---
# System prepended metadata

title: Analysis of structures
tags: [statics, Mechanical Mechanics]

---

# Analysis of structures
![image](https://hackmd.io/_uploads/r1W4qcMExg.png)

## Stable structure analysis
![image](https://hackmd.io/_uploads/Hkfc5qzNee.png)

One truss with two joint
$$m = 2n-3$$
:::success
$$2n = m+3$$
:::
* number of joint : $n$
* number of Truss : $m$
## Mechanism analysis
:::success
$$P = \frac32N-2$$
:::
* number of pairs : $P$
* number of link : $N$

structure : $2P > 3N-4$
mechanism (Kinematic chain) : $2P = 3N-4$
No constraints : $2P < 3N-4$

## Space Stable structure analysis
:::success
$$m = 3n-6$$
:::
* number of joint : $n$
* number of Truss : $m$

## Equilibrium
* statically indeterminate : 
$$\text{unknowns}>\text{equation}$$
* nonrigid : 
$$\text{unknowns}<\text{equation}$$