Civil Engineering Reference
In-Depth Information
Eqn (3.24) is the general one and can even be used for plain beams as
well as beams with and without web reinforcements by deleting the terms
which are not involved. Ray (1980; 1982) observed that this simplified
strength predicted strength very close to that computed by the rigorous Eqn
(3.15). It is, therefore, hoped that Eqn (3.24) will find favour with practising
engineers for their day-to-day design work.
3.12
Ultimate strength in flexure
Knowledge of strengths of beams in both shear and flexure would enable the
designer to fix the dimensions and detailing of the beams. Normally, flexural
failure of beams is affected if the percentage of main reinforcement is kept
below the balance percentage. It has further been observed (Ray, 1980;
1982; 1985) that shear failure in deep beams could be prevented and
flexural failure might be expected if excessive web reinforcements are
provided perpendicular to the plane of rupture. In this particular case, the
support and load bearing regions must be properly strengthened to guard
against any local or anchorage failures.
Determination of the lever arm is highly important in fixing up the
amount of balance reinforcement at initial design. Even the national codes
(CEB-FIP, 1970; BS CP110, 1972; ACI318, 1971, 1978; IS456, 1978) do
not provide any design guidance for beams failing in flexure.
Recommendations put forward by CEB-FIP (1970) are rather conservative
and limited to the case of solid web beams.
Consider simplified stress block, which is in many respects similar to the
one adopted for shallow beams but which accounts for the stress distribution
of concrete on the tension side as well as presence of the web reinforcement.
Its geometry and the associated forces are shown in
Figure 3.14.
The
assumptions made in the derivations are as follows:
i)
Only one neutral axis prior to failure (see also Section 3.3).
ii)
A rectangular stress block (after Whitney, 1940) as used in shallow
beams, for the compression zone,
iii)
A triangular stress distribution for the concrete portion in the
tension zone (in shallow beams, this effect is neglected),
iv)
The effect of web steel in compression zone is neglected,
v)
The tension steel and the web steel below the neutral axis yield at
failure. The contribution of the vertical web steel is also neglected.
Referring to Figure 3.14, the following relations of forces are obtained:
