5. Design of Structures (ACiE05)

5.1 Loads and Load Combinations

Understanding and accurately calculating loads is fundamental to structural design. Structures must be designed to safely resist all foreseeable loads throughout their lifespan.

Dead Load (DL)

Dead load consists of the self-weight of the structure and all permanent attachments. It is calculated based on the material densities and dimensions of the structural elements.

• Beams: Self-weight = (width x depth) x density of concrete.
• Slabs: Self-weight = (thickness x 1m x 1m) x density of concrete per unit area.
• Columns: Self-weight = (cross-sectional area x height) x density of concrete.

Typical density of Reinforced Cement Concrete (RCC) is 24 kN/m³.

Imposed/Live Load (LL)

Imposed loads are variable loads due to the occupancy and use of the building. These are specified by national codes (e.g., NS 105, IS 875 Part 2).

• Residential Buildings: Typically 2.0 kN/m² for floors, 1.5 kN/m² for roofs.
• Office Buildings: 2.5 - 4.0 kN/m² depending on specific area (e.g., general office, storage).
• Hospitals: 2.0 - 5.0 kN/m² (e.g., wards, operating rooms).

Wind Load (WL)

Wind load is a dynamic load caused by the movement of air. Its calculation involves several factors as per NS 030 or IS 875 Part 3.

Design Wind Speed (Vz):

Vz = Vb * k1 * k2 * k3

Where:

• Vb = Basic wind speed (m/s) for a given geographical location.
• k1 = Importance factor (depends on the risk associated with the failure of the building, typically 1.0 for general buildings, 1.15 for important structures).
• k2 = Terrain category and height factor (accounts for ground roughness and building height).
• k3 = Topography factor (accounts for hills, valleys, etc.).

Wind Pressure (pz):

pz = 0.6 * Vz² (in N/m²)

Where Vz is the design wind speed in m/s.

Snow Load (SL)

Snow load is the weight of accumulated snow on roofs. Its calculation is based on ground snow load, roof shape, and exposure, as per NS 031 or IS 875 Part 4.

Ps = μ * S0 * I

Where:

• Ps = Design snow load on the roof.
• μ = Shape coefficient (depends on roof slope and geometry).
• S0 = Ground snow load (specified for different regions).
• I = Importance factor (similar to wind load).

Earthquake Load (EQ)

Earthquake loads are inertial forces generated in a structure due to ground motion. Design for seismic forces is critical in seismically active regions like Nepal.

• Seismic Zone Map of Nepal: Nepal is divided into different seismic zones based on expected ground acceleration, influencing the design seismic coefficient.
• Seismic Coefficient Method (Static Analysis): This method calculates the total design lateral force (base shear) using a seismic coefficient.

  Vb = Ah * W

  Where Vb is the design base shear, W is the seismic weight of the building, and Ah is the horizontal seismic coefficient.

  Ah = (Z * I * Sa) / (2 * R * g) (as per IS 1893)

  Where Z = Zone factor, I = Importance factor, Sa/g = Average response acceleration coefficient, R = Response reduction factor.

• Response Spectrum Method (Dynamic Analysis): A more refined method, especially for irregular or tall structures, where the maximum response of a structure to an earthquake is estimated using a response spectrum curve.

Load Combinations (Limit State)

Structures must be designed to safely resist the most critical combination of loads. Limit state design uses partial safety factors for loads (γf) to account for uncertainties. Common load combinations as per NS/IS codes:

• 1.5 (DL + LL)
• 1.5 (DL + QL) (where QL refers to imposed/live load)
• 1.2 (DL + LL + EQ)
• 1.2 (DL + LL + WL)
• 1.5 (DL + EQ)
• 1.5 (DL + WL)
• 0.9 DL + 1.5 EQ (for overturning/uplift checks)
• 0.9 DL + 1.5 WL (for overturning/uplift checks)

5.2 Concrete Technology

Concrete is a composite material widely used in construction. Its properties are influenced by its constituent materials and mix proportions.

