Lecture 3

Question 1

In this lecture we will look at:
• the maximum and minimum amounts of
reinforcement that are required for a concrete beam
in bending
• How to overcome the limitation of maximum
reinforcement by doubly reinforcing a concrete beam

Answer 1

.

Question 2

Maximum reinforcement

Answer 2

Steel is ductile and concrete is brittle, this is why we want the reinforcement to yield before the concrete crushes.

Question 3

What happens if our beam is too heavily reinforced

Answer 3

The beam will have less rotation which will cause the beam to lose its ductility(ability to deform without losing toughness)) which will cause it to collapse

Question 4

What is the recommenced depth?

Answer 4

you are strongly advised to limit the amount of
reinforcement so that the depth to the neutral axis ≤ 0.45d. This
will ensure our beam is economic, will maintain flexibility in the
design, but most importantly it will enable us to sleep at night
because our beam will be ductile and therefore our structural
system will have reserve capacity

Question 5

Calculations for maximum amount of reinforcement a beam is allowed to have

Answer 5

1. FC
2. FS
3. Fs=Fc
4. Substitute
5. Rearrange for x
6. x=0.45d
7. Find moments around steel
8. rearrange for Asmax(%)

Question 6

The procedure to design a beam from scratch

Answer 6

1. Choose a beam depth and width(d=span/12)(b=d/2)
2. Find area of steel
3. choose a bar diameter and number of bars to
   approximately match this value substitute into the exact
   formula to calculate MRd
4. check that MRd > MEd
5. Check reinforcement ratio

Question 7

Minimum reinforcement

Answer 7

• Since concrete has a small tensile strength when exposed to it, it cracks and the reinforcement takes the load.
• If there is not enough reinforcement then the structure will fracture.
• To avoid this, we have minimum reinforcements.
• This also helps avoid large cracks.

Question 8

Formula for minimum reinforcement

Answer 8

Asmin=fctm/Fyk0.26bd

Fctm= Mean axial tensile strength of Concrete

Fyk= Chracteristic yeild stress

Question 9

Reinforcement ratio

Answer 9

This is used to check if the reinforcement is suitable

Question 10

Ratio:

Answer 10

p=As/bd

Question 11

Doubly reinforcement

Answer 11

• Sometimes you will need more reinforcement than the maximum amount allows
• In this cause you need to make the beam deeper but this is not always possible
• In this case you add compression reinforcement, but this is a last resort

Question 12

Doubly reinforcement

Answer 12

• Sometimes you will need more reinforcement than the maximum amount allows
• In this cause you need to make the beam deeper but this is not always possible
• In this case you add compression reinforcement, but this is a last resort.