Chapter 1 – Yield Line Analysis
for slabs
Concrete materials and structures
chair.

Behavior of slabs loaded to failure in flexure
•
Four or more stages:
i.
Before cracking the slab acts as an elastic plate, and
for short time loads, the deformations, stresses and
strains can be predicted from an elastic analysis.
ii.
After cracking and before yielding of the
reinforcement, the slab no longer has a constant
stiffness, because the cracked regions have a lower
flexural stiffness, EI than the uncracked regions and
the slab is no longer isotropic because the crack
pattern may differ in the two directions.
2

Behavior of slabs loaded to failure in flexure
3
–
Although these conditions violate the assumptions in
elastic theory, tests indicate
that the elastic theory still
predicts the moments adequately. Generally normal
building slabs are partially cracked under service loads.
iii.
yielding of reinforcement eventually starts in one
or more region of high moment and spreads
through the slab as the moments are redistributed
from yielded regions to areas that are still elastic.
The progression of yielding through a slab fixed on
four edges is illustrated in Figure (next slide)

Behavior of slabs loaded to failure in flexure
4

Behavior of slabs loaded to failure in flexure
–
With further load, the regions of yielding known as yield
lines, divide the slab into a series of trapezoidal and
triangular elastic plates as shown in Figure (d) above. The
loads corresponding to this stage of loading can be estimated
by using
yield-line
analysis (plastic method analysis)
iv.
Although the yield lines divide the slab to form a
mechanism, the hinges jam with increased
deformation, and the slab forms a very flat
compression arch as shown in Figure (next slide)(avail
stiff support). This stage of loading usually is not
considered in design
5

Behavior of slabs loaded to failure in flexure
6

•
Yield line method is a plastic method of analysis
of slabs
•
A yield line analysis uses rigid plastic theory to
compute the failure loads corresponding to
given plastic moment resistance in various parts
of the slab
•
A yield line method is an
upper bound method
whereas
the strip method is
lower bound
method
.
Chapter 1 – Yield Line Analysis
for
slabs

•
Upper
bound
theorem
:
If,
for
a
small
increment of displacement, the internal work
done by the slab, assuming that the moment
at every plastic hinge is equal to the yield
moment and that boundary conditions are
satisfied, is equal to the external work done by
the given load for that same small increment
of displacement, then that load is an upper
bound of true carrying capacity.
Chapter 1 – Yield Line Analysis
for
slabs

•
Lower bound theorem
: If, for a given external
load, it is possible to find a distribution of
moments that satisfies equilibrium
requirements, with the moment not
exceeding
the yield moment at any location,
and if the boundary conditions are satisfied,
then the given load is
a lower bound of the
true carrying capacity.