GB2136841A - Portal frame structure having three pivot mounting - Google Patents

Abstract

Each upright support of the arch frame is pivotally mounted at its foot on its respective foundation, and has a strengthened eaves connection provided along an inner face at the upper end thereof to connect the respective roof support beam thereto. The roof support beams extend towards each other to meet at a pivoted ridge connection. In this arrangement the eaves connection effectively acts as a further pivot point. The object of this design is to provide a more efficient use of structural members than is possible with conventional designs.

Description

SPECIFICATION Arch frame This invention relates to an arch frame for a pitched roof comprising a pair of horizontally spaced upright supports having their feet mounted on respective foundations and provided at their upper eaves ends with mountings for a roof-supporting structure, and a pair of roof-support beams mounted one at the upper end of each upright support and extending towards each other to meet at a pivoted ridge connection of a pitched roof.

Conventionally, arch frames have upright support beams, or "stanchions", which are steel beams bolted substantially rigidly at their feet to respective concrete foundations by a series of four or six bolts, and which have haunches provided at their upper eaves ends in order to strengthen the connections of the roof beams thereto. The conventional design of the arch frame is carried out according to a centroidal theory, described in more detail below.

The present invention seeks to provide an arch frame structure, primarily for a pitched roof, which embodies a new design theory and which provides a more efficient use of structural members in the frame than is possible with conventional arch frames designed and constructed according to existing design theories.

Conventional design criteria, and evolution therefrom towards an arch frame structure according to the invention will now be described with reference to Figs. 1 to 1 2 of the accompanying drawings.

The design of buildings by plastic collapse methods dates back to the research work carried out in the 1 940s. Since then and most particularly over the last 20 years-the plastic design of portal frames has been the most popular design method for this type of structure.

The traditional approach to the design of these frames has been by RIGID plastic methods which pre-supposes a collapse load will occur when sufficient plastic hinges have been formed to create a mechanism. The definition of plastic hinges and a mechanism is well-defined. However-whether such a condition in fact results in catastrophic collapse is open to consideration.

It is not necessary in this approach to consider elasto plastic load-deflection time history of the frame and such considerations as strain hardening and PA effects are ignore dor considered of secondary importance.

This approach to design has been proved adequate for relatively straight-forward and simple structures. However---once a reasonable level of complexity and redundancy is apparent-then unique and unambiguous rigorous solutions are more difficult to achieve. In the case of multi bay portal frames then collapse of individual spans of the frame or local joint rotations at a valley condition could constitute failure and the remaining members in the structure will be in some intermediate elasto plastic condition. Such a stress state is not predicted by conventional rigid plastic theory. In consequence the design of such structure is open to interpretation and can be somewhat ambiguous.

In addition to the ambiguities of design interpretation for complex structures-it is also important to highlight some additional areas of ambiguity which are apparent in the traditional design procedures.

It is probably pertinent to list the obvious limitations of the rigid plastic method, making reference to Fig. 1 of the attached drawings.

1 Simplistic centroidal model Fig. 1 2 An upper bound solution for load factor 3 Non-consideration of secondary effects such as PA, strain hardening 4 Consideration of the finite size of members 5 Plastic instability of members and of hinges considered based on the bound solution 6 Unable to consider complex boundary conditions such as super structure, sub structure interaction 7 Considerations such as asymmetrical loading on multi bay frames cannot necessarily be treated rigorously 8 Input to model complex muiti-bay frames It may therefore be pertinent to consider a more rigorous structural model which will allow for the load deflection history of the frame to be predicted; to assess the behaviour of the structure at an intermediate loading condi tionand to be able to consider the finite size of members; complex boundary conditions; second order effects such as PA and strain hardening and to be able to predict the actual rotation of hinges through the load deflection history of the frames. Such mathematical models require sophisticated computing techniques to carry out the numerical calculations and hence these are essentially computer aided methods and not manual aids.

The computer models/system being used for the purposes of the subsequent study are developed and allow for highly sophisticated modelling of line elements in any geometric configuration with internal pins, yielding or non-yielding ties; instability functions; PA effects and strain hardening. The limitations of the rigid plastic approach indicated previously will now be examined with a view to a more sophisticated model.

The simplistic, centroidal model of the rigid plastic approach to analysis and design is quite reasonable when the depth of the member is small in comparison with its length. In the early uniform frame designs for portal buildings this was the case. However more recent forms of portal construction utilise eaves haunching and in consequence although the rafter elements become more slender, the overall haunch depth eaves height ratio has become significantly increased. It is not unusual for the haunch depth to represent in excess of 15% of the overall eaves height of the building.

