Design of a commercial steel-concrete composite building

Design of a commercial steel-concrete composite building

using perforated beams and cost comparison with

conventional solution

Raadi Wazir Mahdi

H00171484

Supervisor:

Dr George Vasdravellis

Submitted for the degree of Structural Engineering with Architectural

Design MEng

Heriot-Watt University

School of Energy, Geoscience, Infrastructure & Society

April, 2016

MEng, 4th Year Heriot-Watt University

Raadi Wazzir Mahdi H00171484 ii

Abstract

Preliminary design has been conducted in a 6-storey building that mimics an

underdevelopment commercial structure in the city of Edinburgh. The structure was

designed according to Eurocode and UK nations annexes. Analysis was carried out to

analysis and design by using SCIA Engineer. Full detailed wind loading calculations

were also carried to perform a global analysis of the steel frame.

Long span beams with perforated openings were also designing in separate software to

investigate the cost saving with regards to the conventional materials. The results

indicated that substantial savings are gained when using cellular beams and sinusoidal

beams, the height maximum height that can be achieved between floor and ceiling was

affected as a result of an increase in the depth of the section.

These of perforated beams provide designers with more cost saving advantages, and

architects with regards to service integration and maximal free space that can be

achieved. However in the absence of detailed designing guidance by Eurocode and

limited understanding of behaviour of perforated beams requires further investigations

to be carried out.


Raadi Wazzir Mahdi H00171484 iii

Declaration

I Raadi Wazzir Mahdi confirm that this work submitted for assessment is my own and is

expressed in my own words. Any uses made within it of the works of other authors in

any form (e.g. ideas, equations, figures, text, tables, programmes) are properly

acknowledged at the point of their use. A full list of the references employed has been

included.

Signed: …………………………….

Date: 04/04/2016


Raadi Wazzir Mahdi H00171484 iv

Acknowledgements

I would like to thank sincerely my dissertation supervisor George Vasderavellis for his

consistent support through the semester to guide me, advise and help me with the

completion of this work. I would also like to thank him for his patience particularly with

the difficulties of finding a suitable software which causes many delays to this work.

Finally, special thanks to my parents who through the course of this work been

extremely supportive and encourage.


Raadi Wazzir Mahdi H00171484 v

Table of Contents

Acknowledgements ....................................................................................................................... iv

Table of Contents ........................................................................................................................... v

-Introduction ................................................................................................................ 8 Chapter 1

Background ................................................................................................................... 8 1.1

Aims ............................................................................................................................... 9 1.2

Objectives ...................................................................................................................... 9 1.3

Chapters outline: ........................................................................................................... 9 1.4

– Literature review ..................................................................................................... 11 Chapter 2

Composite Construction ............................................................................................. 11 2.1

History ......................................................................................................................... 11 2.2

Advantages and market share .................................................................................... 11 2.3

Design process and Eurocode (an overview) .............................................................. 13 2.4

2.4.1 Composite Slabs and beams ...................................................................... 13

2.4.2 Shear connectors ....................................................................................... 14

2.4.3 Composite columns ................................................................................... 15 – Castellated Beams ................................................................................................... 17 Chapter 3

History and Research .................................................................................................. 17 3.1

Type and Manufacturing process ............................................................................... 18 3.2

3.2.1 Castellated beams ...................................................................................... 18

3.2.2 Beam with individual openings ................................................................. 19

3.2.3 Cellular Beams .......................................................................................... 20

3.2.4 Sinusoidal openings .................................................................................. 21 Failure mode of Cellular .............................................................................................. 22 3.3

3.3.1 Lateral torsional buckling (LTB) .............................................................. 23

3.3.2 Vierendeel mechanism .............................................................................. 25

3.3.3 Flexural Mechanism .................................................................................. 26

3.3.4 Web post buckling .................................................................................... 26

3.3.5 Rupture of the Welded Joints .................................................................... 27 Beams with Sinusoidal openings ................................................................................. 28 3.4

Composite cellular beams ........................................................................................... 29 3.5

3.5.1 Assumption in design ................................................................................ 29 – Frame Design ........................................................................................................... 31 Chapter 4

Steel Frame ................................................................................................................. 31 4.1

Design and Structural Analysis software ..................................................................... 32 4.2

4.2.1 SCIA Engineer 15.3.12 (educational version) .......................................... 32

4.2.2 FBEAM 2015.1.4 ...................................................................................... 33

4.2.3 ANGELINA v3.02 .................................................................................... 34 – Results and results interpretation according to Eurocode ..................................... 35 Chapter 5


Raadi Wazzir Mahdi H00171484 vi

Input data .................................................................................................................... 35 5.1

Results ......................................................................................................................... 35 5.2

5.2.1 Secondary beam ........................................................................................ 35

5.2.2 Construction stage ..................................................................................... 35

5.2.3 Composite stage - ULS ............................................................................. 36 Composite columns ..................................................................................................... 40 5.3

FBEAM 2015 ................................................................................................................ 44 5.4

Mass and Cost Saving per whole structure ................................................................. 45 5.5

Angelina ...................................................................................................................... 46 5.6

- Wind Loading ........................................................................................................... 48 Chapter 6

Site location ................................................................................................................ 48 6.1

Basic values (EN 1991-1-4, 4. 2) .................................................................................. 49 6.2

- Conclusion and Recommendations .......................................................................... 57 Chapter 7

Conclusion ................................................................................................................... 57 7.1

Recommendation for further research ....................................................................... 57 7.2

References .................................................................................................................................. 59

Appendices .................................................................................................................................. 94

List of figures

Figure 1: Steel share in the UK's Construction market (steelconstruction.info, 2014) ............................... 13 Figure 2: Re-entrant and trapezoidal steel decking (steelconstruction.info, 2016) .................................... 13 Figure 3: Elastic transformation of composite cross-section (course materials, 2015) ............................. 14 Figure 4: drawing of a Headed stud connector (course materials, 2015) ................................................... 15 Figure 5: Interaction curve of shear and moment resistance ...................................................................... 16 Figure 6: Various type of composite columns (steelcomstruction.info, 2016) ........................................... 16 Figure 7: The Renault Centre (fosterandpartners.com 2015) ..................................................................... 17 Figure 8: An example of castellated beam cutting and rearranging process (wikimedia.org 2015) ........... 18 Figure 9: Resizing of a castellated beam by reversing the top half (Grunbauer 2015) ............................... 19 Figure 10: Wide rectangular openings with stiffeners (.steelconstruction.info) ......................................... 20 Figure 11: Fabrication process of closely spaced cellular opening (ArcelorMittal, 2015) ......................... 21 Figure 12: first drawing of the transformation process from cellular to Sinusoidal opening (THE

SINGAPORE ENGINEER Aug 2008) ...................................................................................................... 21 Figure 13: cutting process of Angelina™ beams (ArcelorMittal 2015) ..................................................... 22 Figure 14: Lateral torsional bucking of a cellular beam (Dervinis and Kvedaras, 2014) ........................... 23 Figure 15: 2T design approach used in lateral (Snock, 2014) .................................................................... 24 Figure 16: Table 6.5 of EN 1993 for recommendation for the selection of LTB for rolled I-sections. ...... 24 Figure 17: Set-up of a cellular beam under 4-point bending (Nseir et al, 20120) ...................................... 25 Figure 18 (right): Vierendeel mechanism and Vierendeel bending moments (Panedpojaman et al, 2015) 26 Figure 19: Web post bucking of web post (scielo.br 2016) ........................................................................ 27 Figure 20: Vierendeel mechanism causing the failure of welded section (scielo.br 2016). ....................... 28 Figure 21: Formation of plastic hinges on sinusoidal opening (Durif et al, 2013) ..................................... 29 Figure 22: Column Grid Line (SCIA Engineer output) .............................................................................. 32 Figure 23: Effective span of concrete flange for composite beam (Eurocode 4) ....................................... 37 Figure 24: A screen shoot of SCIA Engineer steps calculating the effective width ................................... 37 Figure 25: An example of plastic stress distribution for a composite beam with full shear connection