Materials

• Cement:
  • Types: Ordinary Portland Cement (OPC), Portland Pozzolana Cement (PPC), Rapid Hardening Cement.
  • Grading: Fineness (specific surface area).
  • Properties: Setting time, compressive strength, heat of hydration.
• Aggregates:
  • Coarse Aggregates: (e.g., crushed stone, gravel) - provide bulk and strength. Grading (size distribution), shape, surface texture, strength, durability are important.
  • Fine Aggregates: (e.g., sand) - fill voids, improve workability. Grading, fineness modulus, silt content are crucial.
• Water: Must be clean, free from deleterious substances (oils, acids, alkalis, salts, organic matter). Potable water is generally suitable. pH should be between 6 and 9.
• Admixtures: Chemicals added to concrete to modify its properties.
  • Plasticizers/Superplasticizers: Reduce water requirement for a given workability or increase workability for a given water content.
  • Retarders: Increase setting time, useful in hot weather or for long hauls.
  • Accelerators: Decrease setting time, useful in cold weather or for early strength gain.

Properties of Fresh Concrete

• Workability: Ease with which concrete can be mixed, transported, placed, and compacted without segregation.
  • Slump Test: Measures consistency (slump cone). Higher slump indicates higher workability.
  • Compaction Factor Test: Measures degree of compaction achieved under standard conditions.
  • Vee-Bee Consistometer Test: Measures the time required to remould a concrete frustum into a cylindrical shape, indicating workability for very low slump concrete.
• Setting Time:
  • Initial Setting Time: Time until concrete loses its plasticity (typically > 30 minutes for OPC).
  • Final Setting Time: Time until concrete completely hardens and loses all plasticity (typically < 600 minutes for OPC).

Properties of Hardened Concrete

• Compressive Strength: Most important property, determined by cube or cylinder tests. Influenced by w/c ratio, aggregate quality, compaction, and curing.
• Tensile Strength: Much lower than compressive strength (approx. 10-15% of compressive strength). Measured by split cylinder test or flexural strength test.
• Modulus of Elasticity (Ec): Relates stress to strain.

  Ec = 5000 * sqrt(fck) (as per IS 456)

  Where fck is the characteristic compressive strength of concrete in N/mm².

Mix Design (IS/NS Code Method)

The process of selecting suitable ingredients of concrete and determining their relative proportions to produce concrete of certain minimum strength and durability as economically as possible.

1. Determine target mean strength (fck + 1.65 * std_dev).
2. Select water-cement ratio based on target strength and durability requirements.
3. Estimate water content for required workability.
4. Calculate cement content.
5. Determine aggregate content (fine and coarse) using aggregate grading limits.
6. Conduct trial mixes to adjust proportions and verify properties.

Testing

• Cube Test: Standard 150mm cubes tested at 7 and 28 days for compressive strength.
• Cylinder Test: Standard cylinders (e.g., 150mm diameter x 300mm height) tested for compressive strength, often yielding slightly lower results than cube tests (fck_cylinder ≈ 0.8 * fck_cube).
• Non-Destructive Testing (NDT):
  • Rebound Hammer Test: Measures surface hardness, providing an estimate of compressive strength.
  • Ultrasonic Pulse Velocity (UPV) Test: Measures the velocity of ultrasonic pulses through concrete, indicating concrete quality and uniformity.

Quality Control

Ensuring that the concrete produced meets the specified requirements.

• Cube Strength Results: Regular testing of concrete cubes from site batches.
• Acceptance Criteria: As per codes (e.g., IS 456), typically based on the average strength of a group of cubes and the strength of individual cubes (e.g., average of 3 consecutive samples > target strength, and no individual sample < target strength - 4 N/mm²).

5.3 RCC Structures-1

Reinforced Cement Concrete (RCC) combines the compressive strength of concrete with the tensile strength of steel.

Working Stress Method (WSM)

An older design method based on elastic theory, ensuring stresses in concrete and steel remain below permissible limits under service loads.

• Permissible Stresses: Fraction of characteristic strength (e.g., σcbc for concrete in bending compression, σst for steel in tension).
• Modular Ratio (m): Ratio of modulus of elasticity of steel to concrete.

  m = 280 / (3 * σcbc) (as per IS 456 for concrete grades M20 and above)

• Neutral Axis Depth (n): Calculated by equating moments of areas of concrete and transformed steel section about the neutral axis.
• Moment of Resistance (Mr): Calculated based on the stress distribution in the concrete and steel.

Limit State Method (LSM)

The modern design method, which considers the ultimate strength of materials and ensures that the structure remains safe under ultimate loads and serviceable under service loads.

• Partial Safety Factors (γm for material, γf for load):
  • γm for concrete = 1.5, for steel = 1.15.
  • γf for loads = 1.5 for DL+LL, 1.2 for DL+LL+EQ/WL.
• Stress-Strain Curve: Non-linear stress-strain curves are used for both concrete (parabolic up to 0.002 strain, then constant up to 0.0035) and steel (elastoplastic with strain hardening).

Design of Beams

• Singly Reinforced Beams: Designed when the concrete in compression is sufficient to resist the compressive force.

  Ultimate Moment of Resistance (Mu) for an under-reinforced section (as per IS 456):

  Mu = 0.87 * fy * Ast * d * (1 - (Ast * fy) / (b * d * fck))

  Where fy = characteristic strength of steel, Ast = area of steel in tension, d = effective depth, b = width of beam, fck = characteristic strength of concrete.

• Doubly Reinforced Beams: Required when the beam size is restricted, and the concrete section is insufficient to resist the compressive force, necessitating compression reinforcement.
• L- and T-Flanged Beams: Beams cast monolithically with slabs, where a portion of the slab acts as a flange, increasing the effective width of the compression zone. The effective width of the flange is calculated as per code provisions.

Design of Slabs

• One-Way Slabs: Supported on two opposite sides, primarily bending in one direction. Designed as wide beams. Reinforcement is provided mainly perpendicular to the supports.
• Two-Way Slabs: Supported on all four sides, bending in both directions.
  • Marcus Formula / Coefficient Method: Used to determine bending moments in two perpendicular directions based on aspect ratio and support conditions.
  • Reinforcement Detailing: Main reinforcement in both directions, distribution reinforcement, and special reinforcement at corners to resist torsion.

Analysis of RC Beams

• Bending: Calculation of internal stresses and moments to ensure the section can resist the applied bending moment.
• Shear: Checking the beam's capacity to resist transverse forces. Shear resistance is provided by concrete and shear reinforcement (stirrups).
• Deflection: Ensuring that deflections under service loads are within permissible limits to avoid aesthetic and serviceability issues. (Span/depth ratios are primary checks).
• Bond and End Anchorage: Ensuring proper transfer of stress between steel and concrete, requiring adequate development length for reinforcement bars.

Shear Reinforcement

Provided to resist shear forces that concrete alone cannot handle.

• Vertical Stirrups: Most common form, placed vertically around the main reinforcement.
• Inclined Stirrups: Also known as bent-up bars, effectively resist diagonal tension.
• Design involves calculating the shear force to be resisted by stirrups (Vs = Vu - Vc, where Vu is ultimate shear force and Vc is concrete shear capacity) and then determining the required spacing of stirrups.

Code Provisions

All RCC design must comply with relevant national codes, such as NS 205 (Code of Practice for Plain and Reinforced Concrete) and IS 456 (Plain and Reinforced Concrete - Code of Practice), which specify material properties, design procedures, and detailing requirements.

5.4 RCC Structures-2

Design of Columns

Columns are vertical compression members supporting beams and slabs.

• Short vs. Long Columns: Differentiated by slenderness ratio (L_eff / D or L_eff / b). Short columns fail by crushing, long columns fail by buckling.
• Axially Loaded Columns: Designed for pure compression.

  Ultimate axial load capacity (Pu) for a short column with minimum eccentricity:

  Pu = 0.4 * fck * Ac + 0.67 * fy * Asc

  Where Ac = area of concrete, Asc = area of steel in compression.

• Uniaxial and Biaxial Bending: Most columns are subjected to axial load and bending moments. Uniaxial bending occurs when moment is about one axis, biaxial when moments are about both axes.
  • Interaction Diagrams: Graphical tools used to design columns subjected to combined axial load and bending moment, showing the permissible combinations of axial load and moment.

Design of Isolated Footings

Foundations that support individual columns.

• Types: Square, rectangular, stepped, sloped.
• Design Considerations:
  • Bearing Capacity: Ensure soil can safely support the load.
  • Punching Shear: Check for shear failure around the column perimeter.
  • One-Way Shear: Check for beam action shear failure.
  • Bending Moment: Design reinforcement for bending.

Design of Combined Footings

Foundations that support two or more columns.

• Strap Footing: Used when one column is near a property line, connecting an exterior column footing to an interior column footing via a strap beam.
• Common Footing (Mat/Raft Footing): A large slab supporting multiple columns or walls, used when soil bearing capacity is low or column loads are heavy.

Pre-stressed Concrete

Concrete in which internal stresses are introduced to counteract the stresses resulting from external loads, thereby reducing or eliminating tensile stresses.

• Concept: Applying a compressive force to the concrete before or during the application of external loads. This enhances the load-carrying capacity and crack resistance.
• Methods:
  • Pre-tensioning: Tendons are tensioned before concrete is cast. Once concrete hardens, the tension is released, transferring prestress to the concrete via bond.
  • Post-tensioning: Tendons are tensioned after concrete has hardened. Ducts are cast into the concrete, tendons are threaded through, tensioned, and then anchored. The ducts may or may not be grouted.
• Losses of Prestress: The initial prestressing force reduces over time due to various factors.
  • Elastic Shortening: Shortening of concrete when prestress is applied.
  • Creep of Concrete: Time-dependent deformation of concrete under sustained stress.
  • Shrinkage of Concrete: Volume reduction of concrete due to loss of moisture.
  • Relaxation of Steel: Time-dependent reduction in stress in the prestressing steel at constant strain.
• Design Principles: Based on elastic theory for serviceability limit states and ultimate strength theory for ultimate limit states, ensuring adequate compressive stress in concrete and preventing cracking under service loads.

5.5 Steel Structures

Steel structures are known for their high strength-to-weight ratio, ductility, and speed of construction.

Standard Sections and Built-up Sections

• Standard Sections: Commercially available rolled steel sections.
  • I-section (beams, columns)
  • Channel section (purlins, light beams)
  • Angle section (trusses, bracing)
  • T-section
  • Plate (for built-up sections, base plates)
• Built-up Sections: Formed by welding or bolting together plates and/or standard sections to achieve larger sections or specific properties (e.g., plate girders, box columns).

Design of Bolted Connections

Connections using bolts to transfer forces between members.

• Bearing Type Connections: Load transfer occurs by bearing of bolts against the plate and shear in the bolt shank. Bolts are snug-tight.
• Friction/Grip Type Connections (HSFG bolts): High Strength Friction Grip bolts are tightened to a specified tension, creating clamping force that transfers load through friction between connected plates.
• Bolt Capacity: Determined by the minimum of shear capacity (Vsb = (fub * Anb) / (sqrt(3) * γmb)) and bearing capacity (Vpb = 2.5 * kb * d * t * fu / γmb) per bolt.
• Pitch and Edge Distance: Minimum and maximum spacing requirements for bolts to prevent tearing of plates and ensure proper load distribution, as per NS 045 or IS 800.

Design of Welded Connections

Connections formed by fusing metal parts together using heat.

• Fillet Weld: Triangular cross-section weld, commonly used for connecting overlapping plates or members at an angle.
• Butt Weld: Joins two members end-to-end, providing a smooth transition. Can be full penetration or partial penetration.
• Weld Strength: Calculated based on the effective throat thickness, effective length, and ultimate tensile strength of the weld material.
• Effective Throat Thickness: The minimum distance from the root to the face of the weld (for fillet weld, typically 0.7 * weld_leg_size).

Design of Simple Elements

• Ties (Tension Members): Designed to resist axial tensile forces. Checks include gross section yielding, net section rupture (accounting for bolt holes), and block shear failure.
• Struts (Compression Members): Designed to resist axial compressive forces.
  • Buckling: The primary failure mode for slender compression members.
  • Slenderness Ratio: Ratio of effective length to minimum radius of gyration (λ = Le / r_min), which dictates buckling behavior.

Axially Loaded Columns

Columns primarily subjected to axial compression.

• Euler Load (Critical Buckling Load): Theoretical load at which a perfectly straight, elastic column will buckle.

  Pe = (π² * E * I) / (Le²)

  Where E = modulus of elasticity of steel, I = moment of inertia, Le = effective length.

• Effective Length (Le): The length of an equivalent pin-ended column that has the same buckling load as the actual column with its end restraints. Depends on boundary conditions.
• Buckling About Both Axes: Columns must be checked for buckling about both major (xx) and minor (yy) axes, as the critical buckling load is governed by the axis with the larger slenderness ratio.

Column Bases

Interface between steel columns and concrete foundations.

• Grillage Foundation: Consists of one or more tiers of steel beams encased in concrete, used to spread heavy column loads over a larger area.
• Base Plate Design: A steel plate connecting the column to the concrete pedestal, designed to distribute the column load (axial, moment) uniformly over the concrete area, preventing crushing of concrete.

Code References

Design of steel structures in Nepal and India follows codes like NS 045 (Code of Practice for Use of Structural Steel in General Building Construction) and IS 800 (Code of Practice for General Construction in Steel).

5.6 Timber and Masonry Structures

Traditional and widely used construction materials, particularly in Nepal.

Design Principles of Timber Beams

Timber beams are designed for bending, shear, and deflection, considering the anisotropic nature of wood.

• Bending Stress:

  σb = M / Z (where M is bending moment, Z is section modulus)

  Must be less than permissible bending stress (fbt).

• Shear Stress:

  τ = (V * Q) / (I * b) (where V is shear force, Q is first moment of area, I is moment of inertia, b is width)

  For rectangular sections, maximum shear stress is 1.5 * (V / A). Must be less than permissible shear stress (fsv).

• Deflection: Must be within permissible limits (e.g., Span/300) to ensure serviceability, using modulus of elasticity (E) and moment of inertia (I).

Design of Timber Columns

Timber columns are designed primarily for axial compression, considering buckling behavior.

• Euler Load: Applicable for very slender timber columns, similar to steel.
• Permissible Stress Method: Compressive stress in the column must be less than the permissible compressive stress, which is reduced for slender columns based on their slenderness ratio (L_eff / r).

Design of Masonry Structures

Masonry structures are built using units like bricks or stones bonded with mortar.

• Mandatory Rules of Thumb: Simple prescriptive rules for earthquake-resistant masonry, often found in local building codes (e.g., minimum wall thickness, maximum opening sizes, provision of horizontal bands).
• Nepal Building Code (NBC): Provides specific guidelines for the seismic design and construction of masonry buildings in Nepal, including requirements for confined masonry and reinforced masonry.

Properties of Masonry

• Compressive Strength (fm): Primarily depends on the strength of masonry units, mortar strength, and workmanship. It is significantly lower than the compressive strength of the individual units.
• Modulus of Elasticity (Em): Varies widely based on materials and construction, generally lower than concrete.

Failure Modes of Masonry Structures

• Diagonal Tension (Shear Failure): Cracking along the diagonal due to shear forces, common in earthquakes.
• Toe Crushing: Crushing of masonry at the corners or ends of walls under high compressive stresses, often due to combined axial load and bending.
• Sliding: Failure along horizontal mortar joints due to excessive shear stress, especially in poor quality mortar or unreinforced masonry.

Mortar Types and Properties

Mortar is a mixture of binding material, fine aggregate, and water, used to bond masonry units.

• Mud Mortar: Made from soil and water, low strength, used in traditional or low-cost construction.
• Lime Mortar: Made from lime, sand, and water. Offers good workability and breathability, hardens slowly.
• Cement Mortar: Made from cement, sand, and water (and sometimes lime for workability). High strength, fast setting.
  • Proportions: Typically 1:3, 1:4, 1:6 (cement:sand) by volume.
  • Strength: Increases with cement content and decreases with water content.
  • Uses: Most common for load-bearing masonry, reinforced masonry, and modern construction.