In addition-there is an implied inconsistency in modelling the connectivity of the eaves haunch. Modern methods assume a neutral axis/point of rotation of the eaves haunch to be about the compression flange.

In effect this implies that the thrust line for compression is at that point. Consideraton of the base plate would also indicate that the point of rotation on a pin base would be about the outer flange for dead and super loading.

Consideration of Fig. 2 indicates a proposed new model. The lines of compression thrust can be interpreted as being due to arching effect--albeit shallow arching. Consideration of any other materials such as masonry or concrete would accept such arching effects as part of the structural model. Although steel is elastic and ductile--being able to resist compression and tension with easy this still does not preclude that natural load paths will be found.

The shallow arching model can be idealized as a series of centroidal lines and the finite size of the members being represented by rigid arms representing the plane sections phenomenon of bending theory.

An alternative would be an inclined assumed thrust path model and this should give similar correlation with the rigid arm assumptions that second order effects such as PA and strain hardening would require further investigation.

A series of designs and analyses have been undertaken to investigate the correlation between a simple rigid plastic idealization, the centroidal elasto plastic idealization and the new models taking into account finite size members and shallow arching. For simplicity-second order effects, PA and strain hardening have not been considered.

The frames under consideration were simple 30 m span, 6 m eaves height, 1:10 pitched portal. The length of the haunch was varied initially from 2.5 m to 100 mm increments to elevate the collapse load factor and hence investigate other phenomena such as rotation of hinges and load deflection history of the frame. The initial rigid plastics and elasto plastic design and analysis correlated with remarkable accuracy. The proposed new structural models however gave significantly enhanced load factors and also showed they were insensitive to change in haunch length-in the regions considered. Hence it was necessary to carry out additional analysis with reduced haunching. The results of these tests are tabulated in Fig. 3 and indicate the potentially large reserve of strength in frame buildings designed on the traditional centroidal model.It is of course necessary to verify that the shallow arching effects do in effect occur. Recent finite elements modelling has indicated a very high likelihood that this is the case but experimental tests on models or full scale buildings would be valuable to confirm the validity of this approach.

A simple intuitive verification of this model would be to consider the following simple structure, making reference to Figs. 4, 5 and 6.

Figs. 4 5 and 6 indicates a series of frames with pinned rafters and doubly propped at intermediate points. The bending moment diagrams indicated are similar to that of a continuous beam. If these prop members are then raked to the stanchion feet and triangulated then on a centroidal model the same bending moment distribution is evident. These struts are now raked from the rafters to the stanchion at some intermediate height and now the rafter bending moment diagrams remain the same. However the bending moments in the stanchions now become modified because of the introduction to the intermediate point load from the thrust on the strut. Hence this simple triangulated knee brace acts in the same way as a haunch and produces an equilibriating moment by a direct force system and not by flexure.It would therefore be possible to remove the web material from a haunch---ensuring flange stability and result in a bending moment diagram similar to that postulated. It seems reasonable therefore that the flexural distribution of stress/moment around portal frame building is of this nature and that the connectivity of the haunch zone is achieved by a triangulated force system.

The finite element model already referred to indicates this form of stress around the haunch zone. Taking this model further the knee brace is connected on the outer flanges of the rafter and stanchion. The resultant shears from this activity are eccentric to the centroid of the members. Hence the discontinuity of moment similar to that at a crane bracket-will be evident at the underside and the rafter end of the haunch. Fig. 7 Another area of interest and some conten tions concerned with the behaviour in the vicinity of the haunch and what constitutes adequate bracing of this sensitive region.

There do not appear to be any freely available test results nor is there any mathematical model which demonstrates that the number and type of lateral braces is necessary in order to ensure that the desired load factor against collapse is achieved for the frame. The point is that when the collapse load of a pinnedbased frame is achieved, the degree of plasti city present is usually quite small. Arguments as to restraint requirements in this sensitive zone are sometimes based upon the presumption that large degrees of plasticity and associated rotation of the hinge will occur. This is however demonstrably incorrect and in fact the two plastic hinges in a well-designed frame often form with little disparity between the loads at which plasticity occurs.It is therefore questionable whether there is any significant reduction in the carrying capacity of such frames if bracing were provided solely to cater for elastic conditions.

