#### This article gives guidance on how to size concrete and steel structural elements at the initial concept design stages of a project development.

Before selecting a concept and scheme for a new structure, preliminary sizing of all structural elements composed within the structure must be carried out. This is very essential, as no structure can be designed without knowing the loads it must withstand. A bulk of these loads normally result from the structure’s own weight, hence the designer must determine the size of the structural elements towards estimating the loads. However, at the concept design stage, where the designer has to compare different scheme, the designer cannot with utmost precision give the structural elements sizes, a dead-end ensues. To determine the structural loads, he needs to determine the sizes of the structural elements and to determine the sizes of the structural elements he requires the structural loads. Thus, in-order to resolve the dead end, simplified, approximate methods of pre-sizing structural elements have being developed.

Albeit, preliminary sizing of structural elements is not an exact science, aren’t always precise, they are however, pretty accurate and when the rules are followed sensibly, they provide a very good starting point. And, this practice grants a designer the ability to have a feel of the form and performance of the structure, they are designing as well as the changes that may be required during the final detail design stages, should the initial sizing proves too onerous or should there be alterations in the structural requirements.

In this article, guidance on how to size concrete and steel structural elements at the initial concept design stages is presented. The guidance is mostly based on the recommendations of the Concrete Centre manual “Economic Concrete Frame Elements and the (IstructE) manual for steel and concrete.

**Principles of **Preliminary Sizing

The main factor being considered when trying to initially size a structural element is

As said in the last section, preliminary sizing rules are not laws, they are simply* “rules of thumb*” based on experience, used to gain an understanding of the overall concept of a new scheme. A good comprehension of preliminary sizing 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 span** Figure 1** shows some common structural forms in concrete.

**Concrete Slabs**

The factor influencing the size of a concrete slab is the span and 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 ignoring the loads applied. * Table 1* provides guidance on what these ratios are, based on the type of slab being considered and the magnitude of the imposed load applied.

Slab Type | 5kN/m2 | 10(kN/m2) |

Simply supported (one-way) | 27 | 24 |

Simply supported (two-way) | 30 | 27 |

Continuous (one-way) | 34 | 30 |

Continous (two -way) | 44 | 40 |

Cantilever | 11 | 10 |

Flat slab | 30 | 27 |

** Tables 2-4** are slightly more accurate method of estimated depths of one-way spanning slabs. It considers the form of the structure; for a down-stand beam structure, a

^{2}and a superimposed dead load of 1.5 kN/m

^{2}for single and multi-spanning slabs.

Span (m) | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Single span (mm) | 150 | 175 | 225 | 250 | 300 | 350 | 450 |

Multi span (mm) | 125 | 150 | 175 | 200 | 250 | 300 | 325 |

Span (m) | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Single span (mm) | 125 | 125 | 125 | 175 | 200 | 200 | 225 |

Multi span (mm) | 125 | 125 | 150 | 175 | 200 | 250 | 275 |

Span (m) | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Single span (mm) | 200 | 200 | 225 | 250 | 250 | 300 | 350 |

Multi span (mm) | 200 | 200 | 225 | 250 | 250 | 300 | 350 |

##### 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 and the load it supports.

Span Condition | 25kN/m | 50kN/m | 100kN/m |

Simply supported | 18 | 14 | 10 |

Continouos | 22 | 17 | 12 |

Cantilever | 9 | 7 | 5 |

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.

Span (m) | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|

50kN/m | 250 | 300 | 350 | 400 | 475 | 550 | 650 |

100kN/m | 300 | 350 | 425 | 500 | 575 | 650 | 750 |

200kN/m | 350 | 400 | 475 | 575 | 675 | 775 | 875 |

Span (m) | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|

50kN/m | 250 | 300 | 350 | 400 | 500 | 575 | 675 |

100kN/m | 275 | 325 | 400 | 450 | 575 | 675 | 800 |

200kN/m | 325 | 375 | 450 | 525 | 650 | 775 | 925 |

**Concrete Columns**

The factors that influences on the design of concrete columns are the magnitude of axial loads and bending moments being applied to them and their length. Unlike slab and beam elements, preliminary sizing of columns cannot be summarized into a series of tables. Hence, 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 factors that have an impact on the design of stairs are the imposed load, span and whether or not they have multiple spans. Table 8 is for an in-situ concrete staircase with an imposed load of 2 kN/m^{2}, which is typical for residential use. Table 9 is for staircases that support an imposed load of 4 kN/m^{2}. These are more commonly found in commercial buildings such as offices and hotels.

Span (m) | 2 | 3 | 4 | 5 | 6 |

Single span (mm) | 100 | 125 | 175 | 200 | 250 |

Multi span(mm) | 100 | 100 | 150 | 175 | 200 |

Span (m) | 2 | 3 | 4 | 5 | 6 |

Single span (mm) | 100 | 150 | 175 | 225 | 250 |

Multi span(mm) | 100 | 125 | 150 | 175 | 200 |

#### 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 a far less complex endeavor than in concrete. The rule of thumb for steel beams can thus be summarized into ** Table 10**.

Type of Beam | Max floor span | floor beamRatio | Max roof span | Roof beam Ratio |

Primary | 15m | Span/20 | 15m | Span/25 |

Secondary | 12m | Span/25 | 15m | Spab/25 |

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.

No. of Storeys | Column Size |

3 | 203UC |

5 | 254UC |

8 | 305UC |

8-12 | 356UC |

### Worked Example

A concrete structure with a column layout of 9m x 7.5m is to support an imposed load of 2.5 kN/m^{2}. 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 \\ on\quad 7.5m(Table\quad 3)

Permanent\quad action:\quad { g }_{ k }\\ \qquad \qquad Slab\quad =\quad 0.20\times 25=5.0{ kN/m }^{ 2 }\\ \qquad \qquad finishes\ =1.5kN/{ m }^{ 2 }\\ { g }_{ k }=6.5kN/{ m }^{ 2 }\\ \qquad

Varaible\quad action:\quad { q }_{ k }=\quad 2.5kN/{ m }^{ 2 }\\ since\quad { g }_{ k }<4.5{ q }_{ k }\\

Design\quad load\qquad { n }=1.35\xi { g }_{ k }+1.5{ q }_{ k }\\ \quad =\quad 1.35\times 0.925(6.5)+(1.5\times 2.5)\\ =\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)*.

See: Design of Ribbed Slab with EPS

### Citation & Sources

*The Concrete Centre (2009) Economic Concrete Frame Elements to Eurocode 2 Camberley, Surrey: Mineral Products Association.**The Institution of Structural Engineers (2010) Manual for the design of steelwork structures to Eurocode 3 London: Institution of Structural Engineers**The Institution of Structural Engineers (2012) Technical guidance note (level 2): Element size estimation.**Reynolds, C.E. et.al (2007) Reynolds’s Reinforced Concrete Designer’s Handbook 11th ed. CRC Press*

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