Structural Design and Drawing (RCC-II) (CE-702 (D)) - Unit 3 Short Notes

UNIT 3: DESIGN OF SPECIAL STRUCTURES AND PRESTRESSED CONCRETE

I. RETAINING WALLS

Types and Selection

Earth Pressure Theories

Rankine’s Theory (Active/Passive)

• Active Pressure (soil pushes wall):

$$K_a = \frac{1 - \sin \phi}{1 + \sin \phi} = \tan^2\left(45^\circ - \frac{\phi}{2}\right)$$

For cohesive soil: $$\displaystyle P_a = \gamma z K_a - 2c\sqrt{K_a} $$ (at surface, pressure = $$\displaystyle -2c\sqrt{K_a} $$).

• Passive Pressure (wall pushes soil):

$$K_p = \frac{1 + \sin \phi}{1 - \sin \phi} = \tan^2\left(45^\circ + \frac{\phi}{2}\right)$$

• Assumptions: Soil cohesionless, wall frictionless, vertical backfill, ground horizontal.

Coulomb’s Wedge Theory

• Considers wall friction ($\delta$) and inclined backfill ($\beta$).

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

• More realistic but iterative; used for high walls or sloping backfill.

[!TIP] Exam Focus: Rankine for level backfill, Coulomb for sloping. Remember sign of cohesive term in active pressure.

Stability Checks

1. Overturning: Factor of Safety (FOS) ≥ 1.5

   FOS = $$\displaystyle \frac{\text{Resisting Moment}}{\text{Overturning Moment}} $$

2. Sliding: FOS ≥ 1.4

   FOS = $$\displaystyle \frac{\mu R_v + P_p}{P_h} $$, where $\mu$ = friction coefficient, $$\displaystyle P_p $$ = passive pressure.

3. Bearing Pressure:

   • Eccentricity $$\displaystyle e < B/6 $$ (no tension).

   • Pressure distribution: $$\displaystyle q_{max/min} = \frac{W}{B} \left(1 \pm \frac{6e}{B}\right) $$

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

Design of Cantilever Retaining Wall

Stem Design

• Thickness at base: $0.05H$ to $0.07H$ (H = height above base).

• Reinforcement: Design for maximum bending moment at base from active pressure.

  $$\displaystyle M_{max} = \frac{1}{2} K_a \gamma H^2 \times \frac{H}{3} $$ (for triangular pressure).

• Main steel: $$\displaystyle A_{st} = \frac{M}{0.87 f_y (d - 0.42 x)} $$ (limit state).

Base Slab

• Heel: Subjected to downward pressure from soil + self-weight.

  Design for bending (negative moment at stem face) and shear.

• Toe: Subjected to upward soil pressure.

  Design for bending (positive moment at stem face) and shear.

• Thickness: Minimum 0.3m; shear check critical at stem face.

Shear Key

• Provided at toe-base junction to increase sliding resistance.

  Design for shear: $$\displaystyle V = \mu (W + P_p) - P_h $$; provide key depth $$\displaystyle d_k $$ such that shear stress $$\displaystyle < \tau_c $$.

Construction Details

• Joints: Construction joints with keyways; water stops.

• Drainage: Weep holes (75mm dia, 300mm c/c, 4% slope) with filter media (gravel/sand).

• Waterproofing: Impervious membrane or plaster on backfill side; coping on top.

II. WATER TANKS

Types of Water Tanks

Loads and Load Combinations (IS 3370)

• Hydrostatic: Full/empty condition (worst for wall/base).

• Dead Load: Self-weight, roof slab.

• Live Load: On roof (2.5 kN/m² if accessible).

• Seismic: IS 1893; horizontal/vertical acceleration.

• Temperature/Shrinkage: For restrained tanks.

• Combinations: 1.5(DL+LL), 1.2(DL+LL+WL), 1.5(DL+WL) etc.

Design of Circular Water Tank (Rigid Base)

Wall Design

• Hoop Tension (at depth h): $$\displaystyle T = \gamma_w h r $$ per unit height.

  $$\displaystyle A_{st} = \frac{T}{0.4 f_y} $$ (limit state; 0.4 for steel stress in tension).

• Vertical Bending: Due to hydrostatic pressure on wall strip (fixed at base, free at top).