(SCI_P359) ................................................................................................................................................. 38 Figure 26: Plastic stress distribution with partial connection ..................................................................... 38 Figure 27: Various type of composite columns configuration (Eurocode 4) ............................................. 40


Raadi Wazzir Mahdi H00171484 vii

Figure 28: out-put of internal forces from SCIA Engineer for middle columns ........................................ 41 Figure 29: Table 6.4 of Eurocode 4 for equivalent factor .......................................................................... 41 Figure 30: out-put of SCIA Engineer for composite column ..................................................................... 42 Figure 31: SCIA out-put for calculated resistance of cross section for middle column ............................. 42 Figure 32 interaction curve simplification provided by Eurocode 4 (Eurocode 4) .................................... 43 Figure 33: SCIA out-put for 4 points of simplified interaction curve. ....................................................... 44 Figure 34: Optimisation option used in FBEAM ....................................................................................... 44 Figure 35: dimension and cross-section of optimized section. ................................................................... 46 Figure 36: Properties of Angelina beam ..................................................................................................... 46 Figure 37: height of the new angelina beam .............................................................................................. 47 Figure 38: 3D View of the structure ........................................................................................................... 49 Figure 39: Deformed shape of the structure under lateral loading ............................................................. 56 Figure 40: SCIA output showing the maximum lateral deflection of the frame ........................................ 56

List of tables

Table 1: recommended LTB curve selection by (Lakusic et al., 2008) and (Maquoi et al., 2003) ............ 24 Table 2: Load input data ............................................................................................................................ 35 Table 3: properties of non-optimized section ............................................................................................. 44 Table4: Properties of optimized section ..................................................................................................... 45


Raadi Wazzir Mahdi H00171484 8

-Introduction Chapter 1

Background 1.1

Composite frame structures are constructed by using different materials that provide

different advantages with regards to the stability and overall strength of the structure.

The particular type of materials utilized in a composite structural element depends on

the desired use of the structure and the expected loading magnitude. However with

regards to framed structures, steel-concrete beams and columns are used predominantly

because of their characteristic individual abilities, such as their capability to withstand

different compressive and tensile forces that are expected to be carried by the element.

In a steel-concrete composite frame, beams and columns are made of a traditional I-

beam or H-beam supporting a precast concrete slab or a composite slab (in situ concrete

with profiled steel sheeting). The steel with its intrinsic resistance to tensile forces

combined with the high compressive strength of concrete acts together as one member

which enable longer span beams to be produced in comparison to regular concrete and

steel beams. With regards to column design, the resultant composite action of steel-

concrete reduces the diameter of columns and increase their resistance to fire.

When composite beams are used in any structure, external force exerted on them causes

the two different materials to slip over each other. To overcome this issue, shear

connectors (studs) are welded to the top flange of steel beam regular spacing where the

two materials meet. However, the amount of shear connectors provided for a structural

section has a significant effect on the level of interaction between the two materials and

the property of the composite section. For example, when a composite beam consists of

a fewer number of connectors than required, the plastic moment of the section is not

entirely achieved.

As composite beams improve the bending resistance of a section significantly, it has

facilitated the development of long-span composite beams which contribute to

architectural space. Most of the long-span beams are provided with openings to pave the

way for service pipes to run within the depth of the beam and hence maximize the head-

room of each floor. The opening of a beam web can be achieved in various ways, such

as rectangular, hexagonal, sinusoidal or cellular cutting through its web. This also

provides the excellent advantageous regarding material saving and self-weight of the

section.



To fully understand the benefit of composite steel-concrete structures, particularly with

regards to steel framed buildings with cellular beams, a preliminary design of a six-

storey frame will be performed. The design will be carried in accordance to Eurocode

for wind loading and gravity loading by using analysis software SCIA Engineer.

Moreover, to further explore the economic advantages of using composite steel-concert

beams with web openings, two different analysis software, FBEAM® and ANGELINA,

will be used to model long span secondary beam that requiring openings for service

accommodation

Aims 1.2

This dissertation aims at providing an introduction to designing process and analysis of

composite beams with perforated webs according to Eurocode 3 and Eurocode 4. This

paper will take a greater interest in the use of structural analysis and design software

concerning minimize the use of material and reduce the cost of the project will be.

Moreover, to provide a better understand of Eurocode 4 and how composite design

works, results obtained from SCIA Engineer will investigate and compared to Eurocode

4 for composite columns and composite beams.

Objectives 1.3

To provide an introduction to the design of composite perforated beams.

To perform a preliminary design of a 6-storey frame using composite

construction with accordance to Eurocodes 3 and 4, as well as consulting other

research documents.

To model the three-dimensional steel frame using the SCIA Engineer software

to design for lateral loading (wind).

To design a long-span composite cellular beam using FBEAM 2015.1.4

software

To design a long-span composite cellular beam using ANGELINA software

To perform a cost and material saving analysis of the building

Chapters outline: 1.4

Chapter 1 An introduction to the concern topic, aims and objectives of this dissertation.

Chapter 2 Literature review about composite structure including different aspects.

Chapter 3 An introduction to current research in perforated beams



Chapter 4 Frame design

Chapter 5 Interpretations and comparison of software of the results according to Eurocode

Chapter 6 Detailed calculations of wind loading according to Eurocode

Chapter 7 Conclusion and suggested further recommendation for research



– Literature review Chapter 2

Composite Construction 2.1

History 2.2

Composite construction has been used in construction for almost a century now. The

use of steel and concrete was initially used for flexural structural members at the early

of 20 century in America and Canada- this is much credit to an American engineer who

first developed shear connection between at the interface between a steel beam and

concrete slab. This also exploited the full advantages of both materials which worked

together as a stronger material.

The development of composite construction lead engineers to use a similar method to

create vertical composite columns. The encasement of concrete columns within steel

provided a permanent formwork for columns and increased their capacity to withstand

higher axial forces in compression. Moreover, this lead to the reduction in

reinforcement amount need for vertical members and time and expenditure spend on the

process of erecting the structure. This also made it either to connect the columns to steel

beams.

With regards to framed structure, composite construction, despite their advantages was

not the most desirable method of construction until the introduction of metal decking.

This provided a permanent formwork for the concrete slab and better use of

reinforcement within the slab. Regarding construction process, metal decking produced

significant improvement by reducing the time spent in constructing traditional

formwork and was also used as a platform for construction workers

.

Advantages and market share 2.3

Some the advantage of composite use of steel and concrete are outlined below:

Architectural

Shallower beam: less concrete and steel is used resulting in the reduction in the

depth of the concrete beam. Which Increases architectural height of the floor.



Thinner columns: the use of steel around the concrete slab increase overall

compressive strength of the member, hence less material and small diameter.

Longer-span: as the two materials work compositely, the stiffness of the member

is improved, and the beam can span for larger distance without the need for

many supports, thus more room.

Services: particularly when using castellated steel beam, this provide serves

pipes to be integrated which contribute to the height of the floors.

Economical

The speed of construction: as the materials are prefabricated away from the site

and the time spent in construction phase is reduced dramatically.

Less material: as the composite action achieve sound structural integrity without

using many materials as compared to concrete and steel structures. Total

material cost is reduced.

Less labour: as most of the members are already fabricated such as precast

concrete slabs and steel sections and connection, less personal are required in the

construction site.

More floors: as the construction depth of the beam is reduced, more floors are

achieved within the same height of the building.

Less formwork: metal decking act as working platform reducing the need for

expensive and costly formwork. Also, steel encased columns required less or no

fire protection requirements.

The popularity of composite construction has increased within all industries and

particularly construction sector. One reason for such attractiveness to the developer is

the economic benefit. This has been particularly appealing to the construction of multi-

storey offices. A survey carried out by the BCSA and Tata Steel shows that in 2014

showed that showed that 66.8% multi-storey building where constructed of steel

compared to 24.3% ready mixed concrete.



Figure 1: Steel share in the UK's Construction market (steelconstruction.info, 2014)

Design process and Eurocode (an overview) 2.4

2.4.1 Composite Slabs and beams

Composite beams and slabs are made of two different materials that act as one element

so that the characteristic properties of both is fully utilized. To achieve this, various

theories are used simultaneously for designing composite members (mainly bending).

This is mostly because of the two states that the two materials experience during the

loading, which are compression and tension.

Figure 2: Re-entrant and trapezoidal steel decking (steelconstruction.info, 2016)

Composite slabs are constructed in various ways; however, most commonly used types

of composite slab are re-entrant and trapezoidal decking, this method provides

considerable resistance to the shear for that exist between the bottom surface of concrete

and steel sheet and prevent the concrete from slipping longitudinally and vertical



movement (Johnson, 2004). This is achieved by creating an interlocking effect as a

result of embossments, and this also resists horizontal shear forces of concrete.

The design of composite beam is covered by Eurocode 4 (BS EN 1994-1-1:2004) which

is used in conjunction with Eurocode 2 and 3 for concrete and steel structures. This is

due to the different characteristic behavior of the two materials. When the composite

beam is subjected to flexural loading, the concrete can resist high compressive forces

while steel is capable of carrying large tensile forces. Therefore, when using the elastic

theory of bending and plastic theory for designing composite members, concrete in

tension is usually not taken into account in elastic theory and not taken into

consideration in plastic theory. However in the elastic theory, concrete is transformed to

equivalent area of steel (Johnson, 2004):

Modular ratio: 𝑒 = 𝐸𝑎 / 𝐸𝑐𝑚

The equivalent flange width equals 𝑏𝑓, 𝑒𝑞 = 𝑏𝑓 / Shear connections

Figure 3: Elastic transformation of composite cross-section (course materials, 2015)

2.4.2 Shear connectors

Shear connectors are the most important part of the composite construction, and this is

mainly because of the shearing forces that exists between surfaces of two materials, in

this case, concrete and steel flange of the universal beam. To overcome this force shear

connectors were developed which transformed the two separate materials to perform

compositely as one element (Johnson, 2004).

There exist various types of shear connectors each with its pros and cons. the most

common form of shear connection is stud connectors. The reasons for the popularity of

stud connectors is that they are easier to weld to the flange, which expedites the welding



process in site during construction. The Eurocode 4 limits the diameter of welded stud

to 2.5 x thickness of the flange unless the stud is welded directed above the web of the

steel beam. The Eurocode also emphasises on the deformation capacity of shear

connection which is achieved by the use of ductile connectors. The ductility of

connectors depends on its slip capacity and is assumed to be only ductile if the slip

capacity is 6mm or above. This helps with shear to be redistributed between connectors

in the design (Johnson, 2004). The ductility of a shear connector is determined by push-

out test outlined in Eurocode 4.

Figure 4: drawing of a Headed stud connector (course materials, 2015)

2.4.3 Composite columns

Composite columns come in different forms, the most common one being the filling of

steel hollow section with concrete and additional reinforcement. Initially, it was

assumed that the only benefit of steel around concrete was to provide longer fire

protection. However, later it was discovered that it contributed to the effective

slenderness of the column. These types of columns offer significant advantages such as

great axial resistance and more slender columns.

The Eurocode 4 provides a simplified method for designing composite columns, which

is only valid for beams with constant cross-sectional and uniform material and not valid

for members made of unconnected parts. The resistance of the cross-section of a

composite member to combined compression is achieved by an interaction curve

(Figure 5) Npl, Rd (shear resistance) and Mmax, Rd (plastic bending moment)



Figure 5: Interaction curve of shear and moment resistance

Also, when calculated the critical load that can be taken by composite members, the

sum of the all contributing taken into account, including a correction factor which is a

calibration value of results of the simplified in comparison to data found from the test.

To verify members, the second-order linear elastic analysis is used.

Figure 6: Various type of composite columns (steelcomstruction.info, 2016)



– Castellated Beams Chapter 3

History and Research 3.1

Perforated beams which come in various shape and forms have been around for almost a

century now. The earliest known use of steel beams with openings is in the USA by

engineering firm Chicago Bridge & Iron Company in 1910 ( KERDAL 1982).

However, in Europe, the use of Castellated beams came a few years later when the

Skoda factories used them as roof beams with a span of up to 12 meters in the Czech

Republic (Radić and Markulak 2007). In the UK, the earliest use of perforated beams

within steel framed structures was in The Renault Centre design by Structural

engineering firm Ove Arup & Partners (Sonck 20014)

Figure 7: The Renault Centre (fosterandpartners.com 2015)

For the last decades, the use of castellated beams have gone through many types of

modifications; different manufacturers and structural engineering firms have produced

beams with a different opening, from eye-shaped openings to elongated opening, each

serving various purposes. These are used for various applications such as cantilever roof

for stadia, carparks and mixed used steel framed structures such as shopping centre and

office.

In some applications castellated beam with different opening shapes are used for

columns. This practice is limited as the shear resistance of the castellated beams is

decreased during the removal of some portion of the web. These members are most

suitable for application where a long span member is subjected to a universally

distributed load (UDL



Type and Manufacturing process 3.2

There is existed many opening configurations in today’s industry that provide Engineers

and Architects different advantageous.

3.2.1 Castellated beams

Castellated beams are type of steel beam that has been cut into a predetermined pattern.

The beam is then split into two parts and then moved by a distance so that the high point

of the web of the upper section is aligned with the lowers one and welded together. This

produces castellated beams with hexagonal shaped openings. Initially, the cutting of the

patterns was carried out solely by hand which was slow and tiresome - hence making

the production process time-consuming and limited in scale. However, the development

of digitally controlled cutting machines opened the gate for mass production and

decreased the cost, which in return made the use of castellated beam very attractive to

engineers and architects.

Figure 8: An example of castellated beam cutting and rearranging process (wikimedia.org 2015)

Moreover, the cutting of the web can be arranged in a way that will produce a

castellated section with varying depth that will suit different loading situation. For



example, the cutting line of the web can be set at an angle with regards to the length of

the section, when the cutting is finished the upper half is turned around son that the two

higher ends of the section are met and welded together. The load carrying capacity of

the section can be further enhanced by using two different halves of different sizes,

where the upper half is smaller than the lower half. This not only increases the

resistance to load carrying capacity but also reduces the self-weight of the section

significantly.

