Typical dead load values for various types of construction are required. These are available from hand books. Imposed loads are given the code. Some comments on load estimation are as follows.
• Most loads are distributed. Beam and column reactions are point loads. Floor loading is expressed as equivalent uniform loads.
• Loads are assessed on the tributary floor area supported by the member.
• Loads are cumulative from roof down. Imposed loads are reduced depending on the number of floors involved.
• Wind loads generally act horizontally, but uplift due to suction is important in some cases.
• The structure is taken to be pin jointed for load estimation.
3.4 ANALYSIS
The purpose of analysis is to determine the critical actions for design. Some methods that can be used in preliminary analysis are given.
3.4.1
Statically determinate structures Figure 3.1 shows some common types of statically determinate construction.
(a) Floor systems
The floor system (Figure 3.1 (a)) consists of various types of simply supported beams. For uniform loads the maximum moment is WL2/8 where W is the design load and L is the span. This gives a safe design whether the beams are continuous or not or some two-way action in the slab is considered.
Chord at mid-span=WL/8d Web member at support=WS/2d where W is the design load; d is the depth of girder; S is the length of web member.
For a Pitched roof truss (Figure 3.1(c)), force coefficients can be determined for a given truss such as the Fink truss shown.
The axial forces are
Top chord, member 1: F=–1.18W max. Bottom chord, member 2: F=1.09W max. Web members 3, 4: F=–0.23W, +0.47W where W is the total load. Tension is negative, compression positive.
(d)
Three-pinned portal For the three-pinned portal (Figure 3.2),
Horizontal reaction H=WL/8h Eaves moment MX=Ha
where W is the vertical load; L is the span; h is the height to crown; a is the height of columns.
Fig. 3.1 Statically determinate structures: (a) multistorey building; (b) lattice girder; (c) roof truss.
3.4.2
Statically indeterminate structures (a)
General comments
For elastic analysis, if the deflected shape under load is drawn, the point of contraflexure may be located approximately and the structure analysed by statics. The method is generally not too accurate.
For plastic analysis, if sufficient hinges are introduced to convert the structure to a mechanism, it is analysed by equating external work done by the loads to internal work in the hinge rotations. The plastic moment must not be exceeded outside the hinges.
Design aids in the form of formulae, moment and shear coefficients, tables and charts are given in handbooks (Steel Designers Manual, 1986, 1994). Some selected solutions are given.
(b) Continuous beams
The moment coefficients for elastic and plastic analysis for a continuous beam of three equal spans are shown in Figure 3.3.
(c)
Pitched roof pinned-base portal
Portal design is usually based wholly on plastic theory (Figure 3.4). As a design aid, solutions are given in chart form for a range of spans. A similar chart could be constructed for elastic design (Chapter 4 gives detailed designs).
Fig. 3.2 Three-pinned portal.
Fig. 3.3 Continuous beam.
It is more economical to use a lighter section for the rafter than for the column, rather than a uniform section throughout.
The rafter is haunched at the eaves. This permits use of a bolted joint at the eaves and ensures that the hinge there forms in the column.
Let Mp be the plastic moment of resistance of the column and qMp be the plastic moment of resistance of the rafter, where q=0.75 for chart. Then
where
w=roof load per unit length;
L=span;
H=horizontal reaction;
h=eaves height;
g=depth of column hinge below intersection of column and rafter centrelines (0.3–0.5 m for chart);
Φ=roof slope (15° for chart);
x=distance of rafter hinge from support.
Equate dH/dx=0, solve for x and obtain H and Mp.
A chart is given in Figure 3.4(c) to show values of the column plastic moment Mp for various values of span L and eaves height h.
Fig. 3.4 Plastic analysis: (a) frame load and hinges; (b) plastic bending moments; (c) analysis chart.
(d)
Multistorey frames subjected to vertical loads Elastic and plastic methods are given.
• Elastic analysis—the subframes given in Clause 5.6.4.1 and Figure 11 of BS 5950 can be used to determine actions in particular beams and columns (Figure 3.5(a)). The code also enables beam moments to be determined by analysing the beam as continuous over simple supports.
• Plastic analysis—the plastic moments for the beams are ±WL/16. The column moments balance the moment at the beam end as shown in Figure 3.5(b) and hinges do not form there. This analysis applies to a braced frame.
(e)
Multistorey frames subjected to horizontal loads The following two methods were used in the past for analysis of multistorey buildings.
(i) Portal method The portal method is based on two assumptions.
• The points of contraflexure are located at the centres of beams and columns.
• The shear in each storey is divided between the bays in proportion to their spans. The shear in each bay is then divided equally between the columns.
The column end moments are given by the product of the shear by one-half the storey height. Beam moments balance the column moments. External columns only resist axial force, which is given by dividing the overturning moment at the level by the building width. The method is shown in Figure 3.6.
Fig. 3.5 Multistorey frames: (a) elastic analysis; (b) plastic analysis.
(ii) Cantilever method In the cantilever method, two assumptions are also made.
• The axial forces in the columns are assumed to be proportional to the distance from the centre of gravity of the frame. The columns are to be taken to be of equal area.
• The points of contraflexure occur at the centres of the beams and columns.
The method is shown in Figure 3.7.
3.5
ELEMENT DESIGN
3.5.1