You must have a compass, ruler, and protractor for this exam

Transcription

1 ES30 STRENGTH OF MATERIALS FINAL EXAM: WEDNESDAY, MAY 14 TH, 4PM TO 7PM, HUGEL 100 Closed book. Calculator and writing supplies allowed. Protractor and compass required. 180 Minute Time Limit Given: Law of Cosines: C b a Law of Sines: A c B Stress = E = G Bending M/EI = 1/ = -y/ =My/I M=EI M/EI = dv /d I = (/4)r 4 for a solid circular cross-section Stress Transformation Equations σ σ y σ σ y σ ' cos θ τ σ σ y τ ' ' sin θ τ y cos θ y Principal Stresses 1, y sin y y 1, Occur on Principal Planes at Angle p τ y tan θ p σ σ y Maimum Shear Stress is: y θ Torsion = Tc/J = TL/GJ Power P = Twhere T is torque and is angular frequency (rad/s) 1hp = 550 ft-lb/s 1Watt = 1 N-m/s J = (/)c 4 for a solid, circular shape of radius c. Beam Shear Stress = VQ/It q = VQ/I q = F/s I = (/4)r 4 for a solid, circular shape of radius r Pressure Vessels hoop = Pr/t long = Pr/(t) Buckling Deformation due to Temperature: Δ 1 of 10 You must have a compass, ruler, and protractor for this eam

2 Bonus Questions (0.1 points each): Match the quote to the author While it is true that alcohol will not solve your problems, neither will milk or water ut tensio, sic vi ( as is the etension, so is the force ) I want to eat his children. You may beat me, but you will not outwork me. "A mathematician is a blind man in a dark room looking for a black cat which isn't there." He was a wise man who invented beer He may be a son of a bitch, but he s OUR son of a bitch I have come to believe that a great teacher is a great artist and that there are as few as there are any other great artists. Teaching might even be the greatest of the arts since the medium is the human mind and spirit. My choice early in life was either to be a piano-player in a whorehouse or a politician. And to tell the truth, there's hardly any difference. If I owned both Hell and Teas, I d rent out Teas and live in Hell In any fight, it is the guy who is willing to die who is going to win Perfection is not attainable, but if we chase perfection, we may catch ecellence. A life is not important ecept in the impact it has on other lives. Good judgment comes from eperience, and a lot of that comes from bad judgment. Anyone can become angry that is easy, but to be angry with the right person at the right time, and for the right purpose and in the right way that is not within everyone s power and that is not easy. 1. Vince Lombardi. Steve Kurtz 3. Robert Hooke 4. Mike Tyson 5. Dan Gable 6. Charles Darwin 7. Plato 8. Franklin D. Roosevelt 9. John Steinbeck 10. Harry S. Truman 11. W.T. Sherman 1. Al Pacino 13. Jackie Robinson 14. Will Rogers 15. Aristotle of 10

3 EXAM QUESTIONS (7 QUESTIONS: 100 POINTS): 1. (1 points). The wooden joint is subjected to the aial member force of 5kN. Determine the average normal stress acting on sections AB and BC. Assume that the connection is smooth (no FRICTION). The members are 50-mm thick (this is the dimension into the page). Note: BC is horizontal Horizontal 3 of 10

4 . (13 points). The rigid link is supported by a pin at A and two steel wires (E=9000 ksi) at B and C, each having an unstretched length of 1-in and cross-sectional area of in. Determine the aial force in each wire when the link supports the 350-lb vertical load, shown. Assume that the wires remain elastic. 4 of 10

5 3. (17 points). The beam is made from three plastic pieces, glued together at the seams A and B. The glue can safely support a shear stress of 50 psi. The plastic pieces can safely support a shear stress of 80 psi and a normal stress of 150psi. If it is subjected to the uniform loading of 00 lb/ft, as shown, determine if the beam is adequate, considering: The shear strength of the glue The shear strength of the plastic The normal strength of the plastic 5 of 10

6 4. (13 points). A boiler (pressure vessel) is constructed out of 8-mm thick curved steel plates that are fastened together at their ends using a butt joint consisting of two 8-mm cover plates and rivets having a diameter of 10-mm and spaced 50-mm apart, as shown. If the steam pressure in the boiler is 1.35 MPa, determine the average shear stress in the rivets. 8-mm thick steel Butt joint consisting of () 8-mm cover plates, connected with 10- mm diameter rivets 6 of 10

7 5. (18 points). The crane boom is subjected to the load of 500-lb. Determine the state of stress at points A and B. Label these the state of stress on the stress elements, provided below. A B 7 of 10

8 6. (17 points). The frame supports the distributed loading of 00 N/m. AB and BC are both pin-ended members. Determine the normal and shear stresses at point E that act perpendicular and parallel, respectively, to the grains. The grains at this point make an angle of 60º with respect to the horizontal, as shown. Note: graph paper is attached. If used to solve this problem, clearly show all work related to Mohr s Circle, on the graph paper. 60º 8 of 10 Show final answer here (label directions and magnitudes of stresses)

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10 7. (10 points). The truss is made from steel (E=9000 ksi, yield = 36 ksi) bars, each of which has a circular cross-section. If the applied load P=10 kips, determine the diameter of member AB to the nearest 1/8-in. that will not fail by buckling or material yielding. All members are pin-ended. 10 of 10