CIVE 310 Exam 1, Fall 2006

CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 1 QUIZ 1 Fall 2006-07 (Wednesday, November 8, 2006) CIVE310 - MECHANICS OF MATERIALS CLOSED BOOK, 1 ½ HOURS Name: ID#: NOTES • 2 PROBLEMS – 14 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 YOU HAVE SOLVED A QUESTION YOUR COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DO NOT WRITE IN THE SPACE BELOW MY COMMENT(S) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ YOUR GRADE Problem I: _ _ _ /45 Problem II: _ _ _ /55 Other: _ _ _ __________________ TOTAL: /100 CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 2 Problem I: (45 points) The rigid beam ABCD shown Figure (I-a) is subjected to a uniform distributed load w and a concentrated load of 4 kN as shown. Ignore the own weight of the beam and assume linear elastic behavior and small deformations. PART [1] Knowing that w = 4 kN/m, determine the following: 1) The support reactions at B and C. (DOUBLE CHECK YOUR REACTIONS) (10 points) 2) The shearing force diagram (S.F.D) and bending moment diagram (B.M.D) of the beam ABCD. (20 points) Calculations and/or Diagrams: Figure I-a B A C D w 1.0 m 1.0 m 3.0 m 1.0 m 4kN CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 3 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 4 PART [2] The structure given in Part [1] was modified such that the supports at B and C were replaced by steel rods BF and CG as shown in Figure (I-b). Rods BF and CG are pin connected at both ends thus resist only axial loads (Beam ABCD will behave the same as in Part 1). The rods have the following properties: • d1 : Diameter of Bar BF • d2 : Diameter of Bar CG • L = 3.0 m. : Length of Bars BF and CG • E = 200 x 106 kPa (kN/m2) : Modulus of elasticity of steel • σy = 250,000 kPa : Yield stress of steel in tension and compression • F.S = 2.0 : Factor of safety Solve the following: 1) The maximum value of w that the structure can safely carry if the diameter of rod BF is 10mm and the diameter of rod CG is twice as much; i.e., d2=2d1=20mm. Assume the beam is always safe. (15 points) Calculations and/or Diagrams: Figure I-b G F L= 3.0 m B A C D w 1.0 m 1.0 m 3.0 m 1.0 m 4kN CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 5 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 6 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 7 Problem II: (55 points) The steel bar ABC shown in Figure (II-a) has a uniform thickness equal to 10mm and consists of two parts; a tapered bar AB and a rectangular bar BC, as shown. The bar is subjected to the shown concentrated loads, P1 and P2. Figure (II-b) shows that the tapered bar AB will deflect at B a value of 1.73287x10-3mm due to a load of 1kN applied at end B, as shown. Assume small deformation - elastic behavior - and neglect own weight of the bar. The bar has the following properties: • E = 200,000 MPa (N/mm2) : Modulus of elasticity of steel • σyield= 250 MPa (N/mm2) : Yield stress of material PART [1] • Calculate axial stresses at points C and D. (10 points) • Calculate the maximum axial stress in the bar ABC and discuss its safety. (10 points) • Calculate the vertical displacement of points B and C. (10 points) • Compute axial stiffness of the bar ABC. (10 points) Calculations and/or Diagrams: 200mm D Thickness =10mm B A P1=100kN 250mm C P2=50kN 100mm Figure II-a Figure II-b L2=200mm L1=500mm B A 100mm 200mm L1=500mm Thickness =10mm 1kN ∆∆∆∆=1.73287x10-3mm CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 8 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 9 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 10 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 11 PART [2] The rod ABC is made fixed at both ends (indeterminate rod) and the rod was subjected to P1 only as shown in Figure (II-c). (THINK BEFORE YOU SOLVE: THIS MAY SAVE YOU QUITE SOME TIME) • Calculate support reactions at A and C. (15 points) Calculations and/or Diagrams: 200mm Thickness =10mm B A P1=100kN C 100mm Figure II-c L2=200mm L1=500mm CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 12 Calculations and/or Diagrams (cont’d): CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 13 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: CIVE310 - Fall 2006-07 Quiz 1 M. Mabsout & H. Basha 14 EXTRA SHEET: Continued from page _______ Name: ID#: Calculations and/or Diagrams: