Name: Understanding and Analysing Trusses
Uploaded: 2024-07-03T18:19:57.000Z
Duration: 17 min 41 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

They are used in bridges, antenna towers, cranes, even in parts of the International Space Station.

They allow us to create strong structures while using materials in a very efficient and cost-effective way.

It is essentially a rigid structure made up of a collection of straight members.

There are two important assumptions we need to be able to make for a structure to be considered as a truss.

First, we need to be able to assume that all of the joints in the structure can be represented by a pinned connection, meaning that members are free to rotate at the joints.

The members of a truss are often rigidly connected using what is known as a gusset plate.

But if the center lines of all the members at a joint intersect at the same point, like they do here, it's reasonable to assume that the joint behaves like a pinned connection.

The second assumption we need to be able to make is that loads are only ever applied at joints of the truss.

We never have loads acting in the middle of a member, for example.

Because all joints are pinned, the members cannot carry bending moments.

This simplifies the analysis of a truss significantly.

Each member has to be in equilibrium, so the forces acting at each end of a member must be equal and opposite.

Each member is either in tension or in compression.

These assumptions are what differentiate a truss from a frame.

Unlike trusses, frames don't necessarily have pinned joints, and so members can carry bending moments.

A frame can also have loads applied directly to its members.

The base shape of a truss is three members connected to form a triangle.

If a load is applied, the angles of the triangle won't be able to change if the length of each of the members stays the same.

This means that the triangle is a very stable shape which won't deform when loads are applied to it, and so it is a great base from which to build a larger structure.

Joining four members together does not form a stable structure.

The angles between members can change without any change in the length of the members, and so using a four-sided shape as the base for building a truss would be a terrible choice.

An easy way to stabilize this configuration is to add a diagonal bracing member to split it into triangles.

We can start with our triangle and build it out to form a structure.

There are a lot of different ways to build a truss, but there are some particularly popular truss designs that you will see again and again, and so they are referred to by specific names.

The one shown here is a Fink roof truss, but there are many more as you can see here.

Later on in this video, I'll cover how these different designs carry loads in different ways.

The members of these trusses are all located in the same plane.

These are called planar trusses, and we can analyze them as two-dimensional structures.

Even seemingly three-dimensional structures can often be analyzed as planar trusses.

The loads are transmitted from the horizontal floor beams to the two vertical trusses on each side of the bridge.

Each of these trusses only carries loads acting in its plane, and so we can analyze it as a two-dimensional structure.

To be able to design or analyze a truss, we need to be able to determine the force in each of its members.

This allows us to check that the member can carry the loads without failing, or gives us the information we need to select the best cross-section for each of the members.

There are two main methods we can use to do this, the method of joints, and the method of sections.

Let's look at the method of joints first, using the Fink roof truss we saw earlier.

First, you draw a free body diagram, showing all of the external loads acting on the truss, and you use the three equilibrium equations to calculate the reaction forces.

Then, you draw a free body diagram for every single joint, and work through them one by one to solve the unknown forces acting at each Since all of the joints are pinned connections, there are no moments, and so you only need to consider equilibrium of the horizontal and vertical forces.

Remember that we are calculating the forces acting at each joint, not the forces in the member.

If a member is in tension, the internal forces will be acting to make the member longer.

For every action, there is an equal and opposite reaction, which means that a member in tension will be exerting a force on the joint which is acting away from the joint.

For members in compression, the force will be acting towards the joint.

Let's work through an example for a slightly simpler truss.

First, let's draw the free body diagram and determine the reaction forces using our three equilibrium equations.

Taking equilibrium of the horizontal forces, the horizontal force at joint A must be equal to zero, because it is the only force in the horizontal direction.

Taking equilibrium of the vertical forces, the reaction forces at joints A and E must sum up to 20 kilonewtons.

Both joints are located at the same distance from joint C, so taking equilibrium of the moments acting about joint C, we can calculate that they both equal 10 kilonewtons.

Now, let's determine the forces acting on each joint.

Since we don't know yet which members are in tension and which are in compression, it's easiest to just assume that all of the members are in tension, and so we'll draw the internal forces as pointing away from each joint.

If we end up with negative values for these forces, it just means that we guessed wrong, and the member is actually in compression.

Now we can work through each of the joints, starting with joint A.

Analyzing trusses involves a lot of resolving forces to different angles, so if you want to be good at it, you're going to need to remember your trigonometry.

All we have to do is apply the equilibrium equations to determine the forces acting on each joint.

Taking equilibrium of the vertical forces, the 10 kilonewton reaction force must balance the vertical component of the force FAB, and so we can calculate FAB as negative 10 divided by sine of the angle of 60 degrees.

Taking equilibrium of the horizontal forces, we get that the force FAC must balance the horizontal component of the force FAB, and so is equal to 5.8 kilonewtons.

That's all of the forces acting on joint A calculated.

The force in each member is constant, and so we now also know the forces acting on the joints at the other ends of these two members.

We can start by considering equilibrium of the vertical forces, which allows us to calculate the force FBC.

And then we can consider equilibrium of the horizontal forces, to calculate FBD.

We then need to work through all of the remaining joints, but we can save a bit of time by noticing that the truss and the applied loads have an axis of symmetry, and so the forces on the other side of the truss must be identical.

That gives us all of the forces at the joints.

We can show which members are in tension, and which are in compression, like this.

One thing you'll notice as you analyze trusses is that some members don't carry any loads at all.

There are two main configurations where we have zero force members.

The first is where we have three members connected at a single joint, and two of the members are aligned.

Here, only one member has a component in the vertical direction, and so to maintain equilibrium of forces at the joint in the vertical direction, the force in this member must be zero.

The second configuration is when we have only two members connected at a joint, and the members are not aligned.

Only one member has a component in the vertical direction, and so both must be zero force members.

By the way, this is true regardless of how the members are oriented, because we can rotate the orientation of the coordinate system we are using to apply the equilibrium equations.

These two configurations only contain zero force members if there are no external loads acting at the joints.

If we have external loads, there will be components in the vertical direction, and so these will not be zero force members.

At this joint here, we have two connected members.

The members are not collinear, and there are no external loads, so they must be zero force members.

And at this joint, we have three members, of which two are collinear.

The vertical member must be a zero force member.

We can remove these members, and so have a much easier starting point for solving the truss.

You'll notice that we haven't removed the two members at this joint.

That is because there is an external load acting here, and so these can't be zero force members.

You might be wondering why anyone would bother including zero force members in a truss if they carry no loads.

They are usually included to provide stability, for example to prevent buckling of long members which are under compression.

Or they may be used to make sure that unexpected loads won't cause the structure to fail.

Let's look at the other method we can use to solve trusses, which is the method of sections.

The first step is the same as the method of joints.

We draw the free body diagram, and use the equilibrium equations to solve the reaction forces.

Next, we make an imaginary cut through the members of interest in our truss, and we draw the internal forces in the cut members.

The internal and external forces must be in equilibrium, and so we can apply the equilibrium equations to solve the internal forces.

When choosing how to cut your truss, remember that we only have three equilibrium equations.