab (L in m).

• With Wearing Coat:

  • Include 80 mm wearing coat in dead load.

Reinforcement Design

• Bending Moment:

  • Continuous slab: $$\displaystyle M_{\text{max}} = \frac{w L^2}{10} $$ (mid-span).

  • Simply supported: $$\displaystyle M_{\text{max}} = \frac{w L^2}{8} $$.

• Shear Reinforcement:

  • Stirrups if shear stress > 0.5 τ_c (IS 456).

Wearing Coat

• Thickness: 80 mm (as per question).

• Effect on Load Distribution:

  • Increases dead load, reduces effective span for live load distribution.

Detailing

• Main Steel:

  • At tension face, curtailed at L/6 from support.

• Distribution Steel:

  • 0.12% of gross area (transverse).

• Development Length:

  • At supports, $$\displaystyle L_d \geq \text{effective depth} $$.

\boxed{\text{Note: All designs to conform to IS 456, IS 3370 (water tanks), IRC 6 (bridges), IS 1343 (prestressed).}}