Question

Can someone explain to me how my book came up with the free body diagram on the right side from the diagram on the left side. Will rollers always have positive normal force?

Answer 1

@dan815 we need you here dan,

Answer 2

This is the explanation from the book: "In Example 1 the truss is composed of structural elements which,
taken all together, constitute a rigid framework. Thus, we may remove
the entire truss from its supporting foundation and treat it as a single
rigid body. In addition to the applied external load P, the free-body diagram must include the reactions on the truss at A and B. The rocker at
B can support a vertical force only, and this force is transmitted to the
structure at B (Example 4 of Fig. 3/1). The pin connection at A (Example 6 of Fig. 3/1) is capable of supplying both a horizontal and a vertical
force component to the truss. If the total weight of the truss members is
appreciable compared with P and the forces at A and B, then the
weights of the members must be included on the free-body diagram as
external forces.
In this relatively simple example it is clear that the vertical component Ay
must be directed down to prevent the truss from rotating clockwise about B. Also, the horizontal component Ax
will be to the left to
keep the truss from moving to the right under the influence of the horizontal component of P. Thus, in constructing the free-body diagram for
this simple truss, we can easily perceive the correct sense of each of the
components of force exerted on the truss by the foundation at A and can,
therefore, represent its correct physical sense on the diagram. When the
correct physical sense of a force or its component is not easily recognized by direct observation, it must be assigned arbitrarily, and the correctness of or error in the assignment is determined by the algebraic
sign of its calculated value "

Answer 3

The problem I have is in this part "In this relatively simple example it is clear that the vertical component Ay must be directed down to prevent the truss from rotating clockwise about B."

From my point of view to me it looks like the downward force of P and upward force of By cancel each other out so the extra force from Ay will be extra and create a moment.

Answer 4

The vertical component of P and vertical component Ay is equal to upward reaction of the roller at point B... thus the reaction force of the roller at point B is distributed to two vertical components acting downward so as to maintain the truss in equilibrium. There will be no extra force among the vertical components.
\[\sum_{upward}^{+} F = 0\]
\[B _{y}-A _{y}-P _{y}=0\]
\[B _{y}=A _{y}+P _{y}\]

Answer 5

How do you determine the direct of the vertical forces at point A and B with only knowing the force P?

Answer 6

Although not mentioned in the example, dimensions such as distances from either points A, or B, or P is given as well angles between members of the truss, so that another solution to solve forces component is by means of summation of moments be zero... :)