# [RESULTS] Comparison of Local Axis and Global Axis

Hi Sir,

Hope you are doing well!!

First of all, I am sorry for the delay. I know its been a long time.

To answer your last query!!

First regarding static cases like SW

In your model, it is not possible to get the exact results (i.e. local direction results in actual model = global direction results in rotated model) because:

1. The beam end releases are

To explain your last query, I did another Case study of a simple portal frame:

Regarding Simple Static Loads

We have 2 cases:

Case 1 : Load applied in Global X Direction and Frame rotated by an angle 30 degrees.

I applied Nodal Local Axis to all the nodes in the frame

Solid View of the Frame:

Before we come to results :

Nomenclature for Deformations:

DX, DY - Global X and Global Y

dx, dy - Local x and Local y

So, for this frame, if we run the analysis, we check the result of the loaded node:

Global X - DX : 63.054 mm

Global Y - DY : 44.979 mm

Local x - dx: 32.126 mm

Local y - dy : 70.485 mm

Case 2 : Frame rotated by 30 degrees to allign with the Global Axis

The 1000 kN is resolved in Global X and Global Y in such a way that it gives the same effect as the previous case

Also I defined Local x and Local y for all the nodes in such way that it replicates the Global X and Global Y in previous case

So, now we check the results :

Local x - dx : 63.064 mm

Local y - dy : 44.979 mm

Global X - DX : 32.126 mm

Global Y - DY : 70.485 mm

So, to summarise both the cases we got:

So we get exactly the same results for Local and Global and vice e versa for both the cases.

NOW WE DO THE SAME THING WITH RS LOAD CASE:

For Case 1: RS is applied in Global X axis only

For Case 2: RS is applied in 30 degrees to Global X to represent the same case as Case 1:

For Lumped masses for both the cases I applied 100 in Global X and 100 in Global Y

Now we check all the results in same manner we get the following results :

Thre results don't match....the reason is its not similar to static case. Now the deformations are dependent upon 2 things for Dynamic Case:

1. The orientation of Stiffness Matrix

2. The Inertia of masses

Currently both the cases have masses oriented in Global X and Global Y direction, that is why you are getting different results.

So, I did is, I added masses for the CASE 2, in such a way that it has the same effect as 100 and 100 in Global X and Global Y

Hope you are doing well!!

First of all, I am sorry for the delay. I know its been a long time.

To answer your last query!!

First regarding static cases like SW

In your model, it is not possible to get the exact results (i.e. local direction results in actual model = global direction results in rotated model) because:

1. The beam end releases are

To explain your last query, I did another Case study of a simple portal frame:

Regarding Simple Static Loads

We have 2 cases:

Case 1 : Load applied in Global X Direction and Frame rotated by an angle 30 degrees.

I applied Nodal Local Axis to all the nodes in the frame

Solid View of the Frame:

Before we come to results :

Nomenclature for Deformations:

DX, DY - Global X and Global Y

dx, dy - Local x and Local y

So, for this frame, if we run the analysis, we check the result of the loaded node:

Global X - DX : 63.054 mm

Global Y - DY : 44.979 mm

Local x - dx: 32.126 mm

Local y - dy : 70.485 mm

Case 2 : Frame rotated by 30 degrees to allign with the Global Axis

The 1000 kN is resolved in Global X and Global Y in such a way that it gives the same effect as the previous case

Also I defined Local x and Local y for all the nodes in such way that it replicates the Global X and Global Y in previous case

So, now we check the results :

Local x - dx : 63.064 mm

Local y - dy : 44.979 mm

Global X - DX : 32.126 mm

Global Y - DY : 70.485 mm

So, to summarise both the cases we got:

Case 1 | Case 2 | |||

DX | 63.064 | dx | 63.064 | |

DY | 44.979 | dy | 44.979 | |

dx | 32.126 | DX | 32.126 | |

dy | 70.485 | DY | 70.485 |

So we get exactly the same results for Local and Global and vice e versa for both the cases.

NOW WE DO THE SAME THING WITH RS LOAD CASE:

For Case 1: RS is applied in Global X axis only

For Case 2: RS is applied in 30 degrees to Global X to represent the same case as Case 1:

For Lumped masses for both the cases I applied 100 in Global X and 100 in Global Y

Now we check all the results in same manner we get the following results :

Case 1 | Case 2 | |||

DX | 6.657 | dx | 9.162 | |

DY | 7.093 | dy | 3.269 | |

dx | 2.218 | DX | 6.3 | |

dy | 9.472 | DY | 7.412 |

Thre results don't match....the reason is its not similar to static case. Now the deformations are dependent upon 2 things for Dynamic Case:

1. The orientation of Stiffness Matrix

2. The Inertia of masses

Currently both the cases have masses oriented in Global X and Global Y direction, that is why you are getting different results.

So, I did is, I added masses for the CASE 2, in such a way that it has the same effect as 100 and 100 in Global X and Global Y