Figure 9: Resizing of a castellated beam by reversing the top half (Grunbauer 2015)

3.2.2 Beam with individual openings

These type of beams consisted of openings cut to the web of a hot-rolled section with

various shapes such as rectangular, cellular and elongated-circular. The steel section of

this type usually has a symmetrical shape as the opening are individual, and there is no

need to split it into two halves. Other section can be formed by welding three plates to

form a section with isolated openings that has dissimilar shape, for example, a beam

might need to integrate large services like ducts and isolated cellular pipes.



Wider openings will inevitably pose detrimental effect on the shear capacity of the

section, particularly if they are large and located in high vertical force zones along the

span. The use of stiffeners above the opening parallel to the flanges of the section can

improve the transfer of shear and compensate for lost bending capacity by removal of

the web.

Figure 10: Wide rectangular openings with stiffeners (.steelconstruction.info)

3.2.3 Cellular Beams

Probably the most used type of beams with web opening in steel framed building is the

use of cellular beams. The use of these beams is particularly attractive to architect and

designer in office, mixed-used structures, and car parks, usually as secondary beams to

provide the way for service pipes to be buried within structural depth. The

manufacturing process of a cellular beam is very similar to that of other castellated

beams. However as the spacing are regularly spaced, weight reduction per linear meter

is higher than other perforated beams.

Due to

increase in

depth as a

result of

cellular

cutting and

re-welding,

the bending

capacity of



the beam is also increased. Conversely, the shear force capacity of the section is

reduced, and the susceptibility to buckling is increased. This can be easily improved by

introducing vertical interval stiffeners to the web.

Figure 11: Fabrication process of closely spaced cellular opening (ArcelorMittal, 2015)

3.2.4 Sinusoidal openings

The advancement in cutting technology offered designers and manufacturers with the

ability to produce beams with different opening configuration. One of those

manufacturers is ArcelorMittal, which has produced Angelina™ beam. The invention of

these new type of openings came from a collaboration between a French architect and

ArcelorMittal, the purpose of this was to design a more architecturally striking

perforated beam.

Figure 12: first drawing of the transformation process from cellular to Sinusoidal opening (THE

SINGAPORE ENGINEER Aug 2008)



The resulting shape of this modification produced what is known today as Sinusoidal

opening. The results were not only atheistically pleasing but also contributed

significantly to self-weight reduction. This is because the cutting line passes throw a

lower angle (sinusoidal line) than traditional cellular openings. A more popular

advantage of Angelina™ beam is that the cutting procedure can be readjusted, so that

desired height is obtained; this contribute cutting waste of material. Normally the

resulting section is 1.5 time the height of original (ArcelorMittal 2015).

Failure mode of Cellular 3.3

The invention of perforated beams has unquestionably been a valuable development

within structural engineering industry and has contributed enormously to the savings in

costs and materials. The design of these beams also bring some setbacks that engineers

and designers need to consider before application. This is particularly important when

calculating the resistance of the member for lateral stability and bending capacity. When

a portion of the web of steel beam is removed, to produce a cellular opening or any

other shape, the stability of the section is put at risk and clearly the resulting section

would be susceptible to different failure modes (Snock and Belis, 2014).

Over the years, the behaviour of cellular beams under various types of loading have

been studied extensively. Kerdal and Nethercot (1984) produced a comprehensive

overview of the failure mode of castellated beams which is widely believed to be similar

to the cellular beam. Others like Aglan and Redwood (1974) looked at the ultimate load

capacity of web post of castellated beams under critical conditions. More recently

Chung and Lawson (2000) have observed the behaviour of perforated composite beams,

whereas Durifa and Bouchaïra (2012) have investigated the behaviour of more

Figure 13: cutting process of Angelina™ beams (ArcelorMittal 2015)



innovative geometrical opening like Sinusoid shapes.

Although perforated steel beams come with a variety of opening shapes, however,

regardless of the form of opening, it is generally believed within literature that similar

failure modes are introduced to the section when the beam is castellated. The review of

failure modes will only be explored concerning Cellular and Sinusoidal beams, and this

is mainly because these to type beams have been used during this project.

3.3.1 Lateral torsional buckling (LTB)

The cutting and re-welding of an I-section web at an offset results creates a deeper

section than the original one; this deteriorates the capability of the section to withstand

the lateral movement particularly when the upper flange is not fully supported against

lateral moment. Long-span beams are more likely to experience this failure behaviour

because of their height and slenderness, and also because the stiffness of the web

against torsion is decreased as a result of circular opening (Knowles 1985).

Figure 14: Lateral torsional bucking of a cellular beam (Dervinis and Kvedaras, 2014)

A number experimental works have been carried out to ascertain design approach for

the calculation of castellated beams resistance against lateral buckling, (Nethercot and

Kerdal, 1982) tested eight full-scale castellated beams with hexagonal openings. The

found that the effect of opening at the web concerning lateral stability was of let

significance. They also proposed that the resistance to LTB should be determined by

using cross-sectional properties of section calculated at the middle of the hexagonal

opening coupled with approached used to compute a steel section with no openings. The



approach is also known as 2T (Snock, 2014). This method was also used in Annex N of

ENV3 (European Pre-Standard, CEM, 1998) which was never published.

Figure 15: 2T design approach used in lateral (Snock, 2014)

Most of the current design calculation for cellular beam resistance to lateral buckling is

based on 2T. However, experimental tests conducted over the years have suggested a

variety different buckling curve. For example, (Nseir et al, 20120) undertook LTB test

for three beams with different web-opening of various shape ranging from 7.5 to 11 m

span, proposed the use of bucking curve ‘c’ in figure 6.4 of BS EN 1993-1-1:2005.

Figure 16: Table 6.5 of EN 1993 for recommendation for the selection of LTB for rolled I-sections.

Other experimental results from the study of the lateral stability of castellated beams

have also supported the use of 2T, but each of them has recommended a different

approach to LTB curve selection. (Lakusic et al., 2008) and (Maquoi et al., 2003) who

conducted similar LTB test under varying number of point bending recommended the

use of buckling curve

Table 1: recommended LTB curve selection by (Lakusic et al., 2008) and (Maquoi et al., 2003)

H/b ≤ 2.0 H/b > 2.0

Lakusic et al. [17]a b

Maquoi et al. [16]b c



Figure 17: Set-up of a cellular beam under 4-point bending (Nseir et al, 20120)

More recently, (Snock and Belis, 2014) investigated LTB behaviour by employing

numerical parametric study by using of results from two different experiment that used

cellular beams under 4-point setup bending test. The study confirmed that the 2T

approach is valid for calculated buckling resistance moment MRd, but failed to provide

a definitive proposal of a buckling curve. The test also used the MRd equation provided

in Eurocode 3

𝑀𝑅𝑑 = 𝛸𝐿𝑇 𝑊𝑦 𝑓𝑦 / 𝛾𝑀1

Where XLT is reduction factor for later torsion buckling provide in EN 1993 as:

3.3.2 Vierendeel mechanism

This type of failure is usually observed

in the experiments when shallow beams

with small T-sections (the upper and

lower steel T shapes that are results of

cellular web opening). Under normal



bending moment and shear force, forces are transmitted to the web of the steel section,

which in the case are the T-sections. The bending moment is carried by the beam and

the shear force that is transferred through the opening cause the T-section to experience

local bending. This is local bending is caused by the formation of four plastic hinges at

each corner of the opening, this is also known as Vierendeel mechanism, the bending in

the T-section. This is also known as Vierendeel bending moments (Chung et al, 200).

Figure 18 (right): Vierendeel mechanism and Vierendeel bending moments (Panedpojaman et al, 2015)

The Design recommendation for calculating the resistance of T-section with regards to

the Vierendeel mechanism are given in SCI P355 (Lawson et al,2009), and will be

further discussed with regards to composite steel-concrete beams.

