# Internal Forces in Chair Frames

6.2.1.1 Statically Determinate 2-D Structures

By adopting one of the load schemes discussed above, the distribution of internal forces in the system internally statically determinate (Fig. 6.20) can be indicated as follows.

The sums of moments in relation to point B show that:

RaI + F1I1 – F2O1 + *2) = 0; (6.1)

therefore,

Sum of moments in relation to point A,

RbI – F1 (I – h)- F2(h1 + Й2),

leads to the determination of reactions:

 Fig. 6.20 Graph of internal forces: bending moments, cutting forces and normal forces

R, = F'(‘ – ‘■>+ ^ + h2> . ,6:4)

While the sums of projections on the X-axis show that:

Hb = F2. (6.5)

On this basis, for all elements of the construction, a distribution of internal forces can be determined. And so, the bending moments of particular cross sections are illustrated in Fig. 6.20, and their extreme values are, respectively,

Mxi = Ra(I – h>, (6.6)

Mx2 = RaI + Fih, (6.7)

M3 = F2h2, (6.8)

M4 = H, hi. (6.9)

Normal forces can be expressed as follows:

N1 = Ra, N4 = Rb, (6.10)

and cutting forces as follows:

Ti = О, Txi = Ra, Tx2 = Ra + Fu T3 = F2, T4 = H,. (6.11)

On the basis of the characteristics of M, T, N in a selected structural node of a furniture piece (Fig. 6.21), the state of internal forces can be determined, which is necessary for strength calculations aiming to dimension the connectors of furniture joints.

Fig. 6.21 The internal forces acting on the node excluded in thought