Models for Simulating the Seismic Response of Concrete Structures - Dynamic Behavior of Concrete and Seismic Engineering - page 236

are concerned, introducing reinforcements relies on a partial pressure law that
implies non-sliding between steel and concrete [LAB 91]. Thus, inside each layer:

HH H

E b concrete modulus

steel concrete

E a steel modulus

E 1 CE CE a

b

a

a

b b

E homogenized (a + b) modulus

H 1 C H C H

inel .

a

inel concrete .

a

inel steel .

b b

steel area

H concrete inelastic strain

C

inel concrete .

a b

concrete area

H steel plastic strain

inel steel .

beam element

composite layers
(concrete + steel)

Figure 7.2. Principle of discretization by multi-layer beam elements

Following the same principle, multi-fiber discretization is more efficient,
because it makes it possible to study the behavior of structures, for slender elements
at least. We will present the principle behind writing this type of element more
thoroughly, based on a Timoshenko beam element with shear strains ([GUE 97],
[PEG 93]).

The shear and axial strains inside fiber i are written respectively as functions of
the general strains of the beam element and of the section geometry:

In 2D (multi-layer beams):

H H y M

x x i z

i

and