XAM SAMPLES (FROM PAST EXAMS - Sites at … · ES230 2017 – Sample Exam (past exams) for Exam 2 Material Page 2 of 44 This is a compilation of many past exams (some of these were

ES230 2017 – Sample Exam (past exams) for Exam 2 Material

Page 1 of 44 This is a compilation of many past exams (some of these were “Exam 3, in past years”)

NAME: ____________________________________________

EXAM 2, SAMPLES (FROM PAST EXAMS) Updated: 2/17/17

You are allowed to use a calculator and drawing equipment, only. 50 minute time limit

Given Formulae: Law of Cosines:

Law of Sines:

Formulae: Normal stress = F/A, where F is the normal force on the cut and A is the area of the cut. Shear stress avg = V/A, where V is the shear force on the cut and A is the area of the cut. Normal strain = L/L, where L is the change in length and L is the original length (AKA, gauge length) Shear strain xy = the change in angle of x-y, where x-y are initially perpendicular or xy=/2 – ’, where ’ is the deformed angle

between x-y, measured in radians and is obviously . Hooke’s “Law” – = E, where E = modulus of elasticity (AKA Elastic Modulus or Young’s Modulus) Poisson’s Ratio = - (lat/long), where the specimen is loaded in the long direction, resulting in long strain, as well as lat strain. Hooke’s Law for Shear: = G, where G is the shear modulus of elasticity (AKA, the modulus of rigidity) The elastic properties E, G, and are related by:

A B

C

b

c

a



1. (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

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”





2. (6 points). The diagram for human skin is shown. Determine the toughness of human skin and clearly report what the units are:

3. (4 points). Using your knowledge and experience from lab, you know that concrete has a higher Modulus of Elasticity than wood. Circle the answer that is closest to the truth:

a. Concrete E is 1.1 times higher than Wood E b. Concrete E is 3 times higher than Wood E c. Concrete E is 30 times higher than Wood E d. Concrete E is 300 times higher than Wood E

4. (4 points). Given equal-sized bars of 6061 Aluminum alloy and Structural Steel (use your knowledge of these materials from lab), which material will deform more when subjected to axial tension, if it is known that the bars are loaded elastically (i.e., to a stress that is less than the yield stress)? (circle the correct answer)

a. Aluminum 6061 alloy b. Structural Steel





5. (40 points) Determine the rotation of Rigid Beam ABC and report your answer in degrees. Given:

Beam ABC is considered to be rigid. It is supported by pin-ended wires AE and CD, as shown Wire AE is made of aluminum (E=10000 ksi) and has a diameter of 0.2 inches. Wire CD is made of steel (E=30000 ksi) and has a diameter of 0.5 inches. With the load applied, it is known that the wires remain elastic (stresses are below yield)

A C

1 kip

200 in.

D

100 in. 100 in.

B

E

300 in.





6. (26 points). Wood has radically different properties when loads are parallel to the grain versus perpendicular to the grain, as shown:

Given: A 5/8-in.-diameter Wooden rod AB is fitted into a round hole near end C of the wooden member CD, at a distance of 3” from the center of the hole to the edge C. Determine the maximum force P that may be applied without either:

A). Failing the 5/8”-diameter wooden rods in shear, or B). Tearing out the dashed area.

When shear is parallel to grain, it fails at 90psi

Wood Grain

When shear is perpendicular to grain, it fails at 900psi

Wood Grain

P/2

P/2

P

3”





1. (4 points) TRUE or FALSE. The stress-strain behavior of all engineering materials is consistent with Hooke’s Law.

2. (4 points) What is the typical tensile strength of ordinary structural steel, such as that tested in lab? (circle the closest answer):

a. 50 psi b. 500 psi c. 5000 psi d. 50000 psi

3. (4 points) For the stress-strain curves below, circle the correct statement. a. Material 1 has greater toughness, greater elastic modulus, greater ultimate stress u, and greater yield stress y than

Material 2. b. Material 1 has less toughness, lower elastic modulus, lower ultimate stress u, and lower yield stress y than

Material 2. c. Material 1 has greater toughness, lower elastic modulus, lower ultimate stress u, and lower yield stress y than

Material 2. d. Material 1 has less toughness, lower elastic modulus, higher ultimate stress u, and lower yield stress y than

Material 2. e. Material 1 has greater toughness, lower elastic modulus, higher ultimate stress u, and lower yield stress y than

Material 2.

4. (4 points). Which material has a higher Modulus of Elasticity, Concrete or Steel? (circle the correct answer)

a. Concrete b. Steel

5. (4 points). Which material has a higher Modulus of Elasticity, Aluminum (such as 6061 alloy) or Steel? (circle the correct answer)

a. Aluminum (such as 6061 alloy) b. Steel

Stress, (psi)

Strain, , (in/in)

1

2

rupture rupture





1. (25 points) Determine the shear modulus G for the material below. Given: A 100mm-thick sample of the material below (hence, the material’s dimensions are 100mm x 200mm x 150mm) is subjected to a shearing force of 30 kN, as shown, causing the material to distort in shear, moving from its initial position, indicated by the solid lines, to its final position, indicated by the dotted lines.

30 kN

30 kN



2. (25 points) Determine the elastic modulus, yield strength, ultimate strength, maximum strain, and toughness for the following engineering material and plot its stress-strain curve on the graph paper below. Given: The material is a 4”x 4” block that was tested in compression, recording load and deformations over its 8-inch length. Plot compressive stress and compressive strain as positive.

Load (lbs) Deformation (inches)0 0.00

480000 0.01480000 0.10640000 0.20

8”

Evenly distributed compressive load on 4”x4” cross-section

4”

4”

Stress (psi)

Strain (in/in)





3. (30 points) Determine the force P. Given: Position B moves 0.5 inches to the right, due to force P. Rigid pole BC is supported by a pin at C and a steel wire (E=29000 ksi) at point B. The diameter of the wire is 0.2 inches.

P





1. (4 points) Rank the following materials in order of INCREASING elastic stiffness from 1 (lowest elastic stiffness) to 4 (highest elastic stiffness).

_____ Typical Aluminum Alloy (such as the 6061 alloy tested in lab)

_____ Typical Concrete (such as that tested in lab)

_____ Structural Steel (such as that tested in lab)

_____ Typical Wood (such as the Southern Yellow Pine tested in lab)

2. (2 points) Based on the laboratory testing, circle the material that is more brittle:

STRUCTURAL STEEL or ALUMINUM ALLOY (6061)

3. (3 points). Circle the closest answer a. The yield strength of structural steel is about 10 times larger than the yield strength of aluminum alloy (6061).

b. The yield strength of structural steel is about the same as the yield strength of aluminum alloy (6061).

c. The yield strength of aluminum alloy (6061) is about 10 times larger than the yield strength of structural steel.

d. The yield strength of structural steel is about 3 times larger than the yield strength of aluminum alloy (6061).

4. (3 points). Circle the closest answer a. The elastic modulus of typical concrete is about 3 times larger than the elastic modulus of typical wood.

b. The elastic modulus of typical concrete is about the same as the elastic modulus of typical wood.

c. The elastic modulus of typical wood is about 3 times larger than the elastic modulus of typical concrete.

d. The elastic moduli of typical concrete and typical wood were not determined in lab.

5. (4 points). Circle the correct answer, based on the materials tested in lab: a. Structural steel has greater elastic strain than aluminum alloy, but lesser plastic strain than aluminum alloy.

b. Structural steel has lesser elastic strain than aluminum alloy and lesser plastic strain than aluminum alloy.

c. Structural steel has lesser elastic strain than aluminum alloy, but greater plastic strain than aluminum alloy.

d. Structural steel has greater elastic strain than aluminum alloy and greater plastic strain than aluminum alloy.

