Group Number: Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, use the white lined paper provided to you. Work on one side of each sheet only, with only one problem on a sheet. Each problem is worth 20 points. Please remember that for you to obtain maximum credit for a problem, it must be clearly presented, i.e. The coordinate system must be clearly identified. Where appropriate, free body diagrams must be drawn. These should be drawn separately from the given figures. Units must be clearly stated as part of the answer. You must carefully delineate vector and scalar quantities. If the solution does not follow a logical thought process, it will be assumed in error. When handing in the test, please make sure that all sheets are in the correct sequential order and make sure that your name is at the top of every page that you wish to have graded. Instructor s Name and Section: Sections: J. Silvers 8:30-9:30am B. Hylton 2:30-3:20pm J. Jones 11:30am-12:20pm J. Seipel 12:30-1:20pm M. Murphy 9:00-10:15am E. Nauman 9:30-10:20 am K. Li 1:30-2:20pm J. Jones Distance Learning Problem 1 Problem 2 Problem 3 Total
PROBLEM 1. (20 points total) There are three parts to this problem. 1a. Draw a free body diagram of each link or piece of the machine shown below. If a force, P = 45 lbs. is required to crush a can, what input force, F, is required? You may assume the dimensions are given in inches. (8 points) Can Crusher Free Body Diagram Free Body Diagram Free Body Diagram
F = 1b. State Newton s 3 Laws in order as succinctly as possible. (5 points) First Law Second Law Third Law
1c. In the picture shown below, there are two torques applied to the shaft. T 1 = 450 Nm and T 2 = 200 Nm. If x 1 = x 2 = 0.25 m, determine the maximum shear stress at the section located at, x = 0.1 m. The diameter of the thick section, d 1 = 10 cm, and d 2 = 6 cm. (7 points)
Problem 2. (20 points) A beam AB has length L = 12 ft and weight W a = 100 lbs. It is supported at A and B by hanger rods AC and which behave as two-force members. The length of these two hanger rods is 2 ft before loading. A crate of weight W b (in lbs) is placed on the beam as shown in the following diagram. Rod AC is made of aluminum alloy which has diameter d 1 = 0.25 in, yield stress ( ) 1 YP σ = 60 ksi and Young s modulus E 1 = 10 10 3 ksi. Rod is made of brass which has diameter d 2 = 0.125 in, yield stress ( σ 2 ) = 50 ksi and YP Young s modulus E 2 = 15 10 3 ksi. (a) Draw the free body diagram of beam AB and determine the respective axial forces, F AC and F, in Rods AC and in terms of the weight of the crate, W b. (7 points) F
F AC = Tension / Compression (circle one only) F = Tension / Compression (circle one only) (b) Using a factor of safety FS = 2.0, and considering the yield stress in Rod AC, determine the maximum allowable weight of the crate, W b. Give your answer in 3 significant figures. (5 points) W b =
(c) For W b determined in (b), calculate the axial stress σ in Rod. (4 points) σ = (d) Considering the axial stress σ obtained in (c), determine the axial strain ε and the extension Δ in Rod. (4 points) ε = Δ =
ME 270 Exam #3 Name Problem #3 Fall 2013 Version #3 A 4 foot long beam is loaded with a discrete load and a couple at point A and a distributed load from Point B to Point C. The beam is fixed into the wall at Point C. y F A = 10 lb w = 3 lb/ft M A = 20 ft*lb A B C x 2 ft 2 ft Please place your answers in the boxes provided: a. Complete the free-body diagram (sketch the free-body diagram on the figure provided) and determine the reactions at C (6 points) b. Cut a section between points A and B (sketch the free-body diagram on the figure provided, page 2 of this problem) and determine the shear and moment equations for the section from x = 0 to x =2 feet (4 points). c. Cut a section between points B and C (sketch the free-body diagram on the figure provided, page 2 of this problem); and determine the shear and moment equations for the section from x = 2 to x = 4 feet (6 points). d. Complete the shear and moment diagram on the lines provided on the 3 rd page of this problem (4 points). y x A B C a.) C x = C y = M C = lb. lb. ft*lb Problem #1 Version #3 Page #1
ME 270 Exam #3 Name Problem #3 Fall 2013 Version #3 y x A b.) For x=0 to x = 2 V = M = lb. ft*lb y A B c.) For x = 2 to x =4 V = M = lb. ft*lb Problem #1 Version #3 Page #2
ME 270 Exam #3 Name Problem #3 Fall 2013 Version #3 d.) Complete the Shear and Moment diagrams below (original diagram is repeated to help align the Shear and Moment Diagrams): y F A = 10 lb w = 3 lb/ft M A = 20 ft*lb x A B C V x A B C M A B C x Problem #1 Version #3 Page #3
Normal Stress and Strain ME 270 Exam 3 Equations Shear Stress and Strain ( ) Shear Force and Bending Moment ( ) ( ) ( ) ( ) ( ) ( ) ( )
Fall 2013 Exam 3 Solutions 1A. Free Body Diagrams F = 20 lbs 1B. Newton s 3 Laws 1C. max = 1.27 MPa 2 2A. Free Body Diagram F AC = 50 + W b Tension 3 1 F = 50 + W b Tension 3 2B. W b = 2130 lbs to 3 sig. figures 2C. σ = 62.0 ksi 2D. = 4.14 x 10-3 -2 = 9.93 x 10 in The system will fail at Rod 3A. C = 0 lb C = 4 lbs x y M c = -14 ft-lb 3B. V = -10 lbs M = 20-10x ft-lb or 10(2-x) 3C. V = 3 (x - 2) - 10 = 3x - 16 lb M = 20-10x + 3 2 2 (x - 2) ft-lb 3D. Shear & Moment Diagrams