Module 9 · Lesson 9.2
Flat slabs, punching shear and yield lines
The failure that takes buildings down, and the analysis method that finds more capacity than there is if you let it.
Why this matters
Punching shear at a flat-slab column is the most dangerous failure mode in ordinary building structures. It is brittle, it is local, and it is progressive — one column punching through drops the slab onto the floor below, which then punches at its own columns. Several buildings have been lost this way. It deserves more attention than its half-page in most textbooks.
By the end of this lesson you should be able to
- Explain why a flat slab is efficient and what it gives up
- Check punching shear on the control perimeter
- Explain why punching is progressive, and what that implies for detailing
- State what yield-line analysis is and why being an upper bound matters
What you should already know
- Shear as diagonal tension (Module 5)
- Punching perimeter and the empirical resistance (Module 5)
- One-way and two-way action (previous lesson)
The flat slab bargain
A flat slab has no beams. The soffit is flat, which means shallower floors, simpler formwork, easier services and faster construction. On a large building that is worth a great deal.
What it gives up is the beam's ability to collect load gradually. In a beam-and-slab floor, the slab hands its load to a beam over several metres, and the beam hands it to the column over its own depth. In a flat slab the whole panel load arrives at the column through the slab's own thickness, over a perimeter a few hundred millimetres across.
The shear stress at a flat-slab column is the highest stress anywhere in an ordinary building frame, and it is concentrated in the one place where the slab is thinnest relative to the load it is carrying.
That is the bargain, and punching shear is the price.
Worked example
Punching shear at an internal flat-slab column
Given
- 250 mm flat slab, C30/37, 30 mm cover, H20 bars
- Internal column 400 mm × 400 mm
- Design shear transferred to the column VEd = 850 kN
- Flexural reinforcement ratio, mean of the two directions, ρ = 0.8%
Find
Whether punching reinforcement is required.
Assumptions
- β = 1.15 for an internal column, allowing for the moment transferred
- Control perimeter at 2d from the column face
- The empirical resistance expression, whose coefficient is nationally determined
Yield lines, and the direction of the error
A slab does not fail when the first section reaches its moment of resistance. It yields there, redistributes, and goes on carrying load until enough yield lines have formed to turn it into a mechanism.
Yield-line analysis finds the load at which that happens, by assuming a collapse mechanism and equating external work to internal work. For a simply supported rectangular slab with isotropic reinforcement m per unit width:
w = 24m / (Ls² [√(3 + (Ls/Ll)²) − Ls/Ll]²)
which reduces to w = 24m/L² for a square slab.
The critical property is that yield-line analysis is an upper-bound method. Any assumed mechanism gives a collapse load at or above the true one. Assuming a mechanism is equivalent to imposing a constraint the real slab does not have, and constraint can only make the structure appear stronger.
Practice
A 6.0 m square slab is simply supported and reinforced isotropically with m = 25 kNm/m. What uniform load does yield-line analysis predict at collapse, in kN/m²?
Practice
A punching check gives vEd = 0.95 N/mm² and vRd,c = 0.62 N/mm². By what factor is the demand above the resistance?
Practice
What is the length of the basic control perimeter at 2d around a 300 mm square column in a slab with d = 200 mm, in mm?
Check yourself
Bottom reinforcement is required to run continuously through a flat-slab column. What is it for?
Summary
- A flat slab trades beam depth for a severe shear concentration at the columns
- Punching is brittle, local and progressive — one column can take a building down
- Check vEd on the 2d perimeter, and separately the face stress against vRd,max
- Below vRd,max reinforcement is a valid fix; above it, only more concrete works
- Integrity bottom steel through the column appears in no calculation and is essential
- Yield-line analysis is an UPPER bound: an assumed mechanism overestimates capacity
- It found 44% less steel than the elastic model for the same slab — use with judgement
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint