CIVE 310 Exam 2, Fall 2004

CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 1 QUIZ 2 Fall 2004-2005 (Monday, January 10, 2005) CIVE310 - MECHANICS OF MATERIALS CLOSED BOOK, 1 ½ HOURS Name: ID#: P/A; Tc/J; Mc/I bh3/12; ΠR2; 2ΠRt; ΠR4/2; 2ΠR3t NOTES • 3 PROBLEMS – 12 PAGES. • ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QUESTION SHEETS. • TWO EXTRA SHEETS ARE PROVIDED AT THE END. • ASK FOR ADDITIONAL SHEETS IF YOU NEED MORE SPACE. • SOME ANSWERS MAY REQUIRE MUCH LESS THAN THE SPACE PROVIDED. • DO NOT USE THE BACK OF THE SHEETS FOR ANSWERS. • DRAFT BOOKLET WILL BE PROVIDED; BUT DO NOT USE FOR ANSWERS. • BOTH QUESTION SHEETS AND DRAFT BOOKLET SHOULD BE RETURNED. • CHECK BOXES ARE FOR YOU TO CONFIRM THAT HAVE SOLVED A QUESTION YOUR COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DO NOT WRITE IN THE SPACE BELOW MY COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ YOUR GRADE Problem I: _ _ _ /20 Problem II: _ _ _ /35 Problem III: _ _ _ /45 Other: _ _ _ __________________ TOTAL: /100 CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 2 Problem I: (20 points) The block shown in Figure I is made of a magnesium alloy for which the modulus of elasticity E= 50,000 MPa (N/mm2) and Poisson’s ratio ν= 1/3. Assume linear elastic behavior, and given that σX= 180 MPa in compression, determine the following: 1. The magnitude of σY for which the change in height LY of the block is zero. (5 points) 2. The corresponding change in the horizontal area (XZ Plane). (7 points) 3. The corresponding change in volume using 2 different methods and compare. (8 points) Calculations and/or Diagrams: LX = 100 mm LY = 40 mm LZ = 25 mm Y Z σY σX Figure I X CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 3 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 4 Problem II: (35 points) The weightless shaft shown in Figure II is made of a thick tube. Assuming linear elastic behavior, and given that the allowable shear stress τall is 70,000 kPa (kN/m2) and shear modulus G is 200x106 kPa (kN/m2), determine: 1. The maximum torque T which can be applied, and plot the shear stress distribution on the cross section. Calculate the torsional stiffness and the rotation at the free end. (13 points) 2. The maximum torque which can be applied on a solid shaft of same weight and material (i.e. same cost). Compare with question 1 and briefly discuss. (10 points) 3. The diameter and cross-section area of a thin shaft of thickness t=1 cm which will result in the same torque capacity as the thick shaft in Figure II; compare cost and briefly discuss. (12 points) Calculations and/or Diagrams: Din = 10 cm Figure II Dout = 15 cm T L = 2 m CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 5 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 6 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 7 Problem III: (45 points) A steel I-beam with overhanging ends is subjected to a uniformly distributed load w, as shown in Figure III. The dimensions of the beam are shown on the cross-section. The yield stress in tension and compression is σYT = σYC = 200 MPa (N/mm2) and the factor of safety assumed is 1.6. 1. Draw the shear and bending moment diagram of the beam. (10 points) 2. Determine the axial flexural stresses at the critical sections of maximum negative and positive moments, and briefly discuss safety. (10 points) 3. Compute the moment capacity of the section in tension and compression, and determine the maximum additional allowable uniform load ∆w that can be added to the beam safely. (15 points) 4. Compute the maximum permissible concentrated load applied at mid length of the beam (between B and C), in addition to the existing w (without ∆w). (10 points) Calculations and/or Diagrams: 10 2 m 2 m B A 5 m C Figure III w =30 kN/m D 20 200 20 150 Cross-Section (mm) CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 8 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 9 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 10 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 11 EXTRA SHEET 1: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CIVE310 - Fall 2004-2005 Quiz 2 H. Basha &M. Mabsout 12 EXTRA SHEET 2: Continued from page _______ Name: ID#: Calculations and/or Diagrams: