Module 1: Introduction to Structural Analysis and Loads
Structural analysis is the fundamental process of determining how a structure responds to the loads applied to it. In this module, we explore the types of structural systems, identify the design loads defined by building codes, and trace the path these loads take through a structure.
Structural Analysis
The process of calculating the responses of a structure to environmental and operational loads. It involves determining internal forces (shear, axial, moment), stresses, deflections, and stability to ensure the structure is safe and functional.
Limit State Design (LSD) vs Allowable Stress Design (ASD)
Before analyzing the loads themselves, it is important to understand the two primary design philosophies that dictate how those loads will be used to proportion members.
Allowable Stress Design (ASD)
Also known as Working Stress Design. In this older philosophy, structures are designed so that the stresses produced by the expected service loads do not exceed a fraction of the material's failure strength (the allowable stress). It focuses entirely on the elastic range of materials and uses a single factor of safety applied to the material strength.
Limit State Design (LSD)
Also known as Load and Resistance Factor Design (LRFD) in the US. This is the modern philosophy required by the NSCP. It identifies all the possible ways a structure could fail (its "limit states," such as yielding, buckling, or excessive deflection) and applies statistically derived load factors to increase the expected loads, while applying resistance factors to decrease the expected material strengths. It is a probabilistic approach that ensures a more consistent level of safety across different materials and load types.
Key Takeaways
- ASD uses expected service loads and a single factor of safety against failure stress.
- LSD (or LRFD) uses factored loads and resistance factors based on probability to ensure a structure operates safely without reaching various limit states.
- Timber design requires a Load Duration Factor () due to wood's viscoelastic nature.
- Wind load calculations depend on basic wind speed, exposure, and topography.
- Differential settlement induces massive internal forces in indeterminate structures, but merely rotates determinate ones.
Classification of Structures
Structures are generally classified based on their fundamental load-carrying mechanisms. Identifying the type of structure is the first step in determining the appropriate analysis method.
Checklist
- Trusses: Composed of slender members joined at their endpoints. Trusses are analyzed under the assumption that members carry only axial forces (tension or compression), making them highly efficient for spanning large distances.
- Cables: Flexible members carrying loads strictly in tension. They are commonly used in suspension bridges and cable-stayed structures.
- Arches: Curved structures supporting loads primarily through compression. They are highly efficient for masonry and concrete structures.
- Frames: Composed of beams and columns rigidly or semi-rigidly connected. Frames resist loads through a combination of bending, shear, and axial forces, forming the skeleton of most modern buildings.
- Surface Structures: Structures whose thickness is small compared to their other dimensions (e.g., plates, shells, membranes). They carry loads through complex internal membrane stresses and are used for continuous roofs or tanks.
Key Takeaways
- Structures can be classified into trusses, cables, arches, frames, and surface structures based on how they resist loads.
- Timber design requires a Load Duration Factor () due to wood's viscoelastic nature.
- Wind load calculations depend on basic wind speed, exposure, and topography.
- Differential settlement induces massive internal forces in indeterminate structures, but merely rotates determinate ones.
Design Loads per NSCP
According to the National Structural Code of the Philippines (NSCP) and similar international codes like ASCE 7, structures must be designed to withstand various types of loads safely over their lifespan.
Dead Loads
The permanent weights of the building materials. This includes the weight of walls, floors, roofs, ceilings, stairways, built-in partitions, finishes, cladding, fixed service equipment, and the structural frame itself.
Live Loads
Loads produced by the use and occupancy of the building. These loads are movable and transient. Examples include human occupants, furniture, movable equipment, and roof live loads due to maintenance or use. Live loads are typically specified as uniform loads (e.g., kPa) or concentrated point loads.
Environmental Loads
Loads caused by natural forces. These forces can be very complex to evaluate because their magnitudes are mostly unpredictable. Under the National Structural Code of the Philippines (NSCP) and ASCE 7, strict guidelines are provided:
- Wind Loads (WL): Dynamic pressure exerted by wind on the exterior surfaces of the structure. Wind produces positive pressure on windward faces and suction (negative pressure) on leeward faces and roofs.
- Earthquake/Seismic Loads (E): Inertial forces induced in the structure due to ground acceleration during seismic events. Seismic design focuses on mass, stiffness, and ductility.
- Other: Snow loads (where applicable), rain loads (R), and soil/hydrostatic pressure (H).
Load Duration Factor (Timber)
Unlike steel or concrete, wood is a viscoelastic material. Its strength is heavily dependent on how long a load is applied. The allowable stress design of timber structures requires multiplying the base material strength by a Load Duration Factor (). For example, a timber beam can carry a much higher load for 10 minutes (wind gust) than it can for 10 years (dead load) before failing.
Wind Load Fundamentals
Calculating environmental wind loads requires a Basic Wind Speed () based on the geographical location and risk category of the structure. This wind speed is converted into dynamic pressure () and adjusted for factors like:
- Exposure Category: The roughness of the surrounding terrain (e.g., urban vs. open country).
- Topographic Factor: Wind speed-up over hills or ridges.
- Directionality Factor: The probability that the maximum wind speed aligns with the structure's weakest aerodynamic orientation.
Settlement Loads
Differential settlement occurs when different parts of a structure's foundation settle into the soil by unequal amounts. In a statically determinate structure, this simply causes rigid-body rotation without inducing internal stress. However, in a statically indeterminate structure, differential settlement forces the continuous members to bend and warp, inducing massive internal shear forces and bending moments that must be accounted for in design.
Dynamic vs Static Loads
A core distinction in loading is how it applies over time:
- Static Loads: Loads applied slowly or remaining constant over time (e.g., dead loads, typical live loads). Inertial effects are negligible.
- Dynamic Loads: Loads applied rapidly or varying significantly over time (e.g., blast loads, seismic shocks, machine vibrations). These induce significant inertial and damping forces in the structure.
Other Induced Loads
Aside from gravity and environmental forces, structures can experience significant internal forces due to:
- Thermal Loads: If a statically indeterminate structure undergoes a temperature change, the members will attempt to expand or contract. If constrained, this induces thermal stresses.
- Support Settlements: Differential settlement of foundations can induce massive shear forces and bending moments into continuous, indeterminate frames.
Pattern Loading
Also known as checkerboard loading or skip loading. Live loads are transient; they might not cover the entire structure simultaneously. To determine the absolute maximum internal forces (shear and moment) in continuous beams and frames, engineers must arrange live loads in specific patterns (e.g., loaded adjacent spans to maximize negative moment, or loaded alternating spans to maximize positive moment) rather than just applying a full uniform load everywhere.
Load Combinations
Loads are rarely applied individually. Structures must be designed for various combinations of loads to ensure safety under different scenarios. There are two primary design philosophies:
1. Allowable Stress Design (ASD): Focuses on keeping working stresses below a specified allowable limit. Combinations typically use un-factored loads (e.g., ).
2. Load and Resistance Factor Design (LRFD): Also known as Ultimate Strength Design (USD). Focuses on applying load factors (greater than 1.0) to account for overload probabilities, and resistance factors (less than 1.0) to account for material understrength.
Typical LRFD load combinations from the NSCP include:
Checklist
Impact Factors (Dynamic Load Allowance)
When dynamic loads (like moving vehicles or cranes) are applied suddenly, they create internal forces significantly greater than their static equivalents. To simplify analysis, these are often treated as equivalent static loads multiplied by an Impact Factor ().
Equivalent Static Load = Static Load
LRFD Load Combinations Simulator (NSCP 2015)
Input Loads (kN)
100 kN
50 kN
20 kN
60 kN
80 kN
Factored Combinations
Combo 1: 1.4D140.0 kN
Combo 2: 1.2D + 1.6L + 0.5Lr210.0 kN
Combo 3: 1.2D + 1.6Lr + (1.0L or 0.5W)202.0 kN
Combo 4: 1.2D + 1.0W + 1.0L + 0.5Lr240.0 kN
Combo 5: 1.2D + 1.0E + 1.0L250.0 kN
Combo 6: 0.9D + 1.0W150.0 kN
Combo 7: 0.9D + 1.0E170.0 kN
Governing Load Combination:
Combo 5: 1.2D + 1.0E + 1.0L = 250.0 kN
Key Takeaways
- The NSCP outlines the requirements for designing against dead (permanent), live (transient), and environmental (wind/seismic) loads.
- Structures must also be evaluated for thermal loads and support settlements, especially if they are statically indeterminate.
- Load combinations are used to determine the most critical design forces.
- Pattern loading must be considered to find the absolute maximum design forces caused by transient live loads.
- Timber design requires a Load Duration Factor () due to wood's viscoelastic nature.
- Wind load calculations depend on basic wind speed, exposure, and topography.
- Differential settlement induces massive internal forces in indeterminate structures, but merely rotates determinate ones.
Load Path and Tributary Areas
Understanding how loads are transferred through a structure to its foundation is crucial for sizing individual structural members. A clear load path ensures structural integrity.
Checklist
- Primary Load Path: The direct trajectory that a load follows from its point of application to the foundation (e.g., floor slab secondary beams primary girders columns footings soil).
- Secondary Load Path (Redundancy): Alternate routes the load can take if a primary member fails. Indeterminate structures inherently possess secondary load paths, making them more resilient against catastrophic collapse.
- Tributary Area: The specific area of a floor or roof that contributes load to a particular structural member. It is bounded by lines halfway to the adjacent parallel members.
- One-way Slab Action: When a rectangular slab is supported on two opposite edges or has an aspect ratio (length to width) greater than 2, it primarily transfers load in one direction. The tributary area for supporting beams is a rectangle.
- Two-way Slab Action: When a rectangular slab is supported on all four edges and has an aspect ratio of 2 or less, it transfers load in two perpendicular directions. The tributary areas for supporting beams are triangles and trapezoids.
Load Calculations
The load on a member is calculated by multiplying the area load (e.g., in kN/m²) by the tributary width to get a line load (e.g., in kN/m), or by multiplying the area load by the total tributary area to get a point load.
Tributary Area Interactive Simulator
Use this simulation to visualize how grid spacing and column position affect the tributary area and the resulting axial load.
Tributary Area Interactive Lab
Adjust the grid spacing and area load to see how the tributary area and total axial load change for different column types.
Floor Plan View
Tributary Width ($W_x$):6.00 m
Tributary Length ($W_y$):8.00 m
Tributary Area ($A_T$):48.00 m²
Total Axial Load ($P$):240.00 kN
Key Takeaways
- Understanding the primary and secondary load paths is essential for tracking forces down to the earth and ensuring redundancy.
- The tributary area determines the proportion of the total floor or roof load that a specific beam, girder, or column must support.
- Slabs distribute loads either one-way or two-ways depending on their support conditions and aspect ratio.
- Timber design requires a Load Duration Factor () due to wood's viscoelastic nature.
- Wind load calculations depend on basic wind speed, exposure, and topography.
- Differential settlement induces massive internal forces in indeterminate structures, but merely rotates determinate ones.