Civil Engineering Reference
In-Depth Information
Figure 1.3
Space truss model of a concrete beam with longitudinal and hoop steel resisting torsional
forces after cracking, the transverse steel bars in the web would carry tensile forces and the
diagonal concrete struts would resist the compressive forces. The transverse steel, therefore,
serves as the tensile web members in the truss while the diagonal concrete struts become the
diagonal compression web members.
The plane truss model for beams was extended to treat members subjected to torsion as
shown in Figure 1.3 (Rausch, 1929). In Rausch's concept, a torsional member is idealized as
a space truss formed by connecting a series of component plane trusses capable of resisting
shear action. The circulatory shear stresses, developed in the cross-section of the space truss,
form an internal torsional moment capable of resisting the applied torsional moment.
Although the truss models developed by Ritter (1899), M orsch (1902) and Rausch (1929)
provided a clear concept of how reinforced concrete resists shear and torsion, these models
treated the concrete struts and steel ties as lines without cross-sectional dimensions. Con-
sequently, these models did not allow us to treat the beams as a continuous material and
to calculate the stresses and strains in the beam. In other words, the precious knowledge
developed by the scientific discipline of mechanics of materials could not be applied.
In this topic, only a brief, but conceptual, introduction of the struts-and-ties model will be
given in Section 1.4.
1.3.2.4 Equilibrium (Plasticity) Truss Model
In the 1960s the truss model of members with dimensionless linear elements to resist shear
and torsion was replaced by members made up of more realistic 2-D elements. By treating
a 2-D element after cracking as a truss made up of compression concrete struts and tensile
steel ties, Nielson (1967) and Lampert and Thurlimann (1968, 1969) derived three equilibrium
