# 讲解 ME 270 – Spring 2018 Final Exam调试Haskell程序

ME 270 – Spring 2018 Final Exam

PROBLEM 1 (20 points)

1A. For the truss shown, identify all zero-force  members and determine the magnitude of the   load in member CD and whether it is in tension or compression or zero.zer0 F0rce Members    =                                                                                                                                  (3 pts)

FCD      = kN      Tension       Zero      Compression     (Circle One) (2 pts)

1B. For the frame. shown, determine the forces acting at pin B on both members AB and BC. Express both   forces in vector form.

(F(̅)B)0n AB  =  (                         )l(̅) + (                           ) J(̅)  N                                       (3 pts)

(F(̅)B)0n BC  = (                         ) l(̅)  + (                           ) J(̅)  N                                        (2 pts)

1C. A bolt head is made of a material having a shear failure of τ = 120Mpa . Using a factor of safety of F.S. = 2.5 against shear failure, determine the allowable shear stress  (τallow ) and the maximum allowable force P that can be applied to the bolt so that it does not pull through the rigid plate.

1D. Determine the second moment of area about they-axis (Iy) of the shaded shape. Qualitatively, would you expect Ix   to   be  greater  than,   equal  to   or  less  than   Iy?  (No calculations are required).

PROBLEM 2 - (20 points) Partial credit will not be given unless the solution procedure is clearly detailed.

2A. Consider the system in figure where a weight Wis suspended by an inextensible cable connected to a pulley. The pulley is free to rotate without friction around the pinned joint B. A lever is hinged at A and can be actuated by aforce of magnitude F so that the breaking pad can come into contact with the pulley. The coefficient of static friction between the breaking pad and the pulley is μ0.

Draw a complete free body diagram of both the bar and the pulley on the schematic provided below on the right.

Determine the minimum magnitude of the applied force F that will prevent the pulley from rotating under the effect of the weight W.

Assume W = 10 N, a = 0.5 m, b = 1 m, c = 0.1 m, μ0 = 0.3.

Hint: note that the point of contact between the breaking pad and the pulley is at a distance c from the point A. Assume the friction force between the pad and the pulley to be solely in the vertical direction (i.e. the curvature of the pad does not have any effect).

2B. A rectangular cabinet of weight mg rests on an incline. The coefficient of static friction between the incline and the cabinet is μ  = 0.3. A force P is applied to the cabinet as in figure. Find:

●   The magnitude of the force P and the height h (which indicates the point of application of the force P) such that the cabinet will simultaneously slip and tip.

●   How would the value of h change if the plane was horizontal (θ = 0)?

PROBLEM 3. (20 points)

3A. A T-shape cross section is shown right. Determine:

●   The location of the centroid (xc , yc).

●   The second area moment about the horizontal axis which passes its centroid Ic.

3B. A beam is loaded only by concentrated and distributed forces (no external moment applied) . Given the shear force diagram shown below, draw the external loading (both concentrated and distributed forces) and lab their magnitudes on the figure of the beam below. (4pts)

3C. A stepped shaft composed of components AB and BC is shown below. AB and BC are joined by a rigid connector at B. Both AB and BC have a circular cross section, and their diameters are 4 cm and 3 cm, respectively. An external force 2 kN is applied at B. Determine the internal axial stress in AB and BC.

3D. A cantilever beam ABC is subjected to a concentrated force 200 lb at C. The beam has a triangular

cross section. The second area moment of a triangular cross section about its centroid axis is Ic   =  ,

where b and h are the width and height of the shape, respectively. Determine:

●   The normal stress at M within the cross section B, σM .

●   The maximum tensile stress in the cross section B, σmax

PROBLEM 4. (20 points)

4A A solid circular shaft is loaded as shown and is held in static equilibrium by a fixed support at E. Determine the magnitude of the torque experienced in plane AB. Show your free body diagram.

4C If a tubular shaft has an outside diameter do  = 200mm and an inside diameter di  = 100mm, and if the applied torque is T = 5.1 kN-m, determine the polar moment of inertia (J) and the shear stress at points A (τA ) and B (τB) shown on the figure.

4D If a solid circular shaft is replaced by a tubular shaft of the same outside diameter (do),will the maximum shear stress qualitatively increase, remain the same, or decrease given the applied torque is the same for both shafts?  No work needs to be shown.

PROBLEM 5. (20 points)

The cantilever beam is subjected to the loading condition as shown below.

a)  Draw the Free-Body Diagram of the beam and determine the reactions at the wall. Write your answer in the given box.

b)  On the axes provided below, construct the shear force (V vs. x), and the bending moment (Mvs. x) diagrams. Specify the shear & moment values at A, B, C, D, and any maximum and minimum values. (12 pts)

c)  Determine the value of the maximum tensile stress within the beam, and the location of the maximum tensile stress. Write your answer in the given box.