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)

Failure criteria for concrete 43
v
,
0·2~
((tension)
0·4f.' c 0·6f.: c O·Bf.' c f.' c
f (compression)
Fig. 2.5-11 Failure of concrete under combined direct and shear stresses
(a) Triaxial compression: f 1 2:: fz 2:: h. > 0
The maximum compressive stress that can be supported by concrete
in a structure is given by
ft = 0.67feu + 3{1 (2.5-3)
where feu is the characteristic cube strength, and should be divided by
the usual partial safety factor Ym when used in design: thus f 1 =
(0.67feu1Ym) + 3[-, = 0.45feu + 3[,. for Ym = 1.5. Note that the stress
0.67feu1Ym is identical to the peak stress in BS 8110's stress/strain
curve (see Fig. 3.2-2(b)).
(b) Triaxial compression and tension:
(1) ft 2:: f 2 2:: 0; h. < 0 (i.e. only h. is tensile)
(2) ft 2:: fz 2:: f3 < 0 (i.e. at least h is tensile)
For either case (1) or case (2), the maximum compressive stress that
can be supported is
ft = 0.67feu + 20/J (2.5-4)
and the maximum tensile stress that can be supported without cracks
developing is given by
0 f
ft - 0.67feu
> 3 > 20 (2.5-5)
Note that in eqns (2.5-4) and (2.5-5), the sign off3 is negative. Also,
when the equations are used in design, the feu values should be
divided by the partial safety factor Ym• as in eqn (2.5-3).
The apparent clarity of the above summary account might well obscure
the truth, stated earlier, that a universal failure criterion which allows for
all possible stress states has not yet been found. Indeed, from time to time,
observations are reported which may have far-reaching consequences. For
example, Johnson and Lowe [27) have reported triaxial compression tests