aerospace engineering question and need an explanation and answer to help me learn.
I need help with three simple questions.
AEE 4281 Homework #2 Assigned: 19 January Due: 31 January In class, on PAPER. • Be sure to format your homework appropriately, using the Formatting Standards document posted to Canvas. • Note that the use of “services” such as chegg.com to look up answers or event just to “assist” with solutions to homework problems is expressly forbidden (see more details in the course syllabus). 1. Equilibrium Review (10 pts) An airplane has a canard configuration and has a gross weight of 1600kN. It is flying in steady level flight. Locations of the center of gravity of the complete aircraft and the centers of pressure of the main wing and the canard are illustrated below. The main wing produces an aerodynamic moment about the aerodynamic center (a.c.) according to: , where ρ is the density of the air, V is the velocity of the plane, S is the wing area, c is the chord length and CMo is the coefficient of moment (note that as defined in the sketch, Moment is positive when it produces a nose up pitching moment). Given: ρ = 1.225 kg/m3, S = 280 m2, c = 23 m and CMo = –0.010 Because the canard is a symmetric airfoil, assume that the canard generates no aerodynamic moment. a) Determine the lift on the main wing, LW, the lift on the canard, LC, and the aerodynamic moment MW acting on the main wing for each of the following cases: V = 91.5 m/s and V = 183 m/s. b) Explain in words what is the “Aerodyamic Moment.” Physically, what causes it? Continued on next page
2. V-M Diagram Review (15 pts) A simplified representation of loads on an airplane wing are shown in the sketch below. The distributed loading shown includes aerodynamic lift and the weight of the wing and its contents. Point loads corresponding to the weight of the engines are shown at point(s) a and the two 6,990 lb point loads at points b represent the interaction of the fuselage with the wing box. Note that “WS” means “Wing Station,” and is a designation of the location of a given position on the wing, in inches from a reference zero position which is in this case at the center of the fuselage. a) Confirm that the wing is in equilibrium under the given loads (show calculations) b) Determine the internal resultants V and M at WS 0, WS75 and at WS100 based on equilibrium of appropriate free body diagrams. c) Sketch V-M diagrams for the entire wing. Required: All FBDs must be shown in standard form, with the FBD, the V diagram and the M diagram stacked vertically as in the example at http://commons.wikimedia.org/wiki/File:Shear_Moment_Diagram.svg. Numerical values at key points must also be provided. Note: you are not required to obtain equations for V(x) and M(x), only the V-M diagram is required. It is PERMITTED to use a web-based shear-moment diagram tool to obtain the diagrams, but each individual student must operate the tool. Continued on next page 500 lb 500 lb 6990 lb 6990 lb
3. (25 pts) A stiffened web beam is shown in the following sketch. The loads shown are ‘ultimate design loads’ that are greater than the loads actually intended to be placed on the structure by an appropriate factor of safety, hence no further factors of safety will need to be used in this problem. Assume that all parts of the structure are made of aluminum alloy with E = 70GPa and ν=0.33. On wall 10-11 the shear web supports the full shear resultant while there are horizontal reaction forces at 10 and 11 only. a) (10 pts) Determine the shear flows in each of the webs, q1 , q2, q3, and q4 assuming the webs do not buckle. Use the sign conventions in the sketch. b) (8 pts) Sketch the axial load as a function of x (where x is a horizontal axis) for the horizontally oriented stiffener 3-6-9-11. Indicate numerical values of the load at each joint. Use + for tension and ─ for compression. c) (4 pts) Assuming that the thickness of the web 2 is controlled by shear buckling determine the minimum acceptable thickness of web 2 (only). Assume simply-supported boundary conditions on the edges of the panel. d) (3 pts) Consider the longitudinal stiffener loaded in tension, 9-11. If the normal stress in this stiffener is to be limited to a maximum of 275MPa, determine the minimum acceptable cross-section area for the stiffener. The cross-section is uniform along the stiffener.