Coupled onestorey plane frames
As coupled plane frames are defined the plane frames that are connected in such a way that, subject to horizontal forces, they present uniform displacements. The crossbars of the onebay frames illustrated in the following figure have a practically infinite moment of inertia. Both columns of the first frame have moment of inertia Ι whereas the two columns of the second have Ι and 8Ι respectively.
Figure 5.21 Figure 5.21
In conclusion, 73% of the seismic shear force is carried by the fourth column. Example 5.2 : Consider that the first three columns have a typical crosssection 400/400 and are 5.0 m high and that the fourth one differs only regarding one of its sides (800 mm instead of 400 mm/400, Ι _{800/400} =8 Ι _{400/400} ). The seismic acceleration factor is a / g =0.10. H = 4·(0.10·800kN)= 320 kN V_{a} = V_{b} = V_{c} =320 ·1 /11=29.1 kN and V_{d} =320·8/11=232.7 kN M_{a1}=M_{a2}=M_{b1}=M_{b2}= M_{c1}=M_{c2}=29.1·5.0/2=72.8 kNm and M_{d1}=M_{d2}=232.7·3.0/2=349.1 kNm K_{a}=K_{b}=K_{c}= 12 · EI / h ^{3} =12 · 32.8 · 10^{9} · Ν /m^{2} · 21.33 · 10^{4}m^{4}/(5.0^{3} · m^{3})=6.72·10^{6} N / m K_{d}=12E · 8I/h^{3}=8· 6.72·10^{6}N/m =53.74 · 10^{6} N/m Σ (K)=11· 6.72·10^{6}= 73.89 · 10^{6} N/m Therefore, δ = H / Σ (K)=320·10^{3}N/(73.89 · 10^{6} N/m) =4.331 mm In project <B_520> of the related software, the crosssection of columns C1, C2 and C3 is 400/400 and C4 is 800/400. The height of all columns is 5.0 m. The crosssection of the flanged beam is 250/500/1010/150 and its span is 5.0 m.
Figure 5.22: The structural frame model fully stiffened, project <B_520> Figure 5.22: The structural frame model fully stiffened, project <B_520>
Figure 5.23: Elastic line, δ=8.078mm Figure 5.23: Elastic line, δ=8.078mm

Figure 5.24: Shear force diagrams Figure 5.24: Shear force diagrams

Figure 5.25: Bending moment diagrams Figure 5.25: Bending moment diagrams
 It should be noted that the actual displacement of the crossbar δ=8.078 mm is almost twice the value of the corresponding theoretical value δ=4.331 mm assuming fixed end conditions. This is mainly due to the strong column and the normal beam, which results in a significantly smaller actual stiffness. The actual stiffness of columns C1, C2 K_{a}=K_{b}=V_{a}/ δ =44.5·10^{3}N/0.008078=5.51·10^{6} kN/m as well as the actual stiffness of column C3 K_{c}=V_{c}/ δ =52.0·10^{3}N/0.008078m=6.44·10^{6} kN/m differ slightly from the corresponding value (6.72·10^{6} N/m) of the fixedended column. On the contrary, the actual stiffness of column C4 K_{d}=V_{d}/ δ =179.0·10^{3}N/0.008078m=22.16·10^{6} kN/m differs significantly from the corresponding value (53.74·10^{6} N/m) of the fixedended column.
