### SIMLIFICATION OF BUILDING FRAMES

It is very important to simplify building frames, as some building frames are very complex in behavior with the requirement of accounting the possible alternates in load placement. The determination of moments with reasonable accuracy is performed, creating some approximation but reducing substantial amount of computation.

During the life time of a structure, the individual members of its frame must be designed for the most worst combination of loads which can reasonably be expected to occur. The dead loads which can constant but live loads like floor loads from human occupancy can be placed in various ways resulting some worst conditions of loading (moment,shear,torsion etc.) to the member which is larger than that of normal or others.
The distortions of the various frame members are seen to be largest in, and immediately adjacent to, the loaded span and to decrease rapidly with increasing distance from the load. Since bending moment are proportional to curvature, the moments in remote members are correspondingly smaller than those in, or close to, the loaded span.
In addition to investigation of maximum span moments, it is often necessary to investigate minimum span moments. Dead load, acting as it does on all spans, usually produces only positive span moments. But, placement of live load in arbitrary member results to bend the unloaded spans upward, i.e., to produce negative live-load moments are in the span.
If these negative live-load moments are larger than the general positive dead-load moments, a given girder, depending on the load position, may be subjected to at one time positive span moments and another time negative span moments. It must be designed to withstand both types of moments, i.e., it must be furnished with tensile steel at both top and bottom.
In case of column, the largest moment occur at the top or bottom.

ACI 8.9

For negative support moments

For positive span moments

Simplification considering sub frames
For building frames with reasonably regular outline, not involving unusual asymmetry of loading or shape, the influence of side sway caused by vertical loads can be neglected. In the case, moments due to vertical loads are determined with sufficient accuracy by dividing the entire frame into simpler sub frames. Each of these consists of one continuous beam, plus the top and bottom columns framing into that particular beam. Placing the live loads on the beam in the most unfavorable manner permits sufficiently accurate determination of all beam moments, as well as the moments at the top ends of bottom columns and at the bottom ends of the top columns. For this partial structure, the far ends of the columns are considered fixed, except for such first floor or basement columns where soil and foundation conditions dictate the assumption of hinged ends.
ACI 8.9
The live loads may be considered to be supplied only to the floor or roof under consideration and the far ends of the columns may be assumed as fixed.
When investigating the maximum negative moment at any joint, negligible error will result if the joints second removed in each direction are considered to be completely fixed. Similarly, in determining maximum or minimum span moments, the joints at the far ends of the adjacent spans may be considered fixed. Thus individual portions of a frame of many members may be investigated separately.

In regards to columns, the ACI code indicates :

ACI 8.9
1) Columns shall be designed to resist the axial forces from loads on all floor and the maximum bending due to design loads on a single adjacent span of the floor under consideration. Account shall be taken of the loading condition giving the maximum ratio of the bending moment to axial load.
2) In frames or continuous construction, consideration shall be given to the effect of unbalanced floor or roof loads on both exterior and interior columns and of eccentric loading due to other causes.
3) In computing moments in columns due to gravity loading, the far ends of columns built integrally with the structure may be considered fixed.
4) The resistance to moments at any floor or roof level shall be provided by distributing the moment between columns immediately above and below the given floor in proportion to the relative column stiffness and conditions of restraint.