04 Introduction To The Yield Line Method
04 Introduction To The Yield Line Method
04 Introduction To The Yield Line Method
Expended
External energy
expended by the
displacement of loads
(N x )
D
E = D boxing glove analogy
Dissipated
Internal energy
dissipated by the yield
lines rotating
(m x l
)
(N x )
(m x l
)
Similar
triangles
Small angles
L
2
L
max
max
max
(N x )
L
2
1
L
4
(m x l x )
m is the moment
Nb is the
of resistance
displacement
of the
of slab
the centroid
per metre
of length
the slab
(i.e.
region
kNm / m run)
l is the length of the yield line projected onto the axis of rotation.
is the angle of rotation
Summary of the
principles for yield line
theory
Collapse
occurs when yield lines form a mechanism.
1.
2. This mechanism divides the slab into rigid regions.
3. Since elastic deformations are neglected these rigid
regions remain as plane areas.
4. These plane areas rotate about their axes of rotation
located at their supports.
5. All deformation is concentrated within the yield lines: the
yield lines act as elongated plastic hinges.