To investigate this supposition-two simple beam tests were carried out under the action of a central point load. The central portion of one beam was stiffened to simulate a haunch zone whilst the other specimen was for control purposes. Both the stiffening arrangement and the post yield buckling behaviour of the haunch beam can be seen in Fig. 8. The load deflection/rotation characteristics of the two beams are plotted in Fig. 9. It can be seen from this plot that the load carrying characteristics of the beam were not affected by the lateral instability of the hinge zone.In addition-the restraint requirement for plastic hinges of redundant structures such as portal frames must be dependent upon the degree of rotation they undergo to achieve the design load factor not the collapse load factor it if the first hinge to form does so at a load factor of 1.7 then no restraint is necessary to allow the hinge to rotate. Consideration of the performance of the frames already studied will give an indication of the load factors of the formation of the first hinge together with their associated rotations at design load factor. Fig.

10 is a plot of the rotation of the first hinge to form against the load factor of collapse. The results indicated that for the 1:10 pitch frame when the collapse load factor was 1.93-the first hinge formed at the design load factor 1.7. Hence no restraint was required at the hinge position to allow rotation. In addition when the collapse load factor was 1.7 then the first hinge to form had rotated by 1.05 degrees. It can be seen from Fig. 9 that this level of rotation did not severely affect the load carrying capacity of the test specimen.

The 2:10 pitched frames had the following characteristics-collapse load factor of 2.05 first hinge to form 1.7; collapse load factor 1.7; rotation of first hinge at collapse 1.64 degrees.

It is evident therefore that if the previously postulated model of shallow arching and finite size of members has any validity then the load factor at the formation of the first hinge in practice for frames designed by the simplistic, centroidal approach will be in excess of 1.7 and therefore no requirement for positional restraint will be necessary.

The topic of sub-structure super-structure interaction on industrial buildings has received little or no attention, as far as we are aware. It is common practice to consider the effect of tying action of a floor slab to eliminate the horizontal thrust and hence simplify the foundation design. This tie action could in fact be utilized to good effect by acting as an intermediate element and allowing a plastic hinge to occur at the floor level-in effect fixing the base. The resultant equilibrating couple being produced by tie action in the floor slab and passive compression forces is produced between the base and the sub-grade. A simple centroidal model of this has been considered for the example in Fig. 11. The results are tabulated in Fig. 1 2 and it can be seen that a significantly enhanced load factor is achieved by considering this tie force.Studies already carried out (and for expediency not outlined hereFindicate reductions in the order of 15-20% on hot rolled materials when floor tying action is considered. It is necessary to give special consideration of the foundation design. However in the examples consider end no addition in foundation cost would have been necessary to achieve these overall savings.

Finally attention has been focused recently on the design of multi bay frames and the necessity to consider or not asymmetrical laading of symmetrical structure. A series of analyses were carried out on a twin span frame of similar geometry to the 30 m single span frame. It was found that with one span fully loaded-a 30% reduction in the adjacent span super-load could be considered-without any effect on the original dead and super-load design. In addition-further reduction created distress in the centre column only and such a problem could be overcome by suitable detailing to ensure that the central member acting as a pin prop and hence could not attract any moment. In those circumstances-asymmetrical super loading would not have any effect at all on the design.Consideration of a similar problem for the case of valley beams found that the torsional stiffness of such beams in practical circumstances cannot attract significant moment, and therefore would not be considered to be a practical design constraint.

According to the invention there is provided an arch frame for supporting a pitched roof comprising a pair of horizontally spaced upright supports having their feet mounted on respective foundations and provided at their upper eaves end with mountings for a roofsupporting structure, and a pair of roof beams mounted one at the upper end of each upright support and extending towards each other to meet at a pivoted ridge connection of a pitched roof, in which:: at least one of said upright supports is pivotally mounted at its foot on its respective foundation; a strengthened eaves connection is pro vided along an inner face at the upper eaves end of said one upright support to connect the respective roof support beam thereto; and the arrangement of the pivotal mounting of the upright support on its foundation, and of the strengthened eaves connection, are such that the strengthened eaves connection provides a pivotal mounting for the roof support beam on the inner face of the upright at a position vertically spaced from the upper end of the support.

It is preferred that the other of the upright supports is similarly mounted on its foundation, and provided with a similar strengthened eaves connection to said one upright support.

Thus, in respect to each half of the roofsupporting structure, there will be a three pivot type of mounting. Starting at the ridge connection, there is a common pivot for both of the roof beams which provides a first pivot, and then each roof beam is effectively pivotally connected, on a second pivot, to the upper end of its upright support via the respective strengthened eaves connection, and finally the upright support is pivotally mounted, on a third pivot, on its foundation.

Such an arrangement provides a transmission of compressive thrust between the first and second pivots (or bearings) via the roof beam and strengthened eaves connection. Insofar as the second pivot is spaced below the upper end of the upright support, it applies a turning movement in one direction about the third pivot. However, this turning moment is readily resisted by a restoring moment in an opposite direction, via a longer lever arm, provided by the application of tension to the upper end of the support via the strengthened eaves connection. The bending stresses generated thereby are readily absorbed by the upright support, and therefore a simple pivot (the third pivot) type of mounting of the upright on the foundation is both sufficient and satisfactory.

