F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

TT~
b
1--400-l
'
'
T
h ~ -ill
j -r-· Aps.- -2,0
~ ••• __j_
The ultimate limit state: flexure (BS 8110) 357
Fig. 9.5-2 Beam section
(9.5-7)
The coefficient k 2 in eqn (9.5-7), and k1 in eqn (9.5-6), may be read off
from Fig. 4.4-4 or Fig. 4.4-5.
If BS 8110's rectangular stress block (Fig. 4.4-5) is used, then the above
general approach may easily be modified for application to, say, flanged
beams in which the neutral axis lies outside the flange, or to other nonrectangular
beams.
Example 9.5-1
A bonded prestressed concrete beam is of rectangular section 400 mm by
1200 mm, as shown in Fig. 9.5-2. The tendon consists of 3300 mm 2 of
standard strands, of characteristic strength 1700 N/mm 2 , stressed to an
effective prestress of 910 N/mm 2 , the strands being located 870 mm from
the top face of the beam. The concrete characteristic strength is 60 N/mm 2
and its modulus of elasticity 36 kN/mm 2 • The stress/strain curve of the
tendon is as shown in Fig. 9.5-3, with Young's modulus equal to 200
kN/mm 2 for stresses up to 1220 N/mm 2 .
(a)
(b)
Working from first principles, calculate the ultimate moment of
resistance of the beam section.
Suppose, as a result of a site error, the strands have not been
tensioned, i.e. the effective tendon prestress is zero. Calculate the
ultimate moment of resistance of the beam section.
Use BS 8110's rectangular stress block in Fig. 4.4-5.
SOLUTION
(a)
Refer to the strain and force diagrams in Fig. 9.5-1, and reason from
first principles.
A = 400 X 1200 = 4.8 X 10 5 mm 2 Aps = 3300 mm 2
I = -b_ X 400 X 12003 = 5.76 X 1010 mm4
Pc = 3300 X 910 = 3.003 X 10 6 N
e 5 = 870 -
1200/2 = 270 mm