School of Civil, Environmental and Chemical Engineering
Problem 1 Solution
Calculate the extreme fibre stresses at midspan due to
prestressing and applied loads.
P  2000 kN
P.e  2000  250  10 3 kNm
M
wl 2 25  112

 378 kNm
8
8
Stresses due to P (compressive) 
P 2000  10 3

 9.1 MPa  compression 
Ag
220, 000
 t   b  9.1 MPa
Assume tension at top and compression at bottom. Stresses due
to ‘ P.e ’:
t 
P.e. yt 500  106  485

 12.13 MPa
Ig
20000  106
b 
P.e. yb 500 106  415

 10.13 MPa
Ig
20000  106
(tension)
(compression)
Stresses due to M:
t 
M . yt 378  106  485

 9.17 MPa
Ig
20000 106
b 
M . yb 378 106  415

 7.84 MPa
Ig
20000  106
(compression)
(tension)
Combine all the stresses:
 t  9.1  12.13  9.17  6.14 MPa
 b  9.1  10.38  7.84  11.64 MPa
(compression)
(compression)
Concrete Structures 2
168
School of Civil, Environmental and Chemical Engineering
Combined stress diagram is:
Figure S1.1, Extreme fibre stresses at midspan due to prestressing and applied loads,
copyright RMIT University
Concrete Structures 2
169