Civil Engineering Reference
In-Depth Information
Equationss (3.118) and (3.119) are exactly the same as Equations (3.89) and (3.90) for the
design of a singly reinforced beam. The trial-and-error procedure for the solution has been
described in conjunction with Equations (3.92)-(3.93).
Once the steel area for the web
A
s
w
is found, we can calculate the total steel area
A
s
=
A
s
w
+
A
sf
, where the steel area for the flange
A
sf
is obtained from Equation (3.114).
3.2.5 Moment-Curvature (M -
φ
) Relationships
3.2.5.1 Characteristics of
M
-
φ
Curve
We have now studied the linear bending theory in Section 3.1 and the nonlinear bending
theory at ultimate load in Section 3.2. These theories will be used to understand and to cal-
culate the fundamental moment-curvature relationships in the bending of reinforced concrete
beams.
Figure 3.14(a) gives the moment-curvature (
M
-
) curve for a singly reinforced beam using
mild steel bars. Since mild steel has an elastic-perfectly plastic stress-strain relationship as
φ
Figure 3.14
Moment-Curvature relationships
