Answer Happy

This spacecraft has a 6.2-meter-long deployable boom. Assume that the boom consists of three continuous straight longerons - made of glass-fiber- reinforced-composite (E = 40 GPa) with 4-mm-diameter solid circular cross-section - arranged such that centers of the longerons form an equilateral triangle with circumcircle diameter 25 cm, as shown below. Further assume that the truss-like structure between the longerons provides sufficient shear stiffness such that the boom can be modeled as an Euler-Bernoulli beam with uniform cross-section shown below, and that this truss-like structure contributes negligibly to the bending stiffness. a) Where should the x -axis be placed such that the first moment of area vanishes? b) What is the second moment of area of this cross-section? c) During a spacecraft attitude control maneuver, the instrument at the end of the boom imparts an inertial load of +2 N along the xz axis at the tip of the boom. The root of the boom is clamped to the spacecraft. What is the deflection at the tip? X2 Longeron Diameter = 4 mm X3 Circumcircle diameter = 25 cm