Factored moment resistance of a concrete beam

In summary, The equation for factored moment resistance is Mr = fr*As*fy (d - a / 2), where fr is the factor (0.85 for reinforced steel according to CSA guides), As is the area of the steel reinforcement (900mm2 in this case), fy is the yield strength (400), d is the depth from the most compressed part to the centroid of the reinforcement (600 - 40 - 11 - 1/2 diameter of steel, which is 20mm in this case), and a is the depth of the equivalent rectangular stress block. In order to solve for a, it needs to be replaced with B1 - c, where c is the distance to the neutral axis. This
  • #1
steve321
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28mi5ab.png


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
 
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  • #2
anyone?
 

1. What is the definition of factored moment resistance?

Factored moment resistance refers to the maximum bending moment that a concrete beam can withstand before it fails.

2. How is factored moment resistance calculated?

Factored moment resistance is calculated using the formula MR = φMn, where MR is the factored moment resistance, φ is the resistance factor, and Mn is the nominal moment resistance.

3. What factors affect the factored moment resistance of a concrete beam?

The factored moment resistance of a concrete beam is affected by various factors such as the type and strength of concrete, reinforcement type and spacing, beam dimensions, and loading conditions.

4. How does the factored moment resistance of a concrete beam compare to its nominal moment resistance?

The factored moment resistance is typically lower than the nominal moment resistance, as it takes into account safety factors and potential failure modes of the beam.

5. Why is it important to consider the factored moment resistance of a concrete beam?

Considering the factored moment resistance is crucial in designing safe and structurally sound concrete beams, as it ensures that the beam can support the expected loads without failing.

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