The effect of columns differential height
Figure 5.1.41: Frame of common practice, project <B_514> Figure 5.1.41: Frame of common practice, project <B_514>
Figure 5.1.42: 89% of the seismic force is carried by the "short" column. Figure 5.1.42: 89% of the seismic force is carried by the "short" column.
Figure 5.1.43: The bending moment of the "short" column is four times higher than the corresponding moment of the "tall" one. Figure 5.1.43: The bending moment of the "short" column is four times higher than the corresponding moment of the "tall" one.
I.e. 89% of the seismic shear is carried from the first (short) column.
Example 5.1.4: Consider the typical columns 400/400, and seismic acceleration factor a / g =0.10.
Total horizontal force: H = 2·(0.10·800kN)= 160 kN
V_{a}=160 ·8 /9=142.2 kN, V_{b}=160 ·1 /9=17.8 kN
M_{a1}=M_{a2}=142.2·3.0/2=213.3 kNm, M_{b1}=M_{b2}=17.8·6.0/2=53.4 kNm
Left column stiffness: K_{a}=12EI/h^{3}= 31.10·10^{6} N / m
Right column stiffness: K_{b}=1.5E · I/h^{3}=(1.5· 31.10·10^{6} N / m )/12 =3.89 · 10^{6} N/ m
Σ (K)=34.99 · 10^{6} N/ m
therefore δ = H / Σ (K)=160·10^{3}N/(34.99 · 10^{6} N/m) =4.573 mm .
Frame of common practice:
In project <B_514> of the related software, the crosssection of the left column C1 and the right column C2 are 400/400 and 800/400 respectively. Their heights are 3.00 m and 6.00 m respectively. The flanged beam crosssection is 250/500/1010/150 and its span is 5.00 m.
Figure 5.1.44: Elastic line, δ_{max}=6.468 mm Figure 5.1.44: Elastic line, δ_{max}=6.468 mm

Figure 5.1.45: Shear force diagrams Figure 5.1.45: Shear force diagrams

Figure 5.1.46: Bending moment diagrams Figure 5.1.46: Bending moment diagrams

Figure 5.1.47: Axial force diagrams Figure 5.1.47: Axial force diagrams

Modelling of the example with actual fixity degrees on columns i.e. those derived from the structural analysis.
It should be noted that the actual displacement δ=6.468 mm of the crossbar is somewhat higher than the theoretical value δ =4.573 mm assuming fixed end conditions. This is due to the regular crosssection of columns and mainly to the small stiffness of the right column being considerably higher.
The actual stiffness of C1 is K_{a}=V_{a}/δ=(134.3·10^{3}N)/0.006468m=20.73·10^{6} kN/m (against 31.10·10^{6} N/m of the fixedended column).
The actual stiffness of C2 is K_{b}=V_{b}/δ=(25.7·10^{3}N)/0.006468m=3.97·10^{6} kN/m (against 3.89·10^{6} N/m of the fixedended column, i.e. practically the same).
Taking into account the shear effect (Shear effect=ON), the resulting displacement is equal to δ=6.634 mm (against δ =6.468 mm, i.e. the shear effect is minimum).