5.1 Loads and Load Combinations

5.1 Loads and Load Combinations

Introduction to Structural Loads

The primary purpose of a structure is to safely carry and transfer all applied forces (loads) to the ground. These loads can be permanent, variable, or accidental, and their nature, magnitude, and direction govern the entire structural design process. Loads are not applied in isolation; they occur simultaneously in various combinations. Understanding the characteristics of each load type and the principles of combining them realistically is fundamental to ensuring safety, serviceability, and economy in structural design as per standards like NBC (Nepal Building Code) 105:2020 and IS 875.

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1. Types of Loads

Loads are classified based on their origin, duration, and nature of application.

1.1 Dead Load (DL) / Permanent Action

1. Definition: The self-weight of all permanent, stationary components of the structure. These loads are constant in magnitude, position, and direction throughout the structure's life.

2. Characteristics:

   • Constant in Time: Does not vary (except for minor changes due to moisture absorption or creep).

   • Fixed in Location: Acts at specific, unchanging points.

   • Vertical Gravity Load: Primarily acts downwards.

3. Components:

   • Structural Members: Weight of beams, columns, slabs, walls, foundations.

   • Permanent Non-Structural Elements: Weight of floor finishes, ceiling, fixed partitions, permanent mechanical/electrical equipment, waterproofing layers.

4. Calculation:

   • Determined from the dimensions and density of materials.

   • $\text{Dead Load} = \text{Volume} \times \text{Density (Unit Weight)}$

   • Standard unit weights ($\gamma$) are provided in codes (e.g., IS 875-Part 1):

     • Reinforced Concrete: 25 kN/m³

     • Brick Masonry: 18-20 kN/m³

     • Floor Finish (screed): 20-24 kN/m³

5. Significance: Forms a significant portion of the total load, especially for heavy structures. It is always present and must be accurately estimated.

1.2 Imposed Load (IL) / Live Load (LL)

1. Definition: Loads that are not permanent and arise from the intended use or occupancy of the structure. They are variable in magnitude, position, and over time.

2. Characteristics:

   • Variable in Time and Position: Can change in intensity and location (e.g., people moving, furniture being rearranged).

   • Dynamic or Static: Can be static (furniture) or have dynamic effects (crowds, machinery).

   • Primary Direction: Usually vertical, but can have horizontal components (e.g., braking forces).

3. Types:

   • Floor Live Loads: Due to occupants, furniture, movable equipment in residential, office, commercial buildings. Example: 2.0 kN/m² for residential, 3.0-5.0 kN/m² for shops.

   • Roof Live Loads: Due to maintenance personnel, equipment. Typically lower than floor loads.

   • Concentrated Loads: Specific heavy point loads (e.g., from machinery, vehicle wheels).

   • Impact Loads: Dynamic effect due to sudden application (e.g., elevators, machinery).

4. Code Values: Prescribed minimum values are given in IS 875-Part 2 and NBC 105. These are based on the type of occupancy and are conservative estimates to cover most use cases.

5. Significance: Governs the design of floor systems for deflection and vibration (serviceability). May also control design in lightly loaded structures.

1.3 Wind Load (WL)

1. Definition: Loads caused by the pressure or suction exerted by moving air (wind) on the surfaces of a structure.

2. Characteristics:

   • Dynamic and Fluctuating: Wind speed and direction are highly variable, causing fluctuating pressures.

   • Horizontal and Uplift: Can act horizontally (causing sway) or cause uplift on roofs.

   • Pressure and Suction: Can be positive (pressure) on windward faces and negative (suction) on leeward faces and roofs.

3. Governing Factors (as per IS 875-Part 3):

   • Basic Wind Speed ($V_b$): 3-second gust speed at 10m height in open terrain, mapped for different zones (e.g., 33 m/s, 39 m/s, 44 m/s, 49 m/s, 55 m/s in NBC).

   • Risk Coefficient ($k_1$): Based on the structure's design life and importance.

   • Terrain, Height, and Structure Size Factor ($k_2$): Accounts for roughness of terrain (Category I-IV) and building height.

   • Topography Factor ($k_3$): For hills, ridges, or escarpments.

   • Design Wind Speed: $V_z = V_b \cdot k_1 \cdot k_2 \cdot k_3$

   • Design Wind Pressure: $p_z = 0.6 \cdot V_z^2$ (where $p_z$ is in N/m²).

4. Pressure Coefficients ($C_p$ & $C_{pi}$): External ($C_p$) and internal ($C_{pi}$) pressure coefficients are used to calculate the net pressure on cladding and the overall force on the structure.

5. Significance: Critical for the design of tall buildings, long-span roofs, chimneys, towers, and cladding. Governs lateral stability, overturning, and deflection.

1.4 Snow Load (SL)

1. Definition: The vertical load imposed by the weight of snow accumulation on a roof or other horizontal/ inclined surfaces.

2. Characteristics:

   • Variable: Depends on snowfall intensity, duration, wind (which can cause drifting), and temperature (melting/refreezing).

   • Accumulates: Load increases with snowfall duration if melting does not occur.

3. Calculation (IS 875-Part 4):

   • Ground Snow Load ($S_g$): Basic snow load on ground at the site location, based on historical data.

   • Roof Snow Load ($S$): $S = \mu \cdot C_e \cdot C_t \cdot S_g$

     • Shape Coefficient ($\mu$): Depends on roof slope and shape (e.g., 0.8 for flat roofs, reduces for sloped roofs, can be >1.0 for drifts).

