Home Work #7 Due Date:29 April, 2010 (Turn in your assignment at the mail box of S581 outside the ME general office) The solutions must be written on single-side A4 papers only.

HW 7-Problem #1 A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is L= 1.2 m and the height of the bar is h=100 mm. The deflection δ at the midpoint is measured as 3.6 mm. What is the maximum normal strain at the top and bottom of the bar?

HW 7-Problem #2 A freight-car axle AB is loaded approximately as shown in the figure, with the forces P representing the car loads (transmitted to the axle through the axle boxes) and the forces R representing the rail loads (transmitted to the axle through the wheels). The diameter of the axle is d=80 mm, the distance between centers of the rails is L, and the distance between the forces P and R is b=200 mm. Calculate the maximum bending stress σ max in the axle if P=47 KN.

HW 7-Problem #3 Determine the maximum tensile tress σ t (due to pure bending by positive bending moments M) for beams having cross sections as follows: (a) A semicircle of diameter d, and (b) an isosceles trapezoid with bases b 1 =b and b 2 =4b/3, and altitude h.

HW 7-Problem #4 A horizontal shelf AD of length L=900 mm, width b=300 mm, and thickness t=20 mm is supported by brackets at B and C (figure a). The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity q, which includes the weight of the shelf itself, acts in the shelf (figure b). Determine the maximum permissible value of the load q if the allowable bending stress in the shelf is σallow=5.0 MPa and the position of the support is adjusted for maximum load-carrying capacity.