Chapter 20, Problem 20.1P

(a)

To determine

Whether the statement “Higher the variability, higher is the coefficient of variation” is true or false.

Answer to Problem 20.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

Write the equation of coefficient of variation.

$\text{Coefficient of variation}\left(\%\right)=\frac{\text{Standard deviation}}{\text{Mean}}\times 100$ (1)

• From Equation (1), the coefficient of variation is directly proportional to the standard deviation.
• The higher variability in data implies higher standard deviation. Hence, the higher standard deviation gives a higher percentage of coefficient of variation.

Therefore, the statement is $\underset{\_}{\text{true}}$.

(b)

To determine

Whether the statement “Coefficient of variation cannot exceed 100%” is true or false.

Answer to Problem 20.1P

The given statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

From Equation (1):

The coefficient of variation exceeds 100% when the standard deviation is more than the mean. Hence, the coefficient of variation exceeds 100% is possible.

Therefore, the given statement is $\underset{\_}{\text{false}}$.

(c)

To determine

Whether the statement “The loads used in LRFD are greater than those used in ASD” is true or false.

Answer to Problem 20.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

• The allowable strength of the member or component is less than the full strength of member or component.
• In LRFD method, the loads are compared to the full strength of the member; whereas in ASD method, the loads are compared to the allowable strength of the member. Hence, the loads in LRFD method are usually greater than the ASD method.

Therefore, the given statement is $\underset{\_}{\text{true}}$.

(d)

To determine

Whether the statement “The load/resistance factors used for foundations are different from retaining walls” is true or false.

Answer to Problem 20.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

• The method for design of foundation is LRFD; while for retain wall, the standard method is used to design.
• Hence, the load/resistance factors for foundations and retaining walls are different.

Therefore, the statement is $\underset{\_}{\text{true}}$.

(e)

To determine

Whether the statement “The load factors in LRFD are generally greater than 1” is true or false.

Answer to Problem 20.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

• LRFD design method follows limit state of design approach, where no separate factor of safety is used.
• In the limit state design approach, generally, the loads and resistance factors are already adjusted by partial safety factors. In this design method, ultimate loads are compared to actual loads.
• Hence, the load factors are greater than 1 and resistance factors are less than 1.

Therefore, the given statement is $\underset{\_}{\text{true}}$.