Civil Engineering Reference
In-Depth Information
3.15
Extension for uniformly distributed loading
For a truly uniformly distributed load the failure path described by angle ß
may be obtained by minimising the resistance of the concrete as given in the
first part of Eqn (3.15). That is,
This yields a relation between ß and
in the form:
tan 2ß=-tan
f
Once the value of ß is established, evaluation of the ultimate strength of
beam under uniformly distributed load, will follow the usual procedure
(Ray, 1980; 1982).
f
(3.44)
3.16
Recommendations for design of beams for shear and flexure
It is now well known that elastic theory characterises the action and behaviour of
deep beams before cracking in its true perspective, but cannot highlight the
behavioural performance and strength capacity of the beams up to the stage of
collapse, which ultimate load theory can do. Limited crack width, controlled
deformation and deflection are the essential prerequisites for the satisfactory
performance of any structural element. The simplified formulae put forward in the
preceding sections, for
L
/
D
ratio up to 1.5 and shear span/depth ratio varying from
0.22 to 0.47, can predict the strength of beams with web openings at failure condition
either in shear or flexure. For a safe design, the ultimate limit state as well as the
serviceability limit states should be considered. The important codes like CEB-FIP
(1970) ACI (1971; 1978) and UNESCO international code (1971) have
recommended the use of limit state design for the concrete structures. These
recommendations are based on a semi-probabilistic approach in fixing the accepted
values of probability of reaching the limiting states in any structure. This involves
the use of characteristic values and partial safety factors for the various actions and
mechanical properties of the materials. The CEB-FIP (1970), BS CP110 (1972)
and IS456 (1978) have stipulated these factors. Such factors have been used
conveniently in the present formulations for simplified design guide.
Thus, in order to keep the predicted ultimate load capacity of beams under safe
design, a general performance factor (or safety factor) for the ultimate limit state
(UNESCO, 1971; Winter School etc., 1978) is chosen as 0.75 for shear and 0.85
for flexure in order to get reasonable lower bounds on these failures. In addition,
the following partial safety factors (UNESCO, 1971; Winter School etc., 1978) for
loading and materials so as to cover their inherent deficiencies have been used:
g
f
(=partial safety factor for loading)=1.40
g
m
(=partial safety factor for steel)=1.15
g
c
(=partial safety factor for concrete)=1.50