6. (4 points). Gold is the most ductile metal. It has an ultimate tensile strength of about 200MPa. Estimate its ultimate shear strength:





7. (40 points). The jib crane is pinned at A and supports the 900-lb force shown. Beam AC is considered rigid. Pin-ended bar BC has a diameter of ½”. When the 900-lb load is applied, position C deforms downward by 0.153 inches. Determine the elastic modulus E of rod BC. BE CAREFUL WITH UNITS (Feet, inches, lbs, kips).

8. (10 points). Consider the previous jib crane. If the diameter of Pin B is ¼”, determine the shear stress in the pin, due to the

loading.

900-lb

12-ft

8-ft

9-ft

Connection Detail at Pin B





9. (30 points). A circular bar had an initial diameter of ½” and a length of 10 inches. After applying a tensile force P=5.88 kips, the bar was found to have a diameter of 0.499333 inches and a length of 10.040 inches. Determine elastic modulus, the shear modulus, and the Poisson’s ratio.

10”

½” diameter P=5.88 kips



The following questions are based upon your lab experience: 1. (3 points). Which material is tougher (circle one)?

a. Structural Steel b. Aluminum – 6061 Alloy

2. (3 points) Structural Steel is stiffer than Wood (Southern Yellow Pine, tested with the loading parallel to the grain) by about

what factor (circle the closest answer. Assume one digit of precision)? a. About 1 to 2 b. About 2 to 5 c. About 5 to 10 d. About 10 to 50 e. About 50 to 100

3. (3 points) TRUE or FALSE. Concrete is stiffer than Structural Steel

4. (3 points) TRUE or FALSE. Ordinary Strength Concrete is stronger than Wood (Southern Yellow Pine), in compression.

5. (3 points) TRUE or FALSE. Aluminum is stiffer than Structural Steel.

6. (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.

7. (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.

Stress, (psi)

Strain, , (in/in)

1

2

rupture rupture

Figure 1





8. (29 points). A metal tension specimen with a diameter of 0.500-in. was tested to failure while measuring its deformation over a 2.00-in. gage length, resulting in the data, below. A two-bar pin-ended truss is made using the same metal from the tension test, but with 1.500-in diameter bars. Determine the vertical movement of point B due to the 84-kip vertical force at B. Note: graph paper is attached.

Test Specimen

Load (kips)Deformation

(inches)

0.000 0.00001.963 0.00203.926 0.00405.889 0.00607.852 0.00807.852 0.08008.834 0.16009.815 0.2800

84 kips

A B

C

100-in.

100-in.







9. (20 points) Two 1”x3”x6” rubber blocks are bonded to rigid supports and to rigid steel plate AB. When 1 kip is applied to

the plate, it moves by = 0.1”. Determine the shear modulus of elasticity, G, for the rubber. The material is elastic.

1 in.

1 in.

3 in.

6 in.

1 kip

FINAL ANSWER: G = _______________ ksi





10. (31 points) Given: Rigid beam AB supports a uniformly-distributed load w = 2 kips/ft. Rope BC has a diameter of ¼”. If the loading causes position B to go downward by 1”, determine the Modulus of Elasticity E for the rope. BE CAREFUL WITH UNITS (1 foot = 12 inches). The material is elastic.

A B

C

w = 2 kips/ft

8 ft.

6 ft.

FINAL ANSWER: E = _______________ ksi





1. (20 points) Two 1”x3”x6” rubber blocks are bonded to rigid supports and to rigid steel plate AB. The shear modulus of

elasticity for the rubber is G = 0.200 ksi. When 1 kip is applied to the plate, it moves by . Determine this movement . The material is elastic.

1 in.

1 in.

3 in.

6 in.

1 kip

FINAL ANSWER:

= _______________ inches





1. (35 points) A game of tug-of war is devised with a rope that is 300” long when it is unloaded. The rope has a diameter of ½” and

E=200000 psi (= 200 ksi). The teams are arranged over the 100-inch lengths on the left and right ends of the rope with no applied forces along the middle 100-inches. The strongest people are placed on the ends, while the weakest people are placed towards the middle of the rope; consequently, the applied force distribution varies linearly from zero to its maximum value at the ends.

Determine the total length of the rope if it is known that the force in the rope is 1000-lbs in the middle and the condition is static.

100” 100” 100”

Linear increasing force distribution

The Tug-of-War Problem 300” long rope ½” diameter E = 200000 psi Known: 1000 lb internal force in middle What is final length?

Linear increasing force distribution





1. (40 points). A concrete pile with a circular cross-section is embedded in the soil. It is known that the frictional resistance of the soil varies linearly with a function f(x) = 0.01x (units of kips, inches). Hence, the frictional resistance is 5 kips/inch at point A. Determine:

A. Force P B. The change in length of AB.

Given: The pile is known to be elastic. Point B does not move. P is resisted by frictional forces, exclusively (the end of the pile resists no forces). The cross-sectional area of the pile A = 100 in2 and E = 3000 ksi

Ground

P

500 inches

Concrete Pile

B

A

x

Frictional resistance, f(x) = 0.01x (kips/inch





1. (20 points). Determine the internal axial force at a point midway between A and B. Given: Circular concrete pile is embedded in the soil. The pile is 400-inches long and is subjected to a vertical load at point A of 50 kips, directed downward. The vertical force is resisted by a distributed frictional force f(x) that varies linearly from 0 kips/inch at the bottom to fmax at the top.

Ground

50 kips

400 inches

Concrete Pile

Frictional forces increasing linearly (zero kips/inch at bottom, maximum

on top).

B

A





1. (35 points). Determine the vertical displacement of point B. Given: Both members have area A=1in2 and E=500ksi (a plastic material). Connections are pins. Materials are elastic.

6 kip 40 inches

30 inches

A

B

C

40 inches

FINAL ANSWER: Vertical displacement at B, B = __________inches



1. (35 points). Determine the vertical displacement of point B. Given: Both members have area A=1in2 and E=500ksi (a plastic material). Connections are pins. Materials are elastic.

6 kip 40 inches

30 inches

A

B

C

40 inches



2. (25 points). A ½” diameter steel (E=30000ksi) anchor bolt is embedded in concrete. When the upward load P is applied, the wedge-shaped base of the anchor resists a force of 1 kip, while the constant shear stress between the concrete and the 8-inch-long bolt is 0.500 ksi. Determine the extension of the bolt length AB. Materials are elastic.

A

B

8”

P

1 kip Resisted by

Wedge

Constant Shear Stress

Concrete

FINAL ANSWER: Extension, AB = __________inches



2. (25 points). A ½” diameter steel (E=30000ksi) anchor bolt is embedded in concrete. When the upward load P is applied, the

wedge-shaped base of the anchor resists a force of 1 kip, while the constant shear stress between the concrete and the 8-inch-long bolt is 0.500 ksi. Determine the extension of the bolt length AB. Materials are elastic.

A

B

8”

P

1 kip Resisted by

Wedge

Constant Shear Stress

Concrete



1. (35 points). Determine the horizontal displacement of point B.

Given: Both members have area A=1in2 and E=500ksi (a plastic material). Connections are pins. Materials are elastic.

8 kip

30 inches

A

B

C

40 inches

30 inches

FINAL ANSWER: Horizontal displacement at B, B = __________inches



1. (35 points). Determine the horizontal displacement of point B.

Given: Both members have area A=1in2 and E=500ksi (a plastic material). Connections are pins. Materials are elastic.

8 kip

30 inches

A

B

C

40 inches

30 inches

Documents

XAM SAMPLES (FROM PAST EXAMS - Sites at … · ES230 2017 – Sample Exam (past exams) for Exam 2 Material Page 2 of 44 This is a compilation of many past exams (some of these were