Question a please F12 HomeEnd F11 F7 F8 F9 F10 3 F5 F6 Aircr

Question a please

F12 HomeEnd F11 F7 F8 F9 F10 3 F5 F6 Aircraft Structures (1) Junc 23, 2016 Final Exam h e 3 ribs of a 4-stringer box (3096) Loads including concentrated forces and moments are applied to ti beam as shown in Figure 1. Want to analyze the stress distribution of the system. (a) Explain if this is a well posed problem of structural analysis (b) Find the shear stress in the web of the central rib. I. 5000 ib Thickness of panels 0.036in. Stringer areas= l in,\" 307 30 4000 ib 4000 1b Rib 10 600Ib 4000 b 5000 1b 240.000 in.-1b Figure 1

Solution

(a) Total force in x direction = 0

Total force in y direction = 6000+4000-5000-5000 = 0

Total force in z direction = 4000-4000 = 0

Total moment in x direction at a point (top right corner point) = -5000x10 + 4000x10 + 6000x10 -5000x10 = 0

Total moment in y direction at above described point = 4000x(30+30) - 240000 = 0

Total moment in z direction at above described point = 5000x(30+30) - 6000x30 - 4000x30 = 0

Since the total forces and moments in the system are zero, the body is in a state of equilibrium. Hence, this is a well posed problem of structural analysis.

(b) At the central rib,

Area of each web of rib = 10 x 0.036 = 0.36 in²

shear stress at the left web = 6000 / (10 x 0.036) = 16666.67 psi

shear stress at the right web = 4000 / (10 x 0.036) = 11111.11 psi