Loads, Actions and Load Combinations

Introduction

Structural analysis begins with a defensible description of the actions that a structure may experience during construction and use. A structural member does not respond to a load in isolation: actions are transferred through a load path from slabs and cladding to beams, columns, walls, foundations and finally the ground. The engineer must therefore identify actions, establish their spatial and temporal variation, assign appropriate representative values, and combine them in a manner consistent with the governing design standard.

In this chapter, the word action is used in the broad structural-engineering sense: an imposed influence capable of producing stress, deformation or instability. A force is an action, but so may be a support displacement, temperature change or imposed strain. Loads are commonly classified as permanent, variable or accidental; seismic actions are often treated as a distinct dynamic environmental action. Exact factors and combination rules depend on the adopted national code. The principles below are general, while numerical factors must always be confirmed from the current applicable standard.

Learning objectives

By the end of this chapter, a student should be able to:

• identify dead, imposed, wind, snow, thermal, settlement, construction, impact and seismic actions;
• distinguish nominal, characteristic, representative, serviceability and design values;
• trace vertical and horizontal load paths;
• select realistic action combinations for ultimate and serviceability limit states;
• apply partial safety factors without double counting uncertainty;
• explain the limitations of simplified loading assumptions; and
• communicate assumptions clearly in structural calculations and drawings.

1. Actions, effects and load paths

An action is an external influence on a structure. An effect of action is the structural response, such as axial force, shear force, bending moment, torsion, displacement, vibration or bearing pressure. The same action can produce different effects depending on geometry, stiffness, connections and restraints.

A load path is the continuous route by which an action reaches its supporting medium. For a typical building, floor finishes and occupants load a slab; the slab transfers reactions to beams or walls; beams transfer forces to columns or load-bearing walls; columns transfer forces to foundations; and foundations transfer them to the soil. Wind may act on cladding, pass to secondary framing, then to main frames, diaphragms and foundations. A credible analysis must include every significant link in this route.

A useful preliminary check is equilibrium. For a stable structure, the resultant support reactions must balance the applied actions. In a planar system:

Here ∑F_x and ∑F_y are sums of horizontal and vertical forces, and ∑M_O is the sum of moments about point O. These equations describe static equilibrium; they do not by themselves establish strength, stiffness, ductility or dynamic adequacy.

2. Classification of actions

2.1 Permanent actions: dead load

Permanent actions, commonly called dead loads, arise from components that remain in place for the relevant design situation. They include self-weight of structural members, floors, roofs, finishes, ceilings, permanent partitions, fixed mechanical equipment, façade systems and retained earth or water where applicable.

For a uniform material, self-weight per unit volume is:

where w is unit weight in N/m³, ρ is mass density in kg/m³, and g is gravitational acceleration, approximately 9.81 m/s². For an element of volume V, its weight is:

The units are consistent: kg/m³ × m/s² × m³ = kg·m/s² = N. In practice, codes and manufacturers may provide unit weights directly in kN/m³.

Dead load should be calculated from the actual thicknesses and densities expected in the completed structure. A common error is to omit finishes, services or façade weight, or to count an item twice—for example, including a partition in both a permanent area load and a line load. Where dimensions are uncertain, the assumption should be recorded and revised when design information improves.

2.2 Imposed or live actions

Imposed actions are variable actions associated with occupancy, use and movable objects. Examples include people, furniture, stored materials, vehicles, movable partitions and maintenance activity. A code generally provides characteristic imposed area loads by occupancy category, such as residential, office, assembly, storage or industrial use.

An imposed load is not necessarily uniformly distributed in reality. Concentrated loads, partition lines, storage racks and vehicle wheel loads may control local slab design even when the average area load is modest. Load arrangement can also matter: alternate spans may produce more severe bending in continuous beams and slabs than loading every span uniformly.

Reduction of imposed loads for columns or foundations may be permitted because the probability of every floor reaching its maximum simultaneously is limited. Such reductions are code-specific and should not be applied to roofs, storage areas or other categories where they are prohibited or unsafe.

2.3 Wind actions

Wind produces pressure and suction on external surfaces and may also act internally through openings. The pressure on a surface is influenced by wind speed, exposure, height, terrain, topography, turbulence, building shape and local pressure coefficients. A simplified velocity-pressure relationship is:

where q is dynamic pressure in Pa, ρ_a is air density in kg/m³ and V is wind speed in m/s. Codes modify this basic pressure using exposure and aerodynamic coefficients; therefore q alone is not the design pressure on a wall.

A commonly used conceptual expression for net pressure is:

where p_net is net external pressure, q_p is peak velocity pressure, c_pe is the external pressure coefficient and c_pi is the internal pressure coefficient. Sign conventions must be followed: positive pressure acts toward a surface and negative pressure represents suction. The coefficient values depend on geometry and the code.

Wind load paths include cladding fixings, purlins or girts, frames, bracing, floor diaphragms, collectors, hold-downs and foundations. Local cladding design may be governed by peak pressures that are inappropriate for use as a uniform pressure on the entire main frame. Conversely, a global frame analysis must not omit torsion caused by asymmetric wind or accidental eccentricity where required by the code.

2.4 Snow actions

Snow load depends on climate, altitude, roof geometry, drifting, exposure, thermal condition, sliding and exceptional accumulation. A general code model may be represented as:

where s is roof snow load, s_k is ground snow load, μ is a roof-shape or drift coefficient, C_e is an exposure coefficient and C_t is a thermal coefficient. The precise definitions and units are code-dependent, and additional exceptional or unbalanced arrangements may be required.

Snow must be considered on roofs with changes in level, parapets, valleys, dormers or nearby taller buildings because drifting can create highly non-uniform actions. Snow is often treated as a variable accompanying action rather than the leading action in every combination. The governing arrangement may be different for a roof beam, column, connection or global stability system.

2.5 Thermal actions

Temperature changes produce free expansion or contraction. For a uniform temperature change:

where ΔL is free change in length (m), α is the coefficient of thermal expansion (per °C), L is original length (m), and ΔT is temperature change (°C). This relationship assumes a uniform temperature field and small deformation.

If expansion is fully restrained, a simplified uniaxial elastic thermal stress is:

where σ_T is thermal stress (Pa) and E is Young’s modulus (Pa). This expression assumes linear elasticity, complete restraint, uniform temperature and no relaxation, cracking, slip or creep. Real structures frequently have partial restraint, joints and nonlinear behavior, so the formula should not be used uncritically to predict final stress.

Thermal actions arise from seasonal temperature, solar heating, differential temperatures through a section, heat from equipment, fire exposure and construction-stage temperature differences. Movement joints, bearings, sliding connections and flexible detailing can control the action more effectively than simply increasing member strength.

2.6 Settlement and other support movements

Differential settlement is an imposed deformation rather than a conventional applied force. It may result from variable soil stiffness, changes in groundwater, consolidation, excavation, erosion or construction sequence. A support displacement changes the geometry and compatibility conditions of a statically indeterminate structure and can generate secondary moments and shears.

Settlement analysis requires interaction between structural and geotechnical models. Important distinctions include total settlement, differential settlement, angular distortion and rate of settlement. A structure may tolerate a large nearly uniform settlement but suffer damage from a small differential movement. Flexible joints, movement accommodation and staged construction can reduce risk.

2.7 Construction and temporary actions

Construction actions include stacked materials, wet concrete, temporary props, formwork pressure, lifting, striking of formwork, partially completed bracing, construction traffic, wind on incomplete frames and accidental removal of temporary supports. The final structure may be safe while an intermediate stage is unsafe.

Construction is a sequence of design situations. At each stage, stiffness, support conditions, load paths and stability may differ from those in the completed building. Temporary works must therefore be designed, inspected and controlled, not treated as an informal site matter. Loads from fresh concrete are particularly important because formwork may carry fluid pressure before composite action develops.

2.8 Impact and accidental actions

Impact may be caused by vehicles, dropped objects, moving machinery, blast, collision or sudden release of stored energy. It is often modeled using an equivalent static action, a dynamic analysis, local strengthening, sacrificial components or a combination of these measures. An equivalent static force is not a universal material property; it is a calibrated design idealization that must reflect impact speed, mass, deformability and energy dissipation.

Accidental design seeks robustness: local damage should not trigger disproportionate progressive collapse. Strategies include continuity, tying, alternate load paths, compartmentation, redundancy and controlled collapse mechanisms. The appropriate strategy depends on occupancy, consequence class and governing regulations.

2.9 Seismic actions

Earthquake actions result from ground acceleration transmitted through the foundations. Inertia forces develop because structural mass resists acceleration. A simplified lateral force concept is:

where F is inertia force (N), m is mass (kg) and a is acceleration (m/s²). For a single-degree-of-freedom idealization, a code may express base shear as:

where V_b is design base shear, C_s is a code-defined seismic coefficient, and W is seismic weight. C_s depends on hazard, site conditions, period, ductility, importance and structural system; it must not be selected from the equation alone.

Seismic design is governed not only by strength but also by ductility, regularity, drift, detailing and hierarchy of resistance. The load path must be continuous from diaphragms through collectors and vertical resisting elements to foundations. Torsional response, soft storeys, discontinuous walls, pounding and nonstructural components require attention. Seismic actions are dynamic; static equivalent procedures are appropriate only within their code-defined range of applicability.

3. Characteristic, representative and design values

A characteristic value is a statistically or conventionally defined value of an action, usually selected so that unfavorable exceedance is sufficiently unlikely during the reference period. It is not necessarily the largest conceivable action. For permanent actions, the characteristic value may be based on nominal dimensions and density; for variable actions, it often reflects an upper fractile or prescribed occupancy value.

A representative value is the value used to represent an action in a particular combination. For a leading variable action it may be the characteristic value; for an accompanying variable action it may be reduced by a combination or frequent factor. A design value incorporates safety or reliability treatment and is used for verification.

A simplified design action relationship is:

where F_d is design action, F_k is characteristic action, and γ_F is a partial factor. This is a conceptual form; actual standards may use separate upper and lower values for permanent actions and combination factors for variable actions.

Resistance is treated similarly. If R_k is characteristic resistance and γ_M is a material or resistance partial factor:

The design requirement is generally:

where E_d is design effect of actions and R_d is design resistance. The inequality is meaningful only when both sides use compatible limit states, units, models and code rules. Partial factors represent uncertainty in actions, materials, geometry, models and consequences; they are not arbitrary multipliers and must not be mixed between codes without justification.

4. Limit states and combinations

4.1 Ultimate limit states

Ultimate limit states concern collapse, loss of equilibrium, rupture, buckling, excessive instability, mechanism formation and other conditions threatening safety. A generic persistent or transient combination can be written conceptually as:

Here G_k is a characteristic permanent action, Q_k,1 is the leading variable action, Q_k,i are accompanying variable actions, γ_G and γ_Q are partial factors, and ψ_0,i are combination factors. The exact factors and whether favorable permanent actions receive different treatment depend on the governing code and design situation.

The leading variable action should be changed in turn. For example, wind may lead one combination while imposed floor load leads another. Snow, thermal action or construction load may govern a different structural component. One must also check unfavorable and favorable effects of permanent actions, especially in uplift, overturning and sliding.

4.2 Serviceability limit states

Serviceability limit states address usability and performance rather than collapse. They include deflection, cracking, vibration, settlement, rotation, drift, water tightness, appearance and comfort. Typical combination concepts are:

• characteristic combination: used for rare or maximum service conditions;
• frequent combination: used for conditions likely to occur repeatedly; and
• quasi-permanent combination: used for long-term effects such as creep, sustained deformation and appearance.

A generic quasi-permanent action expression is:

where ψ_2,i is a quasi-permanent factor. These factors are not universal constants; they depend on action category and code. Serviceability checks may use unfactored or reduced actions, but “unfactored” does not mean “unimportant.” A realistic service action can govern finishes, partitions, façade performance or occupant comfort.

4.3 Special design situations

Fire, earthquake, accidental impact, blast and construction stages may require special combinations. A generic accidental format may contain an accidental action A_d together with selected permanent and accompanying variable actions. Seismic combinations commonly use the seismic design situation and code-prescribed accompanying actions rather than simply adding a full wind load to full seismic load. The adopted standard must control.

5. Load distribution and idealization

Area loads are converted to line loads using tributary width. If an area load q acts over tributary width b_t, the corresponding line load is:

where q is in kN/m², b_t is in m and w is in kN/m. For a one-way slab supported by parallel beams, an interior beam often receives approximately half the slab span on each side, subject to support conditions and load distribution assumptions.

A point load P at distance a from the left support of a simply supported span L produces reactions, under ideal pin and roller assumptions:

R_A and R_B are support reactions. These equations apply to a statically determinate, simply supported beam with a single vertical point load. They do not account for beam self-weight, stiffness continuity, support settlement or load spreading.

Load idealization must reflect the analysis purpose. A global model may use distributed floor loads, while a connection or local slab model may require concentrated wheel, rack or fixing loads. Blindly smoothing every action can hide local failure modes.

6. Worked example: preliminary floor-beam loading

Consider an interior beam supporting a 3.0 m tributary width of a floor. The floor consists of a 150 mm reinforced-concrete slab, finishes of 1.0 kN/m², services and ceiling of 0.4 kN/m², and an imposed office load of 3.0 kN/m². Take reinforced-concrete unit weight as 24 kN/m³. Ignore beam self-weight initially, then add it separately.

Slab dead load:

Total permanent area load:

Permanent line load on the beam:

Imposed line load:

Using illustrative, not code-prescriptive, factors γ_G = 1.35 and γ_Q = 1.50 for a persistent ultimate combination:

If the beam is simply supported over 6.0 m and carries this uniform design load, the maximum bending moment is:

and each support reaction is:

These results exclude beam self-weight and assume a determinate, prismatic beam with a uniformly distributed load. They are preliminary actions, not a complete design. Beam self-weight, continuity, openings, partition arrangements, vibration, deflection, shear, torsion, fire and connection behavior must be assessed before design is finalized.

7. Applied case: illustrative construction-stage risk

Background

An illustrative four-storey concrete building has a flat slab system, perimeter façade, temporary shoring and a tower crane. The completed structural model indicates adequate strength under permanent, imposed, wind and seismic design situations.

Problem

During construction, materials are stacked on one partially completed floor, while formwork is removed from a lower floor earlier than planned. The temporary stability system is also incomplete. The final-stage analysis does not represent these conditions.

Analysis

The construction manager and structural engineer identify three changed load paths: fresh concrete and stacked materials create concentrated construction loads; the partially cured slab has lower stiffness and strength; and the incomplete frame has reduced lateral stability. A wind action on the unfinished façade is more severe than the enclosed completed-building assumption. The team reviews construction drawings, sequencing, temporary works, concrete age, allowable stacking zones and weather limits.

Approach and solution

A stage-by-stage assessment is prepared. Temporary props remain until the specified strength and stiffness are reached. Materials are distributed rather than stacked over one bay. Crane and delivery loads are assigned to designated supporting zones. Temporary bracing is installed before façade erection, and a site hold point is introduced before removing props or changing the load path. The design team records the construction action combinations and communicates them through drawings and method statements.

Outcome

The revised sequence avoids excessive slab punching and deflection, maintains lateral stability during façade installation and provides inspection evidence before each critical transition. No change to the completed building’s member sizes is required, but the temporary works and sequencing controls become essential parts of the engineered solution.

