exam 6 study guide - lafayette college · spring 2018 es226 exam 6 study guide prof. kurtz 2 of 13...

Spring 2018 ES226 Exam 6 Study Guide Prof. Kurtz

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ES226 EXAM 6 STUDY GUIDE Exam 6 Date: Tuesday, May 1st, 7:30 to 8:30pm, Kirby 104

In Class

Exam Format 60 minute time limit. Closed Book. Centroid and Moment of Inertia formulae given Coverage

Lesson Objectives from Lessons 40 to 48. FRICTION PROBLEMS CENTROIDS MOMENTS OF INERTIA MOMENTS OF INERTIA STRESS, STRAIN HOOKE’S LAW

Solve frictional equilibrium problems. 1. (25 points) Determine the frictional force and the direction of this force at point A if the uniform pole has a weight of 50 lb,

has a length of 26 ft, and is placed against the smooth wall and on the rough floor so that A is 8 ft from the wall. Given: = 0.4. Solution note: it is not known whether or not the pole slides. Hence it is not known that the friction at A is 0.4NA.

Solve “impending motion” problems involving friction

2. (30 points) Determine the coefficient of friction if the pole slips when d = 11 ft. Given: the uniform pole has a weight of 50 lb, has a length of 26 ft, and is placed against the smooth wall and on the rough floor at a distance d from the wall.

3. (30 points) Determine where the man should position his center of gravity G at d in order to exert the maximum horizontal

force on the door and determine the magnitude of this force. Given: the man has a weight of 200 lb and the coefficient of static friction between his shoes and the floor is s = 0.5.

8 ft


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4. (30 points) The movable bracket slides if the force W is close to the pipe, but stays in place due to friction if W is sufficiently

far from the pipe. Determine the minimum distance x at which the load W can be supported. Given: 3-in diameter pipe, =0.25. Neglect the weight of the bracket.

Solve problems in which either sliding or tipping is possible.

5. (35 points) Determine if the 150 lb man can push the 180 lb refrigerator and, if so, determine if it slips or tips. Given: coefficient of friction between the refrigerator and the floor is 0.25, while the coefficient of friction between the man’s shoes and the floor is 0.6.

Solve frictional problems involving multiple free body diagrams.

6. (35 points) The friction tongs shown are used to lift a 750-lb casting. Knowing that h=30-in, determine the smallest allowable value of the coefficient of static friction between the casting and the friction blocks D and D’.


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7. The two blocks A and B, each weighing 60 lbs each, are connected by the weightless linkage shown. If the coefficients of static friction are A=0.2 and B=0.8, determine the largest vertical force P that may be applied to pin C without causing the blocks to slip.


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8. (33 points). Determine the greatest distance d by which the rings can be separated without slipping.

Given: 5kg cylinder is suspended from two equal-length cords. Each cord is attached to a ring of negligible mass, which passes along a horizontal pipe. The coefficient of static friction between each ring and the shaft is s=0.5.


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9. (30 points) Determine angle for which W1 begins to slide downward. Given: W1 and W2 each weigh 100 lbs

and the coefficient of friction for all surfaces is 0.2.


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Describe the physical engineering relevance of moments of inertia.

10. (5 points) The figure below is a drawing of the cross-section of a beam. It has been drawn to scale. Would it be more difficult to bend this beam with a moment about the x-axis or with a moment about the y-axis (using right-hand rule to denote axes of moment)?

Memorize the parallel axis theorem and the formula: , the moment of inertia for a rectangle, taken about its centroid Compute moments of inertia Ix and Iy about an area’s centroid (most commonly) or about any other specified axis using composite parts.

11. (25 points) Determine the moment of inertia Ix with respect to the centroid of the shaded area.

12. (25 points) Referring to the previous problem, determine the moment of inertia Iy with respect to the centroid of the shaded

area.

x

y


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13. (20 points). For the cross-section area shown, determine the moment of inertia Ix about the x-axis with respect to the centroid

of the section. Given: the cross-section is made from top and bottom plates that are 8 in. x 1 in. and side plates that are 12 in. x ½ in.

14. (3 points) TRUE or FALSE. Because natural rubber may be stretched up to 800% of its initial length without ever becoming permanently deformed, it is considered to be an extremely ductile material.

15. (3 points) Referring to the graph below, circle the correct statement.

A. Material 1 is less ductile and has a larger yield stress y. B. Material 1 is less ductile and has a smaller yield stress y. C. Material 1 is more ductile and has a smaller yield stress y. D. Material 1 is more ductile and has a larger yield stress y.

x

y

1 in.

8 in.

1 in.

12 in.

½ in.


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16. (15 points) A thin-walled pipe with a 4.00-inch diameter is subjected to air pressure which causes its diameter to increase to

4.10-inches. Determine the normal strain in the walls of the pipe, caused by this diameter-change. (Ans: 0.025 in/in)

17. (30 points) Determine the elastic modulus, yield strength, ultimate strength, and maximum strain for the following

engineering material and plot its stress-strain curve on the graph paper below. Given: The material is a 0.505” diameter solid cylinder was tested in tension, recording load and deformations over its 2-inch length. .

Stress, (psi)

Strain, , (in/in)

1

2

rupture rupture

Figure 1

Pipe 4-in. original diameter 4.10-in. deformed

diameter

Deformation measured over this

2” length

Load (kips)

0.505”

Load (kips)

Load (kips) Deformation (in)0 0.0008 0.0088 0.1009 0.200


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18. (5 points) Describe the difference between elastic deformation and plastic deformation. 19. (3 points) TRUE or FALSE. Brittleness and ductility are antonyms. 20. (5 points) How can one quantify ductility? 21. (8 points) Draw a qualitative stress versus strain graph for an engineering metal such as steel, indicating linear elastic

behavior, the yield point, strain hardening, and the ultimate stress. 22. (3 points) TRUE or FALSE. For an engineering metal that exhibits yielding (the distinct transition from linear elastic

behavior to plastic behavior at a constant stress), the yield stress and ultimate stress will be the same stress level if no strain hardening is present.

23. (3 points) TRUE or FALSE. (Referring to the stress-strain curve in Figure 2, below), Hooke’s Law is valid between points A and B but it is not valid between points A and C.

Stress (ksi)

Strain (in/in)


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24. (15 points) The tension member shown below has a cross-sectional area of 5 in2. Initially, it was 20 feet long. Determine

the new length of the tension member after a load of 350 kips has been applied (ans: L=21.06 feet) Given: The tension member is made from an engineering metal that has the stress-strain curve shown below.

25. (20 points) A linear-elastic thin-walled steel pipe (E=29000 ksi) with a 4.00-inch diameter is subjected to air pressure which

causes its diameter to increase to 4.005-inches. Determine the normal stress in the walls of the pipe, caused by this diameter-change. (Ans: 36.25 ksi)

26. (20 points). Determine the force P that is required to stretch a structural steel bar to a final length of 530 inches, if its initial

length was 500 inches, prior to applying the load. Given: The stress-strain curves for the steel are given below (2 different horizontal scales provided)

The steel bar has cross sectional dimensions of: 6 inch width, ½” thickness

Stress, (psi)

Strain, , (in/in) A

B

C

Figure 2

350 kips

Length = 20 ft, before applying 350 kip load

Engineering Metal with A = 5 in2

(ksi)

(in/in) 0.006 0.100

60

80

Stress-Strain for Engineering Metal

Pipe 4-in. original diameter 4.005-in.

deformed diameter


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P = ? P = ?

Length = 530 inches, when P is applied

After Load P is Applied

Prior to Applying the Load

Length = 500 inches

Cross Section: 6” x ½”

6”

½”


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exam 6 study guide - lafayette college · spring 2018 es226 exam 6 study guide prof. kurtz 2 of 13...

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