Reinforced Concrete Design / Reinforced-concrete slabs
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.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Checks needed for project use
- A concrete-design reviewer must check the stated first-generation clauses, National Annex choices, detailing rules and factor sets. Numerical agreement alone does not establish code compliance.
- Confirm adjacent orthogonal bar layers, reinforcement-ratio derivation, deductions for loads within the perimeter, beta applicability and the adopted first-generation coefficients/National Annex. Independently verify column-face and reinforced-zone limits, detailing, yield-line formula and competing mechanisms.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
Punching shear can cause a brittle local loss of support at a flat-slab column. If the remaining structure cannot redistribute the load, the failure can spread. The design needs both punching checks and appropriate integrity detailing.
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)
Load transfer at a flat-slab column
A flat slab transfers load directly to columns without downstand beams. Its flat soffit can simplify formwork and service routes and reduce structural floor depth.
The slab must transfer the column reaction through its own thickness. This concentrated load transfer can make punching shear critical around the column. In a beam-and-slab floor, beams collect the slab load and transfer it to the columns through a deeper member.
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
- Passing the column-face limit is necessary but not sufficient; check reinforcement effectiveness, detailing and every relevant perimeter
- 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