Learning points

A structure has more than one design situation. The governing action may occur before completion, and a safe final model cannot validate an unsafe construction sequence. Responsibility must be coordinated among the permanent works designer, temporary works designer, contractor and site supervisor.

8. Professional practice, regulation and technology

The engineer should state the adopted code, reference period, occupancy, environmental parameters, load factors, combination factors, design situations, exclusions and sources of data. National annexes and amendments can change values significantly. Wind and snow maps, geotechnical reports, manufacturer data, survey information and climate records should be traceable.

Computer analysis improves efficiency but does not decide whether a load exists, where it enters the building or whether a load path is complete. Software models can conceal unit errors, duplicated self-weight, incorrect releases, accidental omission of diaphragm action or inappropriate combinations. Independent hand checks should verify reactions, equilibrium, approximate member forces and the reasonableness of deflections.

Building information modelling can associate loads with elements and construction stages, while sensors and digital twins may support monitoring of temperature, movement and construction progress. Artificial intelligence may help classify drawings or identify anomalous model outputs, but it cannot replace code interpretation, engineering judgment, site verification or professional accountability. Data provenance, model version control and human review are essential.

Climate change may alter the relevance of historical wind, snow, rainfall and temperature records. Where regulations require future climatic allowances, they should be incorporated explicitly rather than hidden in arbitrary factors. Resilience also includes durability, repairability, functional recovery and protection of occupants and neighboring property.

9. Common errors and best practice

Frequent errors include confusing mass with weight, using a service load in an ultimate check without appropriate factors, combining mutually exclusive actions, omitting construction stages, applying a roof snow coefficient to an incompatible geometry, treating thermal movement as fully restrained without justification, and failing to design the load path for uplift or diaphragm transfer.

Best practice is to:

1. define the design situations before creating combinations;
2. prepare a load schedule with source, location, units and permanence;
3. distinguish area, line and point actions;
4. map each action to its physical load path;
5. vary the leading variable action;
6. check both global and local effects;
7. verify temporary as well as completed conditions;
8. use code factors exactly as intended; and
9. document assumptions, uncertainties and changes.

Chapter Summary

Structural analysis depends on identifying actions and following them through a complete load path. Permanent actions include self-weight and fixed components; imposed actions arise from occupancy and movable objects; wind and snow are environmental actions; temperature and settlement are imposed deformations; construction, impact and accidental actions require separate design situations; and seismic actions arise from inertia under ground motion. Characteristic values describe representative basic actions, while design values incorporate code-prescribed reliability treatment. Ultimate combinations address safety against collapse, whereas serviceability combinations address deflection, cracking, vibration, drift and long-term performance. Partial factors and combination factors are code-specific and must not be invented or mixed casually. Sound practice combines code compliance, equilibrium checks, realistic staging, clear assumptions, professional coordination and engineering judgment.

Key Terms

Action: An influence capable of causing structural response.

Characteristic value: A code-defined representative value of an action or resistance.

Combination factor: A factor reducing an accompanying variable action in a combination.

Dead load: A permanent action due to self-weight or fixed components.

Design value: A value used for verification after applying relevant code factors.

Differential settlement: Unequal support movement that can induce structural effects.

Dynamic pressure: Pressure associated with moving air, commonly proportional to ½ρV².

Imposed load: A variable action associated with occupancy, use or movable objects.

Inertia force: Force associated with mass resisting acceleration.

Load path: The route by which an action is transferred to the ground.

Partial safety factor: A factor representing prescribed uncertainty and reliability treatment.

Permanent action: An action that remains substantially constant during the design situation.

Representative value: A value selected for a specific design combination.

Seismic action: Structural action induced by earthquake ground motion.

Serviceability limit state: A condition affecting use, comfort, appearance or function.

Snow action: Roof or ground loading caused by snow accumulation and drift.

Thermal action: Response caused by temperature change or gradient.

Ultimate limit state: A condition associated with collapse, instability or loss of safety.