3.3.3 Flexural Mechanism

This failure modes Cellular beams undergo this failure mode when the two T-section

start to yields under the bending moment, and this results in the formation of plastic

hinges. This mode failure is usually observed when beams of medium-span (6 to 7 m)

are put under test (Dervinis et al, 2012). Over years, many experimental works have

been carried out to investigate the flexural stability of steel beams with regular openings

in comparison to that of a plane-web beam. Hallux (1967) based on his work “Limit

analysis of castellated steel beams” stated that the yield of the T-section was not

different from that of a solid beam.

3.3.4 Web post buckling

This failure occurs when the vertical web of the post is exposed to horizontal shear

force as a result of the lateral instability of the post. The distorted shape of the web



yields a double curvature, and this renders the inclined edge of the post to undergo

compression and the other one tension.

Figure 19: Web post bucking of web post (scielo.br 2016)

3.3.5 Rupture of the Welded Joints

As more complex force are introduced to the web after being castellated, the welded

section of the web is exposed to more complicated forces. The welded along the length

where the

two end of

the t

section

meet may

rupture if

the

horizontal

force on

the web

post

become



higher than the resistance of the weld. The likelihood of this failure type is increased in

beams with closely spaced openings. (Demirdjian, 1999) reported that castellated beams

with long horizontal welding length are more susceptible Vierendeel mechanism.

Figure 20: Vierendeel mechanism causing the failure of welded section (scielo.br 2016).

Beams with Sinusoidal openings 3.4

.Modification of opening shapes will undoubtedly effect the overall behaviour of the

section, and this is mainly because each shape will have different size and may increase

or decrease the web area. Therefore, a few experimental test have been carried out to

examine the more recent sinusoidal opening shape. This was confirmed by (Durif and

Bouchaïr, 2012) who conducted a test on three full-scale beams with varying sinusoidal

opening. The test showed that, unlike the circular opening, sinusoidal openings fail in

two ways: yielding of the section at the opening of the small sinusoidal part in the larger

opening and local instability of the lower panel under compression.

Furthermore, (Durif et al, 2013) carried a similar test to investigate further failure mode

and the ultimate values of strength for sinusoidal beams. It was found that beams with

large opening had a similar failure mode to that of rectangular opening with the

formation of 4 plastic hinges at each corner. Whereas the failure mode for beams with

smaller opening showed similar behaviour that reported by (Durif and Bouchaïr, 2012).



Figure 21: Formation of plastic hinges on sinusoidal opening (Durif et al, 2013)

Composite cellular beams 3.5

Cellular composite beam are becoming increasingly the most favoured option for the

architect, this is due to the numerous advantages they provide in terms of span,

accommodation of service pipes, increase in load carrying capacity and weight

reductions in self-weigh of structural members. The behaviour of composite perforated

beam have been study by many (Lawson et al, 2006), (Lawson and Saverirajan, 2011),

(Sheehan et al, 2016), however none of them have produced a final design guide.

SCI P355 publication gives design guidance for beams with large opening and it also

recommends the same guidance to be used for the beam with circular openings. The

design method presented in this publication is based on the analysis given in Eurocode 3

part 1-1 and Eurocode 4 part 1-1. A number if tests have been used to validate this

method with the help of Finite Element Analyses.

3.5.1 Assumption in design

For particle design, SCI P355 (Lawson and Hicks,2011) makes following assumptions

to simply the designing:

In order to take the load of the opening, for uniformly distributed load, vertical

load is established at the higher shear side.

The moment acting at the middle of the opening are used to calculated tensile

forces at the bottom T-section.



The number of shear studs that are place along the length is the opening is taken

into account to establish compression force in the slab.

Composite resistance of the cross-section is taken into account, with bending

resistance of T-sections and component of local composite action of the upper

T-section, to compute the increase the resistance across the opening.

Plastic and elastic resistance of the T-section are based on the classification of

the section.

To simplify the design process, it is assumed that the bottom T-section only

resist tensile force induced by bending moment and the upper Tee resist shear

force.



– Frame Design Chapter 4

Steel Frame 4.1

The steel skeleton of the frame, grid, and steel member’s geometry and over all height

the building are designed to mimic an existing commercial building that is under

construction. The dimensions of the plot area of the building were obtained from

Google map.

To optimize the office area of the building regarding space and material saving, the

space between columns was set to 15 and 8.3 meters, this will provide a column-free

internal space and long-span of 15 meters. The height of the building was based on

assumed height of the surrounding structures on the considered building. To make sure

six floors are achieved within the assumed height, the height of each storey was set to

3.6 meters. This should be enough to leave a target floor-to-ceiling height of just under

3m, which is the required average height for offices

(steelconstruction.info/Concept_design, 2016).



Figure 22: Column Grid Line (SCIA Engineer output)

Design and Structural Analysis software 4.2

Structural analysis and designing software have been used by engineers for many years

to shorting the long process of analysing and designing. Today there is a variety

commercial structural software analysis that is used within the structural industry. The

fundamental purpose of all analysis software’s is essentially the same. However, some

are more suited to be employed for using in Finite Element analysis. The use a

particular analysis software is entirely dependent on the price and individual preference.

4.2.1 SCIA Engineer 15.3.12 (educational version)

SCIA is one of the most used structural analysis software around Europe, it is an

integrated and can analysis a wide variety of different materials. It has a multi number

of functionalities that can be activated to use for designing all kinds of projects such as,

designing multi-storey steel framed building, bridge (pre-stressed and post-tensioned)



and other structures like industrial plants. Other than that, social contains the following

abilities:

Analysis of all kinds of structures built from composite or single materials: steel,

aluminium, timber and composite steel-concrete frames.

Complies with most design standards: all parts of Eurocodes (wind, snow,

earthquake, seismic loading) and also National Annexes to Eurocodes.

Construction stage analysis for composite members.

Detailed designs of steel connection (bolts, welding)

Reinforcement detailing for concrete structures.

Fire resistance design

Detailed out-put of calculations with accordance to relevant Eurocode

Detailing general arrangement drawings

Optimization of cross sections

Library consisting of most of the steel sections and plates from various

manufacturers.

Various type of foundation design.

However, the software requires lots of understanding and practice to be utilized for

optimum design, the software itself provides a semi-full education version for students

with a few limitations: castellated beams needs a different plug-in which needs to be

provided by the steel manufacturers itself. Because of time constraints, by the time the

software was obtained it was not possible to learn how to utilize the software fully.

4.2.2 FBEAM 2015.1.4

FABEAM is a cellular composite beam design software developed by FABSEC that

uses current Eurocode 3 guidance. However, the software does not supply any further

documentation or publications with regards the designing guidance it employs in

ordered to carry relevant checks for designing and analyzing perforated beams.

Therefore, the purpose of using this software is not to attempt at further elaborate on

Literature review provided on perforated beams, but to model cellular beams to look at

the costing saving that can be achieved when using these kinds of structural members.



4.2.3 ANGELINA v3.02

ANGELINA is a beam design software that is developed by ArcelorMittal. The

software is specifically programmed to design openings with sinusoidal shapes. The

designer is taken through a few options that let the designer input various type of

opening dimension with instant graphical feedbacks.

For some reasons ArcelorMittal does not publish any manual on software with regards

as to how the calculations are carried out. This software will only be used to investigate

further the weight and cost savings that can be made by using Sinusoidal beams in

comparison to cellular beams.



– Results and results interpretation according to Eurocode Chapter 5

Input data 5.1

Based on Eurocode standards, the following load were used in SCIA software:

Table 2: Load input data

Load Type value Reference/comment

Dead load ComFlor®60,

Thickness: 1.0 mm

Slab thickness:140 mm

Wet concrete: 2.46 kN/m2

Dry concrete: 2.36 kN/m2

Self-weight of ceiling + raised floor= 0.2 kN/m2

EN 1993-1-1

Variable load Category : office = 2.36 kN/m2

Movable portion: 0.8 kN/m2

EN 1993-1-1

Roof: variable Roof slope < 30 degree = 0.6 kN/m2 EN 1993-1-1

Roof: Dead Load Self-weight of celling and 0.15 kN/m2 EN 1993-1-1

Wind load Windward: 14.6 kN/m

Leeward: -4.5 kN/m

EN 1993-1-4, UK NA

Snow load Snow load: 0.3 kN/m2 UK NA to EN 1993-1-3

Figure NA.1

Results 5.2

5.2.1 Secondary beam

5.2.2 Construction stage

During construction stage, while the concrete is being poured, precaution must be taken

to make sure that steel section is capable of carrying the load from wet concrete,

heaping of concrete, and weight imposed by construction workers. Eurocode 1, EN

1991-1-6: Actions during execution, Table 4.2 provides a value of 0.75kN/m due to the

pouring of the concreting stage for an unsupported member.



To further consider all unfavorable loading situation, EN 1991-1-1, Table A.1

recommends that the value of concrete should be increased by 1kN/m3 to take account

the weight wet concrete.

SCIA Engineers uses basic expression given in Eurocode 3 to account for cross section

requirement for plastic global analysis.

In this case the section was classified to be Class 1.

The majority of design check carried out for construction stage check are according to

Eurocode 3. This is because there is no composite action taking place during this stage.

5.2.3 Composite stage - ULS

When the section is in class one or two, the rigid plastic-plastic theory is used, this is

given in Eurocode 4. Moreover, Eurocode 4 presents engineers with a few assumption

that should be taken into consideration when calculating the plastics resistance moment.

The steel section, reinforcement and concrete are in full interaction with each

other.

The design yield strength of structural steel section is stressed in tension or

compression

The reinforcement in a concrete slab in compression maybe ignored, however

the effective area of longitudinal reinforcement is stress to its maximum design

yield strength.

Plastic resistance Mpl.Rd in full shear connection

Concrete in compression is assumed to resist 0.85 of design cylinder compressive

strength of concrete, and this is assumed over the full depth between the PNA and the

most compressed fib

The contribution of concrete to resistance to binding moment is limited to the beff

(effective with of the concrete flange) and the depth of concrete above the steel

sheeting. beff is calculated as the distributed effective width between the support and

mid-span. Eurocode 4 (5.4.1.2) give the following expression for calculating this

effective width.

beff = b0 + ∑bei



Figure 23: Effective span of concrete flange for composite beam (Eurocode 4)

SCIA Engineer uses the same method to calculate effective width of concrete flange.

Figure 24: A screen shoot of SCIA Engineer steps calculating the effective width



The area of concrete that provides resistance to the bending moment is dependent on the

layout and orientation of the composite slab with regards to the supporting beams. For

example, in secondary beams where the steel sheet is perpendicular to the steel section,

the depth of concrete is taken from the top of the surface of the concrete slab and the top

face of the steel sheet. For primary beams, where the sheet is parallel to steel section,

this is taken as the full depth.

Figure 25: An example of plastic stress distribution for a composite beam with full shear connection

(SCI_P359)

Plastic resistance Mpl.Rd in partial shear connection

When calculating plastic resistance moment in buildings, sometimes full compression

resistance of the concrete flange not required for hogging bending resistance. Therefore,

shear connectors are not expected to transfers a force equal to that of total compressive

resistance of concrete flange.

As the connectors are only required to transverse a certain amount of force, the section

can be provided with a partial shear connection. However, for partial connection to

develop resistance to bending, the Eurocode requires the shear connectors be ductile.

Figure 26: Plastic stress distribution with partial connection

The deformation capacity of shear connectors is based characteristic slip capacity of 6

mm achieved by push-out test.





Composite columns 5.3

Eurocode 4, part 1-1 article 6.7 give design rules for composite columns with sections

enclosed in concrete, partially encased sections and circular tubes filled with concrete.

Figure 27: Various type of composite columns configuration (Eurocode 4)

Article 6.7.3.3 requires the stiffness of all the materials used in composite columns to be

taken into account when calculating the relative slenderises of the plane of bending.

(E I) eff = EaIa +Es Is +Ke Ecm Ic

Ke = correction factor = 0.6

Ia= 2ND

moment area of steel section, Ic = 2nd

moment area of concrete and Is= of steel

reinforcement.

It also indicates that the modulus of elasticity of concrete should be reduced further to

take into account the long-term effects or creep effect on the effective elastic flexural

stiffness.

The final stiffness value is given in 6.7.3.4 which is the analysis of member

imperfection. This takes into account the effective stiffness to determine the second

order effects. However, this time, an additional calibration factor is given.

SCIA Engineer uses this stiffness value to determine the internal forces.



Figure 28: out-put of internal forces from SCIA Engineer for middle columns

The second set of calculation given by the software when designing the columns

according to Eurocode 4, use clause (3) of 6.7.3.4 to take into account the geometrical

imperfections based on column length which are listed in Table 6.5 of 6.7.3.6.

On the other hand, second order effects also needs to be considered. These second order

effects calculated by multiplying largest first-order bending moment by factore called

factor k

k = β/(1- NEd/Ncr,eff) which has to be bigger than 1.0

Where β is the equivalent moment factor given in Table 6.4.

Figure 29: Table 6.4 of Eurocode 4 for equivalent factor

This factor according to the provided table depends on the shape of the bending moment

diagram. For a typical composite column the bending moment diagram will have two



end moments with linear shape, the factor β can be easily calculated for end moments as

shown in the table.

The other moment factor which will be calculated for member imperfection will be

based on a parabolic distribution β

Figure 30: out-put of SCIA Engineer for composite column

Resistance to the axial forces

This check is done by SCIA Engineer following the guidance provide in Eurocode 3 for

checks for axial compression. The only difference is the calculation of NPl,Rd which is

the plastic resistance of composite column. The plastic resistance is increased by the

fact that the concrete is confined in steel tube, and is calculated by considering the

contribution from the plastic resistance of structural steel and rebar reinforcement.

Figure 31: SCIA out-put for calculated resistance of cross section for middle column



Other checks carried out by SCIA, is the resistance of the member to combine uni-axial

and compression bending in accordance to article 6.7.3.6. Which requires the applied

moment to be is smaller than moment resistance reduced for normal forces.

This reduced moment reissuance of normal forces is calculated based on a µd value.

This value can be obtained by an interaction curve between the moment and normal

forces. Eurocode gives a simplified way of generating the interaction curve by

calculating 4 points.

Figure 32 interaction curve simplification provided by Eurocode 4 (Eurocode 4)

SCIA engineer calculates these points and use to fin the µd to be used in finding the

actual

moment

and

correspond

ing normal

force are.



Figure 33: SCIA out-put for 4 points of simplified interaction curve.

Shear reinforcement check of the composite columns

Article 6.7.3.2 (4) states that it may be assumed that the shear force is fully by the

structural section alone, and this also an assumption which also made within SCIA

engineer.

