Number of total reactions in a structure

[fonseh]

Homework Statement

In the example A , Why the author stated the total reactions = 9 only ? How to determine the total reactions for this type of questions ?

Homework Equations

The Attempt at a Solution

we can see that there is a total of 3 reactions (vertical , horizontal and moment) at the cut of the 4 parts , right (circled part) , and 3 reactions below . So , the total reactions is 4x3 + 3 = 15.

 

[CivilSigma]

When ever you have a closed loop as in this frame, you cut it, and you count the set of internal reactions (only once) as reaction forces.

Looking at the loop we get a total of 3+3 reactions (note that the internal reactions of AD and DA are the same and we do not count them as 6 , but 3 unique ones)
Looking at the supports , one is a pin ∴ 2 reactions and the other is a roller ∴ 1 reaction.

In conclusion, we have 3+3+2+1 =9 reactions