4. Internal hinge at C A 10 kN/m B 6 m 2 m IC 12 kN D 2 m 2 m E

Calculate the vertical displacement (downward) at Joint C of the given truss using the method of virtual work. You can use Space Gass to compute the internal forces of the real and virtual systems without manual calculations. (Assume the cross-sectional area and modulus of elasticity of each member are constant.)

The horizontal shaft AD is attached to a fixed base at D and is subjected to the torques shown. A 44-mm-diameter hole has been drilled into portion CD of the shaft. Knowing that the entire shaft is made of steel for which G = 77 Gpa, determine the angle of twist at end A. 44mm -0.6m 60mm C 2000Nm B 30mm 0.2m 0.4m 250Nm A

A beam is subjected to equal bending moments of M₂ = 2700 N-m. The cross-sectional dimensions are b = 100 mm, c = 27 mm, d = 72 mm, and t = 4 mm. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. Answer: (a) y= i ¹₂ = i S = i M₂ (b) σH= i (c) OK= i (d) a max M₂ x mm mm4 mm³ MPa MPa MPa (typ) N b H K