Truss Analysis

- This is the Analysis of forces on
**a single beam**in a system. - There are 2 ways to do this: the
**Method of Joints**and the**Method of Sections**

#### Method of Joints

- This
**isolates**each joint and analyses the forces on the beams connected to it. - With standard force analysis, work out the unknown forces acting on each joint.
- Best methods for analysis are the
**force polygon,**or by**splitting it up into horizontal and vertical components.** **HINT**: It's best to start on a joint with**only one or two unknown**forces.

- Best methods for analysis are the
- Determining the state of the beam can be done by looking at the force's direction.
- If the forces on the beam point away from each other, it is resisting compression (by being in tension) and vice versa.
- Remember that all forces are
**reaction forces**

- Remember that all forces are
**HINTS**:- Remember that the beams carry
**axial loads.**This means that if the force on one joint is in one direction, the force on the 2nd joint it's connected to is opposing that direction. - If a force is pointing
**away**from the joint, the beam is most likely in**tension** - If a force is pointing
**towards**the joint, the beam is most likely in**compression**

- Remember that the beams carry

- If the forces on the beam point away from each other, it is resisting compression (by being in tension) and vice versa.

#### Method of Sections

- This is a way to quickly find the forces on a single member.
- A "Section" is taken through the
**beam that is being analysed**. (In this case, it's Y) - Then, choose the section that is to be used.
- It is optimal to find a section which contains a joint that
**allows the desired beam to be the ONLY unknown force/moment.** - If that is impossible, choose the one with the least unknown forces.

- It is optimal to find a section which contains a joint that
- Once chosen,
**take moments**around a chosen joint to find any**other unknown forces**that could aid in finding the moment.- Remember that
**a force going through a joint cannot have a moment around that joint.** - In the case below, we are trying to find X around the 20kN joint.

- Remember that

Let each truss have a length of 2m.

As $\Sigma M = 0:$

\begin{align} X \times \sqrt{3} + 35 kN \times 1 = 49.17kN \times 2 \end{align}

(2)
\begin{align} X \times \sqrt{3} = 98.34kN - 35kN \end{align}

(3)
\begin{align} X = \frac{63.34kN}{\sqrt{3}} \end{align}

(4)
\begin{align} \therefore X = 36.57kN \end{align}

- Finally, take moments about a (second) chosen moment to find Y.
- For Y's direction, first
**assume**its direction. If it ends up as a negative answer, it's facing the opposite direction. (This is demonstrated below where we take Y to be opposite its direction in the picture) - Below, we are finding Y by taking the moment about the support.

- For Y's direction, first

As $\Sigma M = 0:$

(5)\begin{align} Y \sin{60} \times 2 + 35kN \times 1 + 20kN \times 2 = 36.57kN \times \sqrt{3} \end{align}

(6)
\begin{align} Y \times \sqrt{3} = 63.34kN - 40kN - 35kN \end{align}

(7)
\begin{align} \therefore Y = -6.73kN \end{align}

- Alternatively, we can take the
**horizontal/vertical component**of Y and use the fact that $\Sigma F_{h/v} = 0$ to find out the force on Y.

page revision: 2, last edited: 06 Jul 2011 07:58