7.1 Structural Loads and Forces

Types of Structural Loads

Permanent and Variable Loads

Every structure deals with two broad categories of loads: those that never change and those that do.

Dead loads are the permanent, constant forces a structure carries from its own weight and fixed components. Think of the weight of the concrete floors, steel beams, roof tiles, and permanently installed mechanical systems. These loads don't change once the building is built, which makes them the most predictable type of load to design for.

Live loads are temporary and variable. They come from occupancy, furniture, equipment, and anything that can be added or removed. A classroom full of students creates a live load; an empty classroom at night has almost none. Building codes specify minimum live load values depending on the space's use. For example, residential floors are typically designed for about 40 pounds per square foot (psf), while library stack rooms might require 150 psf.

Environmental loads come from nature and vary dynamically in both magnitude and direction:

• Wind loads push laterally on buildings and increase with height because wind speeds are higher farther from the ground, where there's less friction from terrain and surrounding structures.
• Snow loads add weight to roofs and vary by geographic region and roof pitch. Steeper roofs shed snow more easily, so they're designed for lower snow loads.
• Seismic loads shake structures both horizontally and vertically during earthquakes. Unlike wind or snow, seismic forces originate from the ground moving beneath the structure.

Special Load Considerations

Beyond the standard categories, engineers account for several less obvious load types:

• Impact loads produce sudden, short-duration forces from events like vehicle collisions or explosions. A parking garage column, for instance, must be designed to survive a car striking it.
• Thermal loads arise from temperature changes that cause structural elements to expand or contract. Bridge expansion joints exist specifically to accommodate this movement. Concrete curing also generates significant internal thermal stresses as the chemical reaction produces heat.
• Soil pressure loads exert lateral forces on below-grade structures from surrounding soil and groundwater. Retaining walls must resist soil pressure to prevent overturning, and basement walls in areas with high water tables experience hydrostatic pressure pushing inward.

Force Calculations from Loads

Vector Analysis and Superposition

Structures rarely experience just one force at a time, so engineers need tools to combine multiple forces into a single picture.

Vector analysis determines the magnitude and direction of a resultant force from multiple applied loads. Forces are represented as arrows where the length indicates magnitude and the arrow points in the direction of the force. To find the net effect, you break each force into its horizontal and vertical components, then add those components separately. The result is a single resultant force that captures the combined effect.

The superposition principle says you can analyze the effects of each load separately and then add the results together. This works because most structures behave in a linear elastic manner under design loads, meaning deformations are proportional to the applied force. It's a huge simplification: instead of solving one massive problem with all loads at once, you solve several simpler problems and sum them up.

Moment and Free-Body Analysis

Forces don't just push or pull; they can also cause rotation. A moment is the rotational effect of a force, calculated as:

$M = F \times d$

where $F$ is the force and $d$ is the perpendicular distance from the force's line of action to the pivot point. Moments are critical for analyzing beams, columns, and connections.

Free-body diagrams (FBDs) are the single most important tool for force analysis. To create one:

1. Isolate the structural element you want to analyze by "cutting" it free from the rest of the structure.
2. Draw all external forces acting on it, including applied loads, self-weight, and support reactions.
3. Apply equilibrium conditions: the sum of all forces in each direction must equal zero, and the sum of all moments about any point must equal zero.

These equilibrium equations let you solve for unknown reaction forces and internal forces.

Load Distribution Techniques

Loads applied over an area (like floor weight) need to be distributed to individual structural elements. Two key concepts make this possible:

• Tributary area is the portion of floor or roof area that a particular beam or column is responsible for supporting. You divide the floor plan into zones based on beam and column spacing, then assign each zone's load to its supporting element. For example, if beams are spaced 10 feet apart, each beam carries the load from a 10-foot-wide strip of floor.
• Load path analysis traces how forces travel through a structure from the point of application all the way down to the foundation. Loads on a floor slab transfer to beams, then to girders, then to columns, and finally to the footings and soil. Every link in this chain must be strong enough, and the path must be continuous. A break in the load path is one of the most common causes of structural failure.

Wind and Seismic Load Effects

Wind Load Analysis

Wind loads create dynamic lateral forces that vary with building height, shape, and surrounding terrain. Taller buildings experience higher wind pressures at upper levels, and the overall shape matters too: rounded corners and tapered profiles can significantly reduce the forces a building must resist.

For complex or tall structures, engineers go beyond code formulas:

• Wind tunnel testing uses scale models placed in a controlled airflow to measure actual pressure distributions on the building surface.
• Computational fluid dynamics (CFD) simulations use software to model airflow patterns around buildings digitally.

Both methods help predict how wind will interact with unusual geometries that simplified code equations can't accurately capture.

Seismic Load Considerations

Seismic loads result from ground accelerations during earthquakes. The forces a structure experiences depend on its mass, stiffness, and natural frequency (how fast it naturally vibrates when disturbed).

• Heavier structures generally experience larger seismic forces because force equals mass times acceleration ($F = ma$).
• Stiffer structures tend to attract higher seismic loads because they have shorter natural periods, which often correspond to stronger ground shaking frequencies.

Response spectrum analysis is a key tool for seismic design. It plots the peak structural response against natural frequency for a given earthquake. Engineers use it to determine the design forces for various structural elements based on how the building's natural vibration period interacts with the expected ground motion.

Advanced Seismic Design Techniques

Engineers have developed several strategies to reduce seismic damage:

• Base isolation systems place flexible bearings between the foundation and the superstructure, effectively decoupling the building from ground motion. This reduces the acceleration transmitted upward and is commonly used for critical facilities like hospitals and data centers.
• Damping systems dissipate seismic energy to reduce structural response. Tuned mass dampers (large masses on upper floors that counteract building sway) and viscous dampers (which act like shock absorbers) are two common types.
• Dynamic amplification factors account for the fact that flexible structures can experience forces well beyond what a simple static calculation would predict. Tall buildings may experience 1.5 to 2 times the static equivalent force, making these factors critical for the design of skyscrapers and long-span bridges.

Load Combinations in Design

Code-Specified Load Combinations

No structure faces just one load at a time. A building might simultaneously carry its own dead load, a full live load on several floors, and a strong wind. Load combinations represent realistic worst-case scenarios that capture these simultaneous effects.

Building codes specify which combinations engineers must check. In the U.S., ASCE 7 (Minimum Design Loads for Buildings) provides the standard load combination equations, and the International Building Code (IBC) references them. These combinations account for the low probability that all loads will reach their maximum values at the same moment.

Load and Resistance Factor Design (LRFD)

Not all loads carry the same level of uncertainty. Dead loads are predictable (you know how much concrete weighs), but live loads are much more variable. Load factors are multipliers applied to each load type to account for this uncertainty:

• Dead load factor: typically 1.2 to 1.4 (lower because there's less uncertainty)
• Live load factor: often 1.6 (higher because occupancy and use vary widely)

The LRFD method compares the total factored load demand against the factored capacity (strength) of the structural element. The core requirement is:

$\phi R_n \geq \sum \gamma_i Q_i$

where $\phi R_n$ is the design strength (nominal strength reduced by a resistance factor) and $\gamma_i Q_i$ represents each load multiplied by its load factor. If the design strength exceeds the required strength, the element passes.

Advanced Combination Techniques

Beyond strength checks, engineers also verify serviceability limit states, which ensure structures remain functional and comfortable under normal use. These checks control deflections, vibrations, and cracking, and they typically use unfactored loads or lower load factors since they address everyday performance rather than survival.

For more specialized work, probability-based methods like the First Order Second Moment (FOSM) approach consider the statistical distributions of both loads and material strengths. This enables more refined reliability analysis and can lead to optimized designs.

Finally, load envelopes compile the results of all load combinations into diagrams showing the maximum and minimum forces at every point along a structural element. These envelopes ensure that no critical load scenario is overlooked during design.