Here are the dimensions, sorry for not having them earlier  b = 0.4 m, d =0.5 m , t =0.1 m.   3) The force, FT = 1 kN, and moment, MT = 0.5 kN-m, at the tip are caused by a wing tip vortex and a winglet, not shown. L = 12 m and the spar has an elastic modulus of E = 70 GPa and a Poisson’s ratio of n = 0.33. The mass of the wing is 4000 kg, and the weight of the engine is 107 kN. Use 9.8 m/s 2 for the acceleration due to gravity. a) The aerodynamic center for problem 3 is 0.1 m from the y axis (neutral axis). Calculate the twist angle caused by the lift force.  b) For problem 3, calculate the reactions at the fixed end.  c) Assume the engine in problem 3, applies a torque around the x – axis of the spar of 100 kN-m, calculate the angular delfection of the wing at x = 3 m due to the engine.

]: A horizontal beam with a length of 4.5 m is subjected to the shown loading. The forces are vertical and the couple moment is applied at point D. The figure is not to scale. 3 kN/ m 1 kN/ m 3 kNm A В C D E 1 т 1.5 m 0.5m 1.5m 0.6 KN 1.35KN (a) Motivate with substantiating explanations and clear and applicable calculations why the beam is in equilibrium. (b) Draw the shear force and bending moment diagrams for the beam. Calculate all local maxima and minima, zeros and points where the diagrams change shape, and show these values and points on the diagrams.

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (4) the work done by the reaction force of the pin.____________ (J)

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following.   (2) ) the work done by the couple moment. __________(J) (two decimal places)