CIVE 310 Exam 1 with Solution, Fall 2002

CIVE310 - Fall 2002-2003 Quiz 1 Mounir Mabsout UIZ 1 Fall 2002-2003 (Tuesday, November 19, 2002) CIVE310 - MECHANICS OF MATERIALS CLOSED BOOK, 1 % HOURS Name: Key Key ws: 3000 - G20 NOTES 3 PROBLEMS — 11 PAGES. THE QUESTION SHEETS. Si 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. SPACE PROVIDED. YOUR COMMENT(S) DO NOT WRITE IN THE SPACE BELOW MY COMMENT(S) YOUR GRADE Problem I: _/40 Problem II: _130 Problem Il:___ [30 Other: TOTAL: /100 CIVE310 - Fall 2002-2003 Quiz I Mounir Mabsout Problem I: (40 points) a : 7 Figure I-b The truss modeled and shown in Figure J-b is used to hold a flat horizontal cover of a shop-front (Figure I-a). The total weight of the cover W is carried by each of the two trusses as shown in Figure I-b. It is also possible for the cover to be loaded with snow. Assume linear elastic behavior and be careful with units. The dimensions of the system are given as follows: e L=4m a=2m b=1m e Tubular steel cross-sections of truss bars t Bar AB BC AC © Outside Diameter D (mm) 30 40 20 , Thickness (same) ¢ (mm) 3 3 3 i+ The properties of the system.are given as follows: © oy = 300,000 kPa (ww A: Yield stress in tension and compression of steel tubes e FS : Factor of safety The loading/weight on the system are given as follows: . e W=20kN : Total weight of cover (about 2 Tons) © y=5kN/m’ : Weight density of snow (about 4 of water) eh : Height of snow uniformly distributed above cover © Own weight of truss bars is negligible CIVE310 - Fall 2002-2003 Quiz I Mounir Mabsout 1. Assume NO snow on cover. Discuss the safety of the truss system and briefly comment, assuming that the cover itself is safe. (15 points) Are the bars properly arranged (in terms of cross-sections), and, if not, suggest a more proper arrangement of cross-sections, and briefly justify your choice. (10 points) Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 1 Mounir Mabsout Calculations and/or Diagrams (cont'd): SRD eagebed adn He Sava AC we 2B oy FR. GS | CAS) Loyah. RC... poner = FR 4.344 Same... ef eee eee nneeeneennneneneeees | Clot CIVE310 - Fall 2002-2003 Quiz I Mounir Mabsout 2. The factor of safety is set aAFS=1.5. With the original arrangement of bar cross-sections given on page 2, determine the height h of a uniformly distributed snow above the cover that the truss is allowed to carry, assuming that the cover remains safe. (15 points) Calculations and/or Diagrams: Wy, J + Ws/ hy __- FS2L5 =. 322000 Wea blel K0. CIVE310 - Fall 2002-2003 Quiz | Mounir Mabsout wh hoor Kicdave vis Problem I: (30 points) I Q As) ¢] | | \ Solo} 8 Figure II Your Sketch/e bw The free-standing circular solid column monument shown in Figure II has a height A an diameter D is made of concrete. The properties of concrete are as follows: © E=25x 10°kPa (KN/m?) : Modulus of elasticity © y=25 KN/m : Weight density of concrete (about 2.5 water) © Ox = 30,000 kPa : Ultimate strength in compression © FS=1.5 : Factor of safety For D=1 m Determine the allowable height / of the column so that it is safe under its own weight, and compute the corresponding top displacement. Does your result for height make sense? What problems do you foresee if you decide to build this column and suggest a solution to hold it (think of lateral stability/buckling, make a sketch (above), use your imagination - you may use fantasy and be UN-realistic in your solution). YU What do you expect for A if the problem is tured upside down (much higher, higher, same, lower, much lower). Give an estimate and briefly explain. (22 points) For D=100 m How would your result for / and top displacement change if the diameter is 100 m? Briefly explain. Do you think you need your imaginary solution here? Briefly explain. (8 points) Calculations and/or Diagrams: say wl CIVE310 - Fall 2002-2003 Quiz 1 Mounir Mabsout =<—— Toney esse [28--slaunghk. on —— focal ss [oca]..Gie bme Bp) CIVE310 - Fall 2002-2003 Quiz 1 Mounir Mabsout Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2002-2003 Quiz J Mounir Mabsout Problem III: (30 points) The axial bar of constant cross-section area A. shown in Figure III, is assumed Cveightles) and is made of two equal segments for a total length L. The upper and lower parts have wmodulus of elasticity E; and E, respectively. The bar is loaded at mid height with a load P. Assume linear elastic behavior. Compute the top and bottom reactions and the displacement at mid height and compare reactions for the case with case of E).= E2 with the case when £;.> E2 and briefly comment. (20 points) What happens to the reactions and mid-height displacement when E; (upper part) becomes very large, i.e. E).>>> Ez. Briefly explain. (10 points) Calculations and/or Diagrams: CIVE310 - Fall 2002-2003 Quiz 1 Mounir Mabsout Calculations and/or Diagrams (cont’d): t p A