Exam 3

Please put your answers in the following table.

1

2

3

4

5

6

7

8

9

10

1. An element is cut by an oblique plane with a normal  at an angle  counterclockwise from the  axis. If , , , what is the distribution of shear stress?

A.              B.

C.              D.

2. For the above problem, which of the following statements is not true about the first principle shear stress ?     

A.  The smaller is the mean of , the smaller is the mean of

C.  The larger is the standard deviation of , the larger is the standard deviation of

D.  The larger is the standard deviation of , the smaller is the standard deviation of

D.   is not normally distributed

3. A stress element is subjected to two-dimensional stress as shown in the figure. The Poisson’s ratio is  and the modulus of elasticity is . If  and , determine the mean and standard deviation of the axial strain .

A. ,

B. ,

C. ,

D. ,

4. For problem 3, if the length of the element is  and the maximum allowable axial elongation is , determine the probability of failure.

A.                       B.                           C.                             D.

5. A concentrated load  is applied to a beam with a rectangular cross-section as shown in the figure. The width and height of beam are  and, respectively. And the length of the beam is . What is the distribution of the maximum bending stress?

A.                 B.

C.              D.

6. For the above problem, if the allowable bending stress is , what is the reliability of the beam?

A.                        B.               C.                             D.

7. Two torques are applied to a round shaft as shown in the figure. The diameter of the shaft is . And the modulus of rigidity is  If  and , what is the distribution of the angle of twist at ?

A.              B.

C.              D.

8. For the above problem, if the allowable angle of twist is , determine the probability of failure of the shaft.

A.                       B.                     C.                          D.

9. A shaft is subjected to a torque . If the shaft speed is 2500 rev/min, what is the distribution of the power that the shaft can transmit?

A. ,

B. ,

C. ,

D. ,

10. A force  is applied to a truss as shown in the figure. The rod  has a round cross-section with a dimeter of . If the yield stress of rod  is , determine the reliability of rod .

A.                       B.                  C.                          D.