2.3.1 Equilibrium equations of beam joints

Equilibrium equations of joint T2s. The equilibrium equations of the beam elements at joint or node points set the internal and external reactions $\mathbf{\mathcal{C}_{T2s}}$ equal to the sum of the applied loads (see Fig. 2.17).

Figure 2.17: Equilibrium of joint T2s

$$\left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] \lef... ...rray}{c} Q^{\left( 2\right)}_{A} \\ M^{\left( 2\right)}_{A} \end{array}\right]$$

$$- \left[\begin{array}{c} C_{z} \\ C_{y} \end{array}\right] = \left[\begin{array}{c} F_{z} \\ \mathcal{M}_{y} \end{array}\right] \quad$$ (2.47)

or

$$\mathbf{T_{1}}\cdot \mathbf{s^{\left( 1\right) }_{2L}} + \mathbf{... ...eft( 2\right) }_{2A}} - \mathbf{\mathcal{C}_{T2s}} = \mathbf{\mathcal{F}_{T2s}}$$ (2.48)

        

Equilibrium equations of joint T1s. The external force $F_{z}$ at the joint is not shown in Fig. 2.18.

Figure 2.18: Equilibrium of joint T1s

$$\left[ \begin{array}{cc} 1 & 0 \end{array} \right] \left[\begin{a... ...rray}{c} Q^{\left( 2\right)}_{A} \\ M^{\left( 2\right)}_{A} \end{array}\right]$$

$$- \left[\begin{array}{c} C_{z} \end{array}\right] = \left[\begin{array}{c} F_{z} \end{array}\right] \quad$$ (2.49)

or

$$\mathbf{T^{o}_{1}}\cdot \mathbf{s^{\left( 1\right) }_{2L}} + \mat... ...eft( 2\right) }_{2A}} - \mathbf{\mathcal{C}_{T1s}} = \mathbf{\mathcal{F}_{T1s}}$$ (2.50)