
### 1.0 Introduction

The loading that a structure is subject to during its life is a huge source of uncertainty. So, when designing a structure, one of the first steps is determining what loads or combinations of loads should be assumed in the design.

Helpfully, codes of practice such as the Eurocodes provide a framework that allows designers to systematically determine design loadings that balance efficiency and risk of exceedance. As we saw in the previous lecture, the relevant Eurocodes for determining design loading are:

- BS EN 1990, Eurocode: Basis of structural design (EC0)

- BE EN 1991, Eurocode 1: Actions on structures (EC1)

In order to get an overview of the following discussion, consider a basic design scenario; you are tasked with designing a beam that supports a floor. The floor forms part of an office building. The building is a concrete frame structure with solid concrete floor slabs.

Based on the type of structure (reinforced concrete), we can estimate the **_characteristc permanent load_** applied to the beam due to the self-weight of the structure. Based on the building usage (office building), we can determine from published tables the value of the **_characteristic variable load_** that can be applied to the floor (and indirectly to the beam).

Because the consequences of collapse are potentially catastrophic and we can't be any more specific about what activities will take place on the floor, the characteristic permanent and variable loads are multiplied by **_partial factors of safety_** to obtain the **_design permanent and variable loads_**. The final step is to combine the permanent and variable design loads together to give a final value of the load that can be applied in the beam design calculation.

The values chosen for partial factors, broadly speaking, depend on what **_limit state_** we are designing for; i.e. is our design checking to ensure that the structure will not collapse (an **_Ultimate Limit State (ULS)_**) or are we checking to ensure that the structure will not deflect too much or vibrate too much (examples of **_Serviceability Limit States (SLS)_**)? Each of the concepts identified in the above scenario will be discussed in the following lectures.

### 2.0 Actions (Loads)

The Eurocodes use the term **_Action_** to refer to anything that induces a change in the stress state of a structure (we'll use the term actions and loads interchangeably). Actions can be categorised as direct or indirect. Direct actions are typically loads that are applied directly to the structure, while examples of indirect actions include imposed deformations such as uneven settlement or thermal movement. Indirect actions, therefore, induce a change in the stress state of a structure without the direct application of a force.

Of more importance is the distinction between permanent and variable actions, which are defined as follows:

- **Permanent Action:** An action that is likely to act throughout a given reference period (design life) and for which the variation in magnitude with time is negligible. Historically referred to as _Dead Loads_, examples include the self-weight of the structure and any fixed equipment or fittings.

- **Variable Action:** An action for which the variation in magnitude with time is not negligible. Historically referred to as _Imposed_ or _Live_ loads, examples include loading due to occupancy.

The magnitude stated for a permanent or variable action will unless stated otherwise, usually be the _characteristic_ value. This is the baseline value before partial safety factors are applied. For example, if we consider a concrete beam that is $400 \:mm$ wide and $800 \:mm$ deep, the characteristic permanent loading due to self-weight would be $0.4 \:m \times 0.8\:m \times 25\: kN/m^3 = 8 \:kN/m$.

In order to determine the _design value_ of the permanent load, we multiply the characteristic load by a partial factor of, say, $1.35$, leading to a design permanent load of $1.35 \times 8\: kN/m = 10.8\: kN/m$. This can now be added to the design variable load to obtain a single loading figure that can be used in design. The actual value of the partial factor ($1.35$ above) will depend on the limit state under consideration (discussed later).

#### 2.1 Characteristic Permanent Actions

As already mentioned, characteristic permanent actions, denoted as $G_k$, have minimal variation in magnitude during the structure’s lifetime, a simple example is the loading due to self-weight. If we assume the range of $G_k$ values follows a Gaussian distribution, the variation can be considered small if the standard deviation is less than $10\:\%$ of the mean value.

If the variation cannot be considered small, two different values should be determined; an upper value, $G_{k,sup}$ and a lower value, $G_{k,inf}$. $G_{k,sup}$ is that value of permanent loading that has only a $5\:\%$ chance of exceedance during the lifetime of the structure, assuming $G_k$ follows a Gaussian distribution.

$G_{k,inf}$ is that value of permanent loading with a $95\:\%$ chance of exceedance. For most cases and certainly any designs we undertake in this course, a single value of permanent action will apply.

**Side note: when a load is in units of $kN$, an upper case letter is used, e.g. $G_k = 5\:kN$. If the load is a uniformly distributed/line load, a lower case symbol is used, e.g. $g_k = 5\: kN/m^2$.**

In addition to permanent and variable actions, you should also be aware of _accidental actions_. An accidental action is usually of short duration but significant magnitude. They are unlikely to occur on a structure during the design working life. Nevertheless, some allowance must be made for the potential occurrence of fire, explosions, impacts and localised failures. Determining the magnitude of design accidental actions is beyond the scope of this course, but you should be aware of their existence.

#### 2.2 Characteristic Variable Actions

The characteristic variable action, denoted by $Q_k$ or $q_k$ can usually be determined by considering the proposed usage of the structure. For buildings, four categories are defined:

- Category A: Areas of domestic and residential activities.
- Category B: Office areas
- Category C: Areas where people may congregate not covered by categories A, B and D.
- Category D: Shopping areas

Within each category, there are sub-categories; for the complete table, you should refer to the source document or IStructE manual referred to in the previous lecture. Examples of category/sub-category loadings are shown below as an example:

- Category A / sub-category A1: $(q_k=1.5\:kN/m^2, \:Q_K=2.0\:kN)$, _All usages within self-contained dwelling units. Commercial areas (including kitchens) in blocks of flats with limited use._

- Category B / sub-category B2: $(q_k=3.0\:kN/m^2, \:Q_K=2.7\:kN)$ _Office areas / at or below ground level._

- Category C / sub-category C1 / sub-sub-category C13: $(q_k=3.0\:kN/m^2, \:Q_K=3.0\:kN)$ _Areas where people may congregate / with tables / classrooms._

- Category D / subcategory D1: $(q_k=4.0\:kN/m^2, \:Q_K=3.6\:kN)$ _Shopping areas / in general retail shops._

These are merely a selection of the extensive list of characteristic variable actions specified. If an appropriate sub-category cannot be identified, or where the designer has knowledge that the prescribed loading in the relevant sub-category is not appropriate, sound engineering judgement should be used to determine a suitable (safe and efficient) variable action.

In certain design situations, the characteristic variable action can be multiplied by a number of different factors to facilitate specific design checks, thus, in addition to the characteristic value, $Q_k$, there are three other values that may be used in specific circumstances:

- The combination value, $\psi_0\:Q_k$: When we move on to consider different design limit states in the following lectures, it will become necessary to combine permanent and variable actions. When a number of variable actions act simultaneously, the _leading_ action is chosen as $Q_{k,1}$ and the other _accompanying_ actions are chosen as $Q\_{k,i}$ and are reduced by an appropriate combination factor, $\psi_0$.

- The frequent value, $\psi_1\:Q_k$: This is used to reduce the magnitude of the leading variable action when considering accidental design situations. It is also used when considering serviceability limit states, discussed below.

- The quasi-permanent value, $\psi_2\:Q_k$: This is also used when considering accidental design situations at the ultimate limit state and when considering serviceability limit states.

The frequent and quasi-permanent values for variable actions have only been touched on here. These will make more sense after we discuss the concept of limit state design. The values of $\psi_0$, $\psi_1$ and $\psi_2$ can be determined based on the usage category of the structure, see Fig. 1 below.

<Image
	src="/images/courses/fundamentals-of-reinforced-concrete-design-to-eurocode-2/actions-on-structures/img1.jpg"
	alt="Values of $\psi$ factors for buildings. | EngineeringSkills.com"
	width="1000"
	height="694"
/>

<Caption title="Fig 1. Values of $\psi$ factors for buildings.">
	Fig 1. Values of $\psi$ factors for buildings.
</Caption>

#### 2.3 Partition Loading

The distribution of internal dividing walls or partitions within a structure is often not known when the calculations for the frame and vertical load-bearing system are being completed. Offices, for example, often utilise moveable partitions to subdivide large open floorplans.

To allow for flexibility in the positioning of non-load-bearing partitions, an allowance can be made for them by applying a uniformly distributed loading across the entire floor. This loading is categorised as a variable load and is added to the loading due to occupancy already determined. The value of the partition loading can be determined as follows:

- For moveable partitions with a self-weight $\leq 1.0 \:kN/m$ wall length: $q_k = 0.5\: kN/m^2$.

- For moveable partitions with a self-weight $\leq 2.0 \:kN/m$ wall length: $q_k = 0.8\: kN/m^2$.

- For moveable partitions with a self-weight $\leq 3.0 \:kN/m$ wall length: $q_k = 1.2\: kN/m^2$.

After determining the characteristic values of permanent and variable actions for a given structure and usage category, our next task is to combine these together using partial safety factors to determine the final design actions. The selection of partial safety factors and the combination of permanent and variable loads is determined by the specific _limit state_ being considered. We'll continue in the next lecture by introducing the Ultimate Limit State.


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