## What Method of joints in truss?

The process of analyzing the truss ie. to find the forces in each member of the truss by using joints of the truss and making all forces acting on joints in the equilibrium equation is known as the method of joints. Here we will learn to determine the force in each member of the truss by Method of joints with example.

There are several methods of analyzing trusses but the joint method is one of them which is very easy to solve. Now, let us see the steps of solving the truss.

## Steps to determine the force in each member of the truss by Method of joints

**Step1:-** Find All Reaction using equilibrium equation

Equilibrium Equation are,

∑Y = 0 (Sum of all Vertical Force)

∑X = 0 (Sum of all horizontal Force)

∑M = 0 (Sum of Moments)

**Step-2:-** Analyze the Joints i.e Draw a free body diagram of each joint (Take those joints which do not have more than two unknown reactions).

**Step3:-** Find unknown reaction in each joint again using the equilibrium equation as Step one.

Note that, we should recognize the zero-force member to make our calculation easier. It is not necessary that every truss has zero force members. So, here I have given two rules which will help you to know the zero-force member easily.

**Zero force members** are those which do not possess any force in it neither compression nor tension.

**How to identify Zero Force Member**?

1) In a joint that has three members out of which two members are collinear and there is no external load or support at the joint. Then the non-collinear member will have zero force.

**Example,**

2) In a joint which carries only two members which are non-collinear and does not carry any external load or supports reaction then both the members will possess zero force.

**Example,**

Now, Let us take an example of finding forced in each member of truss.

## Method of joints Example

**Q) Determine the force in each member of the truss. state if the members are in tension or compression.**

**Solution:-**

Force due to given loading (P-forces)

∑M_{B}=0

R_{A }* 10 = 80 * 2.5

Or, R_{A}= **20 KN (↑)**

And, ∑F_{y }= 0

Or, R_{B}= 80 – R_{A} = 80 – 20 = **60 KN (↑)**

### From Joint A

∑F_{y }= 0

Or, P_{AD}Sin60 + 20 = 0

Or, P_{AD} = 23.09 KN (C)

And, ∑F_{y }= 0

Or, P_{AE} + P_{AD}Cos60 = 0

P_{AE} = **11.54 KN (T)**

### From Joint D

∑F_{y }= 0

Or, -P_{AD}Sin60 – P_{DE}Sin60 = 0

Or, P_{AD} + P_{DE} = 0

Or, P_{DE }= **23.09 KN (T)**

And, ∑F_{x }= 0

Or, P_{CD} + P_{DE}Cos60 – P_{AD}Cos60 = 0

Or, P_{CD} + 11.545 + 11.545 = 0

Therefore, P_{CD }= **23.09 KN (C)**

### From Joint B,

∑F_{x }= 0

Or, P_{BC}Sin60 + 60 = 0

Or, P_{BC }= **69.28 KN (C)**

And, ∑F_{x }= 0

Or, – P_{BC}Cos60 – P_{BE }= 0

Or, P_{BE} = **34.64 KN (T)**

### From Joint C

∑F_{x }= 0

Or, P_{BC}Cos60 – P_{CD} – P_{CE}Cos60 = 0

Or, -34.64 – 23.09 = P_{CE}Cos60

Or, P_{CE }= **23.09 KN (C)**

Final Figure of Truss will be given as,

**Force of Each member are given by,**

Member | Force (KN) | Nature (Tension & Compression) |
---|---|---|

AE | 11.54 | T |

BE | 34.64 | T |

CD | -23.09 | C |

AD | -23.09 | C |

DE | 23.09 | T |

CE | -23.09 | C |

BC | -69.28 | C |

I hope this article on “**Determine the force in each member of the truss by Method of joints**” remains helpful for you.

Happy Learning – Civil Concept

**Contributed by,**

**Civil Engineer – Ranjeet Sahani**

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