Exam 2

Please put your answers in the following table.

1

2

3

4

5

6

7

8

9

10

1. A specimen of steel was tested in tension and loaded by an axial force . The yield strength of steel is . And the modulus of elasticity and modulus of rigidity are  and , respectively. Which of the following statements is true about the Poisson’s ratio ?

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

C.  The larger is , the larger is the mean of                 D.  is related to  and

2. For the above problem, which of the following statements is not true about the distribution of the resilience ?

A.   is normally distributed with

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

C.  The larger is , the larger is the mean of

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

3. A solid circular bar is twisted by a torque . The diameter and length of the bar are  and , respectively. Determine the mean and standard deviation of the maximum shear stress .

A. ,

B. ,

C. ,

D. ,

4. For the above problem, if the modulus of rigidity is , what is the mean and standard deviation of the angle of twist ?

A. ,

B. ,

C. ,

D. ,

5. For problem 3, if the allowable shear stress is , what is the probability of failure?

A.                        B.               C.                             D.

6. For problem 4, if the allowable angle of twist is , determine the reliability of the bar.

A.                        B.               C.                             D.

7. If , what is the distribution of the load acting on rod ?

A.              B.

C.             D.

8. For the above problem, if the maximum allowable load of rod  is , determine the probability of failure of the rod.

A.                   B.                           C.                                D.

9. A circular cross-section beam is cantilevered at  and subjected to a concentrated force  and an uniform load of . Determine the distribution of the bending moment at point .

A.              B.

C.              D.

10. For problem 9, if the diameter of the beam is  and the maximum allowable bending stress is , what is the reliability of the beam?

A.                       B.                           C.                          D.