ABSTRACT
This paper portrays a novel retractable roof system that applies the retraction based on
pivot technology used in a park named Miller to a stadium with a shape that is not a circle.
Current retractable roof stadium are studied, and the analysis is applied to offer a hypothetical
engineering structural design for a roof truss and carrier suggestions. To decrease stresses on roof
carriers, the offered approach will most likely necessitate structural solutions that are lightweight
and compact roof trusses. Roof carriers' mechanical designs are highly sophisticated because they
must be capable of rolling in bi-directionally and pivoting in a third direction. The design
provided here is insufficient for implementation in the real, however, it can enlighten engineers in
the future about important architectural considerations.
TABLE OF CONTENTS
ABSTRACT ........................................................................................................................ 2
TABLE OF CONTENTS .................................................................................................... 2
CHAPTER 1: INTRODUCTION ........................................................................................ 3
CHAPTER 2: Methodology ................................................................................................ 4
2.1 Introduction................................................................................................................ 4
2.2 Technical Terms ........................................................................................................ 5
2.3 Retraction System ...................................................................................................... 9
2.4 Structural System ..................................................................................................... 12
CHAPTER 1: INTRODUCTION
Retractable stadium roofs have gained in popularity from 1989 when the installation of the
first retractable stadium roof took place. They have been used for baseball, for football in
America, soccer, and multipurpose stadiums all around the world. The Rogers Centre – a baseball
stadium in Toronto, Ontario previously known as the Sky Dome, Canada, and home of the
Toronto Blue Jays, were the first to have this kind of roof installed. Cowboys Stadium in Dallas,
Texas, home of the Dallas Cowboys, has the most seats, with 80,000. Retractable roof stadiums
are used for some association football matches in Germany, Japan, and Wales, among other
places.
There are various advantages to retractable roofs. They provide dry conditions for games
during stormy weather while yet allowing sunshine during good weather. Retractable roofs,
unlike domes, may be used with natural grass, albeit this raises extra design difficulties. They also
permit year-round usage of the fields.
Today, amongst many other architectural designs in use, panel translation is the most
preferred. In this type of roof, many panels extend in a line to rest below each other at the
stadium's opposing ends. An example is roof of Minute Maid Park. Roofs with panels that pivot,
such as the one at Miller Park in Milwaukee, are built of panels that revolve around a fixed point.
Other varieties that are not as common, which combine both translating and designs that have
pivots for application to stadiums that are not circular in shape. An example of this is fabric roofs
that fold which are outside the boundaries of this document.
This thesis provides a theoretical model for a roof that is able to be withdrawn combining
the concepts of pivoting and translating panels together. This allows panels to revolve around a
3
stationary point while the panels' moveable ends take a path that is not a circle. The panel
supports must be able to move with the panel in such a way in order to stay on track. This
advancement will allow pivoting panel retractable roofs to be used on non-circular venues, such
as football stadiums and soccer arenas,that would otherwise be unable to accommodate typical
pivoting panels.
To begin, this document summarizes the present roof stadiums that are able to be
withdrawn. Second, it analyzes the technological issues that such structures provide. Thirdly, it
discusses the design's various concerns and methodologies. Furthermore, depending on the
preliminary design provided here, it makes observations and recommendations.
CHAPTER 2: Methodology
2.1 Introduction
Roof design is often separated into two stages that are interconnected:
architectural and structural design. Sport rules and aesthetics are taken into mind in the
building design. Because the focus of this thesis is on engineering design, only a few
architectural issues will be explored; the structure will decide the architecture.
A design that allows a component to function and stand is known as a buildings
structural design. These designs must correspond to local construction codes. This will
adhere to the Building Code of 2006 passes internationally. (IBC). Section 3.2 contains a
glossary of key terminology. The engineering design will be divided into two parts: the
retraction mechanism (Section 3.3) and the structural system (Section
3.4).
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2.2 Technical Terms
Axial Loading: A structural component is exposed to forces parallel to its longitudinal
axis.
Axial stress (f): The component of stress that runs perpendicular to its cross - section.
Whenever there is a bending moment, the axial stress varies along the length and crosssection of the member. The axial stress in an axially loaded member can be determined
by f = PA. Here P is the axial load and A signifies the cross-section area of the member.
The maximum axial stress at a given position along a beam is defined by f = Mc I. Here
M is the moment, while c is the distance from the section's neutral axis to its outer fibre,
and I is the moment of inertia of the section.
Beam: Transverse load carrying component
Beam-Column: It carries both transverse and axial loads.
Bogie: A wheel assembly with motorized axles.
Cantilevered Beam: A beam that is fixed at one end but is otherwise unsupported.
Carrier: A wheeled system that both structurally supports and carries the roof along its
track.
Column: is a member that carries axial load exclusively.
Connection: An interface that connects two structural elements.
Dead Load (DL): Loads on a structure caused by its own weight.
Deflection (D): It is known to cause a change in the size and form of a member. Thus a
member will show elongation when exposed to axial stress. Deflection in an axial
member is found by 𝐷 =
𝐴𝐸𝑃𝐿.
Here 𝑃 represents the axial load, 𝐿 is the length
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of the member, 𝐴 is the cross-sectional area of the member, and 𝐸 is Young’s
modulus
Determinate Structure: A structure that can be calculated only by statics.
Engineering Strain (ε): The ratio of a member's deviation to its initial dimension. Strain in
an axial member is given by = 𝐸𝑓, where 𝑓 is the member's axial stress and 𝐸 is
Young's modulus.
Fixed End: A support that can withstand any forces and situations.
Frame: is a load-bearing sequence of linked elements that work as a unit.
Hinge: A connection that is deflectible and so allows the members it connects to spin
freely. A hinged connection does not allow for totally unfettered rotation, yet it
does not prevent structural stresses from rotating. Hooke's Law states that In
materials that are linearly elastic, while 𝑓 ≤ 𝑓𝑦, Young’s modulus, strain, and
stress are related by 𝑓 = 𝐸𝜖
Indeterminate Structure: Statics is not sufficient to evaluate this type of structure.
Live Load (LL): The gravity loads on a structure resulting from factors other than self
weight, i.e. furniture, people, equipment, etc.
Load and Resistance Factor Design (LRFD): It’s a design philosophy based on structures.
In LRFD design, member strengths are multiplied by a resistance factor less than
one, while loads are multiplied by a load factor higher than one. This provides
additional strength to the structure beyond what is apparently needed to
compensate for material imperfections and unusually high loads, material and
load uncertainty
6
Load combination: A derived load is made up of the sum of multiple types of loads
multiplied by their resistance factors, i.e. 1.2DL+1.6LL.
Moment (M): The force that causes a member to bend. It acts as tension on one side of
the cross-section and compression on the other.
Moment Connection: A connection preventing the members from rotating.
Moment Frame: A frame in which the members are connected by moment connections
and can operate as beam-columns.
Moment of Inertia: A cross-sectional geometric property that influences a material's
ability to sustain a moment. 𝐼𝑥 = ∫𝑦2𝑑𝐴 and𝐼𝑦 = ∫𝑥2𝑑𝐴 produce the moment of
inertia.
Nominal Strength (𝑅𝑛): The hypothetical strength of a member in the absence of a
resistance component.
Pin: An ideal support that resists pressures in all directions but not at any one instant.
Poisson's Ratio (𝜐): A material property defined as the transverse strain to axial strain
ratio.
Polar Moment of Inertia: A cross-sectional geometric feature that influences torsion
resistance.𝐽 = ∫𝑟2𝑑𝐴 = 𝐼𝑥 + 𝐼𝑦 denotes the polar moment of inertia.
Reaction: A sustaining force that maintains the balance of a component or system.
Resistance Factor (𝜑): A code-prescribed number larger than one used to calculate a
member's notional strength.
Roller: A perfect support that only resists pressures in one direction and does not resist
any moment.
Shaft: is a member that carries only torsion.
7
Shear (V): The component of a force that acts internally. It is perpendicular to the cross
section of a member.
Shear Connection: A connection that allows its members to rotate freely however restricts
translation
Shear Modulus (G): A measure of material strength, defined as the ratio of shear stress
and shear strain. To calculate it, we use 𝐺 = 2 (1+𝐸 𝜐), where 𝐸 is Young's
modulus and is 𝜐 Poisson's ratio.
Shear stress (τ): A member's stress parallel to its cross-section. It is a component of
appears in the same plane as its cross-section. To determine the maximum shear
stress at any point along a beam, 𝜏 = 𝑉𝐴 is applied where V is the shear and A is
the cross-sectional area of the member. Similarly, the maximum shear stress at a
given position on a particular cross-section along a torsional shaft is given by 𝜏 =
𝑇𝑟𝐽𝐺 where T is the torque, J is the polar moment of inertia, and G is the shear
modulus.
Simply-Supported Beam: A beam which has two supports only. One is a pin at one end
while other is a roller
Stress: A quantity defined as a force per unit area.
Torsion: A event in which loading is done. Here the member twists around its
longitudinal axis.
Traction Drive Mechanism: The impetus for the roof is created by the bogies' wheels
rubbing against the track in this retraction method.
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Transverse loading: An event of loading where a member receives forces that are
perpendicularly acting to its longitudinal axis.
Truss: It is a framework, having posts, struts and supporting a roof or any structure
Ultimate Strength (𝑅𝑢): The maximum load that can be bared by the structure.
Yield Stress (𝑓𝑦): At yield point the value of stress.
2.3 Retraction System
The design components of retractable roofs including its structure and mechanics
must be extremely well integrated. Designers must consider several intricate features,
such as resistance to load in the track, strength, frictional and lateral load resistance in the
assemblies.
A bogie is seen in Figure 4. To transport the roof and provide support, wheels
numbered 52, 54, 56, and 58 are affixed to frame 48. Two driving motors power the
carrier (component 64 as shown). No wire is attached to the bogie as it is powered by
traction, to drag it down the track. Instead, the motors use friction to produce push
between the wheels and track (Allen and Robbie 1986).
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Figure 4
Diagram of a Rogers Centre bogey (Allen and Robbie 1986)
Retraction mechanisms are classified into two types: traction and cable drive
systems. A cable type retraction mechanism’s canopy moves on carriages that have
wheels at each end. Rather than being dragged by the carriers themselves, the roof is
moved by steel wires connected motor’s other end (Waggoner 2008). Since there are
fewer parts, they are less prone to problem with their mechanics and thus ensure easier
maintenance. They are difficult to install on tracks that are not linear. A cable system is
not deemed practicable since the design in this thesis is intended for use on a curved
track.
The carriers themselves generate propulsion for the roof in a traction drive
system. Torque is provided by the axles, and the roof is pushed by the resistance of the
wheels against path (Blumenbaum and White 2011). It is harder to construct bogies and
10
not evenly loaded, serious issues might arise. Overloaded bogies contribute to generation
of excessive force, whereas under loaded bogies cannot supply sufficient propulsion. As a
result, systems must be built mechanically such that to equally transfer roof loads
amongst the bogies.
The retraction mechanism is subjected to two types of loads: fixed and moving
loadings. Static loadings apply to the complete body at all times. Wind loads and selfweight are examples of stationary loads. Operational loads exist when the retraction
mechanism is activated. These loads include torque in the axle, resistance among wheel
and track and engine vibrations. Fixed and operational weights can combine to create
severe weight conditions in specific scenarios.
The bogies' design considerations may be classified separately into types known
as mechanical and structural. One of the concerns of structural design is capacity of the
bogies.
Design challenges(mechanical) include the propulsion system's ability to produce
sufficient force to guide the opening and closing of the canopy of roof.
To guarantee that no carrier is overburdened, a method for equally distributing
loads must be implemented. Load distributors are classified into two types: Individual
suspensions and pivot beams. As shown in figure five, all beams transfer the weight to
bogies (A) at all of the ends. The hinged connectors (B) enable the beam to swivel,
allowing the wheels to always carry the same weight. This technology successfully
distributes loads, however it is uneconomical and load is distributed unevenly. Each
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carrier in independent suspension system.
Roof Structure
A
B
A
B
A
A
Figure 5
An idealized balance-beam assembly in elevation, with bogies (A) and pinned connections at
the pivoted beams (B) (Frazer 2005)
2.4 Structural System
Trusses or frames might be a roof panel’s structural architecture. Structural
components are joined at stiff connections. Every component has the ability to generate
tension and compression, shear, moment, and torsion. Frames necessitates sophisticated,
more costly connections. Instead, plane trusses are to be used in this design.
Each panel must also include some kind of lateral load resisting system (LLRS).
There are two alternatives for the LLRS when utilizing trusses for the structural system:
plane trusses shown on left in figure 6 or space trusses shown in the same figure on right.
Due to the fact that a plane-truss may only withstand loads in its own plane, trusses in
various orientations are utilized. A space truss can endure loads in every coordinate axis
since it is not fully in one plane. In contrast to the previously mentioned trusses, Excellent
durability can be provided by unit space truss in every direction. Space trusses, on the
other hand, are more complicated to construct and require more complex networks as
compare to trusses that are plane.
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Figure
6
Roof supported by plane trusses (left, Waggoner 2008) and space truss (right, encad.ie)
If the limitations of plane trusses are to be bypassed, they have to be built in
different orientations. Loads in all three planes can be sustained if a plane truss is
included perpendicularly. For example, in the architecture seen opposite to right hand
side in showed image, arch trusses of plane are limited by extra trusses extending its
length overall.
Pressure of wind and uplift of wind are major forces operating on the roof. If the
lengths are changing, it will make the design more difficult. Because the loads change
and the truss member forces fluctuate as the roof panels telescope, each member must be
subjected to a variety of potential loads in order to establish the amount of maximum load
that it can bear.
Because many devastating engineering failures, structural designs must have far
more strength than what appears to be essential. Because every structure can be exposed
to loads or material flaws that are unexpected, philosophy has evolved to push engineers
to alter known loadings to promote safety.
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At present, 2 philosophies are made used of in engineering. Allowable Strength
Design (ASD) is an older philosophy strength of designed material shows reduction due
to safety. Calculation of load is done using a variety of strength and combinations. The
largest mixture of bearing loads for each component must be less than the strength
calculated earlier.
The other one is resistance and load factor design, which is analyzed in the
document and the present trend setting (LRFD). The following load combinations
(abbreviations defined in Table 1) must be considered in LRFD designs:
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In structural engineering, currently there are two design methods in use. Allowable
Strength Design (ASD), the original and oldest method, involves the safety factor by
reduction in design strength of component’s material. Calculations of load using variety of
load recipes, safety decreases the strength of component. The calculated strength must be
greater than highest load combination of individual component.
The other philosophy is based on Resistance as well as load factor design, whose application is
shown in thesis and the current state of the art (LRFD). The following combination of loads
(abbreviations defined in Table 1) must be considered in LRFD designs:
1.4(𝐷 + 𝐹)
(1)
1.20 (F + D + 𝑇) + 1.60(H+L) + 0.50(S or R or 𝐿𝑟)
1.20𝐷 + 1.60(S or R or 𝐿𝑟) + ((0.50 or 1.00) 𝐿 or 0.80𝑊)
1.20𝐷 + 1.60𝑊 + (0.50 or 1.00) 𝐿 + 0.50(S or R or 𝐿𝑟)
(2)
(3)
(4)
1.20𝐷 + 1.00𝐸 + (0.50 or 1.00)𝐿 + 0.20𝑆
(5)
0.90𝐷 + 1.60𝑊 + 1.60𝐻
(6)
0.90𝐷 + 1.00𝐸 + 1.60𝐻
(7)
where
Abbreviation
D
F
T
L
H
Load
Dead Load
Fluid Load
Thermal Load
Live Load, except roof Live Load
Load from earth pressures, groundwater pressure, bulk
pressure
Lr
Roof Live Load
S
Snow Load
R
Rain Load
W
Wind Load
E
Seismic Load
Table 1
LRFD load types and their abbreviations (AISC 2006)
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Because the objective of this thesis is to demonstrate a basis for concept of roof design rather than
a fully code-compliant structural design, Only third LRFD combination of load will be used, 1.20D
+ 1.60Lr + 0.80W. (AISC 2006).
2.5 Conclusion
Technical features of design have been discussed in this chapter, that serves as foundation for the
technical choices provided in the above chapter, as well as suggestions offered at the end of this
thesis. In this chapter both engineering and architectural design process will be discussed in detail.
CHAPTER 3: RESULTS
3.1 Architectural Design
Design of the stadium is dependent upon FIFA’s criteria for fields as well as stadiums. The sizes
were calculated as a preliminary estimate of the dimensional requirement to meet FIFA’s pitch
rules while also holding around 49,999 crowd’s capacity (FIFA 2011).
At pitch level, the sizes are 410' (125 m) by 278', including facilities for reserve players
and coaches (85 m). There are 44 rows of chairs, each with 1.5' of space between them
(OC). Height of sitting are is around 52’, every row is around 14" in height and 36" in
depth. For walkways and structural component 10’ was left from both sides, bringing the
overall horizontal dimensions to 696' by 564'. The height of the building was increased by
20'. Building's overall height at the walls was increased to 72', keeping in mind the
visibility issues.
Stadium’s roof is a unique feature (Figure 7). Six panels revolve around a un moveable
pivot located in the middle of walls having high length (Point A). The retraction is driven
by powered bogeys at the other end of each panel. Because the stadium's form isn’t in shape
of circle, around the pivot point, every bogie moves in relation to both its stadium structure
as well as panel. The entirety of the seating space and pitch has direct contact with sunlight
16
when roof is retracted (left). Whole of the sitting and pitch area is protected by harsh
weather when the roof is extended. This thesis includes a preliminary design concept of
the complete roof, as well as a even in-depth look at on one panel, and a speculative one
oof panel’s trusses design.
B
A
A
B
B
Figure 7
Roof plan view with green retractable panels, magenta stationary panels, and white
supporting structure.
Extra services are placed on other end of the structure to overcome extraordinary
overhang in the entirely opened condition (Areas B). Rental Spaces, Canteens, fan stores,
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Parking and many other facilities. Most of the side facilities are covered by stationary
panels as well as by sitting are to some extent. Other panels rotate to rest when the roof is
opened on either end, 124’ is the given maximum overhang, 46’ is the maximum
overhang when the roof is not opened.
Span of the panel must have a maximum length of slightly more than 600', that was curved
to 610'. Span of the truss was 564' when completely closed and 491'3" when fully open. It
has the longest span at a point in the middle, where it must span 601'71/8". The carrier
must initially travel in the direction of panel’s end. when it retracts. Span starts to move in
the direction of pivot as it reaches longest span.
Stadium will support the roof carriers construction on a track. On top of the
carriers will be a second track that will support the roof. There will be an alignment
between the track of the stadium and bottom wheels, and the top wheels will always be
aligned with the span, just as the roof track. Individual wheels do not need to be able to
rotate because to the modest curve of the stadium track across the carrier length, as far as
the track provides around space of an inch between track wall and wheel. Changing angle
between roof track and stadium path, on other To compensate, the carriers must have
some type of rotating mechanism, as will be discussed later.
3.2 Structural Design
The truss closest to the stadium's center, as shown in Figure 9, was chosen for a specific design.
The depth of the truss was chosen to be around 15', including joints separated at 20'4",to remove
hazard of failure of buckling. The truss was designed with a enhanced Pratt geometry to reduce
chord members length and boost its compression forte. Because carrier’s motion in the direction of
18
bottom chord of the truss' would be exceedingly to reduce the carrier’s longitudinal motion, the
truss was believed to be assisted by means of pivot and carrier acting as a roller.
Figure 8
Elevation view of selected truss, parallel to span.
Almost entire parts are sized as W-shaped I-shaped (Figure 9) members with wide flanges. There
is a high modulus to area ratio in W members, resulting compression particularly efficient. The
generated loads in the chords were very substantial due to the panel width and span length,
necessitating big members and high-grade steel. This design was created using guidelines from
AISC 2006. Each and every member of truss are W14 or fewer as design of compression
requirements for the members of W are only supplied by means of members of W14.
Figure 9
Cross-section of a W14x132 member, exemplary of W members
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The self-weight of the members of the dead load of roof (D) (Figure 10) is specified in pounds/foot
in the identification of the member; for example, a 132*W12 member weighs 131.99 plf.
Polytetrafluoroethylene weights (0.720 pounds per square foot), more commonly called as Teflon,
is also included in the dead load. In design, the dead load is a "moving target"; when strength of
the members is increased to match it, the dead load grows, necessitating subsequent member size
increases. As a result, to optimize member of sections, the designer needs frequently iterate member
selection numerous times. As dead loads are solely a product of earth’s gravity, they only shows
downward
force..
Figure 10
SAP2000 interface depicting the undeflected truss geometry with dead loads only
The Lr is calculated using the dimensions in section 1607.11.2 of the 2006
International Building Code.
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R1 & R2 (two reduction factors), are calculated by means of slope and size of roof
to reduce the live load of around 19.99 pounds/ft2. In addition, the roof live load of least
extent must be considered. Because the weight is just 300 pounds, it is insignificant in
comparison to remaining loads and so may be ignored for such cases thesis-based purpose.
The wind loads (W) are calculated using ASCE 7 criteria (ASCE 2010). The method for wind loads
calculation is complicated, as it takes into account the height of the structure, topography of the
surrounding (terrain as well as buildings) profile of roof and slope of roof among other things. A
downward pressure is created as wind rushes up the roof's slope (Figure 11, left). Uplift pressure is
created as water rushes down the roof's slope (Figure 11, right). The horizontal vector of the
pressure of the wind is similar to horizontal velocity of wind, and the factor normal to pressure of
wind is surface of the roof.
Figure 11
Diagram depicting wind directions and the resulting forces
Entirely code compliant stadium is not actually the target of the thesis. As a result,
rather than evaluating all locations of support as well as load cases, this research proposes
one load’s design scenario and location of two supports. LRFD case (3): 1.20D + 1.60Lr
+ 0.80W has been chosen as the situation of the load For scenarios of total four loads, the
2 wind instances having wind in same direction with span.
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SAP2000, was used to conduct the structural analysis (CSI 2004). To calculate the
reactions and member of forces, the structural model is built piece by piece. The
geometry of truss is first entered using truss wizard’s combination that creates the
removal of manual member and a basic geometry basic geometry, addition, change.
Second, in order to determine connection types, restrictions and releases must be defined.
Every joint is liberated to merely reduce linear pressures, with the support of pivot end modelled
similar to pin and the carrier end support modelled similar to roller. Following that, loads are
defined. There is an addition of membrane made up of fabric to the dead loads, although the
software can calculate self-weights of members. The user applies all wind and live loads. SAP200
will itself compute every load situations depending upon member section, Loads applied and
assessments of materials of load combinations when factored – in given case, case (3) – are studied.
3.3 Structural Design Results and Discussion
To resist compression upper members of the chord are one of theW-shape (largest
members) and are made of best quality steel (ASTM A913, fy = 69.99 ksi) due to the
huge member forces created in the structure. According to the support position, some
members experienced both stress and compression. In these circumstances, the smallest
compression member sizes were chosen, and for insufficient section of tensile capacities,
same dept beams were chosen that are larger , giving acceptable compression and tensile
strength.
Diagonal members, Bottom chord, Top chord and vertical members were
separated into four groups. The same section applies to every member of the similar
group. W14x730 is the member of top, W14x605 is the bottom chord member, W10x54
is the vertical chord member, and W12x120 is the diagonal chord member. Many
22
members are over-designed as a result, yet it simplifies construction while also
significantly boosting roof stiffness.
Maximum 13'5" downward span is deflected by the roof when completely
extended under dead load (Figure 12, A). The upper chord is compressed throughout, the
bottom chord is tensioned throughout, and the members web fluctuate. The maximum
deflection of roof is around 5'2" downwards with 1'5" in the upward direction when fully
retracted under dead weight (Figure 12, B) (Figure 12, C). There is a compression in the
upper chord while there is a tension bottom. The upper chord in the cantilever is mostly
in streching, while the bottom chord is mostly in compressed.
From expanded position, the portion which is cantilevered modifies the force distribution, giving
much lower member forces. At the same time design isn't entirely depended upon load (dead).
Unfactored dead in roof deflection and live loads must not be more than 1/240 of the span, which
is around 3'5" in this case, according to code. This structure cannot be compliant with the ASCE
compression member specifications and specified geometry. It is suggested that the design be
iterated
along
less
spaced
trusses.
A
B
C
Figure 12
Roof truss deflected under dead load when fully extended (top) and fully retracted
(bottom)
In fully extended position, the most intense member loads develop. The right side of the truss
develops more extreme because of bigger arm area at the end of carrier, hence the biggest member
23
forces emerge when the wind blows carrier to pivot sides (Figure 13). Near the middle span, having
highest of 18'4" deflection. Red shading below the members indicates compression, while blue
shade over the members indicates tension. The highest compressive and tensile forces were both at
10,700 kips, take near the carriers in the top and bottom chords, respectively. There is a high
pressure to uplift end serves to lower the stresses as when the wind blows pivot o career
sides.(Figure 13).
Figure 13
Closed analysis results for wind blowing left to right; deflected shape (top), member
forces (middle, not to scale), and support reactions in kips (bottom).
The chord loads are not as intense as roof is entirely retracted (Figure 14) , because of
cantilever’s balancing effect. The forces are inverted in the overhanging region, with the
bottom chord members are compressed and top chord members are stretched. larger web
forces occur as a result of this support state, however they are still smaller than the chord
loads. The highest deflection in downward direction is 6'9" (Figure 14, A), While the
highest deflection in upward direction is 1'10". (B). Force’s members are substantially
24
lower in the state of retraction due to the cantilever; yet, this position causes the largest
impact at carrier, about 799 kips.
B
A
Figure 14
Retracted analysis results for wind blowing left to right; deflected shape (top), member
forces (middle, not to scale), and support reactions in kips (bottom).
From a physics sense, the structural design provided here works. But a design that
could be constructed in a practical manner. Steel truss weights a lot when considering the
lengthy span. Even if the construction was completely code-compliant, high-grade steel
and the member sizes would make it prohibitively expensive. While the structure
provided here is not totally practical, it does suggest that the project is doable. More
designed structure is required for professional use in-depth study, such as trusses having
shorter members in order to reduce flexural buckling more cost-effectively. Geometric
optimization is necessary for such a design is well above the undergraduate curriculum
and its scope
25
CHAPTER 4: CONCLUSION
Over the last 25 years, retractable roofs have risen in popularity, and there is no
reason to expect that trend will stop. Engineers have reacted to new issues and built
methods to handle diverse geometries, as the slope roof at phoenix stadium’s university to
rotational roof at Miller Park. There are definitely challenges in creating the roof shown
in this thesis, and there are lessons to be gained from it.
Because of the light-weight roof covering, the number of trusses employed in this
thesis (three per panel) was chosen so there must be less distance between roof trusses.
Because of the quite a lot distance between them and 610' span, the loads were
substantially higher than predicted.
Lighter materials, such as aluminum, should be used to construct the trusses.
Because self-weight made up the majority of the load on the intended truss, reducing it
will drastically reduce the carrier’s load
The shape of the truss must be changed to reduce length of member. Compression
chord's biggest members were controlled via buckling rather than crushing. Small
sections are allowed by reduced member length, lowering cost as well as weight.
From a practical sense, this roof concept isn't particularly important; a simplified
designed panel (translating) can be used, and the quantity of coverage supplied by the
roof is unaffected. However, this proposal provides designers with a fresh choice for
shape. The revolving roof's aesthetic can be implemented to a variety of stadium design
by its means.
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The last conclusion of thesis includes that is necessary for every civil engineer to learn. there's a
reason for engineers not getting licenses early with their degrees. In his (or her) profession, Sense
of intuition and experience is key for success as an engineer, that helps him (or her) in decisions
just as much as his academic education. That experience and intuition are informed by learning
from unrealistic and incorrect designs like the one given here. In the end, an ability of engineer is
summary of his schooling, achievements as well as failures .
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