Determine the moments in the frame shown in Figure 11.20 for a value of W = 0.01375 PE. All the members are of uniform section.

Question

Determine the moments in the frame shown in Figure 11.20 for a value of [latex]W = 0.01375 P_{E}[/latex]. All the members are of uniform section.

Accepted Answer

As a first approximation, the axial force in each column is taken as 10 W and in the beam as zero. The stiffness, carry-over factors, and initial sway moments are:

[latex]\begin{aligned}s_{23} &=6 E I / l \s_{21} &=n E I / l \&=0.5 E I / l \c_{21} &=o / n \&=-1.27 / 0.5 \&=-2.54 \M_{12}^{F} &=M_{21}^{F} \&=-m W l / 4 \&=-0.282 Wl\end{aligned}[/latex]

The distribution factors at joint 2 are [latex]d_{23}=12 / 13[/latex] and [latex]d_{21}=1 / 13[/latex], and the final moments are:

[latex]\begin{aligned}M_{23} &=0.282 Wl imes 12 / 13 \&=0.260 Wl \M_{12} &=-0.282 Wl-2.54 imes 0.022 Wl \&=-0.338 Wl\end{aligned}[/latex]

The corresponding values obtained when the axial forces in the columns are neglected are:

[latex]\begin{aligned}M_{23} &=0.25 Wl imes 6 / 7 \&=0.214 Wl \M_{12} &=-0.25 Wl-1 imes 0.036 Wl \&=-0.286 Wl\end{aligned}[/latex]

Question 11.2.7: Determine the moments in the frame shown in Figure 11.20 for...

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