Shear force and bending moment diagram for aircraft wing

Question 1

A group of engineering students are venturing to build a human powered aircraft as shown in Fig .1. The aircraft is to be designed with a wing span of 30 meters to achieve sufficient lift. The main load bearing element on the wing is an aluminium spar that extends along the length of the wing. The cockpit and supporting structures (without the wing) is expected to weigh 32 kg excluding a pilot of 70 kg, the propeller mass is 28kg. Accordingly, to aid with the design of the wing apply the principles of engineering mechanics to analyse the following cases.

( Wing Cockpit Pilot Propeller Cockpit supporting structures Aluminium spar )

Fig. 1a

i. If the wing is to be designed with 4 aerofoil ribs of mass 328 grams each attached to the aluminium spar as shown in Fig 1b. Calculate the necessary support reaction to keep the aircraft in vertical equilibrium with the pilot assuming that the aircraft is simply supported at the wing ends. (Note: we are analysing for this case as this is the worst case of bending for the aluminium spar.)

[10%]

( Total weight supported by the wing at the centre including pilot Rib 1 Rib 2 Rib 3 Rib 4 7.5 m 7.5 m 15 m A B )

Fig. 1b

ii. Analyse the shear forces in the aluminium spar shown in Fig. 1b by drawing a shear force diagram.

[10%]

iii. Analyse the bending moment distribution along the length of the aluminium spar shown in Fig. 1b using a bending moment diagram.

[20%]

iv. If the maximum bending stress the aluminium spar can withstand before yielding is 40 MPa, predict the smallest possible diameter for a solid aluminium spar without any factor of safety. (Material performance of aluminium: Young’s modulus = 68.9 MPa, Shear Modulus = 26 MPa, Poisson’s ratio = 0.3).

[10%]

v. If the solid spar is to be replaced by a hollow spar of external diameter 2.5 times the internal diameter. Predict the internal and external diameter for the hollow spar and compare the compressive and tensile bending stresses along the thickness of the spar (take 4 points along the thickness of the spar) using an ‘Excel’ type graph.

[20%]

vi. Using the dimensions for the hollow spar analyse the support reactions, shear force and bending moment diagram for the case shown in Fig. 1b including the self-weight of the spar. Take the density of aluminium.

[30%]

Question 2

A 12 mm diameter steel rod is connected to a 30 mm wide by 8 mm thick aluminium rectangular bar as shown in Fig. 2a. Determine the force P required to stretch the assembly by 10 mm. Take theYoung’s modulus of aluminium as 328 MPa and Steel as 32GPa.

[15%]

( 0.5 m 1.5 m P P )

Fig. 2a

Question 3

The joint shown in Fig. 3a is under tension along the major axis with a force of 533kN. The safety factor (FS) of 4 will be applied to the rivets securing the joint. Assume the material has an ultimate shear stress of 190 MPa.

Fig. 3a

i. Calculate the design stress for the rivet.

[5%]

ii. Calculate the number of 10 mm diameter rivets that will be required to secure the joint for the design stress evaluated above.

[10%]

Question 4

A heavy-duty punch is used to make perforations on sheet of thickness 7 mm. The total pressure on the punch was measured to be 328N/m2 on an area of 50 mm2 applied along the axial direction. If the diameter of the punch is 35 mm. Determine the shearing stress induced in the material.(Material data for steel: Young’s modulus = 210 GPA and Shear Modulus = 74 MPa).

[15%]

Question 5

The steel machine part show in Fig. 5a is subjected to a compressive force of 32kN at an angle to the horizontal. Determine the average compressive stress along the areas of contact defined by XY and YZ. (Material data for steel: Young’s modulus = 210 GPA and Shear Modulus = 74 MPa).

[15%]

( 3 kN X Y Z )

Fig. 5a

Question 6

The rotating shaft of a human powered drivetrain is suddenly coupled to a freewheeling drum of a propeller shaft via a friction clutch. The moment of inertia of the drivetrain shaft is equivalent to a mass of 40 kg acting with a radius gyration of 328 mm. The freewheeling drum has a mass of 28 kg and a radius of gyration of 285 mm. The initial velocity of the drivetrain shaft before coupling is 32 rev/s and the freewheeling drum is initially at rest.Find the velocity of drivetrain shaft and freewheeling drum immediately after coupling.

[15%]

Question 7

A golf ball is struck at an angle of 50degree with respect to horizontal, at a velocity of 32 m/sec. The golf course is perfectly level and the golf ball stops instantaneously when it hits the ground.

i. Determine the horizontal distance travelled by the golf ball

[10%]

ii. Determine the maximum height attained by the golf ball

[5%]

iii. If the golf ball is to travel a vertical distance of 28 m, using the same initial trajectory, determine the required initial velocity.