ME 323: Mechanics of Materials Name Last quiz December 8, 2017 Table # For this quiz, you are presented with ten questions from a hypothetical ME 323 exam, along with answers that were provided by one student in the class. Unfortunately, all ten answers by the student are incorrect. As a grader for the exam, you are asked to provide a concise explanation to the student as to why each question is incorrect. You are to be graded on the quality of your explanation. Question 0 Problem: For the loading on the beam shown, determine the

maximum normal stress on the cross section shown for two values of Young’s modulus: i) E, and ii) 2E.

Student’s answer:

The student’s answer indicated that σ

max,ii= 2σ

max,i.

Why is that answer wrong? Question 1 Problem: For the beam shown loaded by its weight,

determine the deflection at end C, δC , for two values of beam length: i) L, and ii) 2L.

Student’s answer:

The student’s answer indicated that δC ,ii = 2δC ,i .

Why is that answer wrong? Question 2 Problem: The rod shown is made up of steel (a ductile

material). Determine the load P that will cause the member to fail.

Student’s answer:

The rod cannot fail due to this loading since ductile materials fail due to shear stress, and a rod with an axial load experiences only normal stress.

Why is that answer wrong?

C B

C B

P

τ

σx

y

σ x

τ xy

C B

C B

P

τ

σx

y

σ x

τ xy

C B

C B

P

τ

σx

y

σ x

τ xy

Question 3 Problem: For the stress state shown, draw Mohr’s circle.

Student’s answer:

The student’s Mohr’s circle is as shown.

Why is that answer wrong? Question 4 Problem: Consider the loaded truss shown. Member (1) is

made of steel. Determine the stress σ1 experienced in member (1) if member (2): i) is made up of steel, ii) is made up of aluminum.

Student’s answer:

The student’s answer indicated that σ1,i >σ1,ii .

Why is that answer wrong? Question 5 Problem: Consider the state of plane stress provided. The

material of the body experiencing this stress is ductile. Determine the factor of safety (FS) against failure using: i) maximum shear stress theory, and ii) maximum distortional energy theory.

Student’s answer:

The student’s answer indicated that FSi > FS ii .

Why is that answer wrong?

C B

C B

P

τ

σx

y

σ x

τ xy

C B

C B

P

τ

σx

y

σ x

τ xy

x

y

σ x

τ xy

L

2( )

1( )

2( )1( )

P

x

y

σ x

τ xy

L

2( )

1( )

2( )1( )

P

Question 6 Problem: Consider the truss shown. There are no applied

loads; however, the temperature of member (1) is increased with the temperature of (2) being held constant. Determine the stress in member (1), σ1 , if the length of member (1) is: i) L, and ii) 2L.

Student’s answer:

The student’s answer indicated that σ1,i <σ1,ii .

Why is that answer wrong? Question 7 Problem: Consider the clamped-free beam loaded as shown.

Make a sketch of the deflection of the beam.

Student’s answer:

Shown above.

Why is that answer wrong? Question 8 Problem: Consider shaft shown with axial force P and axial

torque T loadings. Draw the components of stress for the element at point “a” on the surface of the shaft.

Student’s answer:

As shown to the right.

Why is that answer wrong?

x

y

σ x

τ xy

L

2( )

1( )

2( )1( )

P

x

C B

P T

y

x

y

z x

C B

P T

y

x

y

z

x

C B

P T

y

x

y

z

a

Question 9 Problem: Consider the cantilevered beam with a point load

at end C. Determine the shear stress at point “a” on the beam for two values of point load: i) P, and ii) 2P.

Student’s answer:

The student’s answer indicated that τ

ii> τ

i.

Why is that answer wrong? Question 10 Problem: Consider columns (i) and (ii) shown for which we

will consider in-plane buckling (buckling about an axis perpendicular to the page). These columns have radii of gyration related by rii / ri = 2 .

Determine the critical buckling load Pcr for each column.

Student’s answer:

The student’s answer indicated that Pcr ,ii > Pcr ,i .

Why is that answer wrong? POST-QUIZ SURVEY- On a scale of 1-10, how effective was this quiz at identifying (or re-identifying) gaps in your knowledge of ME 323 concepts (1 = not useful, 10 = very useful)? 1 2 3 4 5 6 7 8 9 10 Do you think offering regular quizzes like this would improve your understanding and prevent you from making these common mistakes in the future? Yes or No

Additional comments/suggestions:

C B

a

P

L

(i)

P

L

(ii)

C B

a

P

L

(i)

P

L

(ii)