Chapter 4 - Flexural Analysis & Design of RC Beams with Flanges

Question 1

What is the compressive stress disribution during flexure in a flanged RC beam?

Answer 1

Flexural compressive stress is higher at the webs and lower at the flanges.

Question 2

What is the equation for beff,i? (State what each term means)

Answer 2

beff,i = 0.2bi + 0.1l0 < 0.2lo and bi

Where:
bi = half the clear space between t-beam webs.
l0= the distance between points of zero moment for the section in question.

Question 3

What is the value of l0 for: simple-simple, simple-continous, continous-continous and free end?

Answer 3

Simple-simple = 1.0L
Simple-continous = 0.85L
Continous-continous = 0.7L
Free end = 1.15L

Question 4

Describe the analysis process of a T-beam to determine if the depth of the neutral axis is in the flange or web of the section for a positve bending moment.

Answer 4

1. Assume the neutral axis is within the concrete flange.
2. Use force equilibrium Fst = Fc to calculate the value of the neutral axis depth.
3. If the height of the flange (hf) > 0.8x, the neutral axis is in the flange of the section.
   If hf < 0.8x, the neutral axis is in the web of the section.

Question 5

Describe the analysis process of a t-beam when the depth of the neutral axis is within the concrete flange.

Answer 5

1. Calculate Fc using the efffective width of the flange (beff).
2. Calculate the lever arm between the tension steel and the compression force where z = d - 0.5hf.
3. Calculate the moment resitance of the section using MRd = Fstz = Fcz.

Question 6

Describe the analysis process of a t-beam when the depth of the neutral axis is within the concrete web.

Answer 6

1. Use equilibrium of forces where Fcw + Fcf = Fst to calculate the new depth of the neutral axis in the concrete web.
2. Calculate the moment resistance of the section using MRd = Fcw(d-0.4x) + Fcf(d - 0.5hf).

Question 7

Describe the design process of a t-beam?

Answer 7

1. Calculate K from the applied moment (MEd).
2. Use your K value to calculate the lever arm of the section. Therefore use z = d - 0.4x to calculate the value of 0.8x.
3. If 0.8x < hf, design the section a normal rectangular beam with width = beff.
   If 0.8x > hf, proceed with the next steps.
4. Find the compression force in the concrete flanges (Fcf) and multiply by the flange lever arm (zf) where zf = d - 0.5hf to get the moment resistance of the concrete flanges (Mcf).
5. Use MEd = Mcw + Mcf to obtain the moment resisted by the concrete web (Mcw).
6. Caluculate a K value for the moment resisted by the concrete web (Kw) and a lever arm (zw) using this value.
7. Divide Mcw by zw to obtain the compressive force in the concrete web.
8. Use Fst = Fcw + Fcf to obtain the force in the tension steel and use this to calculate the area of tensiom steel required.