UNIVERSITY OF PISA
Department of Civil and Industrial Engineering
AEROSPACE ENGINEERING COURSE
MASTER THESIS
FEASIBILITY AND STRUCTURAL STUDY OF AN
AIRSTAIR SYSTEM FOR SHORT-MID RANGE
AIRCRAFT
Candidate
Supervisors
Marco Ciuffarin
Dott. Ing. Vittorio Cipolla
Ing. Carlo Viganò
1 Introduction ... 1
1.1 Scope of the thesis ... 1
1.2 General use of airstairs in the aviation industry ... 2
1.3 THE PRANDTLPLANE ... 5
1.4 THE SUKHOI SUPERJET 100 ... 6
2 Certification requirements for airstairs ... 8
2.1 OVERVIEW ... 8
2.2 THE CS-25 ... 9
2.2.1 SUBPART B – FLIGHT ... 10
2.2.2 SUBPART C – STRUCTURE ... 11
2.2.3 SUBPART D – DESIGN AND CONSTRUCTION ... 12
2.2.4 SUBPART F – EQUIPMENT ... 14
2.3 THE SAE ARP 836 ... 14
3 Airstair conceptual design ... 19
3.1 Overall size definition ... 19
3.2 CAD modeling of the airstairs ... 22
3.3 CAD Assembly of airstairs with SSJ-100 FUSELAGE ... 24
4 SSJ-100 Airstair preliminary design ... 27
4.1 CHOICE OF THE DEPLOYMENT SYSTEM ... 27
4.2 STRUT SUPPORTS ... 29
4.3 CENTRAL REINFORCEMENT SUPPORTS ... 30
4.4 COMPLETE OVERVIEW OF THE STRUCTURE ... 33
4.5 Preliminary structural sizing ... 33
4.5.1 LOAD VERIFICATIONS OF THE STRUCTURE ... 34
4.5.2 DEFINITION OF THE CONSTRAINT REACTIONS IN THE SUPPORT SYSTEM ... 35
4.5.3 STRUT SUPPORT VERIFICATION ... 39
4.5.4 CENTRAL REINFORCEMENT BEAMS VERIFICATION ... 44
4.5.5 PULLEYS VERIFICATION ... 46
4.5.6 REAR SUPPORTS ... 48
4.5.7 OMEGA-SHAPED SUPPORTS VERIFICATION ... 50
5 FEM analysis ... 60
5.1 STOWED STAIR ANALYSIS ... 60
5.1.1 UPWARD LOAD RESULTS ... 61
5.1.2 FORWARD LOAD RESULTS ... 63
5.1.3 REARWARD LOAD RESULTS ... 64
5.1.4 SIDEWARD POSITIVE LOAD RESULTS ... 65
5.1.5 SIDEWARD NEGATIVE LOAD RESULTS ... 67
5.1.6 DOWNWARD LOAD RESULTS WITH REINFORCEMENT BEAMS 68 5.1.7 DOWNWARD LOAD RESULTS WITHOUT CENTRAL REINFORCEMENT BEAMS ... 71
5.2 DEPLOYED STAIR ANALYSIS ... 74
5.3 PULLEY ANALYSIS ... 77
6 PrandtlPlane Airstair preliminary design ... 79
6.1 DIMENSIONS EVALUATION AND CAD ASSEMBLY ... 79
6.2 DEPLOYMENT AND INSTALLATION SYSTEM ... 82
6.3 RELIMINARY STRUCTURAL SIZING ... 85
6.3.1 CONSTRAINTS REACTION DEFINITION ... 86
6.3.2 SYSTEM SUPPORTS VERIFICATION ... 88
6.3.3 PULLEYS VERIFICATION ... 100
6.3.4 OMEGA SUPPORT VERIFICATION ... 101
6.4 DEPLOYED STAIR VERIFICATION ... 103
6.4.1 STEP VERIFICATION ... 103
6.4.2 TOTAL DEPLOYED STAIR VERIFICATION ... 104
6.5 SUMMARY CHART OF THE PRP AIRSTAIR DIMENSIONS ... 106
7 Conclusions ... 107
1
1
Introduction
1.1 SCOPE OF THE THESIS
The purpose of this thesis is to define a possible airstair system solution for two different airplanes, the PrandtlPlane (or PrP), studied in the Parsifal Project, that can be collocated in the mid-range sector, and the Sukhoi Superjet-100 (SSJ), a jet aircraft belonging to the regional sector and main product of the Superjet International Company. Part of this work has been developed inside the SJI headquarters as a trainee lasted six months. The work analyses the feasibility and the structural aspects of an airstair installed inside the fuselage of the airplane, starting from the benefits that can be obtained from this system and the requirements that must be complied, not only for its specific use but also for the stowing inside the airplane. The starting point for the conceptual design has been a first preliminary model made for the PrP, from which a new airstair type in CAD assembly for the adaptation of the SSJ case has been produced. The design and study of the parts needed for the installation and movement of the stair, together with a preliminary verification, has taken some time as represented the most challenging passage of the work, with different solutions tried in order to find the best one. Then, the results obtained with the use of the FEM analysis confirmed the acceptability of such system for the airplane structure and finally, a solution for the PrP has been also possible to produce. Other important aspects related to an airstair, like the choice for the supply system or considerations regarding the fatigue life, have not been faced due to time limits, but discussions and evaluations have been done for such topics as well.
The role of the SJI company in this work has been important, not only for the facilities made available, but mostly for the precious advices given by experts of the sector that made the results obtained possible. The SJI company has been very interested in this thesis also because if in a near future it would be decided to develop a similar project for the airplane, those results would surely be a good point to begin from.
2
1.2 GENERAL USE OF AIRSTAIRS IN THE AVIATION
INDUSTRY
Looking at the examples of airstairs that have been adopted during the years in commercial aviation, thus apart from private jets where it is considered a necessary item for their equipment, it is clear that most of them had been designed for the narrow-body sector, since such type of system has to face many obstacles and difficulties when used in widebody airplanes. This is because the passengers’ cabin doors are significantly above the ground than the narrow-body ones, so it makes it very complicated to use airstairs. In addition, bigger airplanes typically do not use little airports with poor infrastructure. Despite this, there have been cases in which commercial widebody aircraft were equipped with airstairs, like:
• The Ilyushin Il-86 (Figure 1): it had featured three lower-deck airstairs that were deployed from the luggage area in order to allow the passengers to drop off their baggage before entering the passenger cabin; [1]
• The Lockheed L-1011 Tristar: only a few models of this were equipped with airstairs that permitted passengers boarding to the lower deck, just like the former one; this one was used for such airplane in airports without jetways or mobile stairs for widebodies. However, there had been also built an airstair coming out from under the right aft passenger door, giving direct access to the main cabin. This clearly shows that there have been very poor examples of widebody planes using airstairs; on the other side, many narrow-body airplanes were equipped with it, most of them characterized by the T-tail, like:
• Douglas DC-9
• McDonnell Douglas MD-80 Series (Figure 2) • Boeing 717, 727 and 737
• BAC 1-11
• Airbus A319 and A320
The T-tail airplanes have also the particularity to have both an airstair in correspondence of the forward passenger door and a ventral airstair lowering from the fuselage in the tail. The important difference is that, whereas in T-tail ones all had airstairs, in airplanes like the 737, which actually is the only one that uses it, the airstair
3 is offered to the airline as a plus item, depending on where it will be deployed, which routes it will cover and in which type of airports it will land and departure from.
Figure 1. The airstair adopted for the Ilyushin II-86 [2]
4 So why an airline would choose an airplane equipped with airstairs? Different points of view have been analysed, like:
• The cost of the airstair itself (purchase, maintenance, etc.) vs. cost saving for handling service
• Reduction of max. payload and/or range due to higher empty weight vs. reduction of turnaround time
• Reduction of max. payload and/or range vs. access to minor airports without handling services and less impact on airport saturation
Figure 3. The opening of the airstair installed inside the L-1011 for the Pacific Southwest Airlines [4]
In some cases, airlines have decided to get rid of airstairs installed in their aircraft, in order to save costs: for example, PSA Airlines decided to order 5 L-1011 equipped with airstairs for its use in the Los Angeles-San Francisco route, that in those years was facing a rapid growth in passengers number and at peak times the schedule was conditioned by ground congestion. The first two were delivered in 1974 and the other three were to be delivered the following year, but in the period between the order and the delivery, the fuel had triplicated its price per gallon together with a drop in the passenger market. This led the airline to withdraw the first two airplanes after just eight months and the other three were never taken in service.
Today, airstairs are chosen mostly by many low-cost airlines that are continuously looking for a decrease in ground operation costs, but for mainline carriers, which operate
5 in bigger airports like the hubs, a configuration without airstairs is preferred as those airlines want to have a direct access to the airport terminal, using the airbridges, despite higher costs.
1.3 THE PRANDTLPLANE
Figure 4. Artistic view of the PrandtlPlane studied in the PARSIFAL Project [5] The PrandtlPlane (hereafter called PrP) bases its design and concept development on what Ludwig Prandtl, after whom is named, studied and illustrated in a publication dated 1924 [6]: he defined that the “best wing system” that gives minimum induced drag for given lift and wing is the box-wing configuration. From this starting point, in 1990 Pisa University made a research that obtained the exact solution to Prandtl’s problem, proving in particular that the lift on the horizontal wings results of the superimposition of a constant and elliptical distributions and, on the vertical wings, is butterfly shaped, already shown by Prandtl [7]. So, this has permitted to apply such concept to aircraft design and the Prp is the result of it.
The PARSIFAL project ("Prandtlplane ARchitecture for the Sustainable Improvement of Future Airplanes”) was funded by the European Union under the Horizon 2020 Program. The project, which started in May 2017 and concluded in July 2020, has been coordinated by the University of Pisa (Italy), with partners ONERA (France), TUD (Netherlands), ENSAM (France), DLR (Germany) and SkyBox Engineering (Italy). The consortium has been supported by an external Advisory Board made up of experts from the aircraft manufacturers (Leonardo, Airbus), airport management companies (Milan and Tuscany airports), airlines (KLM), and aeronautics professionals, who have
6 contributed to steer the research towards concrete objectives with attention to market interests.[8]
The PrP has 36 metres of wingspan, like the A320 or the B737, but a capacity between 250 and 320 passengers, enabling this airplane to belong to the upper-class sector of the category. The cabin adopts a doble aisle configuration and offers a setup configuration of 8 or 10 seats per row, and the fuselage owns a non-circular cross-section. This modification of the cross-section is necessary in order to maintain the same length of the competitors but also to be able to carry a large number of passengers. Furthermore, the cargo compartment is one-piece and not divided in two parts like most of the cases, moving the luggage faster and in a more efficient way. The study of the use of airstairs can bring important benefits like the decrease in costs per passenger and to speed up the ground operations with the consequent reduction in turnaround times, given the opportunity to carry more passengers with the same dimensions of the competitors. The PrP proposes the installation of airstairs for each of the three exit doors, that especially in a high-density configuration of 308 passengers can give an important advantage in the autonomous boarding and disembarkation of the airplane. Moreover, deciding to place the rear airstair in the tail cone increases the maximum configuration to a total of 324 passengers.
1.4
THE SUKHOI SUPERJET 100
7 The SSJ-100 is a regional jet that has been developed by the Sukhoi Civil Aircraft Company (Russia) in partnership with Leonardo Company (Italy), two of the most known and renowned companies in the aviation industry. Together, they formed the Superjet International Company in 2007, a joint venture dedicated to marketing, sales and support of the SSJ-100 worldwide. The SJI company has introduced this model in order to satisfy the demand of commercial airlines in the segment between regional and mainline markets, establishing as a prefixed goal to become the market leader in the 100 seats aircraft sector. The headquarters are in Tessera, Venice, near Marco Polo International Airport, whereas the assembly line of the aircraft is in Komsolmosk on Amur, Russia [10]. It is 29.94 m long and has a wingspan of 27.80 m; its maiden flight took place in 2008, whereas it entered commercial operations in mid-2011. Now, more than a hundred SSJ100s have been delivered to different airlines, most of them were Russian or belong to the eastern market, but some of them were also western carriers like the Mexican airline Interjet which decided to order and deploy it in its routes.
Technically speaking, the SSJ-100 offers the ultimate aircraft technologies like a full digital fly-by-wire system; a flight deck like the Airbus 350, one of the newest planes in commerce; innovative avionics that reduce consistently the crew workload. In addition, the company has been focused on introducing wingtips in order to reduce fuel consumption and improve performance in the last years. For this reason, the Saberlets have been designed and will equip the airplane very soon.
Regarding the use of airstairs, the SSJ-100 project does not provide such system as a component in its basic equipment, so a similar one has not been considered for its development. In any case, the company has conceived a preliminary design of an airstair placed inside the cabin in order to save time when it has to be installed, aside the forward cabin door, and addressed to the business version of the airplane. On the other hand, the development of an airstair located under the cabin floor and in correspondence of the forward cabin door has been also both an innovation and at the same time it has brought many complications for the SSJ. This is mainly because it is an airplane which has reached ten years of operations and a modification of this type can be defined as major one for the entire structure, needing thus the approvement not only of the design sector of the company, but also, and most importantly, of the certification agencies. At the same time, trying to develop this project for a detailed airplane as the SSJ-100 can help the PrP, which is instead at only the preliminary design, to consider which are the analysis and the components that an airstair installed inside the fuselage should need, and which could be the possible impacts on the airplane and its environment.
8
2
Certification
requirements for airstairs
2.1 OVERVIEW
In every project regarding the aeronautical context, the first step to face is the analysis of what the main regulatory authorities require in their documents about the project of interest; this is obviously because every single part of an airplane must answer exhaustively to specific requests that can relate to different aspects. The document that is issued from the authority to a new airplane is called Type Certificate and certifies the airworthiness of an aircraft design in his totality. After being issued to the airframer, the design can be changed only in two cases:
1. When requesting a Supplemental Type Certificate (STC) 2. When creating a completely different design.
The choice depends on how much the change can be considered as a new design, in other words, if the change introduces risks that were not considered in the first design of the aircraft. Normally an STC is cheaper than a completely new design, and inside the document is reported which is the product change and the effect on the existing part design. All is indicated with serial numbers that make recognizable every single part. The modifications made with a STC are also permitted to an operator or a company that are not the ones who own the Type Certificate of such airplane.
