CIVE 310 Exam 2, Fall 2002

CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 1 VERY IMPORTANT I AM AWARE THAT THE CIVE310 FINAL EXAM IS NOW RE- SCHEDULED TO Tuesday, January 21, 2003, at 3:00 PM, in Wing D Your Signature, please: QUIZ 2 Fall 2002-2003 (Thursday, January 9, 2003) CIVE310 - MECHANICS OF MATERIALS CLOSED BOOK, 1 ½ HOURS Name: ID#: NOTES • 3 PROBLEMS – 17 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. YOUR COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DO NOT WRITE IN THE SPACE BELOW MY COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ YOUR GRADE Problem I: _ _ _ /50 Problem II: _ _ _ /15 Problem III: _ _ _ /35 Other: _ _ _ __________________ TOTAL: /100 CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 2 Problem I: (50 points) A simply supported beam is loaded as shown in Figure I. Two options (1 and 2) of cross- sections will be studied having the same cross-sectional area; they are each made of two equal pieces arranged as shown. Assume linear elastic behavior and that the beam is safe in shear. The dimensions of the beam are given as follows: • L = 6 m • a = 0.20 m • b = 0.60 m The following are the properties of the system: • E = 20 x 106 kPa (kN/m2) : Modulus of elasticity • σYT = 40000 kPa : Yield stress in tension • σYC = 40000 kPa : Yield stress in compression The following loads/weights are to be considered: • w = 50 kN/m : Distributed load including own weight of the beam • P : Load positioned at mid-span C Figure I Option 1 B A L w P L/2 Cross-Sections Option 2 b a Dimensions of 1 piece CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 3 1. Let P = 200 kN Draw the shear and bending moment diagrams in the beam. (10 points) For each option, show the stress distribution due to bending on the critical cross-section, and discuss the safety of the beam for bending. Compare safety between the options and briefly comment (20 points) Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 4 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 5 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 6 2. If a factor of safety of FS=1.5 is desired, determine the maximum allowable load P in each of the options and compare. Do your comparisons in Question 1 and 2 make sense with each others? (20 points) Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 7 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 8 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 9 Problem II: (15 points) This problem is unrelated to Problem I, though solving Problem I first can help. No calculations are needed. A beam is subjected to a positive bending moment as shown in the longitudinal section in Figure II. Each of the cross-sections used is made of the same two equal pieces (each piece is 0.2x0.6 m) arranged as shown (Options 1 to 4), i.e. they have the same cross-sectional areas. 1. Rate the sections from best to worse for bending, assuming that the allowable stresses in tension and compression are equal. (7 points) Best: 2nd: 3rd: Worst: Figure II Option 1 Option 2 Option 3 Option 4 Beam Longitudinal Section CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 10 2. Assuming that the allowable stress in tension is larger than the allowable stress in compression. Circle the correct answer. (8 points) - Option 1 is better than Option 3 for Bending: TRUE FALSE - Option 2 is better than Option 4 for Bending: TRUE FALSE CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 11 CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 12 Problem III: (35 points) The thick tube shown in Figure III is to be replaced by an equivalent (i) solid tube (ii) thin tube (thickness = 1 cm = 0.01 m) 1. Determine the radii of the solid and thin tubes which will have the same rotation at the free end as the thick tube. Evaluate the savings or the additional cost (comparing solid and thin vs. thick, in percentage) that this will entail, assuming that cost is dependent only on the amount of material used. (15 points) Calculations and/or Diagrams: Figure III T L Thick Tube Inner Radius = 0.3 m Outer Radius = 0.4 m CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 13 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 14 2. Determine the radii of the solid and thin tubes which will have the maximum shear stress as the thick tube. Compare savings or additional cost with Question 1 and briefly comment. (15 points) Draw the shear stress distribution on the cross-sections for the three tubes for T = 100 kNm. (5 points) Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 15 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 16 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 2 Mounir Mabsout 17 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: