Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

DEPARTMENT OF MECHANICAL ENGINEERING

EXAMINATION

MECH2413: ENGINEERING MECHANICS

December 12, 2024

Time: 2:30 p.m. — 5:30 p.m.

SECTION A

A1. (a) Construct the shear and moment diagrams for the beam subjected to the concentrated force and torques and the triangular load. What are the values of the shear force and bending moment at B? (10 marks)

(b) Determine the center of gravity of a C beam. (5 marks)

(c) For the stress state (in MPa) shown, calculate the principal stresses and principal stress angles. (5 marks)

A2. The cantilever is clamped on the wall at the left end with the free end on the right-hand side, which is subjected to a concentrated force Fi as shown in Figure A2.

(a) Sketch the reactions provided by the left walls. (3 marks)

(b) Determine and sketch the shear force and bending moment diagrams of the cantilever, in terms of F1, reactions and L. (5 marks)

(c) Determine the deflection of the cantilever as a function of x, in terms of F1, L and any other quantities that are relevant. (7 marks)

(d) Determine the moment of inertia, in terms of w and t. (3 marks)

(e) Calculate the maximum deflection of cantilever. A 150 cm long, 1 cm width, 1 cm thickness cantilever with a uniform cross-section is subjected to downward force of F1=100N at nght end. The Young's modulus is E = 190 GPa. (2 marks)

A3. Figure A3 shows a circular stepped shaft which is clamped at point A. The shaft consists of two solid sections AB and BC, which are 60 and 30 mm in diameter, respectively. The applied torques Mi, Mz and M3 are 600, 500 and 200 N-m, respectively. The shear modulus of the shaft is G = 80 GPa.

(a) Determine the polar moments of inertia of sections AB and BC. (4 marks)

(b) Determine the end reaction, MA, due to the applied torques M1, M2, and M3. (4 marks)

(c) Determine the angle of twist at B and C. (6 marks)

(d) Calculate the maximum shear stress and its location. (6 marks)