Transcript Home Work #1 - Hong Kong University of Science and Technology

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 σmax in the axle if P=47 KN.
HW 7-Problem #3
Determine the maximum tensile tress σt (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 b1=b
and b2=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.