BLDG $2014-$ Assignment $9$

Why are there minimum values for clear cover and spacing when considering the placement of reinforcing bars in concrete?

An interior beam with a rectangular cross section $450mm$ in height and $250mm$ in width is to be reinforced with $15M$ bars. The concrete has a compressive strength of $30$MPa and the steel has a tensile strength of $400$MPa. What are the maximum and minimum number of bars that could be used before risking brittle fracture? Assume one layer of reinforcement for this question. $($Hint: Find max and min area of reinforcement first.$)$

If $6$ bars and an aggregate size of $25mm$ is used for question $2,$ will they need to be divided into two layers of reinforcing? $($show your work$)$ If so$,$ will two layers be enough? $($Hint: consider min cover and spacing.$)$

What is the maximum bending moment that can be carried by the beam from question $2$ with the reinforcement placement you determined in question $3?$