     • Exposure Coefficient ($C_e$): Accounts for wind exposure and terrain.

     • Thermal Coefficient ($C_t$): Accounts for heat loss through the roof (less load for heated buildings).

4. Significance: A major design load for structures in mountainous and cold regions like parts of Nepal. Governs the design of roof members and their connections.

1.5 Earthquake Load (EQ/EL) / Seismic Load

1. Definition: Inertia forces generated in a structure when the ground beneath it moves suddenly during an earthquake.

2. Nature: Dynamic, cyclic, and reversible. The load is not a force applied from outside but an internal force resulting from the structure's own mass and stiffness resisting ground motion.

3. Governing Principles:

   • Inertia Force: $F = m \cdot a$, where 'a' is the earthquake-induced ground acceleration.

   • The force depends on:

     • Mass (m): Greater mass leads to greater force.

     • Stiffness (k): Affects how the structure responds to ground motion (period of vibration).

     • Damping: Ability to dissipate vibrational energy.

4. Equivalent Static Force Method (as per IS 1893 & NBC 105):

   • This method simplifies the complex dynamic analysis by representing earthquake effects as a static horizontal force applied at the base of the structure.

   • Design Base Shear ($V_B$): $V_B = A_h \cdot W$

     • Seismic Weight (W): Summation of full dead load + appropriate percentage of imposed load.

     • Design Horizontal Seismic Coefficient ($A_h$): $A_h = \frac{Z \cdot I \cdot S_a/g}{2 \cdot R}$

       • Zone Factor (Z): Represents peak ground acceleration (e.g., 0.36 for Zone V - severe, per NBC).

       • Importance Factor (I): Based on the structure's functional use (e.g., 1.5 for hospitals).

       • Response Reduction Factor (R): Accounts for ductility and overstrength of the structural system (e.g., 5 for Special RC Moment Frame).

       • Spectral Acceleration Coefficient ($S_a/g$): Depends on the natural period (T) of the structure and the soil type (I, II, III, IV).

5. Distribution of Base Shear: The base shear $V_B$ is distributed vertically to each floor level as lateral forces, proportional to the mass and height of that floor.

6. Significance: The most critical lateral load in seismically active regions. Governs member sizes, ductile detailing of reinforcement, and the overall lateral load-resisting system (frames, shear walls, bracing).

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2. Load Combinations

Loads do not occur individually at their maximum values simultaneously. Load combinations define realistic scenarios of concurrent loads for design checks against ultimate limit states (strength) and serviceability limit states (deflection, cracking).

2.1 Fundamental Principle

A structure must be designed to be safe for the most adverse, yet probable, combination of loads it may experience during its design life.

2.2 Partial Safety Factors ($\gamma_f$)

1. Purpose: To account for:

   • Uncertainty in Load ($\gamma_{f,load}$): Possible overloads and imperfect load modeling.

   • Uncertainty in Material Strength ($\gamma_{m}$): Variability in material properties and workmanship.

2. Load Factors ($\gamma_f$) as per IS 456 and NBC:

   • Dead Load (DL): $\gamma_f = 1.5$ (if it increases the stress effect). $\gamma_f = 0.9$ (if it provides beneficial stability).

   • Imposed Load (LL): $\gamma_f = 1.5$.

   • Wind/Earthquake Load (WL/EL): $\gamma_f = 1.5$.

2.3 Common Ultimate Limit State (ULS) Combinations

For reinforced concrete design as per IS 456:2000 and similar codes, the following are typical: (Note: All loads are factored, i.e., multiplied by their respective $\gamma_f$)

1. 1.5 DL + 1.5 LL

   • The most common combination for gravity load design of beams, slabs, and columns where wind/seismic is not dominant.

2. 1.5 DL + 1.5 WL or 1.5 DL + 1.5 EL

   • For design when wind or earthquake load acts alone with dead load.

3. 1.2 DL + 1.2 LL + 1.2 WL/EL

   • For design where gravity loads and one lateral load are considered to act simultaneously.

4. 1.5 DL + 1.05 LL + 1.05 WL/EL

   • An alternative combination for concurrent gravity and lateral loads.

5. 0.9 DL + 1.5 WL/EL

   • Critical for Overturning/Uplift Check. The stabilizing dead load is reduced (0.9), and the destabilizing lateral load is maximized (1.5).

2.4 Key Considerations for Load Combinations

1. Imposed Load Reduction: Codes allow a reduction in the total imposed floor load for the design of columns, foundations, etc., as the probability of all floors being fully loaded simultaneously is low.

2. Simultaneity of Lateral Loads: Wind and Earthquake loads are not considered to act simultaneously in most design codes. The structure is designed for the more severe of the two, unless located in a region where both are significant (e.g., a tall building in a seismic zone with high winds).

3. Direction of Lateral Load: Earthquake/Wind loads must be considered to act in any horizontal direction. Structures must be checked for loading along both principal axes and in some cases, diagonally.

2.5 Serviceability Limit State (SLS) Combinations

These are used to check deflection and cracking, using unfactored (characteristic) loads.

• DL + LL (for long-term deflection).

• DL + 0.8 LL or DL + 0.5 LL (for cracking checks or shorter-term effects).

• DL + WL/EL (for drift/sway limitations).

Conclusion: The process of identifying all applicable loads, estimating their magnitudes as per relevant standards, and applying them in appropriate combinations forms the very foundation of structural design. This systematic approach ensures that the final structure possesses adequate strength to resist collapse (Ultimate Limit State) and remains functional and comfortable for its users under everyday conditions (Serviceability Limit State).