Preliminary Sizing of Structural Elements

Introdution

Haven decided on the concepts and scheme for a structure, preliminary sizing of the structural elements composed within the structure commences. This post provides guidance on how to initially size structural elements prior to carrying out the full detailed design. This practice grants the designer the ability to have a feel of the form of the structure, as well as the changes that may be required during detail design, should the initial sizing prooves too onerous or should the client requirement change.

Estimating Principles

The main factor being considered when trying to initially size a structural element is it span. The other factors that may have an impact are the permanents actions and variable actions applied, support conditions and the material from which the element will be made from.

The following rules that will be provided in this post are simply “rules of thumb” used to gain an understanding of how to preliminarily size structural elements. A good comprehension of this, allows the structural designer to become accustomed to spotting undersized structural elements as well as being able to avoid oversizing structural elements. The rules, however, are simple guidelines and sometimes not precise.

Preliminary Sizing of Concrete Elements

Outside the variables that impact on the preliminary sizing of elements describes in the preceding section, the sizing of concrete elements is influenced by an additional factor which must be considered before the size estimation. That being the chosen structural form. This can vary from one-way spanning slabs with down-stand beams, ribbed slabs with band beams, flats slabs and so on and so forth. Figure 1 shows some common structural forms in concrete.

FIG 1: STRUCTURAL FORMS OF COMMON CONCRETE STRUCTURES

Concrete Slabs

Generally, the thickness of a concrete slab is dependent on the manner in which it spans, either one way or two way, the magnitude of the load applied upon it and the structural form of the frame.

As an initial step, it is possible to estimate the depth of a slab based purely on its span/ depth ratio. Table 1 provides guidance on what these ratios are, based on the type of slab being considered.

TABLE 1: SPAN/DEPTH RATIO FOR CONCRETE SLABS (Reynold designer handbook).

Tables 2-4 are slightly more accurate estimated depths of one-way spanning slabs for a down-stand beam structure, a bandbeam structure and a flat slab respectively. They assume a blanket imposed load of 2.5 kN/m2 and a superimposed dead load of 1.5 kN/m2 for single and multi-spanning slabs.

TABLE 2-4: SPAN/DEPTH RATIO FOR SLAB ( The Concrete Centre publication)

Concrete Beams

Concrete beams can be grouped into two types with respect to preliminary sizing: down-stand beam and band beams. As with concrete slabs, it is possible to estimate the depth of a beam when considering its span/depth ratio. Table 5 provides guidance on what these ratios are, based on the type of beam structure.

The figures given in Tables 6 and 7 provide more accurate estimated sizes for down-stand ‘T’-beams and band beams respectively. In order to use Tables 5-7, the reader must have calculated an ultimate line load/m length. All depths include the thickness of the slab the beams are supporting.

TABLE 6: Estimated depth for concrete T beams 600mm wide

TABLE 7: Estimated depth for concrete band beams 2400mm wide

Concrete Columns

The elements that impact on the design of concrete columns are the magnitude of axial loads and bending moments being applied to them and their length.

Unlike the slab and beam elements, columns cannot be summarised into a series of tables. As such the reader is directed to Economic Concrete Frame Elements to Eurocode 2 for further guidance

Concrete Stair

The thickness or ‘waist’ of the stair and its landings are the only elements that are designed as far as the structural engineer is concerned. The treads are considered to be a super-imposed dead load i.e. a finish and are not therefore reinforced. The criteria that have an impact on the design of stairs are the imposed load, their span and whether or not they have multiple spans. Table 8 is for an insitu concrete staircase with an imposed load of 2 kN/m2, which is typical for residential use. Table 9 is for staircases that support an imposed load of 4 kN/m2. These are more commonly found in commercial buildings such as offices and hotels.

Estimating sizes of Steel Elements

A majority of the steel structures are braced frames as a result elements are typically simply supported and do not have bending moment transfer issues that are prevalent in concrete design. Thus, estimating the sizes of elements in steel structures is less complex than their concrete counterpart. The rule of thumbs for steel beams can thus be summarized into Table 10.

With regard to columns, their size is dependent on the number of storeys they have to support, from which an initial size can be established. Table 11 is a rough guide to column sizes based on the height of structure they are supporting for braced structures.

Worked Example

A concrete structure with a column layout of 9m x 7.5m is to support an imposed load of 2.5 kN/m2. Estimate the depth of floor slab if band-beams and flat slab structural solution were adopted. In addition, for the band-beam structure, determine the estimated beam depth for a 2400mm wide beam.

Band-Beams Solution:

Multi-span\quad slab:\quad Depth=200mm\quad approx\quad \\ \qquad \qquad \qquad \qquad \qquad \qquad based\quad on\quad 7.5m(Table\quad 3)\\ Beam\quad depth:\quad udl\quad on\quad beam\quad must\quad be\quad calculated\\ \qquad Permanent\quad action:\quad { g }_{ k }\\ \qquad \qquad Slab\quad =\quad 0.20\times 25=5.0{ kN/m }^{ 2 }\\ \qquad \qquad finishes\quad say\quad \quad \quad \quad =1.5kN/{ m }^{ 2 }\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad { g }_{ k }=6.5kN/{ m }^{ 2 }\\ \qquad Varaible\quad action:\quad { q }_{ k }=\quad 2.5kN/{ m }^{ 2 }\\ \qquad \qquad since\quad { g }_{ k }<4.5{ q }_{ k }\\ Design\quad load\qquad { n }=1.35\xi { g }_{ k }+1.5{ q }_{ k }\\ \qquad \qquad \qquad \qquad \quad =\quad 1.35\times 0.925(6.5)+(1.5\times 2.5)\\ \qquad \qquad \qquad \qquad =\quad 11.87kN/{ m }^{ 2 }\\ Udl\quad on\quad Beam\quad =\quad 11.87\times 7.5\quad =89.0kN/{ m }^{ 2 }

The Band-Beam depth is therefore (span = 9m) = 675mm approx. (Table 7)

Flat Slab Solution

Longest span = 9m; Depth = 300mm (Table 4).

This post has dwelled on the guidance from the Concrete Centre publication (Economic Concrete Frame Elements to Eurocode 2). Please click on the download link Download to get a free copy.

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