Conveniently, the strengthened eaves connection is provided by a haunch, which may take a generally triangular form, and which contributes to the strength, and to the mounting of the roof beam on the upright support.

The haunch provides a path for the line of compressive thrust transmitted between the first and second pivots.

In a preferred arrangement, the haunch includes a substantially vertical end plate (forming one side of the triangular arrangement) which is secured by any suitable fasteners, preferably bolts, to the upper region of the inside face of the upright support. The bolts are arranged in vertically spaced array, with a lowermost bolt or bolts effectively forming the "second pivot". The remaining bolts connect the haunch (and the roof support beam) to the upper end of the support, but are not required to contribute to any appreciable extent in providing vertical support for the roof load, which is borne substantially by the (pivot) bolt. The remaining bolts are stressed in tension, thereby providing the restoring moments referred to above.

It is preferred that the third pivot is located with respect to the longitudinal central axis, or neutral axis of the upright support, on this axis or within a distance outwardly (with respect to the interior of the arch frame) in a range of up to 3 times the lateral extent (depth) of the upright support.

The upright supports and the roof beams are preferably made of standard section steel beams e.g. RSJ etc.

The means by which it is ensured that the strengthened eaves connection provides the second pivot may take any of the suitable (and simple) forms available. For example, packing may be inserted between the inside face of the upright support and the eaves connection.

As an alternative and/or addition to a haunch arrangement for the strengthened eaves connection, a knee joint arrangement may be provided.

It is preferred that the second pivot is spaced vertically from the upper end of the upright by a distance which lies in a range from 10 to 40% of the overall height of the support.

By providing a novel construction of arch frame according to the invention, embodying a new theory of construction, it is possible for there to be more efficient material use i.e.

higher permissible loadings for given steel sections, or else smaller sections for a given loading than is possible with conventionally fabricated arch frames.

One embodiment of arch frame according to the invention will now be described in 'detail, by way of example, with reference to Fig. 1 3 of the accompanying drawings.

Referring now to Fig. 13, there is shown a schematic side illustration of an arch frame, in which only one half is shown in any detail, with the other half being shown in dash-dot outline. Only one half of the construction will be described, and it should be understood that the other half will be of similar construction.

The arch frame is designated generally by reference numeral 10 and serves to provide support for a pitched roof, the frame comprising a pair of horizontally spaced upright sup ports or stanchions 11. Each stanchion 11 has its foot 1 2 mounted on a respective foundation, usually concrete, and is provided at its upper eaves end 1 3 with a mounting for a roof-supporting structure. A roof beam 14 is associated with each stanchion 11 and is mounted at the upper end 13 thereof. The pair of roof-support beams 4 extend towards each other to meet at a pivoted ridge connection 1 5 of a pitched roof.

The stanchions 11 and roof-support beams 14 are conveniently provided from any suit able standard steel section.

At least one of the stanchions 11, and preferably both, is pivotally mounted at its foot 1 2 on its respective foundation. This pivotal mounting is not shown in detail, but may comprise any suitable bearing or knife edge type of pivotal mounting. The neutral axis of the stanchion 11 is shown by dash-dot line 16, and it is essential that the pivot (which comprises a third pivot for each half of the arch frame) is arranged along the line of the axis 16, or else is spaced outwardly of the arch frame in the direction of the arrow X within a range of distance of up to three times the lateral extent or depth d of the stanchion 11.

The pivotal mounting of the stanchion 11 on its foundation is all that is required for the arch frame to function satisfactorily, though, subsequent to assembly of the frame, any conventional sealants may be introduced into any space available between the lower face of the foot 1 2 and the upper face of the foundation.

At the upper end 1 3 of the stanchion 11, there is a strengthened eaves connection which is designated generally by reference numeral 1 7 and which is provided along an inner face 18 at the upper eaves end of the stanchion 11. The eaves connection 1 7 serves to connect the respective roof support beam 14 to the upper end 13 of the stanchion 11.

As illustrated in Fig. 13, the eaves connection 1 7 takes the form of a generally triangular haunch 1 9 which is welded to the eaves end of the beam 14 so as to contribute to the overall strength of the roof-supporting construction. The haunch 1 7 is secured by suitable fasteners, preferably bolts, to the inner face 1 8 of the stanchion 11, and the bolts are provided in an array such that a lowermost bolt or bolts effectively forms a pivot or bearing via which compressive thrust is transmitted from the beam 14 to the upper region of the stanchion 11.

