Mechanics of Materials I
Fall 2018
Final Exam
Monday, December 17, 2018
15:00-18:00 PM
Student ID:
1 (10)
2 (10)
3(10)
Name:
4 (10)
5(10)
6 (15)
7 (15)
8 (10)
9 (10)
Total (100)
1. If the shaft is subjected to a uniform distributed torque of t = 20 kN×m/m, determine
the maximum shear stress developed in the shaft. The shaft is made of 2014-T6
aluminum alloy and is fixed at A and C. Take G = 27 GPa. (10pts)
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2. Determine, to the nearest millimeter, the smallest allowable diameter of the shaft
which is subjected to the concentrated forces. The journal bearings at A and B only
support vertical forces. The allowable bending stress is σallow = 150 MPa. (10 pts)
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3. The beam is subjected to a shear of V = 150 kN. Determine the amount of this force
that is supported by the web B. (10 pts)
4. The cap on the cylindrical tank is bolted to the tank along the flanges. The tank has an
inner diameter of 1.5 m and a wall thickness of 18 mm. If the largest normal stress is
not to exceed 150 MPa, determine the maximum pressure the tank can sustain. Also,
compute the number of bolts required to attach the cap to the tank if each bolt has a
diameter of 20 mm. The allowable stress for the bolts is (σallow)b = 180 MPa. (10pts)
5. Determine the state of stress at point B on the cross section of the pipe at section a-a.
(10pts)
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6. The solid propeller shaft on a ship extends outward from the ship. During operation it
turns at w = 15 rad/s when the engine develops 900 kW of power. This causes a thrust
of F = 1.23 MN on the shaft. If the shaft has an outer diameter of 250 mm, determine
(a) the principal stress at any point located on the surface of the shaft, and (b) the
maximum in-plane shear stress at any point located on the surface of the shaft. (15pts)
7. The 60° strain rosette is attached to point A on the surface of the support. Due to the
loading the strain gauges give a reading of εa = 300(10-6), εb = -150(10-6), and εc = 450 (10-6). Determine (a) the in-plane principal strains, and (b) the maximum in-plane
shear strain and the associated average normal strain. Specify the orientation of each
element that has these states of strain with respect to the x axis. (15 pts)
8. The strain gauge is placed on the surface of a thin-walled steel boiler as shown. If it is
12 mm long, determine the pressure in the boiler when the gauge elongates 5(10-3)
mm. The boiler has a thickness of 12 mm and inner diameter of 1.5m. Also,
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determine the maximum x, y in-plane shear strain in the material. Take Est = 200 GPa
and nst = 0.3. (10pts)
9. Select the lightest-weight steel wide-flange overhanging beam from Appendix B that
can safely support the loading. Assume the support at A is a pin and the support at B
is a roller. The allowable bending stress is σallow = 168 MPa and an allowable shear
stress of τallow = 100 MPa. (10pts)
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