  Max +ve moment at base: $$\displaystyle M = \frac{w h^2}{12} $$ (w = water pressure per unit height).

• Thickness: $t \geq 100$ mm; $$\displaystyle t \geq \frac{h}{30} $$ for plain concrete; increased for reinforcement.

Base Slab

• Flexible Base (assumed): Wall and base act independently.

  Base designed for radial and circumferential moments from soil pressure + water pressure.

• Continuous Base (rigid): Wall and base act monolithically; edge moments reduced.

Ring Beam (Top)

• Provided if opening > 1/3 diameter.

  Design for hoop thrust from wall + wind/seismic.

Design of Intze Tank

Top Dome

• Shape: Circular (radius $$\displaystyle R_d $$) or parabolic ($$\displaystyle y = \frac{4h}{d^2}x^2 $$).

  Membrane stresses:

  Meridional: $$\displaystyle N_\phi = \frac{\gamma_w h r}{2 \sin \phi} $$

  Circumferential: $$\displaystyle N_\theta = \frac{\gamma_w h r}{2} \tan \phi $$

• Thickness: Based on meridional stress; min 100 mm.

Ring Beam (Below Dome)

• Location: At dome-cylinder junction.

  Thrust from dome: $$\displaystyle H = N_\phi \sin \phi $$ at springing.

  Design for combined bending and axial.

Cylindrical Wall

• Similar to circular tank but with reduced height (below ring beam).

  Hoop tension from water pressure + ring beam thrust.

Joints and Waterproofing

• Construction Joints: Keyways, water stops (PVC/metal).

• Expansion Joints: Flexible filler, sealant; allow movement.

• Waterproofing: External coating (bitumen, epoxy), internal plaster.

• Leakage Prevention: Proper compaction, curing, crack control.

III. SILOS

Pressure Distribution (Janssen’s Equation)

• Lateral Pressure at depth z:

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

where $\gamma$ = unit weight, $R$ = radius, $\mu$ = coefficient of friction.

• Vertical Pressure:

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

• Max Lateral Pressure (at great depth): $$\displaystyle p_{h,max} = \frac{\gamma R}{\mu} $$ (independent of height).

• Effect of Filling/Emptying:

  • Filling: Janssen pressure (frictional drag).

  • Emptying: Rankine active pressure if mass flow; $$\displaystyle p_h = K_a \gamma z $$ (higher than Janssen near top).

Design of Cylindrical Wall

• Horizontal Reinforcement (hoop tension):

  $$\displaystyle T = p_h \times r $$ per unit height; $$\displaystyle A_{sh} = \frac{T}{f_y} $$.

• Vertical Reinforcement: For bending due to differential settlement + vertical load.

  Provide nominal 0.25% of concrete area.

• Wall Thickness: Based on hoop tension; min 150 mm for large silos.

Factors Influencing Pressures

• Coefficient of Friction ($\mu$): Between stored material and wall.

• Angle of Repose ($\phi$): Affects $$\displaystyle K_a $$ for emptying.

• Unit Weight ($\gamma$): Directly proportional.

• Rate of Filling/Emptying: Dynamic effects; increase pressure by 10-30%.

Hopper Bottom Design

• Shape: Transition from cylindrical to outlet; conical or pyramidal.

• Angle: > angle of repose for mass flow; steeper for cohesive materials.

• Reinforcement: For bending and shear; provide stiffeners if span large.

IV. PRESTRESSED CONCRETE

Basic Concept

• Pre-compression: Apply compressive stress ($$\displaystyle f_{cp} $$) to counteract tensile stress from external loads.

• Effective Prestress: $$\displaystyle f_{pe} = f_{pi} - \text{losses} $$ (stress in tendon at service).

Methods of Prestressing

Systems of Prestressing

• Freyssinet: Multi-wire cables in steel duct; conical anchor.

• Gifford-Udall: Single wires in sheathing; wedge anchor.

• Magnel-Blaton: Parallel wires; hydraulic jacking from both ends.

• B.B.R.V.: Bar system with nut anchor.

Advantages and Disadvantages

Stress Concept & Losses

Transfer of Prestress

• Bonded: Stress transferred by bond along length.

• Unbonded: Stress transferred only at end anchorages.