The pivotal connection at the ridge 1 5 between the pair of beams 14 forms a first pivot for each half of the arch frame. The manner by which the haunch 1 7 is mounted at the upper region of the stanchion 11 provides, effectively, a second pivot which is located substantially at the position designated by arrow reference 20. When a roof loading is applied, compressive thrust is transmitted along a line between the first and second pivots, and there will be a tendency for the haunch 1 7 to pivot in a clockwise direction (for the left-hand half of the arch frame shown in Fig. 13) about the second pivot. This will generate tension in the remainder of the fastening bolts.The compressive thrust passes through the material of the beam 14, and also through the haunch 17, and the vertical roof loading is borne substantially by the bolt or bolts which provide the second pivot. The remaining bolts are placed in tension as a result of the clockwise turning moment of the assembly about the second pivot. Conveniently, the haunch 1 7 includes a vertical end plate which lies alongside the inner face 1 8 of the stanchion 11, and resists the clockwise turning moment by bending stresses generated therein.

Any convenient means may be provided in order to ensure the manner by which the haunch 1 7 has a simple pivotal type of mounting at the upper eaves end of the stanchion 11. This may comprise the insertion of suitable packing from above or below and/or between the underside of the foot 1 2 and the foundation.

It is envisaged that the second pivot provided at position designated by reference 20 should be located below the upper end of the stanchion 11 by a distance which lies in the range from 10 to 40% of the overall height h of the stanchion 11.

The arch frame illustrated in Fig. 1 3 embodies a novel theory of construction, and also provides a unique combination of features in an arch frame, namely the arrangement of the first pivot (15), second pivot (20) and third pivot at the foot mounting of the stanchion.

While it is preferred that the feature of the invention be provided in an arch frame for a pitched roof, it is envisaged that the invention will be applicable also to a flat roof construction, in which one or more roof beams 14 extend generally horizontally and substantially perpendicularly from the upper end of the stanchion 11.

Claims (11)

1. An arch frame for supporting a pitched roof comprising a pair of horizontally spaced upright supports having their feet mounted on respective foundations and provided at their upper eaves ends with mountings for a roofsupporting structure, and a pair of roof beams mounted one at the upper end of each upright support and extending towards each other to meet at a pivoted ridge connection of a pitched roof, in which:: at least one of said upright supports is pivotally mounted at its foot on its respective foundation; a strengthened eaves connection is provided along an inner face at the upper eaves end of said one upright support to connect the respective roof support beam thereto; and the arrangement of the pivotal mounting of the upright support on its foundation, and of the strengthened eaves connection, are such that the strengthened eaves connection provides a pivotal mounting for the roof support beam of the inner face of the upright at a postion vertically spaced from the upper end of the support.

2. An arch frame according to claim 1, in which the other of the upright supports is similarly constructed and arranged as said one upright support.

3. An arch frame according to claim 1 or 2, in which the pivoted ridge connection forms a first pivot, the or each strengthened eaves connection forms a second pivot for a respective roof beam and the foot mounting of the or each upright forms a third pivot.

4. An arch frame according to claim 3, in which the or each strengthened eaves connection comprises a haunch arranged to provide a path for a line of compressive thrust between the first and second pivots.

5. An arch frame according to claim 4, in which the haunch comprises a generally triangular arrangement.

6. An arch frame according to claim 5, in which the haunch includes a substantially vertical end plate which forms one side of the generally triangular arrangement, said end plate being secured to the upper region of the inside face of the respective support.

7. An arch frame according to claim 6, in which the end plate is secured to said inside face of the respective support by means of a vertically spaced array of bolts, with the lowermost bolt effectively forming said second pivot.

8. An arch frame according to claim 7, in which packing is inserted between said inside face of the upright support and the strengthened eaves connection so that the latter affords said second pivot.

9. An arch frame according to any one of said claims 3 to 8, in which the third pivot is located, with respect to the longitudinal central or neutral axis of the upright support, on this axis or within a distance outwardly (with respect to the interior of the arch frame) in a range of up to three times the lateral extent (depth) of the upright support.

10. An arch frame according to any one of the preceding claims, in which the or each strengthened eaves connection includes a knee joint arrangement.

11. An arch frame according to any one of claims 3 to 8, in which the or each second pivot is spaced vertically from the upper end of the respective upright by a distance which lies in a range from 10 to 40% of the overall height of the support.

1 2. An arch frame according to claim 1 and substantially as hereinbefore described with reference to, and as shown in the accompanying drawings.

1 3. A pitched roof supported by a plurality of arch frames according to any of the preceding claims.