FBEAM 2015 5.4

This software was used for to re-design the 15-meter composite beam with cellular

openings. The purpose was to look at the material and cost saving that can be achieved

by introducing these beams to the structures.

The secondary beam that was design in SCIA Engineer was UKB 533 X 312 X 151.

This section was used in FBEAM to and optimised.

Figure 34: Optimisation option used in FBEAM

The same profiling sheeting were used with the same loading that were input into SCIA.

Table 3: properties of non-optimized section

Depth

(mm)

Top

Flange

Width

(mm)

Top

Flange

Thickness

(mm)

Bottom

Flange

Width

(mm)

Bottom

Flange

Thickness

(mm)

Web

Thickne

ss (mm)

Gross

Mass

(kg/m)

542.5 312 20.3 312 20.3 12.7 149.5



The software also provide instant feedback with regards to cost and material saving. As

seen above

Table4: Properties of optimized section

Mass and Cost Saving per whole structure 5.5

Total number of Secondary beam in the

frame

406

Total mass of secondary beams 926585 kg

Total weight of optimized beams 402549 kg

Weight saved 524036

Cost saving 44.9%

However apart from money-saving a reduction in floor-to-floor have been introduced.

With height of the new composite cellular beam increasing 690 mm, the original

expected height has been compromised about money and material savings.

Depth

(mm)

Top

Flange

Width

(mm)

Top Flange

Thickness

(mm)

Bottom

Flange

Width

(mm)

Bottom

Flange

Thickness

(mm)

Web

Thicknes

s (mm)

Gross

Mass

(kg/m)

690 220 10 220 10 6 66.1



Angelina 5.6

To further investigate the advantages of the sinusoidal beams, the same bem was

modelled in Angelina software. The new beam was provide with the same number of

openings and the same opening height.

Figure 35: dimension and cross-section of optimized section.

Figure 36: Properties of Angelina beam



The new mass and height of the sinusoidal beam decreased notably. The original mass

of was 2265 kg and the new mass was found to be m = 1841 kg. When compared to

cellular beam, the cellular beam has more advantages interim of minimum depth, mass

reduction and money saving. The height of the new Angelina beam has increased to

724.5 mm, this can have significant impact on the maximum number of storey that can

be achieved.

Figure 37: height of the new angelina beam



- Wind Loading Chapter 6

Site location 6.1

location of site of the

structrd.

Dimension of the

Building

Total length: b 60 m

Spacing: s 15 m

Bay width: d 49.8 m

Height (max): h 25.2m

Roof slope: 0°

Height of each Story 3.6 m



Basic values (EN 1991-1-4, 4. 2) 6.2

Wind velocity

The following expression is given for calculating basic wind velocity

vb = cdir × cseason × vb,0 (4.1)

Where: vb= is thebasic wind velocity (based on

Terrain Category II)

Cdir= is the directional factor

Cseason= is the seasonal factor

vb,0 = is the fundamental value of the basic wind velocity

vb, 0= 25 m/s (UK wind velocity map, Edinburgh, Figure N.A 1)

Cdir= 1 (As recommended by EN 1991-1-4 and NA.2.6)

Cseason= 1 (For sex month winter period, EN 1991-1-4, 4.2, Note 3)

vb = 1 × 1 × 25= 25 m/s

Mean wind (EN 1991-1-4, 4. 3)

Figure 38: 3D View of the structure



vm(z) = cr(z) × co(z) × vb

cr(z) = is the roughness factor (4.3.2)

co(z) = is the orography factor, normally taken as 1,0. Or specified in (4.3.3)

Terrain roughness (4.3.2)

𝑐𝑟(𝑧) = 𝑘𝑟 . ln(𝑧/𝑧0) for zmin ≤ z ≤ zmax

Terrain category IV (TABLE 4.1)

z= 23.8, z0= 10, z0,11= 1, zmax= 200 m

Based on above table and Annex A terrain effects, A.1, and the location of the building,

category IV is chose, mainly because the site is surrounded by existing building with

average height of above 15 meters. The structure will be only exposed to wind from the

northern side where St square is located.



UK national to (EN 1991-1-4, 4. 3) part N.A. 2.11 provides Figure N.A. 3 for

determining roughness factors for based on the distance upwind to shoreline from town

terrain, Cr (z-his).

Google earth, shortest upwind distance was measure to be 3.66 km

Annex A, A.5 displacement height, Note 1, give the condition for calculated for raised

ground

x =25.9 (was measured from google

earth)

have = 15 m (as recommended )

z= 25.2 (height of the building)



as x ≤ 2 ⋅ have ( 25.9 ≤ 30), therefore hdis is the lesser of 0,8 ⋅ have or 0,6 ⋅ h = (12 or

15.12)

hdis= 12

Cr (z-his) = (25.2 – 12), therefore, Cr= 13.2 at 3.66 km (to be used in figure NA.3)

Using values, From figure NA.3, value of cr(z) = 1.08

NA. 4 gives a correction factors value for those site in town terrain.

Assuming the site is 2km inside the town:

Roughness correction factor = Cr,T = 0.79

NA.2.11 recommends the cr(z) to be multiplied by Cr,T for Town train category

IV.

cr(z) = 0.79 x 1.08 = 0.853

co(z) = 1 ( orography factor as recommended by NA.2.13)

Finally, Vm(z) = cr(z) × co(z) × vb = 0.853 x 1 x 25 = 21.325 m/s

wind Turbulence

UK. NA.2.16 give the following expression for calculating turbulence intensity

( Iv) at height (z) for Towen terrain:

IV (z) = IV (z) flat x k I, T,

NA.5 Give value for IV (z) flat based on (z-hdis) and distance up wind to

shoreline.

From previous, (z-hdis ) (25.2 – 12) = (13.2) , plotting this to NA.5 yields:

IV (z) flat = 0.189 at 3.66 km

And the same procedure for k I, T, on NA.6 yields:



k I, T = 1.56 at 3.66 km

IV (z) = IV (z) flat x k I, T = 0.189 x 1.56 = 0.295

Peak velocity pressure

NA.2.17 provides a different expression (NA.4b) for calculating peak velocity for

structure that have a height of less than 50m

𝑞𝑝 ( 𝑧) = [1 + (3 𝑥 𝐼𝑉 (𝑍)]2

𝑥 0.5 𝑥 𝜌 𝑥 𝑣𝑚2

𝑞𝑝 ( 25.2) = [1 + (3 𝑥 0.295]2 𝑥 0.5 𝑥 0.01226 𝑥 21.3252 = 0.991 kn/m2

Wind pressure on surfaces

Wind pressure on external walls

we = qp(ze) × cpe where, ze is the reference height for the external

pressure

cpe is the pressure coefficient for the external pressure

EN 1991-1-4 (7.2, figure 7.4) provides velocity pressure profiles with regards to ze

based on the relationship between height and width of the building:

For h b (25.2 49.8)

The profile equals to:

Keys for vertical walls (figure 7.5, EN 1991-1-4)



Table 7.1 give values for cpe,10 cpe,1 for coefficents for vertical walls of rectangular

walls,

For ℎ/𝑑 = 25.2/49.8 = 0.51

There fore: D = +0.8 and E= -0.5

Wind pressure on internal

walls

wi = q (zi ) ⋅ cpi

where: qp(zi) is the peak velocity

pressure

zi is the reference height

for the internal

cpi is the pressure

coefficient for the internal pressure

Section 7.2.9 (6) give internal

coefficient values for building

without a dominant face, and NOTE 2 recommends cpi values to be the more onerous

of +0,2 and -0,3 in the absence of full information with regards to the permeability to of

the walls.