Examples of the most important regulatory authorities are: • FAA or Federal Aviation Administration (USA) • EASA or European Aviation Safety Agency • CAAC or Civil Aviation Administration of China
For the topic of this thesis, the main document taken into consideration has been the CS-25 [11] where CS stands for Certification Specifications, the typical document released by the EASA for turbine powered large aeroplanes and that has been used by Superjet
9 International for the SSJ-100. In particular, the CS-25 Amendment 23, dated 15 July 2019, has been the base for the definition of which requirements need to be satisfied when designing an airstair. Secondly, documents regarding criteria for a boarding airstairs from SAE International [12] have been also taken into consideration for the development of the project, remembering that is not a requirement document as the CS-25 but a recommended practice, and gives important information about how to size properly an airstair and its parts. On the other hand, the document does not provide enough information regarding how an airstair shall be installed inside an airplane.
2.2 THE CS-25
As stated before, the Certification Specification is the main document, produced by EASA, that defines the guidelines that an airframer must follow in order to obtain the airworthiness certificate. The first point of this document, the 25.1, it clearly underlines that “These Certification Specifications are applicable to turbine powered Large
Aeroplanes”. Specifically, the document is divided into two books, that are:
• Certification Specifications (CS): as definition by the EASA [13], contains non-binding technical standards adopted by the agency to meet the essential requirements for the basic regulation
• Acceptable means of compliance (AMS): as definition by the EASA, are non-binding and serve as a means by which the requirements contained in the CS can be satisfied
In both books the same numeric system is used, in order to connect properly every CS with the corresponding AMS. Each book is divided into subparts (indicated with letters A-J) that represent different categories of the aircraft that need to be faced, like:
• Flight • Structure
• Design and Construction • Powerplant
• Equipment
• Operating Limitations and Information • Electrical Wiring Interconnection System • Auxiliary Power Unit Installations
10 Many appendices are included after these parts, and illustrate, as an example, the atmospheric icing conditions or the emergency demonstration instructions. Despite not being clearly mentioned in a specific subpart, the categories that contain important requirements for an airstair are flight, structure, design and construction, equipment. In the following subchapters each category will be study in deep.
2.2.1 SUBPART B – FLIGHT
This is the first category faced in the CS-25 for the project’s interest, regarding, as the 25.21 point says, the satisfaction of each point in “each appropriate combination of
weight and centre of gravity within the range of loading conditions for which certification is requested”. So, installing an airstair that increases the empty weight of the airplane
brings appropriate verifications to do in this context, evaluating if the limits imposed in the airplane are respected or not.
In particular, the following points are involved:
NUMERATION COMMENT
25.21 Proof of compliance, how to show the verification for the loading conditions
25.23 Load distribution limits
25.25 Maximum weights in different conditions
25.25 Minimum weight definition
25.27 Centre of gravity limits
25.29 Empty weight and corresponding centre of gravity
11
2.2.2 SUBPART C – STRUCTURE
Together with the subpart D, this is one of the most important parts for the airstair in terms of loads verification and analysis; the main points of interest are the following:
NUMERATION COMMENTS
25.301 Loads, definition of limit and ultimate load 25.303 Factor of safety for the limit load
25.305 Strength and deformation, vibrations
25.307 Proof of structure
25.321 Flight loads, general considerations
25.365 Pressurized compartment loads
25.471 Ground loads, general considerations
25.561 Emergency landing conditions, general considerations 25.571 Damage tolerance and fatigue evaluation of the structure
25.581 Lightning protection
Table 2. Main points considered in subpart C of the CS-25 document
The 25.365 is important because covers the theme of pressurization and compartment loads inside the airplane. This requirement can be considered negligible for the airstair itself, whereas important considerations must be done for the fuselage door. So, it is helpful to illustrate what contents: at subpoint (a) is required that the structure
“must be strong enough to withstand the flight loads combined with pressure differential loads from zero up to the maximum valve setting”, whereas subpoint (b) indicates that “external pressure distribution in flight, stress concentrations and fatigue effects must be accounted for”. In the other subpoints, indications regard landing conditions with a
compartment pressurised (c), the multiplying factor for the pressure differential loads (d), conditions to avoid failure and interference in flight of any structure, component or part inside or outside the pressurised compartment (e), The subpoint (f) indicates that “the
fail-safe features of the design may be considered in determining the probability of failure or penetration and probable size of openings” and finally in subpoint (g) the indications
are for bulkheads, floor beams and partitions in pressurised compartments with occupants. For the requirements 25.301 and 25.561, in the chapter regarding the load’s verification will be more illustrated.
12
2.2.3 SUBPART D – DESIGN AND CONSTRUCTION
The points of interest are the following:
NUMERATION COMMENTS
25.601 General considerations
25.603 Materials, suitability and durability
25.605 Fabrication methods
25.607 Fasteners
25.609 Protection of the structure
25.611 Accessibility conditions, for inspection and parts replacement
25.613 Material strength properties and material design values
25.619 Special factors
25.621 Casting factors
25.623 Bearing factors
25.783 Fuselage doors
25.787 Stowage compartments
25.843 Test for pressurized cabins
25.865 Fire protection
Table 3. Main points considered in subpart D of the CS-25
As underlined in the chart, the first requirements of particular interest are the 25.601 and 25.603 that introduce the materials matter. In the first one is written that design features or details with a hazardous or unreliable experience should not be considered for an airplane, so the suitability mut be demonstrated by tests. In the second one is indicated that the suitability and durability of materials used for parts, in order to prevent failures for safety reasons, must be “established on the basis of experience or
tests”, “conform to approved specifications that ensure their having the strength and other properties assumed in the design data (AMC 25.603 (b)” and “take into account the effects of environmental conditions” expected in service. For typical materials, like
aluminium, the correspondent AMC is the 25.603, whereas for composite materials the AMC 20-29 are considered. In the 25.613 requirement, subpoint (a), the material strength properties “must be based on enough tests of material meeting approved specifications” in order to obtain design values on a statical basis, whereas at subpoint (b) “material
design values must be chosen to minimise the probability of failure due to material variability”. For this reason, except subpoints (e) and (f), the selected material design
13 values must show compliance and corresponding strength as “99% probability with 95%
confidence” in case of a single member of an assembly has applied loads that in case of
failure could bring to the loss of the entire component, whereas a “90% probability with
95% confidence” is requested for a redundant structure where, if a an individual element
fails, this “would result in applied loads being safely distributed to other load carrying
members”. Subpoint (c) regards the effects of the environmental conditions, like
temperature and moisture, for materials applied to essential component and structure that must be considered “where these effects are significant within the aeroplane operating
envelope”. The last two points (e) and (f) cover greater material design values and other
material design values that could be acceptable for the agency.
In the 25.787 requirement, as the airstair clearly needs a proper stowage compartment, this and others that are usually used for baggage, carry-on articles and equipment “must
be designed for its placarded maximum weight of contents and for the critical load distribution at the appropriate maximum load factors corresponding to the specified flight and ground load conditions”. In addition, the compartments must be designed if
the breakage of one of them and the consequent loosing of the contents placed inside can
“cause direct injury to occupants”, “penetrate fuel tanks or lines or cause fire explosion hazard by damage to adjacent systems” or “nullify any of the escape facilities provided for use after an emergency landing”, the last one according also to the 25.561 (b). In
addition, an AMC is required “to prevent the contents in the compartments from
becoming a hazard by shifting under the loads specified in (a)”, and lastly, if lamps are
used inside the compartment, “each lump must be installed so as to prevent contact
14
2.2.4 SUBPART F – EQUIPMENT
This category is addressed more to the choice that must be done for the airstair’s power source. The stair can be powered by a supply battery or by the airplane electrical system itself; the points of interest are the following:
NUMERATION COMMENTS
25.1301 Function and installation
25.1302 Installed systems and equipment for use by the flight crew
25.1309 Equipment, systems and installation
25.1310 Power source capacity and distribution
25.1351 Electrical systems and equipment, operation without normal electric power
25.1353 Electrical equipment and installation
25.1360 Precautions against injury
25.1365 Electrical appliances, motors and transformers Table 4. Main points considered in subpart F of the CS-25
2.3 THE SAE ARP 836
This document is provided by SAE International, formerly Society for Automotive
Engineers, an American professional association that gives technical standards and
recommended practices for the design, construction and characteristics of motor vehicle components. In addition, ARP stands for aerospace recommended practice, specifying that this document is for such category. The practice considered is the number 836 and is intitled “Design and Safety Criteria for Passenger Boarding Stairways”; the parts used are the following:
• Description of basic types of stairways • Basic stair design dimensions
• Recommended dimensions for design • Design safety considerations
Various terms are introduced in this document, and they indicate the airstair parts’ proper dimensions; these are:
15 • Tread depth T1: theoretical horizontal dimension from one stair nosing to the
adjacent stair riser nosing
• Effective tread depth-T2: effective horizontal dimension from one stair nosing to
the adjacent stair riser, T2>T1
• Riser height R: the vertical distance between the surface of the tread of one step and the surface of the tread of a step above or below when measured perpendicularly between the tread surfaces
• Riser to tread ratio R/T1: an arithmetical ratio of the height of one of the risers to
the depth of the tread, which ratio is equal of the angle of inclination of the stairway
• Angle of inclination A: the angle formed by a line joining the stair nosings of one flight of stairs and the horizontal, A=tan-1 R/T
1
• Step width W: the width of the step surface as measured along the nosing of the step
• Handrail height H: the distance to the center of the handrail as measured at the nose of the step and perpendicular to the tread surface
Obviously every one of these points have been considered, but the first two from where the dimension of an airstair begins are the tread depth and the riser height.
The document defines two basic types of airstairs: adjustable fixed-riser stair and variable-riser stair. The first type is composed by a lower section that is fixed, whereas the upper one is extendible and can slide or roll behind and parallel to the lower section; there is also a platform that represents the intersection between the lower and the upper sections. Surely, using an airstair like this can bring a big advantage, like the possibility to use it for different elevations, but at the same time this represents the biggest disadvantage as there are limitations in the increments of the stairs’ risers when used for different aircraft. Even the use of a mid-platform could bring some problems for the deployment of the stair. The other type considered for a stairway is the variable-riser model that uses the parallelogram principle, consisting in maintaining the parallelism between the stair treads and the upper platform at any angle. The advantage for this type is that offers a continuous range of elevation adjustments and does not need an intermediate platform; the disadvantage instead is the range of elevation adjustments that are allowed by the acceptable design dimensions.
So, the main difference between these two types is that for a fixed raiser one the riser to tread ratio is a constant that results in a fixed angle of inclination, whereas for a variable
16 riser model the variation is allowed and as a consequence also that for the angle of inclination. Both of the stairs designs can be included in the fixed riser category, leaving apart the considerations about the mid-platform for clear reasons, because only one model cannot satisfy both airplanes due to different elevation values of the passenger boarding door.
The basic proportions that are generally accepted for the project of an airstair are:
Table 5. Value limits for a basic stair proportion
As seen from table 5, the point 5.2 of the document regards the formula used for a basic stair proportioning, showing that for every selected tread depth, within the limits, a best riser height for best proportion can be determined. The formula is:
𝑅 𝑇1
= tan [𝑅 − 3 8 ] °
Several couples of values of riser height and tread depth are reported in the document.
Another important table is the stair design data chart, that allows to determine the acceptable characteristics for an airstair in a quicker manner: is formed by two graphics put side by side, in order to connect the tread depth and the possible corresponding riser height, as well the number of risers and treads necessary. This will be more accurately explained in the following chapter where the chart has been used.
For the design safety cases (table 7), design loads and safety factors are considered. Whereas the airstair designed does not have a platform, the design load per step and the design concentrated load at any point of step becomes the major value to verify in the structure. The concentrated load is formed by the sum of the step itself and a passenger that usually has an average weight of 77 Kg.
17 Table 6. Recommended values for a fixed riser stair
Table 7. Design loads and safety factors recommended for mobile and built-in airstairs
Other safety considerations regard:
18 • Elevation safety: a safety lock is needed to ensure the holding of the adjusted
elevation
• Safety placards: stairways need to be equipped with placards indicating the maximum load capability and the maximum number of passengers allowed at one time
• Lighting: regards the adequate lighting for the airstair and near-by area
• Handrails: must include means to prevent passengers from fallings and indicates the measure for the maximum clear opening under the main handrail
• Acceptance inspection: in the purchase specification must be included as a requirement a test for the demonstration of the design load carrying capability.
19
3
Airstair conceptual
design
3.1 OVERALL SIZE DEFINITION
The starting point of the conceptual design has been the preliminary airstair model made for the PrP; after a careful evaluation of dimensions and section types, the platform on the top of the stair has been removed as reputed unnecessary because not proper for the ideal deployment of the stair. The basic shapes of the step and the stair supports have been maintained, but obviously have been modified in their dimensions in order to follow the SAE document.
Figure 5. The initial preliminary stair design for the PrP
20 Figure 6. Section dimensions for a typical regional jet aircraft
A typical regional jet aircraft has a section (fig.7) with a diameter of little more than three metres, so considering this and depending on how long the airstair could be, the choice has been made between a foldable airstair and a non-foldable one. The height from ground of the cabin door and the angle of inclination formed by the stair with the ground are the first two values considered to estimate the length of the airstair. For the angle of inclination, values suggested by the SAE ARP document are typically between 20 and 40 degrees, preferable 30-35 degrees; 30,35 and 40 degrees have been evaluated, in this case the last one has been chosen because lower values have given higher length values for the stair. Considering an height from ground of the cabin door equal to 2850 mm, the calculation for the definition of the length has been the following:
𝑥 = 2850
sin 40°= 4434 𝑚𝑚
As clearly shown, using the maximum acceptable value for the inclination gives a remarkable length, so the only possibility to insert and stow a stair with these dimensions is to fold it. Next to this, taking as example the model for the steps of the PrP stair, the SAE ARP document is considered for the dimensioning of the step. The two points that first need to be defined are the tread depth and the riser height that will
21 determine the number or steps needed; in order to do this, the stair design data chart is analysed in the following mode:
Table 7. The stair design data chart
Knowing both the elevation difference, or the elevation from ground, and the length of the stair, the first thing to do is to draw a curve for the elevation needed, similar to the others presented, because there is not one for the case in study. The curve drawn intersects different horizontal lines corresponding to the numbers of risers available; in this case the lines intersected correspond to the values going from 24 to 14 risers. From the intersection point, moving down vertically, the corresponding riser height can be determined; this value is algo linked with the “tie lines” to the corresponding optimum tread depth for such riser height. In the case in study, the length of the stair is also known, so starting from this value on the corresponding length of stair axe, an horizontal line is drawn in order to intercept the oblique one coming from the value of number of treads equal to 13; this last value has been also defined because is the horizontal tie with the 14 value for the risers. From the intersection point between the oblique line and the horizontal one for the stair length, moving down vertically, the tread depth can be defined, equal to approximately 32.5 cm; at the same time, returning at the value 14 for the number of risers, the riser height value defined is equal to approximately 20.3 cm. These two
22 values are not united by the tie lines, in fact to a 32.5 cm value for the tread depth corresponds a riser height of approximately 17 cm, whereas for a riser height of 20.3 cm corresponds a tread depth of 24 cm. So, despite not being optimal values, this resulted fine for the stair also because the length of the stair is known, and it is not necessary to follow the procedure completely. In addition, as the document differentiates the tread depth and the effective tread depth, and considering also the disposal of the step compared to the stair supports, the one assumes a final value of 27.5 cm whereas the second becomes the 32.5 cm measure.
3.2 CAD MODELING OF THE AIRSTAIRS
The next phase defines, using the program CATIA, a 3D model of the unfolded stair, in order to distribute equally the 13 steps (obviously as a tread corresponds to a step), whereas, in the second case, the stair has been split into two parts in order to make possible its stowing inside the fuselage. For the opening and closing the stair, it has been analysed the airstair model used for the Boeing 737, with brochure material and videos that show the displacement of it outside the plane; Monogram systems, a branch of Zodiac aerospace (now property of Safran) has developed this model. A hinge has been adopted for the opening and closing of the stair, that permits the lower part of the stair to retract under the upper part of itself. [14]
For the other measures regarding the step, like the height or the thickness, no mentions are written inside the SAE ARP document , so the decision was to reply the measures decided for the preliminary stair of the PrP.
23 Table 9. Value references for the 2024-T3 Aluminium [15]
Regarding the choice of the material, talking about the stair itself and the components used for its installation, the possibilities that have been considered are composite materials and aluminium alloys, both regularly used in this sector. As the certification says in the subpart D materials section, the chosen material needs proper tests in order to verify if it responds correctly to stresses. For this reason, the choice made was made for the 2024-T3 Aluminium (table 9), a well-known material used in the aeronautical sector that has already been certified and represents a material ready to use. On the other hand, choosing a composite material is not so convenient in comparison with aluminium because needs the certification tests, thus increasing the time of analysis; in addition, if used for a stair, it should be strong enough in all the three directions of reference, and this is very difficult to obtain as composite materials typically guarantee good results along the plane, with important transversal limits. An airstair is continuously stressed by the movement of the passengers and luggage over it, causing some damage, and as the composites are more delicate to impacts this will result in long run problems. In order to protect the structure from impacts and consequently the delamination of the composite layers, several layers would be necessary, increasing at the same time the weight and not guaranteeing protection in the long run. Another important consideration is that the steps are fixed to the stair supports with screws, and for a composite material this can be a
24 drawback as it would be necessary more material and consequently an increase of weight in the structure. Applying the material to the structure model, the total preliminary weight is 108 Kg. As the model designed does not have handrails, correspondent measures and limits that can be adopted in order to design it are defined inside the SAE ARP document.
Figure 8. The final preliminary stair design adopted for the SSJ-100
3.3 CAD ASSEMBLY OF AIRSTAIRS WITH SSJ-100 FUSELAGE
The decision to stow the stair inside the forward fuselage zone of the SSJ have brought different drawbacks that needed to be face properly: the main problem in this part of the airplane is the presence of the drainpipes coming from the toilet placed near the cockpit and the ventilation ducts for the passenger cabin; in addition, the stow space is next to the electric box unit, separated with a bulkhead. Being this a complete limitation for the insert of the stair, it is clear that in a real development of an airstair for the SSJ-100, a solution in correspondence of the forward cabin door cannot take place; this because the position of these ducts should be changed, making such operation forbidding as the space is limited. So, the only solution, in order to move the project forward, has
25 been not to consider these obstructions, supposing that there is enough free space available for the stair. This is a clear example where projecting a primary modification for an airplane that has been flying during the last years is very difficult when facing these problems, because are modifications not so easy to do, and the builder should consider the convenience of the modification very carefully, especially in terms of loads and costs. Without these two obstructions, the space available is still occupied by some struts that sustain the floor beam right above. Also in this case, the only way to make room is to remove them temporarily, because the struts are a sustain and a way to discharge the loads coming from the floor beam, and a reorganization of the structures is necessary for the distribution of the loads.
A major change that had to be done to the fuselage structure is the opening for the deployment of the stair. Doing such modification is considered as primary for the certification agencies since removing a considerable part of the fuselage needs important evaluations regarding the pressurization, the loads distribution and the possible emergency situations that could happen to the airplane. One frame, together with several stringers that intersect it, needed to be cut in the opening zone. The space has a delimitation of 932x634 mm, with a little clearance between the stair and the opening (fig.9). The reorganization of the structure could be done like the reinforcement adopted for the cabin doors, doubling the structure in order to assure a complete resistance to loads and pressurization. For the door of the stairs opening, a smaller model like the luggage compartments can be considered, moving the door down and not up for the deployment of the stair. At the same time, on the internal side of the door, proper constraints need to be applied to maintain fixed the forward part of the stowed stair and to avoid contact between the door and the stair itself that could bring some damage in case of movement inside the compartment.
26 Figure 9. Front view of the fuselage opening with also the airstair stowed
27
4
SSJ-100 Airstair
preliminary design
The preliminary design of the airstair regards the choices done for the installation of the system inside the fuselage space available and how it would be stowed and deployed outside the airplane. After this part, the loads verification is illustrated explaining which are the values that must be considered and how are applied to the different components of the installation system. In the last part of the chapter, the verifications done for the opened stair are illustrated.
4.1 CHOICE OF THE DEPLOYMENT SYSTEM
Having defined the opening sizing in the fuselage, the next step has been the determination of an appropriate system of supports for the stowed stair that allow not only a proper fixing to the surrounding fuselage components but can also sustain a useful deployment system for the stair itself. After evaluating the zone nearby the positioning of the stair, the decision has been to create four supports (two for each side, figures 12 and 13) joint to the lateral struts supporting the floor beams; in addition, in order to avoid possible bending in the central zone of the stair and torque effects due to load conditions, two vertical C-shaped cross section beams have been added, connecting the floor beam to the frames. Otherwise, the option to design a floor panel only for the sustain of the stair below it could offer a better distribution of its weight but, at the same time, could increase considerably the weight of the total airplane itself.
For the deployment of the stair, the most convenient logical system is one that permits a slip movement outside the fuselage; this can be done using, for example:
• Rollers • Conveyor belt • Pulleys
In order to design a light and least bulky system, the ideal option is to use pulleys that can move inside tracks joint to each side of the stair with screws. The pulley structure is
28 composed by a simple wheel, made of galvanized steel, joint to a galvanized steel stem that supports it. It is important to define a minimum number of pulleys that not only allow the stair movement but also, when stowed, have to sustain the weight of the stair itself, not only in static conditions but mostly during the airplane load conditions. Every pulley is fixed to a support that is a little longer than the length size of the folded stair, across the fuselage; in total, two supports, one for each side, are placed. Each support beam has an omega-shaped cross-section, in order to be easily joint with the C-shaped strut connectors. In addition, four stiffeners are added to the support beam, in order to prevent local deformations and to increase the stiffness of the structure.
Figure 10. The four stiffeners used for the omega-shaped supports
29
4.2 STRUT SUPPORTS
Having decided to join the stowed stair and its deployment system to the four struts, the structure does not allow many solutions because of their geometry. So, the choice has been to design a pursuant support to it, composed of two parts to give enough stiffness along the three axes:
• A fitting bracket, directly joint to the strut, designed with a C cross-section, partially closed on the back
• A clip, connecting the top of the bracket to the top of the omega-shaped supports
Figures 12-13. Front and lateral view of the strut support
Both the joints between these different parts are made with an adequate number of fasteners, the 2117-T4 AD 5/32 type ones. More precisely:
30 • 12 fasteners (3 rivets for 4 rows) join the side of the bracket with the strut side • 6 fasteners are placed between the top side of the clip and the bracket
• 3 fasteners are placed between the clip and the omega-shaped supports and other 3 between the bottom side of the bracket and the omega-shaped supports
All these parts have been evaluated with the loads of interest.
4.3 CENTRAL REINFORCEMENT SUPPORTS
As introduced before, as the airstair completely occupies all the space along the transversal section of the fuselage, the entire structure could bend not only in static conditions but especially when stressed in flight load conditions (fig.14). For the same reasons, the airstair, together with the movement system, could sustain important torque moments. So, the solution considered has been to design two C-shaped beams, each with a thickness of 3 mm, 1110 mm long and 55 mm wide, that join the lower part of the frames to the two floor beams. For the upper junction (fig.15), with surface dimensions 55x48.5 mm, between the reinforcement beams and the floor beams the same solution has been assumed in both sides, using 2 rows of 2 rivets each. On the other, different solutions have been used for the junctions with the frames (fig. 16-17).
Figure 8. Preliminary study of the possible bending of the omega-shaped supports together with the pulleys, value in mm
31 Figure 9. Upper solution for the junction between the reinforcement and the floor beams
Figure 10. Lower solution between the reinforcement beam and the frame, left side of the airstair
In the figure 16 is showed the solution adopted for the junction with the frame placed immediately under the left side of the stair, looking at it from the fuselage opening. The frame in this point has not a flat shape but is curve, so, as the support adopted has a T-shaped cross-section, the side in contact with the frame, the web, needs to assume the same curvature in order to adhere perfectly. The two flanges adhere respectively one to the reinforcement beam and the other to the frame. Having in total three junctions, the total number of fasteners that can be applied is: in the two flanges, having a surface of 45x45 mm, is possible to place 2 rows of 2 rivets each, whereas for the web is used a single row of 2 rivets.
32 Figure 11. Lower solution for the junction between the reinforcement beam and the
frame, right side of the airstair
On the other side, as the frame has a more complex shape and geometry, the design chosen has been a stiffened bracket as the image above shows, that extends itself over the frame surface for 95 mm. In the side joining the bracket and the beam are used 2 rows of 2 rivets each, whereas on the base is placed a single row of 4 rivets. The two reinforcement beams are then joint to the omega-shaped supports with the following solution:
Figure 12. C-shaped connector between the reinforcement beam and the omega-shaped support
A C-shaped connector, similar to the ones adopted for the struts, is designed, where the two fins, with a section of 22x45 mm, provide the junction with the omega-shaped supports with 3 fasteners for each fin. On the other side of the C connectors, the face joint
33 to the reinforcement beams has a section of 85x45 mm. In the complex, the C connectors have the following measures: 71.5x85x45 mm. 4 rows of 3 rivets each are placed for the junction with the reinforcement beams.
4.4 COMPLETE OVERVIEW OF THE STRUCTURE
Figure 13. The result of the stowed stair installed inside the fuselage
The image shows the result of stowage and constraint system inside the fuselage of the SSJ. On the left it is visible the fuselage opening done for the exit of the stair, whereas under and on the right of the image are visible the two frames where the rear struts, the floor beams and the reinforcement beams are joint.
4.5 PRELIMINARY STRUCTURAL SIZING
Starting from an overview about how the load values for the verification should be determined, considering not only the ones defined by the CS-25 but also the values obtained from the flight load envelopes, the verification regards the constraints definition in each direction of the reference system considered, the support brackets together with the rivets used and the deployment system composed by the omega-shaped supports and the pulleys. Secondly, the verification for the opened stair is presented, regarding the single step, the hinge and the complete opened stair.
34
4.5.1 LOAD VERIFICATIONS OF THE STRUCTURE
Figure 14. The reference system adopted by the SSJ-100
The CS demands that the sizing must be done considering the highest load that can be reached in the operational life of the airplane; this is well defined in the requirement 25.301, subpoint (b), which says that “the specified air, ground and water loads must be
placed in equilibrium with inertia forces, considering each item of mass in the aeroplane”
and “these loads must be distributed to conservatively approximate or closely represent
actual conditions”. So, a combination between loads is necessary: the landing conditions
are given by the CS itself in the requirement 25.561, whereas for the flight load conditions, these are defined from the diagrams given by the builder company. The load conditions envelope represents a typical airplane of the regional sector in vertical ultimate load factor situation and lateral limit load factor for gust and continuous turbulence situations. The values on the diagram change depending on the point of the airplane considered along its fuselage, so the zone of interest identified corresponds to the one where the stair has been stowed. In the 25.301, subpoint (a), the CS defines the limit load as “the maximum load to be expected in service” and the ultimate load as “limit loads
multiplied by prescribed factors of safety”, in this case a factor of 1.5 has been applied.
In addition, for pressurized compartments, the only situation that could be considered is a traction effect due to the fuselage dilatation that could do traction on the supports, but such case can be negligible. The conditions are represented by accelerations along the three axes system referred to the airplane, as:
• Upward and downward loads along the y axis • Sideward load along the z axis
35 The requirement 25.561, subpoint (b)(3), indicates that “the structure must be
designed to give each occupant every reasonable chance of escaping serious injury in a minor crash landing when the occupant experiences the following ultimate inertia forces acting separately relative to the surrounding structure:
• Upward, 3g • Forward, 9g
• Sideward, 3g on the airframe and 4g on the seats and their attachments • Downward, 6g
• Rearward, 1.5g”
Remembering that stowage compartment musts satisfy these requirements, together with requirement 25.787, and with all the values needed, the last thing to do is to define which is the highest load for every condition. So, the values from the envelope of the vertical ultimate load factor are compared with the upward and downward values of the requirement, whereas the values from the envelope of the gust and continuous turbulence, after being multiplied for the correspondent factor, are compared with the sideward ones. The final values of the load conditions at which the structure is submitted are the following: • Upward: 3g • Forward: 9g • Sideward: ±3g • Downward: 6.5÷6.8 g • Rearward: 1.5÷1.65 g
For the last two loads, having a range of values, the one that is considered is the highest for each range, so for the downward will be 6.8g whereas for the rearward will be 1.65g.
4.5.2 DEFINITION OF THE CONSTRAINT REACTIONS IN THE SUPPORT SYSTEM
The first thing to do is to determine the constraint reactions in correspondence of each support system, along all the three axes, with the verification loads. The stair section is simplified as a rectangle.
36
XY plane: looking from the opening, left side of the airplane fuselage, forward load
Figure 15. Forward load condition, the beam represents the transversal section of the stowed stair
The value of 4770 N is obtained multiplying the half weight of the stair (because the other half is sustained by the rear supports) and the correspondent value of the load. The constrains obtained are:
𝑥𝐴 = 𝑥𝐵 =
4770
2 = 2385𝑁
XY plane: looking from the opening, left side of the airplane, rearward load
Figure 16. Rearward load condition representation
In the same manner as the forward one, the reactions obtained are the following:
𝑥𝐴 = 𝑥𝐵= 874
37
YZ plane: looking towards the front of the airplane, transversal view of the fuselage, downward load
Figure 17. Downward load condition, the beam represents the lateral side of the stowed stair
The three constraints along the z axis represent the supports joint to the frames at the two extremes, whereas the one at the centre, near the application point of the load, represents the reinforcement beam. In addition, the vertical constraints along the y axis represent the exit door on the left, whereas the other represents the right-side fuselage. Having three unknowns for the reactions and two equations available, one for the vertical equilibrium and the other of the bending moment, there is not only one solution. So, supposing that the load is equally divided in the three constraints, a medium value of the constraint reaction can be considered equal to 2401 N, thus split into two parts as the downward load represents the entire weight of the stair in this case.
7204.5
3 = 2401 𝑁 → 2401
2 = 1200.5 𝑁
YZ plane: looking towards the front side of the airplane, transversal view of the fuselage, upward load
The situation is similar to the downward one; a medium value of the reaction can be defined as equal to 1059 N.
38 Figure 18. Upward load condition
YZ plane: looking towards the front of the airplane, transversal view of the fuselage, sideward load (in both directions)
Figure 19. Sideward load condition
The determination of the constraints value is equal for both loads; the result gives that:
𝑧𝐴 = 𝑧𝐵 = 1590
39
4.5.3 STRUT SUPPORT VERIFICATION
Figure 20. The strut support solution design
Each strut support, together with the fasteners applied, need to be verified properly with the loads defined. As the material chosen is the 2024-T3 aluminium, the reference values are:
𝜎𝑦 = 450𝑀𝑃𝑎 𝜎𝑡𝑢 = 620𝑀𝑃𝑎
The verifications will be done with the last value, as the loads defined are ultimate, therefore the structure admits plastic deformation.
40
XY plane: looking from the opening, support placed at the right side of the stowed stair
Figure 21. Strut support view in the XY plane
Forward load
The critical sections are represented by the clip side and the bracket bottom side, both attached to the omega-shaped supports. These are in traction when the forward load is applied, giving a bending moment in the two fins. Supposing that the traction in the y axis direction splits in the two fins, for each one the value is:
𝑁 =2385
2 = 1192.5𝑁 So, the correspondent moment is:
𝑀 = 𝑁 ∙ 6.5 = 7751.25 𝑁𝑚𝑚
The critical zone is the rectangular one of the fins, 13x52 mm, so we obtain: 𝜎 =𝑀 ∙
𝑦 2
𝐼𝑧 = 5.29 𝑁 𝑚𝑚⁄ 2 ≤ 𝜎𝑡𝑢
On the other hand, the left side front support receives a compression from the forward load in the side joined with the strut; it can be verified that:
𝜎 =𝐹 𝐴 =
2385
41
Rearward load
In the rearward case, the effects are inverted, in fact for the right support there is a compression:
𝜎 =𝐹 𝐴 =
437
4000= 0.11 𝑁 𝑚𝑚⁄ 2 ≤ 𝜎𝑡𝑢 Whereas for the left support we see the bending moment at the fins:
𝑁 =437 2 = 218.5𝑁 𝑀 = 𝑁 ∙ 6.5 = 1420 𝑁𝑚𝑚 𝜎 =𝑀 ∙ 𝑦 2 𝐼𝑧 = 0.97 𝑁 𝑚𝑚2 ⁄ ≤ 𝜎𝑡𝑢
YZ plane: looking towards the rear of the airplane, support placed on the right side of the stowed stair
Figure 22. Strut support view in the YZ plane
Sideward load
In the sideward case, along the z axis, shear and bending moment are present on the two fins:
𝜏 = 3𝑇𝑦 2𝑏ℎ=
3 ∙7952
42 Where Ty is the half of the sideward load, for one fin, whereas b and h represent the
measures of the section fin (13x52 mm). The moment given in each fin is: 𝑀 = 795 2 ∙ 65 = 25837 𝑁 ∙ 𝑚𝑚 𝜎 = 𝑀 ∙ 𝑧 2⁄ 𝐼𝑦 = 25837 ∙ 26 152325 = 4.41 𝑁 𝑚𝑚⁄ 2
And this gives the ideal tension equal to:
𝜎𝑖𝑑= √𝜎2+ 3𝜏2 = 4.68 𝑁 𝑚𝑚⁄ 2 ≤ 𝜎𝑡𝑢
Downward load
For the downward case, shear and bending moment are present; the verification gives that: 𝜏 = 3𝑇𝑦 2𝑏ℎ= 3 ∙ 2401 2⁄ 2 ∙ 70 ∙ 85 = 0.3 𝑁 𝑚𝑚⁄ 2 𝑀 = 1200.5 ∙ 71.5 = 8.5 ∙ 104𝑁⁄𝑚𝑚2 𝜎 =𝑀 ∙ 𝑦 2 𝐼𝑧 = 4.19 𝑁 𝑚𝑚2 ⁄ 𝜎𝑖𝑑= √𝜎2+ 3𝜏2 = 4.22 𝑁 𝑚𝑚⁄ 2 ≤ 𝜎𝑡𝑢 Upward load
There is a situation like the previous one, and the verification gives that: 𝜏 = 3𝑇𝑦 2𝑏ℎ= 3 ∙ 1059/2 2 ∙ 70 ∙ 85 = 0.13 𝑁 𝑚𝑚⁄ 2 𝑀 =∙ 71.5 = 3.8 ∙ 104𝑁 𝑚𝑚2 ⁄ 𝜎 =𝑀 ∙ 𝑦 2 𝐼𝑧 = 0.19 𝑁 𝑚𝑚⁄ 2 𝜎𝑖𝑑= √𝜎2+ 3𝜏2 = 0.3 𝑁 𝑚𝑚⁄ 2 ≤ 𝜎𝑡𝑢 Rivets verification
As said before, the 2117-T4 AD 5/32 rivets, with a strength of 270 Kg, are chosen for fitting the different parts. 6 rivets are placed for the joint of the clip with the top of the bracket; the verification done is about the shear given by the downward load:
43 𝑇 =1200.5 ∙ 71.5
85 = 1009.8 𝑁
This value is divided into the number of rivets used, 6: 𝑇
6 = 168.3 𝑁 < 𝑇𝑚𝑎𝑥 = 2646 𝑁
In the bracket side in contact with the strut, 4 rows of rivets, 3 for each row, are placed; the verification gives the following bending moment value:
𝑀 = 1200.5 ∙ 71.5 = 8.5 ∙ 104𝑁𝑚𝑚
The two central fastener rows have a distance of 29 mm between them, whereas the two rows at the top and at the bottom have a distance of 61 mm between them. The bending moment varies its value from one row to another, so is necessary to determine at the extreme and at the middle the corresponding loads. A system of equations is imposed, indicating with x the value at the extremes and with y the value at the middle:
{ 𝑀 = 61𝑥 + 29𝑦 29 𝑦 = 61 𝑥
The first equation regards the total moment, the second is an equation indicating a proportion between the arms and the unknowns loads.
{𝑥 = 1136.2 𝑁 𝑦 = 541.05 𝑁
As these values correspond to the complete row, for each fastener the corresponding load is: { 𝑥 3= 378.7 𝑁 𝑦 3= 180.35 𝑁
For the fitting of the clip and the bracket with the omega-shaped support, 3 fasteners are placed for each part; for the downward load, the following value is defined:
𝑇 = 1200.5 ∙ 71.5
85 = 1009.8 𝑁 → 𝑇
44 For the sideward load:
𝑇 = 795 ∙ 71.5
53 = 1072.3𝑁 → 𝑇
3 = 357.5𝑁
Figure 29. Strut support view in the XZ plane
Finally, the clip part in contact with the top of the bracket is verified to the sideward load: 𝑇 = 1072.3𝑁 →𝑇
6= 178𝑁
And to the forward load:
𝑇 =1192.5 ∙ 85
71.5 = 1418𝑁 → 𝑇
6= 236𝑁
4.5.4 CENTRAL REINFORCEMENT BEAMS VERIFICATION
Rivets verification
The central reinforcement beams represent an additional constraint for the stowed stair, so the different loads are divided by 6 as the number of total constraints increase. Starting from the upper solution for the junction with the floor beams (fig. 15), with section 55x48.5 mm, 2 rows of 2 rivets each are placed; the verification in the downward condition, considering a medium value, gives that:
𝑇 = 1200 ∙ 55
48.5 = 1360.8 𝑁 → 𝑇
4 = 340.2 𝑁 At the same time, for the sideward condition, the verification gives that:
45 𝑇 =265 ∙ 48.5
55 = 𝑁 → 𝑇
4 = 233.7 𝑁
For the lower left-side support (fig. 16), the T-shaped one, the verification of the forward condition in the web, having a row of 2 rivets, gives that:
𝑇 =1590 ∙ 45
20 = 3577.5 𝑁 → 𝑇
2 = 1788.5 𝑁
And for the sideward condition:
𝑇 = 265 ∙ 20
45 = 117.8 𝑁 → 𝑇
2 = 58.9 𝑁
On the other hand, for the flanges, having 2 rows of 2 rivets each, the verification for the downward condition gives that:
𝑇 =1200 ∙ 45
45 = 1200 𝑁 → 𝑇
4 = 300 𝑁 And the sideward condition gives that:
𝑇 =265 ∙ 45
45 = 265 𝑁 → 𝑇
4 = 66.2 𝑁
In the right-side lower support (fig. 17), the base has a single row of 4 rivets; the forward verification in this case gives that:
𝑇 =1590 ∙ 95
16.5 = 9154.5 𝑁 → 𝑇
4 = 2288.6 𝑁 Whereas for the sideward verification, the result is:
𝑇 = 265 ∙ 16.5
95 = 46 𝑁 → 𝑇
4 = 11.5 𝑁
The side in junction with the reinforcement beam has 2 rows of 2 rivets each applied; the downward verification gives that:
46 𝑇 = 1200 ∙ 48
29 = 1986.2 𝑁 → 𝑇
4 = 496.5 𝑁 Whereas the sideward verification gives that:
𝑇 = 265 ∙ 29
48 = 117.8 𝑁 → 𝑇
4 = 29.4 𝑁
Finally, for the C-shaped connectors, the verification done for the strut supports can be considered valid also for this part, as its uses the same number of rivets in the fins and in the side joint to the reinforcing beam.
4.5.5 PULLEYS VERIFICATION
The pulleys used for the movement of the stair have also the important function to sustain the stair when stowed; for this reason, the downward load could be a problem and a minimum number of pulleys is defined to prevent it. Some systems in commerce have been evaluated [16], but as the materials used are not the same for this purpose, the decision has been to assume a pulley structure composed by a wheel made of galvanized steel, where each wheel must sustain 200 N. The pulley needs to be properly produced for this use, with a certification if the material has not been verified yet. So, knowing that the downward load equals to 7204.5N, 42 wheels are connected to the omega supports used, 21 for each side. The omega profile is long 2300 mm in order to go from one strut to the other, whereas the tracks connected to the stair are 2000 mm long. The distance between each pulley and the following one is 97 mm; the verification, supposing that a wheel gives away whereas the others continue to sustain the load, is done in the following manner:
7204.5
41 = 175.7𝑁 < 200𝑁
The wheel has a diameter of 24 mm. The connection between the wheel and the omega support is done with a galvanized steel cylindrical support, long 11 mm and with a diameter of 14 mm; this suffers both the upward and the downward loads respectively:
3178
47 7204.5
42 = 171.5𝑁
where both loads are divided into the number of pulleys in each side and the cylindrical support is simplified as a cantilever beam.
Figure 30. Representation of the pulley as a cantilever beam with the downward load applied
Figure 31. Upward load applied to the pulley
Each pulley is fixed to the omega-shaped support with a proper screw in order to facilitate a quick change of the part in case of failing.
48 Figure 32. View of the omega-shaped support with the pulleys joint
4.5.6 REAR SUPPORTS
At the rear of the stowed stair, proper constraints are defined in order to face the sideward load, whereas at the front supports are also used, but their shape should be related to the design of the exit door. Looking along the XZ plane, the situation is the following at the front:
Figure 33. Front view of the stowed stair in the XZ plane
𝑧𝐴 = 𝑧𝐵=
3175
2 = 1587.5𝑁
The same situation is obviously present at the rear too; as the stowed stair occupies all the transversal section of the fuselage, the rear supports can be fixed to the fuselage with a base in aluminium, preferably joint to the nearby frames. The material applied is galvanized steel because such part might get worn due to the continuous contact with the
49 stairs. Adopting a safety factor of 1.5, a minimum area of pression is defined in order to model the constraint:
𝜎𝑎𝑚𝑠 =500 1.5 = 333 𝑁 𝑚𝑚⁄ 2 𝐹 𝐴≤ 𝜎𝑎𝑚𝑠 → 𝐴 ≥ 𝐹 𝜎𝑎𝑚𝑠 → 𝐴𝑚𝑖𝑛 = 1587.5 333 = 4.8 𝑚𝑚 2
For this reason the supports can have the following shape, long 100 mm and with a section of 50x55 mm:
Figure 34. The rear support design and are placed in contact with the stair in the following mode:
