# and F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points)

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1 ME rd Sample inal Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) IND: In your own words, please state Newton s Laws: 1 st Law = 2 nd Law = 3 rd Law = PROBLEM 1B. (5 points) IND: Two forces, 1 and 2, are applied to a bracket as shown. The magnitude of force 1 is 300 N. The resultant force acts in the positive y-direction, i.e., R = R j. 2

2 ME rd Sample inal Exam PROBLEM 1C. (5 points) GIVEN:The loaded truss ABCDE is supported by a pin joint at A and a roller support at E. A 16 kn horizontal force acts at joint C. IND: a) Identify two zero-force members (2 points) b)solve for the reactions at A and E: express your answers in vector form relative to the coordinate axes shown in the figure (4 points) c) the force carried by member AC (3 points); is AC in compression or tension (1 point) a) Zero-force Members: b) = A = E c) AC = Circle One: Tension Compression

3 PROBLEM 1D. (5 points) GIVEN: The circular disk with a square-shaped hole. IND: The y-coordinate of the centroid of the shaded area. Y = PROBLEM 1E. (5 points) GIVEN: Block A weighs 100 N. orce P is applied to the mass-less wedge B. Block A is constrained to move vertically by frictionless rollers. rictionless rollers are also present under the wedge. IND: The force P required to raise block A, in N. P =

4 PROBLEM 1. (5 points) GIVEN: Water, with density of 1,000 kg/m 3, fills a cave located beneath the surface. IND: The hydrostatic pressure at points A 1, B 1, and C in kpa (note: 1 kpa = 1,000 N/m 2 ). P A = P B = P C =

5 NAME: PROBLEM 2A. (5 points) IND: The wood joint shown has a width (into the page) of 150 mm. Determine the average shear-stress developed along planes a-a and b-b. τa = (2 pts) τb = (3 pts) PROBLEM 2B. (5 points) IND: Rigid bar AB is supported by a steel rod AC having a diameter of 20 mm and an aluminum block having a cross-sectional area of 1800 mm2. The 18-mm diameter pins A and C are subjected to single shear. Assume ( ) st fail = 680 MPa, ( ) al fail = 70 MPa, and ( )fail = 900 MPa. If a factor of safety S = 2 is utilized, determine the largest load Pmax that can be applied to the bar. Pmax = (5 pts)

6 PROBLEM 2C. (5 points) IND: The assembly shown consists of an aluminum tube AB having a cross-sectional area of 400 mm 2 and a steel rod BC having a diameter of 10 mm and passing through tube AB. Assume E st = 200 GPa and E al = 70 GPa. If a load of 80 kn is applied to rod BC, determine the strain in tube AB and rod BC. ε AB = ε BC = (2 pts) (3 pts) PROBLEM 2D. (5 points) IND: The assembly consists of two sections of galvanized steel pipe connected together using a reducing coupler at B. The smaller pipe (AB) has an outer diameter whereas the larger pipe (BC) has an outer diameter of 0.75 in and an inner diameter of 0.68 in., whereas the larger pipe (BC) has an outer diameter of 1 in. and an inner diameter of 0.86 in. If the pipe is securely attached to the wall at C, determine the maximum shear-stress in each section of the pipe. τ AB = τ BC = (2 pts) (3 pts)

7 PROBLEM 2E. (5 points) IND: Determine the centroid of the T-beam and the second area moment of inertia about the centroidal axis y y y = I = (2 pts) (3 pts)

8 PROBLEM 3 (25 points) NAME: kn 2 m GIVEN: Beam ABCD is supported by a pin support at B and a roller support at C. The beam is loaded A with a concentrated moment at D and a B uniformly distributed load between A and B as C shown. Assume the beam has a rectangular 2m 4m 2m cross-section of width 0.05 m and height of m. 8kN-m D IND: a) Determine the reactions at supports B and C. (4 points) b) On the graph provided, sketch the shear-force diagram for the load condition shown. At each interface along the beam (A, B, C, D), label the magnitude of the shear-force on the diagram. (7 points) c) On the graph provided, sketch the bending-moment diagram for the load condition shown. At each interface along the beam (A, B, C, D), label the magnitude of the bending moment on the diagram. (7 points) d) Identify (if any) the location(s) along the beam where pure bending exists. (2 points) e) Calculate the maximum normal stress due to bending in the region of pure bending. At what location(s) does this maximum stress occur? (5 points)

9

10 PROBLEM 4. (25 points) GIVEN: The distributed load acts on a frame ABCDE. The frame is supported by pin joints B, C, D, and E, and by a roller support at A. IND: a) Draw complete free body diagrams of the geometries given; replace the distributed load with a single point load. (5 pts) b) The magnitudes of the forces supported by pin joints B and E. (6 pts) c) The reaction forces at A, C, and D; express your answers in vector form relative to the coordinate system given in the figure. (9 pts) E BD 2 BD 1 E D B BD 3 A B C

11 Sample inal Exam Answers 1A. Definitions 1B. 2 = N 1C. Zero-orce Members = AB, BC, D, C A = -16i = 5 j kn AC = 6.40 kn B = 5 j kn Tension 1D. y = in 1E N 1. P A = kpa P B = kpa P C = kpa 2A. ( τ ) = 200 kpa ( τ ) a Avg b Avg = 160 kpa 2B. P max = 168 kn ; ( P max ) = 171 kn Rod AC ( P ) = 168 kn ( ) max Block B P = 183 kn max Pin A or C 2C. ε AB -3 = x 10 m/m ε BC -3 = x 10 m/m 2D. τ AB = 7.82 ksi τ BC = 2.36 ksi 2E. y = 8.55 in from base of T-beam I = 646 in 4 3A. B x = 0 B y = 3 kn C y = 1 kn 3B. Diagram 3C. Diagram 3D. Pure Bending occurs between C and D 3E. σ max = 96 MPa σ max occurs between C and D

12 4A. BDs 4B. BE = kn (Compression) 4C. D = i +50 j kn A = 37.5 j kn C = i j kn

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