Introduction to the yield line method

Dr Gareth Whittleston

Yield line theory – work method

E = D

Expended = Dissipated

External energy expended by the

displacement of loads

Internal energy dissipated by the yield

lines rotating =

Σ (N x δ) = Σ (m x l x θ)

E = D boxing glove analogy

Simply supported, one-way-spanning slab

b

L

δmax

L2

L4

δmax δ1

L2

δmax θ

Σ (N x δ) = Σ (m x l x θ)

Σ (N x δ) Σ (N x δ)Nb δ is the displacement of the centroid of the slab region

Σ (N x δ)

Similar triangles

Σ (m x l x θ) Σ (m x l x θ)m is the moment of resistance of the slab per metre length (i.e. kNm / m run)

l is the length of the yield line projected onto the axis of rotation.

Σ (m x l x θ) Σ (m x l x θ)

θ is the angle of rotation

Small angles

=

Summary of the principles for yield line theory

1. Collapse occurs when yield lines form a mechanism.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.