Therefore,



External Coeff, Internal Coeff, Case 1 Case 2

D = cpe = +0.8 D = cpi = +0.2 or -

0.3

+0.8 + 0.2 = 1 +0.8 + (-0.3) = 0.5

E= cpe = -0.5 E= cpi = +0.2 or -0.3 -0.5 + 0.2 = -0.3 -0.5 + (-0.3 )= 1

Sum = 0.7 Sum = 0.5

From above table, Case 1 will give the largest value of wind loading or the worst case

scenario where (cpi = +0.2) is used.

Wind forces

The following expression is given in 5.3 (3) for calculating the summation of external

and internal forces on vertical walls.

𝐹𝑊 = 𝑐𝑐𝑐𝑑𝑥 (𝐶𝑝𝑒 + 𝐶𝑝𝑖) 𝑥 𝑞𝑝 𝑥 𝐴ref

Where, 𝑐𝑐𝑐𝑑 is the structural factor given as 1 (6.2 (1) (d))

𝐴ref = is the reference area, in the case it is the distance between vertical columns on the

windward face and leeward face.

Therefore:

Winward: 𝐹𝑊 = 𝑐𝑐𝑐𝑑𝑥 (𝐶𝑝𝑒 + 𝐶𝑝𝑖) 𝑥 𝑞𝑝 𝑥 𝐴ref = 1 x ((+0.8) + 0.2) x 0.911 x 15 =

14.87 kN/m

Leeward: 𝐹𝑊 = 𝑐𝑐𝑐𝑑𝑥 (𝐶𝑝𝑒 + 𝐶𝑝𝑖) 𝑥 𝑞𝑝 𝑥 𝐴ref = 1 x ((-0.5) + 0.2) x 0.911 x 15 = 4.5

kN/m

After these load were applied to the structure, the maximum lateral movement was

found to be mm, this is less than the recommended value of height of the building/300

(25200/300 = 84) in NA.2.24 Table NA.3



Figure 39: Deformed shape of the structure under lateral loading

Figure 40: SCIA output showing the maximum lateral deflection of the frame



- Conclusion and Recommendations Chapter 7

Conclusion 7.1

Insight has been given to the recent development of perforated beams within this thesis.

This was particularly explained regarding cellular and sinusoidal shaped openings.

Design and analysis software’s were used to perform a preliminary design of a six-

storey framed structure, with regards to lateral movement and gravitational loading.

Others software will also use to model beams with different openings configuration to

investigate the cost and mass saving of the whole structures. The out results of the

global analysis were fully interpreted with regards to Eurocode. Based on the

preliminary design undertaken in this thesis, the following conclusion can be made:

• The use of perforated beams has shown to have a considerable effect on the total

saving of the structure. However, the use of cellular beams has also demonstrated that

when using then compromise will be made concerning the maximum roof-to-t ceiling

height than can be achieved.

• The use of these beams also showed to increase on the column-free space that will

be obtained if these beams are used, particularly when used as secondary long-span

beams.

• The use of composite circular concrete infilled columns significantly decreased the

cross-sectional area of the column.

• Current research and literature have shown that further investigation is needed to

examine the behaviour of sinusoidal beams, particularly regarding the Vierendeel

mechanism around the sinusoidal openings.

Recommendation for further research 7.2

This thesis gave an introduction to the current literature and research of perforated

beams; it was found a high number of experiential work was aimed at understanding the

behaviour of castellated beams with very limited work on sinusoidal beams. Further

tests can be carried look at the behaviour of sinusoidal opening with regards to

composite slabs with profiled sheeting, and this will be very beneficial particularly for

understanding the contribution of the shear connectors to the resistance of upper

sinusoidal plate. Furthermore, more experimental work can be done to look at ways of



minimizing the height if these beams while at the same time to wider and higher

openings.



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Appendices

Appendix – c – unity check for optimized cellular beam from FBEAM

Combination Unity

Factor

Resu

lt CheckName Message

Construction Pass Weld Size Ratio Limit Weld Size : 5mm, Limit : 7.2mm

Construction 0.8572809

7

Pass Interaction Of Bending

Moment and Vertical Shear

Critical moment capacity 525.34kNm at point 26


01

Pass Vertical Shear Critical shear resistance 378.91kN at point 1


51


Moment and Vertical Shear at

Openings

Critical moment capacity 506.74kNm at opening 10


22

Pass Vertical Shear at Openings Critical shear resistance 244.05kN at opening 19


94

Pass Vierendeel Bending Moment capacity at opening 10 : 5.11kNm


91

Pass Web Post Buckling Max unity factor at the right side of post 1


42

Pass Web Post Horizontal Shear Max unity factor at post 19

Construction 0 Pass Web Post Flexural Max unity factor at post 1

Normal 6.10a Pass Weld Size Ratio Limit Weld Size : 5mm, Limit : 7.2mm

Normal 6.10a 0.6272234

32




Normal 6.10a 0.4286950

23


Normal 6.10a Pass Degree of Shear Connection Partial Shear Connection : 65.0% at analysis point 26

(Minimum Degree : 61.0%)

Normal 6.10a 0.2825984

66

Pass Concrete Longitudinal Shear

Resistance

Critical Plane : a-a overall span

Normal 6.10a Pass Transverse Reinforcement No further reinforcement is required. 12mm²/m

surplus reinforcement. Deck Continuous therefore

used in Reinforcement.

Normal 6.10a 0.7936336

99



Openings


Normal 6.10a 0.5155231

36


Normal 6.10a 0.5112715

36


Normal 6.10a 0.8501548

17


Normal 6.10a 0.3820796

31


Normal 6.10a 0 Pass Web Post Flexural Max unity factor at post 1

Normal

6.10b

Pass Weld Size Ratio Limit Weld Size : 5mm, Limit : 7.2mm

Normal

6.10b

0.7204784

15




Normal

6.10b

0.4924329

82


Normal

6.10b

Pass Degree of Shear Connection Partial Shear Connection : 65.0% at analysis point 26

(Minimum Degree : 61.0%)

Normal

6.10b

0.3246149

42

Pass Concrete Longitudinal Shear

Resistance

Critical Plane : a-a overall span

Normal

6.10b

Pass Transverse Reinforcement No further reinforcement is required. 12mm²/m

surplus reinforcement. Deck Continuous therefore

used in Reinforcement.



Normal

6.10b

0.9116304

52



Openings


Normal

6.10b

0.5955347

42


Normal

6.10b

0.5921006

2


Normal

6.10b

0.9765551

09


Normal

6.10b

0.4388868

51


Normal

6.10b

0 Pass Web Post Flexural Max unity factor at post 1

Serviceability

6.14b

0.4372978

81

Pass Imposed Load Deflection

Limit L/360

Maximum deflection : 18.2mm at analysis point 26,

Limit : 41.7mm

Serviceability

6.14b

0.4388937

65

Pass Total Deflection Limit Maximum deflection : 65.8mm at analysis point 26,

Limit : 150mm

Serviceability

6.14b

0.9302325

25

Pass Natural Frequency Natural Frequency : 4.3Hz, Limit: 4.0Hz

Serviceability

6.14b

0.1150166

99

Pass Concrete Compressive Stress Maximum stress : 2N/mm² at analysis point 26

Serviceability

6.14b

0.4867490

23

Pass Steel Top Stress Maximum stress : 134N/mm² at analysis point 26

Serviceability

6.14b

0.8069891

33

Pass Steel Bottom Stress Maximum stress : 222N/mm² at analysis point 26