Civil Engineering Reference
In-Depth Information
Use of Graphs and Tables
In Section 3.4 the following equation was derived:
1.7
f
y
1
M
u
A
s
f
y
d
1
c
f
If
A
s
in this equation is replaced with
bd
, the resulting expression can be solved for
bd
2
.
M
u
/
1.7
f
y
1
M
u
bdf
y
d
1
c
f
and from this
1.7
f
y
M
u
1
bd
2
f
y
1
c
f
c
For a given steel percentage
and for a certain concrete
f
and certain steel
f
y
, the
bd
2
can be calculated and plotted in tables, as is illustrated in Appendix Ta-
bles A.8 through A.13 or in graphs (see Graph 1 of Appendix A). SI values are provided
in Appendix Tables B.8 to B.9. It is much easier to accurately read the tables than the
graphs (at least to the scale to which the graphs are shown in this text). For this reason
the tables are used for the examples here. The units for
M
u
/
value of
M
u
/
bd
2
in both the tables and the
graphs of Appendix A are pounds per square inch. In Appendix B, the units are MPa.
Once
M
u
/
bd
2
is determined for a particular beam, the value of
M
u
can be calculated
as illustrated in the alternate solution for Example 3.1. The same tables and graphs can be
used for either the design or analysis of beams.
Barnes Meadow Interchange, Northampton, England. (Courtesy of Cement and Concrete
Association.)