Variable action: An action whose magnitude or position changes significantly with time.

Wind action: Pressure, suction or force generated by atmospheric airflow.

Review Questions

Short Answer Questions

1. Distinguish an action from an effect of action and give one example of each.
2. Why must construction stages be checked separately from the completed structure?
3. Define characteristic value and design value.
4. State two differences between ultimate and serviceability limit states.
5. What is meant by a structural load path?

Long Answer Questions

1. Explain the classification of permanent, variable, accidental and seismic actions, including appropriate building examples.
2. Discuss the factors influencing wind pressure and describe how wind is transferred from cladding to foundations.
3. Explain thermal action and support settlement as imposed deformations rather than ordinary applied forces.
4. Describe the principles of ultimate and serviceability load combinations and the role of leading and accompanying variable actions.
5. Evaluate the role and limitations of software, BIM and AI in action assessment and combination generation.

Analytical / Application Questions

1. A beam supports a 2.5 m tributary width carrying a 0.18 m concrete slab, 0.8 kN/m² finishes, 0.3 kN/m² services and a 2.5 kN/m² imposed load. Using a concrete unit weight of 24 kN/m³, calculate the characteristic permanent and imposed line loads, excluding beam self-weight.
2. A 30 m steel member has α = 12 × 10⁻⁶/°C and experiences a uniform temperature rise of 35°C. Calculate its free expansion and explain why the restrained thermal stress formula may not represent the actual stress in a building.
3. Develop a design-situation matrix for a small building containing floors, roof, façade, temporary works and seismic bracing. Identify at least four leading actions and explain which load-path checks would be required for each.

Multiple Choice Questions with Answers

Question 1

Which statement best defines a structural load path?

A. The route by which an action is transferred to the ground

B. The maximum load a member can resist

C. The sequence used to calculate material density

D. The distance between adjacent columns

Correct Answer: A. The route by which an action is transferred to the ground

Question 2

For a material of density ρ and gravitational acceleration g, the unit weight is:

A. ρ/g

B. ρg

C. g/ρ

D. ρ + g

Correct Answer: B. ρg

Question 3

A 150 mm concrete slab has unit weight 24 kN/m³. Its area dead load is:

A. 0.16 kN/m²

B. 3.60 kN/m²

C. 16.0 kN/m²

D. 36.0 kN/m²

Correct Answer: B. 3.60 kN/m²

Question 4

In a combination with one leading variable action, accompanying variable actions are commonly represented using:

A. Combination factors

B. Air-density factors only

C. The resistance factor γ_M

D. The slab thickness

Correct Answer: A. Combination factors

Question 5

Which action is most directly associated with occupant use and movable furniture?

A. Permanent action

B. Imposed action

C. Thermal action

D. Seismic action

Correct Answer: B. Imposed action

Question 6

The simplified free thermal expansion relationship is:

A. ΔL = αLΔT

B. ΔL = L/(αΔT)

C. ΔL = Eα/ΔT

D. ΔL = ρgV

Correct Answer: A. ΔL = αLΔT

Question 7

For a simply supported beam carrying a uniform load w over span L, the maximum midspan moment is:

A. wL/2

B. wL²/8

C. wL²/2

D. w/L²

Correct Answer: B. wL²/8

Question 8

Which condition is primarily a serviceability concern?

A. Member collapse

B. Excessive deflection affecting finishes

C. Formation of a collapse mechanism

D. Loss of equilibrium

Correct Answer: B. Excessive deflection affecting finishes

Question 9

A seismic base-shear expression V_b = C_sW uses W to represent:

A. Wind pressure

B. Seismic weight

C. Section modulus

D. Water pressure

Correct Answer: B. Seismic weight

Question 10

Why must temporary construction stages be assessed?

A. The completed structure always has lower strength

B. Stiffness, supports and load paths can differ before completion

C. Construction loads are always zero

D. Codes prohibit analysis of completed structures

Correct Answer: B. Stiffness, supports and load paths can differ before completion