18 - Element Size Estimation

› Note 17 Level 1

32

TheStructuralEngineer October 2012

Technical Technical Guidance Note

Element size estimation Introduction

Once the concept and scheme for a structure has been settled upon, the initial sizing of the elements that it is made up of commences. This Technical Guidance Note provides a set of hints as to how to initially size elements, prior to carrying out the detailed design. This process allows the engineer to gain an appreciation of the form of the structure and the changes that may be required if element sizes prove to be too onerous following this size estimation process.

Estimation principles The primary variable that is considered, when attempting to estimate the size of an element prior to carrying out the detailed design, is its span. The other factors that have an impact are the imposed load (or Variable Action as they are described in the Eurocodes), the super imposed dead loads (or Permanent Actions), the support conditions and the material the element is to be made from. Note that the following are simple 'rules of thumb' that can be used to develop an appreciation of how to estimate a member size in a structure. By gaining a good understanding of this, the structural engineer will become attuned to spotting elements that are undersized in structures before carrying out detailed design, as well as avoid making uneconomic decisions by over sizing elements. These rules however are only guidelines and should therefore not be treated as sacrosanct.

N Figure 1 Typical forms of concrete structure

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ICON LEGEND

W Estimation principles

W Worked example

W Further reading

W Web resources

Estimating sizes of concrete elements

Concrete slabs

Much of this text has been based on the guidance included within The Concrete Centre’s Economic Concrete Frame Elements to Eurocode 2. The reader is strongly encouraged to read this reference text alongside this Technical Guidance Note.

The depth of a concrete slab is dependent on the manner in which it spans, i.e. one-way or two-way, the magnitude of load being placed upon it and the form of the frame it sits on. If the structure is a flat slab for example, then there are no beam elements to consider, other than the beam and column strips that exist within the depth of the slab.

As well as the variables that impact on element size estimation described previously, concrete structures have one additional variable that must be established at the very start of the size estimation process. That being the form the structure is going to adopt. This can vary from one way spanning slabs with down-stand beams to pre-stressed flat slabs. Figure 1 is a selection of the most common concrete structural forms that are currently favoured. The form of the structure is determined at the concept design stage of a project. This is the stage where the geometry of the structure is largely established as well as other key aspects of the design criteria such as soil conditions and the structure’s anticipated use.

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 ratios for insitu concrete slabs (from Reynolds’s Reinforced Concrete Designer’s Handbook)

Slab type

5 kN/m2 Imposed load

10 kN/m2 Imposed load

Simply supported one-way

27

24

Simply supported two-way

30

27

Continuous one-way

34

30

Continuous two-way

44

40

Cantilever

11

10

Flat slab

30

27

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Table 2: Estimated depths of insitu concrete slabs spanning one way between down-stand beams Span

4m

5m

6m

7m

8m

9m

10m

Single span thickness

150mm

175mm

225mm

250mm

300mm

350mm

450mm

Multi span thickness

125mm

150mm

175mm

200mm

250mm

300mm

325mm

Table 3: Estimated depths of insitu concrete slabs spanning one way between band-beams Span

4m

5m

6m

7m

8m

9m

10m

Multi span thickness

125mm

125mm

125mm

175mm

200mm

200mm

225mm

End span thickness

125mm

125mm

150mm

175mm

200mm

250mm

275mm

Table 4: Estimated depths of insitu concrete flat slabs with no column heads Span

4m

5m

6m

7m

8m

9m

10m

Multi span thickness

200mm

200mm

225mm

250mm

250mm

300mm

350mm

Table 5: Span/depth ratios for insitu concrete beams (from Reynolds’s Reinforced Concrete Designer’s Handbook) Beam span condition

Ultimate line load 25 kN/m

Ultimate line load 50 kN/m

Ultimate line load 100 kN/m

Simply supported

18

14

10

Continuous

22

17

12

Cantilever

9

7

5

Table 6: Estimated depths of insitu concrete single span T-beams (600mm wide) Span

4m

5m

6m

7m

8m

9m

10m

50 kN/m UDL

250mm

300mm

350mm

400mm

500mm

575mm

675mm

100 kN/m UDL

275mm

325mm

400mm

450mm

575mm

675mm

800mm

200 kN/m UDL

325mm

375mm

450mm

525mm

650mm

775mm

925mm

Table 7: Estimated depths of insitu concrete single span band-beams (2400mm wide) Span

6m

7m

8m

9m

10m

11m

12m

50 kN/m UDL

250mm

300mm

350mm

400mm

475mm

550mm

650mm

100 kN/m UDL

300mm

350mm

425mm

500mm

575mm

650mm

750mm

200 kN/m UDL

350mm

400mm

475mm

575mm

675mm

775mm

875mm

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› Note 17 Level 1

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TheStructuralEngineer October 2012

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 super-imposed dead load of 1.5 kN/m2 for single and multi-spanning slabs.

Concrete beams There are two varieties of concrete beams: down-stand and band-beam. Down-stand beams that form part of a solid reinforced concrete frame are regarded as more traditional. They are more difficult to form, but do create a very robust frame. Band beams are much shallower and are therefore easier to construct.

Technical Technical Guidance Note

"To estimate the size of the column requires an understanding of the interaction between the floor structure and the columns"

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.

column is less influenced by applied bending moments than those located at the perimeter of the structure. To estimate the size of the column requires an understanding of the interaction between the floor structure and the columns. This is due to the transfer of bending moments from one element of the structure to another. In the first instance the axial load the column is expected to support must be determined. In addition, bending moments that are likely to be applied from the floor structure are calculated via analysis. This will likely include the use of moment distribution and sub-frame analysis methods. This is then cross checked against the concrete strength and amount of reinforcement in the column. 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.

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.

Concrete stairs 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.

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. Bending moments are dependent on pattern loading within the structure. The strength of concrete can also alter their size with higher axial loads benefiting from increased concrete strength. The location within the structure is also important, as an internal

Table 8: Estimated depths of waists to insitu concrete staircases with an imposed load of 2 kN/m2 Span

2m

3m

4m

5m

6m

Single span waist thickness

100mm

125mm

175mm

200mm

250mm

Multi span waist thickness

100mm

100mm

150mm

175mm

200mm

Table 9: Estimated depths of waists to insitu concrete staircases with an imposed load of 4 kN/m2 Span

2m

3m

4m

5m

6m

Single span waist thickness

100mm

150mm

175mm

225mm

250mm

Multi span waist thickness

100mm

125mm

150mm

175mm

200mm

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Table 10: Span/depth ratio tables for steel beams located in the floor and roof (from Tata Steel Europe website) Type of beam

Maximum floor span

Depth of floor beam

Maximum roof span

Depth of roof beam

Primary beams

15m

Span/20

15m

Span/25

Secondary beams

12m

Span/25

15m

Span/25

Estimating sizes of steel elements Steel structures are less complex than their concrete brethren when estimating their size. They are typically simply supported structures and hence do not have the bending moment transfer issues that are prevalent in concrete design. The exceptions to these are portal and sway frames, which do transmit moments through their connections. It is thanks to this that the rules-of-thumb for steel beams can be summarised 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.

Table 11: Column size estimate based on storey of structure (from section 5.3 of The Institution of Structural Engineers’ Manual for the design of Steel Structures to Eurocode 3) Number of storeys

Column size

3

203x203 UC

5

254x254 UC

8

305X305 UC

8-12

356X356 UC

"Steel structures are less complex than their concrete brethren when estimating their size" Glossary and further reading Span/Depth ratio – The ratio between the span of an element and its overall depth

Waist – The thickness of a staircase

Worked example A concrete structure with a column layout of 8m x 6m is to support an imposed load of 2.5 kN/m2. Estimate the depth of floor slab if a down-stand beam and a flat slab structural solution were adopted. In addition, for the down-stand beam structure, determine the estimated beam depth for a 600mm wide beam.

Further Reading The Concrete Centre (2009) Economic Concrete Frame Elements to Eurocode 2 Camberley, Surrey: Mineral Products Association Reynolds, C.E. et.al (2007) Reynolds’s Reinforced Concrete Designer’s Handbook 11th ed. CRC Press The Institution of Structural Engineers (2010) Manual for the design of steelwork structures to Eurocode 3 London: Institution of Structural Engineers

Eurocode 0.

Web resources

The Institution of Structural Engineers library: www.istructe.org/resources-centre/library Tata Steel Europe: www.tatasteelconstruction.com/ en/reference/teaching_resources/ architectural_studio_reference/elements/ design_of_beams_structural_steel/ estimating_sizes/ The Concrete Centre: www.concretecentre.com/

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