Design of a Steel Structures for a Large Span Roof

General geometry

Steel Structures for a Large Span Roof Focusing on roof structures, those that span more than 20 – 25 meters are often more economical if designed as trusses instead of portal frames [2]. Savings stem from the fact that trusses are lighter, using less steel, than solid profiles. Indeed, for the same weight, better performance in both of resistance and stiffness is managed when considering trusses. Although aesthetics is a matter of taste, the general consensus is that trusses are of a superior appearance when compared to portal frames. However, relating to the installation process, hot rolled beams are less time consuming as they have much fewer connections. For a cost effective truss, the engineer has to balance several aspects such as equipment, man-hours, and cost of steel. Steel Structures.

As with beams, the ratio depth to span of flat trusses at mid span, otherwise known as slenderness,
should range from 1/7.5 to 1/12 [2] so that good structural performance, regarding deflection and forces
on each element, is achieved. Moreover, efficient layouts should consider point loads applied only at
nodes with diagonals connecting with chords at 35º to 55º. The reason behind these two numbers is a
simple one. As the inclination of each diagonal increases (becoming more vertical) so will the number of
total diagonals in the truss. Thus, for the same loading, the axial force on each element will decrease
making the case for savings by means of a less robust cross-section. Evidently, the validity of this line of
thought breaks down when the total number of additional diagonals and connections result in such
additional cost that the savings in material are outweigh.

Cross-sections of members

There are two main families of cross-sections used in truss members: open sections and closed sections.
Open sections offer greater ease to establish connections as they require little to no welding, resorting
primarily to bolts. For small to intermediate spans, a popular design is using single angles for diagonals
and T profiles for chords. In this choice of design, it is recommended that vertical and diagonal members
be placed on the same side of the T section as to avoid additional bending of the web and twisting of the
chords [2]. For large spans and member forces, a popular design is using double angles or channels
back-to-back spaced intermediately with battens for the diagonal members and I or H profiles (i.e. IPE,
HEA, HEB) for the chords. The chords can be placed either vertically (standing up) or horizontally (flat). In
both layouts there are advantages to be noted. First, in the horizontal layout the obvious advantage is
that, for chords in compression, it is easier to increase in-plane buckling resistance, by shortening the
buckling length by means of additional diagonals, than to increase out-of-plane buckling resistance. In the vertical orientation, the advantage stems from the fact that it is easier to establish a connection between the purlins and chord. Steel Structures

Closed sections have several advantages that need mentioning. Primarily, CHS and RHS sections are
much more efficient cross-sections under compression when compared with open cross-sections. The
radius of gyration is the same in all directions, hence greater efficiency. They are considered to be more
aesthetic and are generally better appreciated by the public at large. As maintenance is regarded, tubular
trusses require less paint per linear meter [2], reducing the cost of the corrosion protection treatment

General overview

In deciding the appropriate layout of a roof structure the major problem is to find the right balance between economy and structural efficiency. There is little difficulty in assuming a truss structure instead of a I beam as it has already been noted that with increasing spans the latter become less efficient. Other
questions arise such as what is the ideal spacing of the main trusses? What is the best slope of the
chords and should both have the same slope? What is the best layout for the different truss? Is it
preferable to have transverse or longitudinal purlins? What is the best type of cross-section to adopt?

Members and materials

All structural steel members, including gusset plates, have the same grade of steel.

The members that make up the structure are summarized in Table 2. As is shown in the table, all the
diagonals of the bracing truss have the same profile and the same is true for the main truss. The main
reason for this decision is to reduce the complexity of the installation on-site. It would be possible to adjust the robustness of the profiles according to the internal forces but so has not been done.

The connections are established by welding and bolting. For the latter, depending on where the
connection is, several types of bolts are adopted so to best fit the needed resistance.

General overview

Connections are perhaps the most critical of parts in the design process. Indeed often enough, the cause
of structural failure is due to poorly designed and detailed connections [3]. Modern steel structures are
connected by welding or bolting – either high-strength or standard. Rivets were common in the past, but
since the publication in 1951 of the first specification from the Council of Riveted and Bolted Structural
Joints authorizing the substitution of rivets for high strength bolts, their use has plummeted [3].

The choice between welding and bolting depends on several factors. A possible shortlist includes
customer acceptance, cost of both material and installation/execution, and safety. Welding and bolting
have their advantages that should be considered in the design process.

Despite the interest in analysing all of the above, only the continuity chord connection, gusset to chord
and diagonals to gusset will be fully analysed in this document. Although not fully analysed, a brief discussion on particular aspect of the connection of the main truss to the columns follows.

Main truss to columns

The main truss is designed as simply supported on the columns. So, one of the chord members could be
omitted (namely the first lower chord member, with the arrangement of diagonals as shown in this case);
however, it is advantageous to keep this member at the connection of the truss to the column in order to
supply lateral stability to the lower chord of the truss. Thus, in order to enable the global in-plane rotation, the connection of one of the chords to the column must allow for relative horizontal displacement. Usually, the horizontal displacement is released at the node where the diagonal does not meet – in this case, the lower node.

In the truss being studied, the horizontal displacement in node B shown in Figure 5 (with no member 1-1
in the structural model) due to the gravity loads is +36 mm. Thus, a possible solution for the connection of member 1-1 to the column is as shown in Figure 5, comprising a plate welded to the column with a hole that has enough length (say, 50 mm) to accommodate the expected displacement.

Continuity of the chords

When designing large spans, one has to consider the maximum length of the members provided by the
fabricator. These typically limit the length at about 12 meters due to the nature of the transportation
method – trucking has limited allowable length, therefore limiting the length of profiles to be transported.

The proposed structure has a 36 meter span and therefore, in order to guaranty continuity, the connection has to be rigid and there are several options that can be considered.

Bolted connections are usually adopted instead of welded, the reason being that welded connections
need a greater control in quality, and so better efficiency is achieved in shop rather than on site. Two
types of bolted connections are possible with different implications: end-plate and splice-plate
connections. End-plate connections are possible for I, H, and hollow profiles. Here, bolts are in tension
and, with increasing force, the transverse plates will tend to bend in a complex three-dimensional manner.
A simplified approach may be considered in the analysis of such connections, based on the so-called
‘equivalent T-stub model’. Splice-plate connections are generally used for I, H, T, L and U profiles. The
main difference from the end-plate type is that bolts are loaded with shear instead of tension.

In the adopted solution, splice-plates are considered.

Diagonals to chords

Depending on the assumptions considered in modelling the structure, as well as on the type of profiles
chosen as diagonals, welding and bolting may be considered. It is common to use gusset plates as
additional elements in the structure to assist in connecting diagonals to chords. These plates may be
bolted or welded to the chords and the diagonals may as well be bolted or welded to the gusset.

For chords that are of T or U profiles a typical connection is shown in Figure 7 – left, with the gusset
connected to the chord with bolts.

For chords that are I or H profiles the gusset is typically connected to these through welding and the
diagonals may be bolted or welded to the chords (Figure 7 – centre and right).

The chords may be arranged vertically (standing up) or horizontally (flat), with the gusset connecting to
the flange or web respectively. The discussion on the implications of a vertical or flat layout of the chords
is provided further in section 4.2.2.

Relating to the gusset plate design and analysis, EN1993 does not give any specific indication on safety
checking of these members. In mid twentieth century, Whitmore and Thornton developed methods for
analysing cross-sectional resistance as well as buckling of gusset plates that are adopted in this
document.

Design Loads and Modelling

Loads

The only loads considered are the dead, live, wind and snow loads. Temperature has been opted out as
the structure is modelled as a series of 2D statically determinate structures with slotted holes in the
connections.

Dead Load (DL)

The main components of DL on roof trusses in single story industrial buildings are the self-weight of the
following elements: cladding, purlins, chords, diagonals and connection elements such as bolts and
gusset plates. Steel Structures

Live load (LL)

The gravity load due to maintenance is regarded as the main LL on roof trusses. In accordance to EN
1991-1-1, the roof is of category H and as such the characteristic value is defined in Table 6.

Snow load (SN)

Snow loads are quantified with the assumptions indicated in Table 7, according to NP EN 1991-1-3.

Wind load (WL)

Given the slope of 5º, and in accordance to EN 1991-1-4, the predominant wind load on the roof truss is
uplift force perpendicular to the roof, due to the suction effect of the wind blowing over. Hence, the wind
loads act contrary to gravity loads and with greater magnitude. To illustrate this result, Table 9 and Table
10 provide the design wind pressures in the roof (with the wind velocity and the division into zones according to NP EN 1991-1-4) already taking into account the results of Table 8 and the internal
pressures. Steel Structures

Load Combinations | Steel Structures

The load combinations are summarized in Table 11 and Table 12, in accordance to EN 1990. As the
temperature is not considered in the model the partial safety factors are not indicated.

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