((3) pinned at top, fixed at bottom (4) top free, bottom fixed

Column dimension b b = smaller dimension of column cross-section

Rectangular cross-section b = lcr/14

Beams

Beams are structural members primarily loaded in bending. The magnitude of the bending moments influences the dimensions (depth, slenderness, shape of cross-section) and the type of reinforcement (conventional or pre-stressed). Structural beams occur in various forms - with ends fixed, simply-supported, continuous, above the floor (upstand), below the floor (downstand) and in frames.

The conventional rectangular beam is rather rare in i n situ concrete because it is frequently cast monolithi-cally with a floor slab (T- or L-beam) and then functions together with this. If the compression zone in such a beam is wholly within the slab, the depth of the beam is less than that of a standard rectangular member.

Abb. 52: Precast concrete beams in a framed building

Angelo Mangiarotti: industrial building, Bussolengo Barese (I), 1982

Owing to the cost of formwork, adjusting the beam sizes to suit the loads exactly is only advisable in precast-ing works, where forms can be reused economically. For example, the depth of a beam can be designed to track the bending moment diagram, the width can be varied in line with the shear force diagram. On large spans the cross-section can therefore be optimised to save material

(valid as approximation if buckling is not critical)

in. dimension for in situ concrete b = >200 mm in. dimension for precast concrete b = >150 mm

Column dimension for multi-storey column column grid 7.5 x 7.5 m, storey height 3.60 m (normal loading, e.g. offices)

1 floor above column:b = 250 mm

2 floors above column:b = 350 mm

3 floors above column: b = 400 mm

4 floors above column: b = 450 mm in. dimension for in situ concrete b = >200 mm in. dimension for precast concrete b = >150 mm

Column dimension for multi-storey column column grid 7.5 x 7.5 m, storey height 3.60 m (normal loading, e.g. offices)

1 floor above column:b = 250 mm

2 floors above column:b = 350 mm

3 floors above column: b = 400 mm

4 floors above column: b = 450 mm

and hence weight and the beam constructed as a girder or trussed beam (trussing above or below).

The function of a column is to transfer the vertical loads to the f oundation. Carrying horizontal loads simultaneously (shear forces due to wind, earthquakes) calls for correspondingly large cross-sections.

Thanks to the mouldability of concrete, the shape of the cross-section can be chosen virtually at will, but the cost of the formwork and the fixing of the reinforcement place practical limits on this. The "perfect" form is circular because the flexural strength is the same in all directions. However, i n situ concrete columns are frequently square or rectangular to make the f ormwork easier and less costly. An in situ column must be at least 200 mm wide, a precast column 150 mm. The latter are cast horizontally, the surfaces are trowelled smooth or given subsequent treatment depending on the quality required. Spin-casting can be used for both square and round precast concrete columns. In this method the form is filled, closed and rotated to compact the concrete. This results in an absolutely smooth and consistent surface finish.

Slender columns loaded in compression are at risk of buckling; in other words, the more slender a column is, the lower is its permissible load (buckling load). The length of a column is therefore governed by its relationship to its smallest cross-section dimension. The buckling length depends on the type of support at each end, and maybe shorter (= high buckling load) or longer (= low buckling load) than the actual length of the column. Normally, however, columns with pinned ends are met with in superstructure works.

cr cr cr cr

cr cr cr

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