CIVE 310 Exam 2, Fall 2001

CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout QUIZ 2 Fall 2001-2002 (Monday, January 14, 2002) CVEV 041 – MECHANICS OF MATERIALS CLOSED BOOK, 1 ½ HOURS Name: ID#: NOTES • ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QUESTION SHEETS. • 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. YOUR COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DO NOT WRITE IN THE SPACE BELOW MY COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ YOUR GRADE Problem I: _ _ _ /50 Problem II: _ _ _ /50 Other: _ _ _ __________________ TOTAL: /100 CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout Problem I: (50 points) A simply supported beam is loaded as shown in Figure I. The cross-section dimensions are also shown in the figure. Assume linear elastic behavior and that the beam is safe in shear. The dimensions of the beam are given as follows: • L = 6 m • b1 = 0.60 m b2 = 0.20 m • h1 = 0.20 m h2 = 0.40 m The following are the properties of the system: • E = 20 x 106 kPa (kN/m2) : Modulus of elasticity • σYT = 10000 kPa : Yield stress in tension • σYC = 20000 kPa : Yield stress in compression The following loads/weights are to be considered: • w = 25 kN/m : Distributed own weight of the beam • P = 100 kN : Moving load positioned at “a” between (A) and (B) Figure I h2 b2 h1 b1 B A L w P a Cross-Section CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout 1. Determine the moment capacity of the section. (15 points) Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout 2. Let P be applied at a = L/4 = 1.5 m Draw the shear and bending moment diagrams in the beam. (10 points) Show the stress distribution due to bending on the critical cross section, and discuss the safety of the beam for bending. (10 points) Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout Calculations and/or Diagrams (cont’d): CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout 3. Discuss the beam safety for a worst-case condition of P. Show that condition. (15 points) Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout X Problem II: (50 points) The circular shaft shown in Figure II is indeterminate to the first degree. Assume linear elastic behavior and neglect the own weight of the shaft. The dimensions, properties and torque load of the shaft are given as follows: • L1 = 3 m L2 = 2 m • D1 = 0.50 m D2 = 0.30 m • G = 10 x 106 kPa (kN/m2) : Shear modulus of elasticity • Τ =50 kNm : Torque applied at B 1. Solve for the angle of rotation at B. (15 points) Compute and draw the shear stress distribution at B. (10 points) Calculations and/or Diagrams: C T L2 D1 B A L1 Circular Cross-Section Diameter D1 or D2 D2 Figure II CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout Calculations and/or Diagrams (cont’d): CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout 2. The shaft was subjected to an experiment and the maximum shear strain at a section just to right of B was measured as 0.0001535. Compute the reactions of the shaft and the angle of rotation at B. Compare with question 1 and briefly comment. (15 points) Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout 3. What is the uniform diameter D of a shaft of total length (5 m) which will give the same angle of rotation at B computed in question 1. Compare D to D1 and D2, and very briefly comment. (10 points) Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CVEV 041 - Fall 2001-2002 Quiz 2 Mounir Mabsout EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: