Civil Engineering Reference
In-Depth Information
Table 5.3
Top fi bre
Bottom fi bre
σ
partial
σ
cumulated
σ
partial
σ
cumulated
Self weight
+3.72
-6.61
Prestress
-2.98
+0.74
+23.02
+16.41
Finishes
+0.76
+1.50
-1.35
+15.06
Live load
+8.48
+9.98
-15.06
0
5.9 Table of stresses
It is always necessary to check the stresses after any sizing exercise in order to confi rm
the suitability of the beam under the applied loads and to assist in checking for mistakes
in the calculation. By far the best format for tabulating stresses is shown in Table 5.3.
All stresses are in MPa. '
partials'.
This presentation has the great advantage that it shows visually how the stresses
build up stage by stage, and makes it very easy to spot mistakes in the calculation, or
to assess the effects of any change, of load or of prestress.
Many of the calculations required for designing a prestressed concrete bridge
can be readily carried out using spreadsheets. However, it is very important that the
spreadsheets are set out in such a way that the tabulation of stresses maintains the
clarity of the presentation shown above.
One principal aim of the preliminary design calculations described in this topic is
to illuminate the changes that may be made to the design to improve its performance.
Methods of calculation or modes of presentation of calculations that simply publish the
fi nal result are of no use in this endeavour. It is essential for the engineer to understand
the difference between calculations that are aimed at checking the compliance of an
established design, and those essentially exploratory calculations carried out during
the true 'design' phase.
Table 5.3 shows that when the prestress is combined with self weight alone, the
stresses on the top and bottom fi bres respectively are +0.74 MPa and +16.41 MPa.
The maximum compressive stress on the top fi bre under the effect of live load is
+9.98 MPa, while on the bottom fi bre the stress falls to zero, in accordance with the
sizing calculations.
σ
cumulated' gives the running total of the '
σ
Table 5.4
Top fi bre stresses
Bottom fi bre stresses
σ
partial
σ
cumulated
σ
partial
σ
cumulated
Self weight
+3.72
-6.61
Initial prestress
-3.43
+0.29
+26.47
+19.86
Prestress loss
+0.45
+0.74
-3.45
+16.41
Finishes
+0.76
+1.50
-1.35
+15.06
Live load
+8.48
+9.98
-15.06
0
