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

k;ok 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.

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The reason is simple: the axial and shear forces and bending moment on opposite sides of the cuts are the same. So you don't have $4\times3$ unknowns along the cut, but just $2\times3$. Add that to the three support reactions and you get nine unknowns.

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