Questions $117$ are focused on developing a mix design for concrete to be used as a box

culvert. The designer has determined the design strength to be $4,200$ psi. It is expected that the

culvert will carry only fresh water and will not be exposed to freeze$/$thaw$.$ The structural cross

section is shown in Figure $1.$

Figure $1.$ Concrete Box Culvert Dimensions $($Not To Scale$).$

Answer the following questions with regard to the above scenario. State any assumptions or

tables from the notes that you use in answering each question.

$1.$ Assuming that $28-$day compressive strength test data are available from $20$ samples with a

standard deviation of $200$ psi, what should the measured average strength exceed to meet the

culvert strength requirement?

$2.$ If there were no compressive strength test data available, what should the measured average

compressive strength of a new mix exceed to meet the strength requirement?

Note: Use your answer from question $2$ where fcr$$ is needed for the remaining problems.

$3.$ What is the required water$-$cement ratio for this mixture?

$4.$ What is the maximum size aggregate that should be used?

$5.$ The available aggregate has a fineness modulus of $2\mathrm{.}80.$ What is the proportion of coarse

aggregate to unit volume of concrete that should be used?

$6.$ What is the recommended range of slump for this type of structure. Justify your answer.

What is the approximate amount of mixing water $($lb$/$yd$3$ concrete$)$ required for this mixture?

$7.$ What is the approximate amount of entrapped air for this mixture?

$8.$ What is the minimum cement content required for this mixture?

$9.$ For a cubic yard of concrete, what is the weight and volume of dry coarse aggregate?

Assume the unit weight of the coarse aggregate is $104$ pcf and the specific gravity is $2\mathrm{.}580.$

$10.$ For a cubic yard of concrete, what is the weight and volume of water?

$3$ ft

$4$ in$.$