Factored moment resistance of a concrete beam

[steve321]

hi,

this is a sample question.. I'm having trouble with part a)

google has led me to believe that the equation i need for factored moment resistance is

Mr = fr*As*fy (d - a / 2)

fr is the factor, and i think it's .85 for reinforced steel according to those CSA guides

As is the area of the steel reinforcement. according to the answer, it is 900mm2. no idea where this comes from.

fy is 400

d is the depth from the most compressed part to centroid of the reinforcement (i think), which is 600 - 40 - 11 - 1/2diameter of steel.. again, I'm told the diameter is 20mm but am not sure how to get this from the diagram.

a is the depth of equivalent rectangular stress block, and this is also where i start getting a little confused. why do you need to know this anyway? how does an equivalent material factor into what I'm doing right now? and how do you solve for a?

in the answer, a is replaced with B1 - c, and c is supposedly the distance to the neutral axis (i think).. it gets a little confusing to me at this point.

if anyone can clear up any of these points i'd appreciate it.

thanks

 

[steve321]

anyone?