Civil Engineering Reference
In-Depth Information
Section 2.5
P
= 22 MN;
e
= -1.161 m;
M
p
= +11.5 MNm
Table 6.5
Top fi bre
Bottom fi bre
σ
partial
σ
cumulated
σ
partial
σ
cumulated
Self weight
+1.81
-2.94
Prestress
-1.32
+12.33
Mp
+2.34
+2.83
-3.80
+5.59
Finishes
+0.57
+3.40
-0.93
+4.66
Live load +
ve
+2.36
+5.76
-3.84
+0.82
Live load -
ve
-1.26
+2.14
+2.05
+6.71
Section 3.0
P
= 22 MN;
e
= 0.675;
M
p
= +10 MNm
Table 6.6
Top fi bre
Bottom fi bre
σ
partial
σ
cumulated
σ
partial
σ
cumulated
Self weight
-3.53
+5.35
Prestress
+6.30
-1.11
Mp
+1.98
+4.75
-3.00
+1.24
Finishes
-1.13
+3.62
+1.71
+2.95
Live load +
ve
+0.85
+4.47
-1.29
+1.66
Live load -
ve
-3.35
+0.27
+5.08
+8.03
It may be seen that the stress on the top fi bre under the full live load has a residual of
0.27 MPa. This is because the
M
p
at 10 MNm is greater than the minimum acceptable
fi gure of 8.7 MNm. The margin is 1.3 MNm. With
z
t
= 5.041, this margin gives rise
to a top fi bre stress of 0.26 MPa, confi rming that if
M
p
had in fact been 8.7 MNm, the
stress on the top fi bre would have fallen to zero. This is the type of simple check that
designers should be carrying out all the time to confi rm the accuracy and consistency
of their calculations.
The
M
p
at section 2.0 is 13 MNm, slightly greater than 50 per cent of
Pe
at the
adjacent section 2.5. It would be possible to redefi ne
M
p
as say 12 MNm and calculate
the required
P
. However, the 13 MNm will be accepted for the purpose of this
example.
6.16.5 Choice of tendons and tendon arrangement
We have seen in
5.13
that strand is available in nominal 13 mm and 15 mm sizes, and
that for preliminary design purposes, the working force for each size is 100 kN and
