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.

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1 Please review the followg statement: I certify that I have not given unauthorized aid nor have I received aid the completion of this eam. Signature: INSTRUCTIONS Beg each problem the space provided on the eamation sheets. If additional space is required, use the white led paper provided to you. Work on one side of each sheet only, with only one problem on a sheet. Each problem is worth 20 pots. Please remember that for you to obta maimum credit for a problem, it must be clearly presented, i.e. The coordate 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 deleate vector and scalar quantities. If the solution does not follow a logical thought process, it will be assumed error. When handg the test, please make sure that all sheets are 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 Jones 9:30-10:20AM P Sojka 1:30-2:20PM J Silvers 3:30-4:20PM J Jones Distance Learng Problem 1 Problem 2 Problem 3 Total ME 270 Eam 3 Page 1

2 PROBLEM 1 (20 pots) Prob. 1 questions are all or nothg. 1A. The frame shown below is made up of lks AC and BD. A leraly-varyg distributed loadg is applied to lk AC, where p 0 is the value of the loadg at end C. Consider a perpendicular cut through lk AC at location E. For the cut face on segment AE, determe the shear force V and the bendg moment M. Leave your answer terms of the given parameters of the problem, but simplify your fal answer as much as possible. V = E M = E (2 pts) (3 pts) 1B. A square press that is punches a hole a ¼ ch thick staless steel metal plate with a shear resistance of τ ma = 36 ksi. The plate has the followg material properties: 2 σ yp = 42 kips/, 2 σ u = 84 kips/, ensure the hole can be fully punched? 2 E = 28,000 kips/. What is the mimum force required to F m = (5 pts) ME 270 Eam 3 Page 2

3 1C. A horizontal bar is attached to a fied bracket through two rubber pads onto the upper and lower ner surfaces of the bracket, as shown the figure. The rubber has a shear modulus of G. A horizontal load P acts on the free end of the bar. Determe the shear stress the rubber pads where they meet the bar. Use the followg parameters your analysis: P = 450 N, b = 60 mm, w = 100 mm, and G = 0.6 M Pa. τ = (Show solution Pa) (5 pts) 1D. Determe the maimum shear stress and shear stra on the bolt just below the head for the followg parameters, P = 75 lbs, = 13 ches, d = ches. Sketch the shear stress distribution over the cross-section of the bolt. Assume the Shear Modulus (G) is psi. (1pt) τ ma = (2 pts) ɣ ma = (2 pts) ME 270 Eam 3 Page 3

4 PROBLEM 2. (20 pots) GIVEN: The truss shown is made of structural steel (σ yield = 36 ksi; E = ksi; ν = 0.29). Beam BH has a cross-sectional area A BH = 0.5 2, and beam EF has a cross-sectional area A EF = The truss is subjected to a 10 kip load at B and a 60 kip load at E. FIND: a) Determe the forces members BH and EF. Include any free body diagrams used, and identify if the members are tension or compression. (5 pts) b) Determe the normal stress, aial stra, and transverse stra BH. (6 pts) c) Determe the normal stress EF. Has yieldg occurred? (3 pts) d) If the 10 kip load remas constant at pot B, determe the maimum allowable load at pot E so that EF will not yield; use a factor of safety of 1.5. Under this loadg, will BH yield? (6 pts) a) F BH = T or C F EF = T or C b) Values for BH Normal stress Aial stra Transverse stra c) Values for EF Normal stress Yieldg? Yes or No d) Ma load at E Will BH yield? Yes or No ME 270 Eam 3 Page 4

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6 PROBLEM 3. (20 pots) GIVEN: Beam ABCD is held static equilibrium by a p support at A and a roller support at C. The beam is loaded with a concentrated force and couple at B and uniformly a distributed load between C and D as shown. The beam cross-section is rectangular with a height of 10 cm and a width of 6 cm. FIND: a) Determe the reactions at supports A and C. (4 pts) b) On the graph provided, sketch the shear-force diagram for the load condition shown. At each terface along the beam (A, B, C, D), label the magnitude of the shear-force on the diagram. (6 pts) c) On the graph provided, sketch the bendg-moment diagram for the load condition shown. At each terface, along the beam (A, B, C, D), label the magnitude of the bendg moment on the diagram. (6 pts) d) Determe the second area moment of ertia (I) of the rectangular cross-section and the maimum stress that acts on the beam the section where pure bendg occurs. (4 pts) 8 kn-m 6 kn 2 kn/m B C D a) A B C D A = A = y C = y ME 270 Eam 3 Page 6

7 8 kn-m 2 kn/m B C D b) 6 kn A B C D c) A B C D d) I = MAX σ = (2 pts) (2 pts) ME 270 Eam 3 Page 7

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9 Normal Stress and Stra ME 270 Eam 3 Equations Shear Stress and Stra ( ) Shear Force and Bendg Moment ( ) ( ) ( ) ( ) ( ) ( ) ( ) ME 270 Eam 3 Page 9

10 ME 270 Eam 3 Equations 1A. V B = 2 pol/3 2 M B = 5 pol /9 1B. F m = 72 kip 1C. τ = Pa τ = psi γ ma = ( ) 1D. ma 2A. F BH = 10 kip Tension F EF = 75 kip Tension 2B. σ = 20 ksi 2C. σ = 37.5 ksi -4 ε = ( ) Yieldg has occurred. -4 ε y = ( ) 2D. Ma load at E is: 38.4 kip BH will not yield. 3A. A = 0 kn 3B. Shear-Force Diagram 3C. Bendg-moment diagram 3D I = 5 10 m = 500 cm A y = -6 kn (σ MAX ) = 40 MPa C y = 4 kn ME 270 Eam 3 Page 10