Structural Loads Handbook Pedro Albuquerque Undergraduate Student of Aerospace Engineering Instituto Superior Técnico – Technical University of Lisbon In collaboration with: OGMA, Indústria Aeronáutica de Portugal, SA Alverca do Ribatejo October 2011 Abstract From the design viewpoint, the determination of the loads acting on an aircraft is of outmost relevance, because their critical combinations are the designer’s limit constraints. The present work aims to enhance the work developed by the OGMA, Indústria Aeronáutica de Portugal, SA Engineering, Design and Modifications Office by developing a Structural Loads Handbook to enable the estimation of the maximum loads acting on an aeroplane using a thorough analysis that can work both as an alternative and a validation of the most commonly used methods, namely Computational Fluid Dynamics and Finite Element Methods commercial softwares. So as to materialize this purpose, a number of Microsoft Excel® workbooks that evaluate the structural loads acting on a generic aircraft have been developed. The user is required to introduce the geometry and operational conditions of the aeroplane. The most relevant loads acting on the landing gears, wing, horizontal stabilizer, vertical stabilizer and fuselage are then analysed. In order to demonstrate the results obtained with the methods implemented in Microsoft Excel® throughout this work, the shear force, bending moment and torsion are plotted along each of the main components of a Lockheed Hercules C-130H . Symbols Symbol Description Unit Symbol Description Unit Damping ratio - Angular velocity $ ξ Air density ! Undamped natural frequency rad /s ͧ Ultimate tensile strength kg /m !) rad /s Angular velocity tension ͦ ͈/͡ Ω rad /s Aeroplane lift curve slope Time ͯͥ ͕ Damping Coefficient ͕ͦ ͘ t Fuselage relative thickness ͧ- ̽ Maximum lift coefficient -͈ͧ /͡ t/c Reference gust velocity ̽ ĠĔī Laplace Transform - ͏- ! Design Cruise Airspeed m/s s Pressure coefficient - ͐ Design Dive Airspeed m/s + ̽ Gravity acceleration ͐ Design Dive Airspeed m/s ͦ ͛ Moment of Inertia ͡/ͧ ͐ Wing loading m/s ͦ ͦ $ ̓ Spring constant kg /m ͫ Displacement ͈/͡ ͟ Mass ͈/͡ x Velocity m m Aeroplane Mass kg ͬʖ Acceleration m/s ͦ M Load factor - kg ͬʗ m/s ͢ 1. Introduction modifications can be made at any point of the aeroplane without putting at risk its integrity, thus From the design viewpoint, the determination working in compliance with both the aeroplane’s of the acting loads on an aircraft is of outmost flight manual and the applicable legislation. relevance, because their critical combinations are the designer’s limit constraints. 2. Structural Loads Handbook The loading conditions are those found in- flight, in the ground and during landing and take-off. 2.1. Flight Envelope Since it is impossible to investigate all the loading According to both CS-25 [1] and FAR-25, the conditions that each aeroplane will have to strength requirements must be met at each withstand during its life cycle, it is normal to select combination of airspeed and load factor on and those that will be critical for each member of the within the boundaries of the representative structure. These conditions are usually found from manoeuvring envelope. This envelope, also known investigation and experience and then included in as V-n diagram may also be used to determine the updated version of the legislations. In Europe, the aeroplane’s structural operating limits. current legislation for large aeroplanes is the European Aviation Safety Agency (EASA) Certification Specifications for Large Aeroplanes (CS-25). There are four main load sources acting on an aeroplane – aerodynamic forces, inertia, ground reactions and thrust. The goal of the current work is it to determine its critical combinations. Not until all these load sources are determined shall the criticality of a particular aeroplane modification be Figure 1 - Typical Flight Manoeuvring Envelope [1]. known. Once all the loads have been determined, In level flight (1g) the stalling speed is the challenge is to assess which critical load given by: combinations are likely to happen to conclude about the maximum loads that may be taking place at ©½ (1) ¯̊½ ̊ each point. ² Ɣ ǯ̋û¯¨Ã·Î At other load factor values, the stall speed is 1.1. Objectives given by . This will give the positive stall ͐ Ɣ ͐ͥ" ͢ curve of the flight√ envelope. The negative design The present research aims to enhance the manoeuvring speed is: work developed by the OGMA, Indústria Aeronáutica de Portugal, SA Engineering, Design ͯ©½ (2) ²¯ͯ̊½ Ɣ ̊ and Modifications Office by developing a structural ǯ̋û¯¨Ã¿Ä At other load factor values, the stall speed is loads handbook to enable the estimation of the given by , where n vary between zero maximum structural loads acting on an aircraft using ͐ Ɣ ͐ͯͥ" Ǝ͢ and the minimum admissible√ load factor. This will a thorough analysis that can work as an alternative give the negative stall curve. and a validation of the most commonly used methods, namely Computational Fluid Dynamics In terms of the stresses acting on the wing and Finite Element Methods commercial softwares. on each of these conditions, it is noticeable that the PHAA will reflect the maximum compression in the The main purpose of this Master Thesis is to upper flange of the forward longeron, which means enable a much faster analysis of the maximum the maximum tension will be acting on the lower loads acting at each point of the aeroplane, so that 2 flange of the rear longeron. For the same reasons, it Once the manoeuvring and gust envelopes can be stated that the NHAA will impose the highest have been determined, the combined flight compression in the forward longeron lower flange envelope should be drawn, which is shown in Figure and the highest tension in the rear longeron upper 4. This is the most relevant plot, since it does flange. establish the true limit loads that the aeroplane’s In the PLAA condition, the centre of pressure structure may experience in the advent of being will be at its rear most position, which means it will subject to gust loads coming from any direction and be critical for compression of the rear longeron on any flight condition. upper flange and for tension in the forward longeron lower flange. With an analogous reasoning it can be stated that the NLAA will cause maximum compression in the lower flange rear longeron and in the upper flange forward longeron. Figure 4 - Typical Combined Flight Envelope. The limit loading conditions with a black dot in Figure 4 are critical for almost all the aircraft’s structure. Each stringer and longeron is thus designed for the maximum tension or compression of each of these conditions. It is usually common Figure 2 Limit Load Cases [2]. place to neglect other loading conditions since the The gust envelope, commonly known as V-g structure is likely to withstand all intermediate diagram is determined in a similar pattern to the loadings provided that it bears the limit load manoeuvring envelope, except that the boundaries conditions shown. are determined by the gust load factor at cruise airspeed (V ) and dive airspeed (V ). The C D 3. Specific Load Analysis equivalent gust velocity is defined in CS-25 [1] and FAR-25 [2] to be a function of the aeroplane’s equivalent airspeed and operating altitude. The gust 3.1. Landing Gear Loads load factor may be computed as follows: From all the loads that may act on the landing gears’ structure, the most important loads ̊ (3) ̋û̉²·§½±È»¼ involved in ground, landing and take-off must be Ä Ɣ ̊ Ə ©½/¯ where is the gust alleviation factor and is defined determined. as: §½ ̋Í Ground Loads ̉.̑̑ û¹·½ (4) ½ ̋Í § Ɣ ̎.̌ͮû¹·½ In what concerns to the landing gears ground loads, the following conditions must be investigated (in accordance with CS-25 [1]): • Static Load • 2-Points Braked Roll • 3-Points Braked Roll • Sudden braking • Ground Turn Figure 3 - Gust Envelope [1]. • Reversed Braking 3 • (7) Nose wheel yaw and steering ̋ ÉÊ • Unsymmetrical Braking ʚÃÉ ƍ ¹É ƍ Áʛ´» Ɣ ̉ The non-trivial solution results in the roots of • Pivoting the polynomial between brackets on equation. • Towing Accordingly: Landing Loads ̋ ¹ ǭ¹ ͯ̍ÃÁ (8) When computing the landing gear force É̊,̋ ƔƎ ̋à Ə ̋à Three different possibilities may happen, reactions in landing, the following conditions must depending on the values of the aeroplane’s mass, be investigated [1]: spring constant and damping coefficient. • 1-Point Landing Overdamped system response ( ): • 2-Points Landing Ɨ 1 ʚ ʛ ʚ ʛ (9) ͯøăÄÊ ̋ Îʖ ̉ ͮøăÄÎ ̉ ̋ Ä Ä • ÎʚÊʛ Ɣ» ƭÎʚ̉ʛ ̨̣̯̳Ƴă ǭø Ǝ ̊ÊƷ ƍ ̋ ̨̳̩̮Ƴă ǭø Ǝ ̊ÊƷƱ Side Load Landing ăÄǯø ͯ̊ Critically damped system response ( ): • 3-Points Landing Ɣ 1(10) ͯăÄÊ According to CS-25, in order to compute the ÎʚÊʛ Ɣ» ʞÎʚ̉ʛʚ̊ ƍ ăÄÊʛ ƍ Îʖ ʚ̉ʛÊʟ Underdamped system response ( ): landing loads acting on the landing gears, the Ƙ 1 ʚ ʛ ʚ ʛ (11) ͯøăÄÊ ̋ Îʖ ̉ ͮøăÄÎ ̉ ̋ Ä Ä aeroplane lift can be assumed null. In order to ÎʚÊʛ Ɣ» ƭÎʚ̉ʛ ̣̯̳Ƴă ǭ̊Ǝø ÊƷ ƍ ̋ ̳̩̮Ƴă ǭ̊Ǝø ÊƷƱ ăÄǯ̊ͯø determine the force acting on the landing gear the From the displacement response it is following conditions must be studied – one-point possible to compute the maximum loads acting on landing, two-points landing, side load landing and the system in each of the conditions to be analysed three-points landing. throughout the landing loads study. At each landing gear a system with one or two degrees of freedom can approximate the physics of the problem.