Chapter 3 - Flexural Design of RC Beams

Question 1

What is K and what is the equation for it? (State what each term means)

Answer 1

K is the normalised value of design moment resistance. It is a measure of if a section is over or under-reinforced.

K = MRd/(fckbd^2)

Where:
MRd = maximum bending moment resistance of a section.
fck = cylindrical characteristic strength of concrete.
b = wdith of the section.
d = effective depth of the section.

Question 2

What is K’ and what does it mean if K > K’ or K < K’ ?

Answer 2

K’ is the normalised moment resistance of a balanced section.

If K < K’, the section is under-reinforced.
If K > K’, the section is over-reinforced and requires compression steel.

Question 3

What are the 3 possible K’ values depending on x/d limitations?

Answer 3

When x/d = 0.617, K’ = 0.211.

When x/d = 0.6, K’ = 0.207.

When x/d = 0.45, K’ = 0.167.

Question 4

What is the design process for a single reinforced concrete beam?

Answer 4

1. Find the K value for an applied moment (MEd).
2. Confirm the section is under-reinforced i.e. K < K’.
3. Find the lever arm (z) using your K value in the lever arm equation.
4. Use MEd = Fst * z to work out the force in the tension steel and therefore the area of steel required to resist the applied moment.

Question 5

How can over-reinforced beams be changed to become under-reinforced?

Answer 5

They can either have compression reinforcement added or the section depth increased.

Question 6

What is the design process for a double reinforced concrete beam?

Answer 6

1. Find the K value for an applied moment (MEd).
2. Confirm the section is over-reinforced i.e. K > K’.
3. Calculate the moment resistance of a balanced section (MRd,bal) using the eqaution: MRd,bal = K’bd^2*fck.
4. Calculate the area of tension steel to resist the balanced section moment (As,bal).
5. Calculate the moment resisted by the compression steel (M’) where M’ = MEd - MRd,bal.
6. Use M’ = Fsc*z2 (where z2 is the lever arm between the tension and compression steel) to calculate the force in the compression steel.
7. Calculate the area of compression steel required (As2).
8. Find the total area of tension steel required (As). This is equal to the sum of As2 and As,bal.
9. Check the compression and tension steel have yielded.