Structures are loaded in many different ways. For example, earthquake load or wind load might destroy a structure that has safely withstood its own weight and the weight of its occupants for many years.
So already we can list four types of loads:
- Earthquake loading
- Wind loading
- Dead load (the self weight of the structure)
- Live load (the load associated with the normal use of a structure (e.g. people and furniture in a building, cars on a bridge)
There are many other types of loading, eg. earth pressure, liquid pressure, thermal loading, snow loading. In this unit we will only discuss dead load and live load.
Dead Load
This is perhaps the easiest load to calculate, and the one whose value we are the most certain about. The dead load of a bridge can be obtained by calculating the volume of all of the materials used in the bridge, and multiplying by the density of the materials. Densities of two common materials are:
density of concrete 2400 kg/m3 = 24 kN/m3
density of steel 7850 kg/m3 = 78.5 kN/m3
A small problem is this;
In order to design the bridge you need to know how much it weighs (the dead load), but you do not know how much it weighs until you have designed it! Therefore all design must begin with an estimate of the size, shape, and density of the structure so that the dead load can be estimated. This requires experience, and the ability to learn from similar structures that are already completed.
Example
Let us decide that the bridge will be made of concrete. Each bridge beam (a beam spans from pier to pier) will be 30 metres long, 1.5 metres deep, and 0.7 m wide.
Volume of one beam = 30 x 1.5 x 0.7 = 31.5 m3 density of concrete = 2400 kg/m3
Therefore, mass of one beam (dead load) = 31.5 x 2400 = 75,600 kg (= 75.6 tonnes)
Weight of one beam = 75,600 x 9.81 Newtons (say x 10) = 756 kN
OK, we have a number, but how confident are we about that value? For example, concrete is a variable material, our concrete may weigh 2200 kg/m3, or worse, it may weigh 2600 kg/m3, in which case our bridge will have a greater load than we have designed for.
All load calculations involve uncertainty, and so we can use the principles of probability to control the risk that we take when we choose a value for a load. Most data samples approximate to a Normal (Bell) Distribution Curve. This curve is symmetrical about the mean/average, and the standard deviation (σ) is used to indicate the degree of spread of values from the mean. In a normal distribution curve, 68% of values occur within (mean ± σ) and 90% of values occur within (mean ± 1.65σ). Accepted practice is to choose a value for the density that only has a 5% chance of being exceeded (i.e. (mean + 1.65σ)). Therefore, on average, 1 design in 20 will have assumed a material density less than that of the actual material used.
This value is called the CHARACTERISTIC DEAD LOAD.
Live Load
The calculation of live load is more uncertain than the calculation of dead load, but a similar principle applies. Think of the case of a domestic house. How much should we allow for the live load (ie people and furniture)? This obviously varies very much from house to house, and yet when you are designing the house you cannot know how much ‘stuff’ the people will put into it. The large variation in live load values means that the live load probability density curve spreads further than the dead load one – the standard deviation is higher.
With live loads, the accepted practice is to choose a value of the load that has a 5% chance of being exceeded once in 50 years. 50 years is chosen, because that is the design life of most buildings. This is called the CHARACTERISTIC LIVE LOAD.
Some characteristic live load values from the standard are:
- Domestic Houses: 1.5 kPa (150 kg/m2)
- Car Parks: 3.0 kPa (300 kg/m2)
- Offices: 3.0 kPa (300 kg/m2)
- Grandstands: 5.0 kPa (500 kg/m2)
Load Factors
We now have a rational basis for choosing values for the dead and live loads:
- Dead load: choose a characteristic value for the density that only has a 5% value of exceedance.
- Live load: choose a characteristic value of the load that has a 5% chance of being exceeded once in 50 years
Should you design your structure for these characteristic values? If you do, then on average one structure in 20 will be designed for less than its actual dead load, and one structure in 20 will receive more than the design live load during a 50 year period. There would be structures collapsing everywhere! To maintain an acceptable level of safety, we apply load factors to the characteristic dead and live load. These vary depending on the circumstances, and the limit state that we are designing for.
Video Link 2: Dead and live loads.
Limit States
When we design a structure we must think of a ‘checklist’ of things to design for, e.g.
- Is it safe against collapse?
- Will it deflect too much?
- Will it vibrate annoyingly?
- Will it withstand a fire?
These different conditions are called ‘limit states’. If, during its lifetime, the limit state of ‘collapse’ is exceeded, the consequence will be severe – loss of life usually. If the limit state of ‘deflection’ is exceeded the consequence is not so great – people may not feel comfortable, or cracking might occur. Because the seriousness of the consequences varies, the acceptable risk of exceeding the limit state varies also. This variation in risk is achieved by using different load factors for different limit states.
For example, the load factor for the limit state of collapse (commonly called an ultimate limit state) is typically in the range 1.2 to 2. This reduces the chance of the design load being exceeded from 1 in 20 to say 1 in 100,000. The load factor for the limit state of deflection (commonly called a serviceability limit state) is often less than 1.0 With this limit state we are concerned about ‘average’ rather than ‘extreme’ load events. Using a load factor less than 1.0 will increase the chance of the design load being exceeded from 1 in 20 to say 1 in 5 or 1 in 10.