Prestress Losses (Total = Sum; typical 15-30%)

1. Elastic Shortening: $$\displaystyle \Delta f_{pES} = \frac{E_p}{E_c} \cdot f_{cp} $$ (simultaneous tension).

2. Creep of Concrete: $$\displaystyle \Delta f_{pCR} = \phi \cdot f_{cp} $$ ($\phi$ = creep coefficient).

3. Shrinkage of Concrete: $$\displaystyle \Delta f_{pSR} = \epsilon_{sh} E_p $$.

4. Relaxation of Steel: $$\displaystyle \Delta f_{pR} $$ (from manufacturer’s curve).

5. Friction (post-tensioning): $$\displaystyle \Delta f_{pF} = \sum (K x + \mu \alpha) $$.

6. Wedge Draw-in (post-tensioning): $$\displaystyle \Delta f_{pD} $$ (anchor slip).

Effective Prestress:

$$f_{pe} = f_{pi} - \Delta f_p$$

Tendon Profiles

• Concordant: All tendons have same eccentricity diagram → no secondary moments.

• Non-concordant: Different profiles → induce secondary moments.

Types of Prestressing

1. Full Prestressing: No tensile stress under service loads (Class 1, IS 1343).

2. Partial Prestressing: Controlled tensile stress allowed (Class 2, 3).

   Permits higher prestress; used for crack control.

3. Composite Prestressing: Prestressed + non-prestressed reinforcement.

V. BRIDGE DESIGN

Types of Bridges

IRC Loading (IRC 6)

• Class AA:

  • Tracked vehicle: 700 kN (axle load 140 kN each).

  • Impact factor: 25% for spans ≤ 45m.

• Class A:

  • Standard truck: 70 kN (axle load 14 kN each).

  • Impact factor: 25% for spans ≤ 45m.

• Load Distribution to Deck Slab:

  Effective width $$\displaystyle b_{eff} = b_0 + L_0/2 $$ (for slabs), where $$\displaystyle b_0 $$ = width of tire, $$\displaystyle L_0 $$ = span.

Design of Solid Slab Bridge

Effective Span:

• For simply supported: $$\displaystyle L_{eff} = \text{clear span} + \text{width of bearing} $$.

• Depth: $D \geq L/20$ (IRC); typically 0.6-0.8m for 8m span.

Reinforcement Detailing

• Bending Moment: Design for maximum moment from wheel load + impact.

  $$\displaystyle M_{max} = \frac{P}{2} \times \frac{S}{2} $$ (P = wheel load, S = effective width).

• Shear: Check at $d$ from support; provide shear reinforcement if $$\displaystyle V > \tau_c b d $$.

• Reinforcement:

  • Main steel: $$\displaystyle A_{st} = \frac{M}{0.87 f_y z} $$

  • Distribution steel: 0.12% of gross area (IRC).

Wearing Coat & Parapet

• Wearing Coat: 50-80 mm bituminous concrete; provides smooth surface.

• Parapet: 0.8-1.0m height; reinforced concrete; designed for impact load (IRC 6).

Design Example: Simply Supported Solid Slab (Class AA)

1. Data: Clear span = 8m, roadway width = 7.5m, wearing coat = 80mm.

2. Effective Span: $$\displaystyle L_{eff} = 8.0 + 0.2 = 8.2 $$ m (assume bearing width 0.2m).

3. Depth: $$\displaystyle D = 8.2/20 = 0.41 $$ m → adopt 450 mm (including wearing coat).

4. Loads:

   • DL: Slab (25 kN/m³ × 0.37m × 1m) = 9.25 kN/m.

   • LL (Class AA tracked): 700 kN over 3.0m width → distribute to 7.5m width.

   Impact = 25%.

5. Maximum Moment: At mid-span from wheel load.

   Calculate $$\displaystyle b_{eff} $$ per wheel, then $$\displaystyle M_{max} $$.

6. Steel Area: Compute $$\displaystyle A_{st} $$ using M20, Fe415.

7. Shear Check: At support; provide shear reinforcement if needed.

8. Detailing: Main bars (dia 12-16mm @ 150-200mm c/c); distribution bars (10mm @ 200mm c/c).

[!TIP] Common Pitfall: Forgetting impact factor on live load; incorrect effective width calculation for wheel load.

Note: All designs to be as per relevant IS codes (IS 456, IS 3370, IS 1343, IRC 6). Use limit state method for RCC design.