Load Paths and Structural Forms
After working through this lecture you should be able to: discuss a range of structural forms, both for two dimensional and three dimensional structures sketch the load path for a given load on a given structural form divide a two dimensional structure into a series of members and joints to enable it to be mathematically modeled
Before we can analyse a structure we must understand how the forces move through it.
Structures can be classified into different structural forms, each carrying the load in a different way.
For a structure to be successful, it must carry the applied loads through to the support along a load path, maintaining equilibrium at every point along the way.
Consider your current situation sitting in a chair.
1. the load (your weight) acts on the seat of the chair 2. the seat carries the load to the chair legs 3. the legs push down on the floor which
transfers the load to the walls 4. the walls carry the load to the footings 5. the footings carry the load to the earth So the load path is s eat-leg s -floor-walls -footing earth.
If any part of this load path is not present, then the structure will fail to carry the load (it will collapse).
For any situation you must be able to trace the load path from the point of application of the load, to the ultimate reaction (usually the earth)
Consider yourself sitting on a bicycle. Trace the load path from your backside to the ground. Now start pedalling – this introduces new loads. How are these transferred to the ground?
Consider again the example of the load path when you sit on a chair.
1. the load (your weight) acts on the seat of the chair the seat carries the load by bending 2. the seat carries the load to the chair legs the legs carry the load by axially compressing 3. the legs push down on the floor which transfers the load to the walls the floor carries the load by bending 4. the walls carry the load to the footings the walls carry the load by axially compressing 5. the footings carry the load to the earth the footings and earth carry the load by compressing
There are five load paths - two which involve bending and three which involve axial compression .
Bending and axial compression are called the
s tructural actions .
Beams are the most common type of structural form.
Beams divert a load, thus creating an open space beneath them. This causes curving of the beam - in this case the top of the beam gets shorter and the bottom gets longer.
Cables are far more efficient than beams - the same amount of material will carry a much greater load. The problem is that a cable only works in tension, and so the load must be in line with the cable. Thus cables are not as useful, and hence not as popular, as beams.
The most famous examples of cable structures are suspension bridges, where the main cable supports many hanger cables.
Another form is the cable stayed bridge where the cables connect directly to the deck.
Cables have the unique property that the shape of the cable changes as the load changes, so that the cable always carries tension only.
Because cables change shape to suit the load (always carrying the load by tension and never by bending moment, shear or torque), we give cables a special name – funicular structures.
An arch carries load by compression. It is helpful to think of the arch as the opposite of a cable, because a cable carries its load by tension.
Arches have an additional complication when compared to cables. Because the arch is in compression, the arch wants to buckle. For this reason, an arch can never be as slender as a cable. To prevent buckling an arch needs to have some bending stiffness. Because an arch has bending stiffness, it cannot change shape to suit the load as a cable does.
For a given load there is one particular shape of arch which would carry that load by pure compression in the arch, and this is the most efficient arch shape for that load. This shape is the funicular shape. The easiest way to find the funicular shape is to put the load on a cable, and see what shape the cable takes up (this will be pure tension). Flip that shape upside down and you have the shape of an arch that carries the load by pure compression. When the shape of an arch is not the correct funicular shape for a given load, the arch will carry the load by a combination of compression and bending moment. The further away the shape is from the funicular shape, the more bending moment there will be in the arch.
A truss can be thought of as a particular type of beam, where all the inner workings of the beam are exposed. Trusses divert a load, in the same way that beams do, thus creating an open space beneath them. The truss curves like a beam (with the top in compression and the bottom in tension for the example shown). The unique thing about a truss is that while the truss as a whole curves, each individual member carries its load by tension or compression. Therefore, individual members get shorter or longer (with no curving), but this causes the truss as a whole to curve.
Beams, cables, arches and trusses are all two dimensional structural forms. They are useful because when engineers develop mathematical models of real structures we treat them as a series of repeated two dimensional structures joined together to form a three dimensional structure. This makes them easier to analyse and easier to build. However, there are times when a structure is truly three dimensional - a load is dispersed along load paths which exist in all three dimensions.
Slabs and Plates When a beam is extended into the third dimension it becomes a slab, or a plate. These bend in two directions at the same time.
Nets or Membranes When a cable is extended into three dimensions a net is created if the cables are kept discrete. If the cables merge together to from a continuum, a membrane is created. Nets and membranes but exciting structures.form some of the worlds most unusual Because of the efficiency of the structure (carrying the load in pure tension), these structures can cover very large areas with very light structures.
Shells and Domes When an arch is extended into three dimensions a shell or dome is created. Like all three dimensional structures, shells and domes provide many alternative load paths for any applied load, and by dispersing the load paths through the structure, thinner and more elegant structures are possible with three dimensional compared to two dimensional structures.
Space frames When a truss is extended into three dimensions aspace truss or space frame is created. These can span large distances because the load is dispersed through many load paths.
Folded Plates A folded plate is an uncommon three dimensional structure, but it illustrates well the importance of shape in determining the strength and stiffness of a structural form. A flat sheet of paper is useless as a beam, but when folded into a series of peaks and valleys it becomes very much stiffer and stronger. This principle has been used to create long span concrete roofs.
Two Dimensional Structural Forms •To create a mathematical model of a structure we need to divide the structure up into a series of linear members. •The members are joined together at nodes. •Certain of the nodes will be restrained against movement these are the supports. •Other nodes are left free to move as the structure deforms.
There is no limit to the number of nodes that can be used when dividing up a structure, however a node must be provided at the following positions, · at every point where the structure is supported · everywhere that the structure changes direction · everywhere that a member changes shape or size The process of modelling a two dimensional structure by dividing it up into a series of members is called discretising the structure - ie modelling it as a series of discrete members.
Three Dimensional Structural Forms Models of three dimensional structural forms are created by dividing the structure up into a series of elements. These elements can be plates, shells etc. This process is more complex than for two dimensional structures. The process of modelling a three dimensional structure by dividing it up into a series of elements is calleddiscretising the structure – ie modelling it as a series of discrete elements.
Beams, cables, arches and trusses are all examples of two dimensional structural forms with the loads being carried by different types of load paths. Plates, slabs, nets, membranes, shells, domes, space trusses and space frames are all examples of three dimensional structural forms with the load being carried by different types of load paths.
Two dimensional structures are modelled by dividing the structure into a series of members
connected at nodes .
Three dimensional structures are modelled by dividing the structure into a series of elements
connected at nodes .
Load path: The way that a load is carried through a structure to the supports.
S tructural actions : All loads are carried by a combination of axial compression or tension, bending moment, shear and torque.
S tructural forms : The elements that make up a structure, and from the load path can be grouped into structural forms, of which beams, cables, arches and trusses are the most common.
Modelling : In order to develop mathematical models we idealise a structure by ‘discretising’ it into members connected at nodes.
