Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
1
Lecture ten
Yield Line Method
To understand the yield line method, the concept of plastic hinge shall be defined first.
Any section in the frame member reaches its ultimate moment strength; it will behave
like hinge, where it cannot resist moment any more.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
2
The yield line method is used to find the ultimate load capacity of reinforced concrete
slabs, where the plastic hinges will be yield lines. It depends on estimation of the failure
mechanism of the slab of certain geometry and boundary conditions. Failure mechanism
is a pattern of yield lines form and cause the slab collapse.
Yield lines are cracks in reinforced concrete across which the reinforcement bars have
yielded and along which plastic rotation occurs. There are two types of yield lines:
positive, which occur due to positive moments and negative, which occur due to negative
moments near supports. The following symbols will be used to define the failure
mechanism:
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
3
To estimate a failure mechanism, the following rules shall be applied:
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
4
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
5
There are two methods to find the ultimate load capacity using the yield line method:
1- Virtual Work Method.
2- Equilibrium Method.
Virtual Work Method
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
6
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
7
Orthotropic and Isotropic Slabs
Slabs are usually reinforced in two perpendicular directions, so it may be classified into
two types:
Orthogonally reinforced slabs, where the moment resistances are different in
both directions.
Isotropically reinforced slabs, where the moment resistances are equal in both
directions.
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
8
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
9
Concrete Design Ali N. Attiyah, Ph.D.
Fourth Year 2015-2016
10
Example: