F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

42 Properties of structural concrete
m
8
~E! ,~
~-o-,
1·2 / t,2
1·0 --- - - - - ---,(
0·8
0·6
r/
/I
~
Tension
m
Compression
Fig. 2.5-10 Biaxial strength of concrete [26]
(c)
Combined compression and tension may appreciably reduce both the
tensile and compressive stresses at failure.
Many designers neglect the interaction of / 1 and f 2 in a biaxial state, and
assume for simplicity that failure occurs whenever a principal stress reaches
the uniaxial compressive strength f~ or the uniaxial tensile strength, which
is often taken as O.lf~. This failure criterion, based on uniaxial strengths, is
represented by the dotted square in Fig. 2.5-10: it can be unsafe for
combined compression and tension (region III), although it is conservative
for biaxial compression (region I)-see also Johnson and Lowe's research
as described in the paragraph below eqn (2.5-5).
Using Fig. 2.5-10, a failure diagram may be derived for a plane element
under combined normal and shear stresses; such a diagram (Fig. 2.5-11)
shows that in the presence of a shear stress v, concrete will fail at a lower
compressive stress f than the uniaxial compressive strength n. or the
uniaxial tensile strength / 1 (taken here as 0.1/~).
Today, in the absence of a generally acceptable failure criterion, the
strength of concrete under triaxial stresses (/ 1 ;::: / 2 ;::: f,) is often
investigated by making use of the following observation (after Hobbs,
Pomeroy and Newman [25] ): 'The influence of the intermediate principal
stress / 2 on the failure of concrete has been found to be small and for
practical purposes can be ignored.' Accordingly, Hobbs et al. [25]
have made the following design recommendations for various stress
combinations: