18 - element size estimation

TheStructuralEngineer32

Technical Guidance Note

Technical

October 2012

Note 17 Level 1

›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 1Typical forms of concrete structure

Element size estimationIntroduction

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.

W Estimation principles

W Worked example

W Further reading

W Web resources

ICON LEGEND

Estimating sizes of concrete elementsMuch 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.

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 fl at 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.

Concrete slabsThe 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 fl at 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 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 type5 kN/m2 Imposed

load

10 kN/m2 Imposed

load

Simply supported one-way

27 24

Simply supported two-way

30 27

Continuousone-way

34 30

Continuoustwo-way

44 40

Cantilever 11 10

Flat slab 30 27

TSE10_32-35.indd 32TSE10_32-35.indd 32 24/09/2012 09:5324/09/2012 09:53

www.thestructuralengineer.org

33

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


50 kN/m UDL 250mm 300mm 350mm 400mm 500mm 575mm 675mm



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

Span 6m 7m 8m 9m 10m 11m 12m




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



End span thickness 125mm 125mm 150mm 175mm 200mm 250mm 275mm

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 4: Estimated depths of insitu concrete fl at slabs with no column heads



TSE10_32-35.indd 33TSE10_32-35.indd 33 24/09/2012 09:5324/09/2012 09:53

TheStructuralEngineer34

Technical Guidance Note

Technical

October 2012

Note 17 Level 1

›

Tables 2-4 are slightly more accurate estimated depths of one-way spanning slabs for a down-stand beam structure, a band-beam structure and a fl at 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.

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

Concrete beamsThere 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 diffi cult to form, but do create a very robust frame. Band beams are much shallower and are therefore easier to construct.

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 fi gures 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 columnsThe 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 benefi ting from increased concrete strength. The location within the structure is also important, as an internal

column is less infl uenced 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 fl oor structure and the columns. This is due to the transfer of bending moments from one element of the structure to another. In the fi rst 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 fl oor 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.

Concrete stairsThe 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 fi nish 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 offi ces and hotels.

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

TSE10_32-35.indd 34TSE10_32-35.indd 34 24/09/2012 09:5324/09/2012 09:53

www.thestructuralengineer.org

35

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

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/

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 fl oor slab if a down-stand beam and a fl at slab structural solution were adopted. In addition, for the down-stand beam structure, determine the estimated beam depth for a 600mm wide beam.

Estimating sizes of steel elementsSteel 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 10: Span/depth ratio tables for steel beams located in the fl oor and roof (from Tata Steel Europe website)

Type of beam Maximum fl oor span Depth of fl oor beam Maximum roof span Depth of roof beam

Primary beams 15m Span/20 15m Span/25

Secondary beams 12m Span/25 15m Span/25

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"

TSE10_32-35.indd 35TSE10_32-35.indd 35 24/09/2012 09:5324/09/2012 09:53

18 - element size estimation

Documents