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ME104Q – ENGINEERING OF BRIDGES F2013 1st EXAM - 31 October 2013 – 7:30 –9:30 p.m – Hoyt Auditorium.

EXAMINATION RULES: Please read carefully. The exam is “closed book.” Calculators, triangles and one letter-size page cheat-sheet are allowed. Pages for scratch work will be provided. The exam consists of 3 parts (100 points total)

Part 1 (25 points) – two free-body diagram problems, Part 2 (25 points) – one equilibrium problem, Part 3 (50 points) – two truss problems, and One bonus problem.

There are 12 numbered pages in the exam. Show all your work on the attached numbered pages only. Write your name on the front page of the exam, and on all the exam pages.

Do not start the examination until told to do so!

NAME: ______________________________________________

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PART 1 (25 points): Draw the free-body diagram (F-BD) for each of the two systems shown below. Draw first a coordinate system and then be accurate in drawing the F-BD.

1.1) A bar AB weighing 1000 N is supported by a post CD and a cable as shown in the figure. Assume that all surfaces are smooth. Draw the F-BD of bar AB. Be accurate. Show as clearly as possible the direction and location (point of application) of each applied and reaction force.

Free-Body Diagram for bar AB

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Draw the F-BD of the cylinder

1.2) A cylinder is pressed against a vertical surface by a bracket as shown in the figure. The horizontal force P is applied to the bracket. The mass of the cylinder is 50 kg. Ignore the mass of the bracket. All surfaces are smooth.

Draw the F-BD of the bracket

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PART 2 (25 points): A vertical force of 1,000 N is applied to the structure shown in the figure below. The structure consists of two straight bars connected by a hinge at B. We ignore the mass of the bars. Since the 1,000 N force is not applied at a hinge, this is not technically a truss. However, we can still analyze it using our knowledge of truss equilibrium. Find the unknown reactions at the supporting hinges A and C.

• Set up a coordinate system and draw the free-body diagram for the entire structure. • Write the equilibrium equations, then solve the problem analytically. • Draw the free-body diagram with the actual forces at equilibrium. • Verify that your solution is indeed in equilibrium.

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PART 3 (50 points): 3.1) The truss shown in Fig. 3.1 is made of wooden bars joined by pins. The force

€

P = 200 kN and

€

Q = 200 kN are applied at joint 3 and 4, as shown. All bars have square cross sectional area

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A = 225 cm2. Ignore the weight of the bars. 1. Set up the FBD for the entire truss and compute the support reactions. (Show the equilibrium

equations and verify your solution). 2. Find the axial force in bars 13, 23, and 24 by considering the equilibrium of an isolated portion of

the truss that cuts through those bars and includes joints 3 and 4 (and thus the desired forces can be regarded as externally applied to this portion of the truss.)

3. Using the graphical approach, determine the forces for the bars at joint 2 by constructing the force polygon.

4. Tabulate the forces in the truss elements (give magnitude and indicate whether tension or compression) and determine the maximum tensile and compressive stresses in the truss.

Fig. 3.1

Fig. 2

Fig. 2

Fig. 3.1

NAME:_______________________________________ page 9 3.2) Figure 3.2 shows the forces transmitted on each bar of a truss bridge as measured experimentally by load cells. All bars are made with the same material and have identical cross-sections. The forces transmitted are due only to the 200 kN downward loads applied at joints 2 and 3 (the mass of the bars can be neglected.) The truss is pinned at joints 0, 1, 4, and 5. Negative forces are in compression. Based on your understanding of how bars deform elastically in this truss: 1. Sketch the deformed shape of the truss on top of the un-deformed truss geometry given in Fig.

3.3. Be as accurate as possible. Use a pencil. 2. Can you trust the experimental results? Explain your reasoning for the deformations of bars 02,

12, and 23.

Fig. 3.2

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Fig. 3.3

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BONUS PROBLEM:

A force F = 250 N is applied to the bracket as shown in the figure. The bracket is fully constrained at point A. Ignore the mass of the bracket.

• Set up a coordinate system and

draw the free-body diagram. • Determine the moment generated

by force F with respect to point A. • Find the reactions at A and

redraw the free-body diagram with all the external forces in equilibrium.

• Verify equilibrium.