CIVE 310 Exam 2, Fall 2003

CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 1 QUIZ 2 Fall 2003-2004 (Thursday, January 8, 2004) CIVE310 - MECHANICS OF MATERIALS CLOSED BOOK, 2 HOURS Name: ID#: FORMULAS/EQUATIONS: GENERAL FORM (USE CAREFULLY) P/A; Tc/J; Mc/I; bh3/12; ΠR4/2; 2ΠR3t NOTES • 2 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: _ _ _ /60 Problem II: _ _ _ /40 __________________ TOTAL: /100 CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 2 Problem I: (60 points) A fixed beam is loaded as shown in Figure I. Two options of cross-sections will be studied: Option 1 is a hollow square box shape, and Option 2 is a solid square shape. Assume linear elastic behavior and that the beam is safe in shear. Neglect the own weight of the beam. The dimensions of the beam are shown on the Figures. The following are the properties of the system: • E = 20 x 106 kPa (kN/m2) : Modulus of elasticity • σYT = 40,000 kPa : Yield stress in tension • σYC = 30,000 kPa : Yield stress in compression The following loads are to be considered: • w : Distributed load through L • P : Concentrated load at tip of beam Figure I Option 1 B A L=4 m w P Cross-Sections (meter) Option 2 0.20 0.20 0.20 0.20 0.20 0.20 a a CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 3 1. Let w = 50 kN/m and P = 100 kN. Let a = 0.60 m for Option 2. • Draw the shear and bending moment diagrams, and sketch the deflected shape 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 cost and safety between the two options and briefly comment. (20 points) • Calculate the curvature of the beam at A. (5 points) Calculations and/or Diagrams: CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 4 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 5 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 6 2. Determine the moment capacity for Option 1? How does this moment capacity correlate with Option 1 in Question 1? (10 points) Find “a” for Option 2 which will lead to the same moment capacity as Option 1. Compare cost for Options 1 and 2, and comment on the effect of the inner void in Option 1. (10 points) Calculations and/or Diagrams: CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 7 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 8 3. How would Questions 1 and 2 change if Option 1 is replaced by the I shape below? Explain very briefly. This is a 3 mn, 3 lines question with no calculations needed. (5 points) Calculations and/or Diagrams: 0.20 0.20 0.20 0.10 0.40 0.10 CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 9 Problem II: (40 points) • Design (find cross-section and length) of the thin tubular steel shaft shown in Figure II, given the loading, properties and constraints below. (25 points) • Draw the stress distribution on the cross-section along the circumference, and calculate by integration the equivalent to torque and compare to the applied torque. (15 points) • This should be a thin tube with t/D< 1/20 • Ignore own weight • T = 1,000 kNm • G = 100 x 106 kPa (kN/m2) : Shearing modulus of elasticity • γallowable = 0.001 : Allowable shear strain • Rotation limited to 0.01 rad Calculations and/or Diagrams: Figure II T L D t Cross-Section CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 10 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 11 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 12 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CIVE310 - Fall 2003-2004 Quiz 2 Mounir Mabsout 13 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: