Factored moment resistance of a concrete beam

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SUMMARY

The discussion centers on calculating the factored moment resistance (Mr) of a concrete beam using the equation Mr = fr * As * fy * (d - a / 2). The factor fr is established as 0.85 for reinforced steel according to CSA guidelines. The area of steel reinforcement (As) is specified as 900 mm², with fy being 400 MPa. The depth (d) is calculated as 600 mm minus the effective depth adjustments, while the equivalent rectangular stress block depth (a) and the neutral axis distance (c) are also critical components in the calculation process.

PREREQUISITES
  • Understanding of reinforced concrete design principles
  • Familiarity with CSA standards for concrete structures
  • Knowledge of stress block concepts in structural engineering
  • Ability to perform calculations involving moment resistance
NEXT STEPS
  • Study the CSA A23.3-14 standard for reinforced concrete design
  • Learn about the equivalent rectangular stress block method in concrete analysis
  • Explore the calculation of neutral axis depth in reinforced beams
  • Review examples of factored moment resistance calculations in structural engineering textbooks
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in concrete design and analysis will benefit from this discussion, particularly those focused on moment resistance calculations in reinforced concrete beams.

steve321
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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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