One-storey plane frames

Fixed-ended column:

Frames are composed of connected columns and beams behaving as one uniform structure i.e. plane frames comprise many columns connected through beams or slabs. Engineers or engineering students are more familiar with the effects of gravity loads due to their daily exposure to gravity, in contrast to the effects of horizontal seismic forces that are not a daily phenomenon

One-end-fixed column:

The fixity degree of a column end, in a specific direction, depends on the relative stiffness between the column and its framing beams.

The fixity degree varies from fixed to pinned. When a weak column (e.g. cross-section 300/300) is connected to strong beams (e.g. concrete beams with height 800mm) the connection could be considered as fixed. On the contrary, when the column top is connected to a plain slab and the column base is connected to weak footing in soft soil without foundation beams, the connections could be idealised as pinned.

In the case of a column pinned at both ends, the equivalent member is not subjected to bending thus carrying neither bending moments nor shear forces. Indicatively, the case of a pin-ended column could be met at a storey without beams, at the roof and at the floor.

80% of the seismic force is carried by the fixed-ended column

In case of seismic action, each column top would be forced to develop identical displacement δ regardless of its stiffness.

89% and 11% of the seismic action are carried by the strong column (800/400) and the weak column (400/400) respectively

In the one-bay frame of the figure, the second column is considered having eight times higher moment of inertia than the first one.

The structural frame model without rigid bodies but fully stiffened

Elastic line, δ_max=1.366 mm

Shear force diagrams

Bending moment diagrams

Axial force diagrams

In the one-bay frame of the following figure, the second column is considered having two times the height of the first one. The crossbar moment of inertia is infinite. Such cases are met in practice e.g. at a store with a mezzanine or in case of a split level foundation.

89% of the seismic force is carried by the “short” column.

The bending moment of the “short” column is four times higher than the corresponding moment of the “tall” one.

In project <B_514> of the related software, the cross-section 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 cross-section is 250/500/1010/150 and its span is 5.00 m.

Elastic line, δ_max=6.468 mm

Shear force diagrams

Bending moment diagrams

Axial force diagram