T2: Plastic Analysis of Slabs

Question 1

What are the two main methods of plastic analysis?

Answer 1

Yield Line analysis
- Johansen

Strip method of analysis
- Hillerborg

Question 2

What is Johansen’s YL method?

Answer 2

An upper bound (or kinematic) method of analysis

“If, for any assumed plastic failure mechanism, the external work done by the applied loads is equal to the internal work done by the plastic hinges, then the load is either equal to or greater than the load at failure (or collapse)”

Question 3

Where are the hogging yield lines located?

Answer 3

Along the continuous edges

Question 4

Which edges are simply supported, and which are continuous

Answer 4

xxx = continuous
/// = simply

Question 5

What are the five general rules for yield line analysis?

Answer 5

1. Axes of rotation lie along supports (hogging) and pass over columns
2. Yield lines are straight
3. Yield lines between adjacent rigid sections must pass through the point of intersection of the axes of rotation of those regions
4. Yield lines must end at a slab boundary
5. Continuous supports repel yield lines; simple supports attract them

Question 6

Which support type attracts yield lines, and which repels them?

Answer 6

Simply supported = attracts
Continuous = repels

Question 7

What does this equation represent?

Answer 7

Moment capacity from a given area of steel (ULS)

Question 8

Which value of ‘m’ needs to be determined, and why?

Answer 8

The highest

Because M_max => largest steel area

Can predict the load at which the slab will buckle and collapse