Portal Frames - Structural Forms.

By far the most common form of structure for single-storey structures is the portal frame, the principal types being shown in Fig. 1.20.

Spans of up to 60m can be achieved by this form of construction, the frame generally comprising hot-rolled universal beam sections. However, with the increase in understanding of how slender plate elements react under combined bending moment, axial load and shear force, several fabricators now offer a structural frame fabricated from plate elements. These frames use tapered stanchions and rafters to provide an economic structural solution for single-storey buildings, the frame being ‘custom designed’ for each particular loading criterion.

Portal-frame structures
Fig. 1.20 Portal-frame structures

Roof slopes for portal frames are generally of the order of 6° but slopes as low as 1° are becoming increasingly popular with the advent of new cladding systems such as standing seam roofs. It should be noted, however, that frame deflections at low slopes must be carefully controlled, and due recognition must be taken of the large horizontal thrusts that arise at the base.

Frame centres are commonly of the order of 6–7.5m, with eaves heights ranging from 6 to 15m in the case of aircraft hangars or similar structures.

Resistance to lateral loading is provided by moment-resisting connections at the eaves, stanchion bases being either pinned or fixed. Frames which are designed on the basis of having pinned bases are heavier than those having fixity at the bases, although the increase in frame cost is offset by the reduced foundation size for the pinned-base frames.

Parallel-flange universal sections, subject to meeting certain physical constraints regarding breadth-to-thickness ratios of both flanges and webs, lend themselves to rapid investigation by the plastic methods of structural analysis. The basis of the plastic method is the need to determine the load applied to the frame which will induce a number of ‘plastic hinges’ within the frame, thereby causing failure of the frame as a mechanism.

This requirement is best illustrated by the following simple example.

Considering the pinned-base frame shown in Fig. 1.21(a), subject  to a uniform vertical load, w, per unit length: the reactions at the foundations are shown in Fig. 1.21(b). The frame has one degree of indeterminacy. In order  that the frame fails as a mechanism, at least two plastic hinges must form (i.e. the degree of  indeterminacy + 1) as shown in Fig. 1.21(c). (It should be noted that although four hinges are shown in Fig. 1.21(c), due to ‘theoretical’ symmetry only one pair either side of the apex will in fact form, due to the obvious imperfections in both loading and erection conditions.)

Structural behaviour of pinned-base portal
Fig. 1.21 Structural behaviour of pinned-base portal

In many structures, other than the most simple, it is not clear where the plastic hinges will form. There are several methods available to the design engineer which greatly assist the location of these hinge positions, not least the abundance of proprietary software packages specifically relating to this form of analysis. Prior to the
use of these packages, however, it is imperative that the engineer fully understands the fundamentals of plastic analysis by taking time to calculate, by hand, several design examples. The example which follows uses a graphical construction as a means of illustrating the applications of the method to a simple portal frame.

The frame shown in Fig. 1.22(a) has one degree of indeterminacy. It is made  statically determinate by assuming a roller at the right-hand base as shown in Fig. 1.22(b), and the free-bending moment diagram drawn as shown in Fig. 1.22(c).

Application of graphical method
Fig. 1.22 Application of graphical method

The reactant line for the horizontal force ‘removed’ to achieve a statically determinate structure must now be drawn as follows:

Therefore, by rotating the reactant line through point O, the positions of the bending moment of equal magnitude in the positive and negative regions can be found and the member sized accordingly based on this value of bending moment.

Having found the positions of the reactant line which gives the number of hinges required for a mechanism to form, in this case two, the reactant  line for the stanchions can be drawn through point O, a distance h1 from the end of the free-bending moment diagram. The unknown reaction, H, is then calculated as H = MD/h1.

In a majority of instances, portal frames are constructed with a haunch at the eaves, as shown in Fig. 1.23(a).

Depending on the length/depth of the haunch, the plastic hinges required for a mechanism to form are shown in Figs. 1.23(b) and (c). The dimensional details for the haunch can be readily investigated by the graphical method by superimposing the dimensions of the haunch on the free-bending moment diagram. The reactant line can then be rotated accordingly until the required mechanism is achieved and members sized accordingly.

Alternative hinge locations for haunched portal frames
Fig. 1.23 Alternative hinge locations for haunched portal frames

Haunches are generally fabricated from parallel beam sections (Fig. 1.24). In all cases, the haunch must remain in the elastic region. A detailed check is required along its length, from a stability point of view, in accordance with the requirements laid down in the relevant code of practice. In some instances, bracing of the bottom flange must be provided from a purlin position within its length, as shown in Fig. 1.25.

Haunch fabrication
Fig. 1.24 Haunch fabrication
Bottom flange restraint
Fig. 1.25 Bottom flange restraint

Portal frames analysed by the plastic methods of structural analysis tend to be more economical in weight than their elastically designed counterparts. However, engineers should be aware that minimum weight sections, and by inference minimum depth sections, have to be connected together to withstand the moments and forces induced by the applied loading. Particular attention should be paid at an early stage in the design process to the economics of the connection. Cost penalties may be induced by having to provide, for example, gusset plates between pairs of bolts should the section be so shallow as to necessitate a small number of highly-stressed bolts. In addition, end plates should not be much thicker than the flanges of the sections to which they are attached.

Provided the engineer is prepared to consider the implications of his calculated member sizes on the connections inherent in the structure at an early stage, an  economic solution will undoubtedly result. Leaving connection design solely to the fabricator, without any consideration as to the physical constraints of providing  a number of bolts in an extremely shallow depth, will undoubtedly result in a con- nection which is both difficult to design and fabricate, and costly.

Having sized the members based on the previous procedure, it is imperative that an analysis at serviceability limit state is carried out (i.e. unfactored loads) to check deflections at both eaves and apex. This check is required not only to ascertain whether deflections are excessive, but also as a check to ensure that the deflections and accompanying frame movement can be accommodated by the building envelope without undue cracking of any brickwork or tearing of metal cladding sheets at fixing positions. Excessive lateral deflections can be reduced by increasing the rafter size and/or by fixing the frame bases. It should be noted that the haunch has a significant effect on frame stiffness due to its large section properties in regions of high bending moment.

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