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)

Design procedure for rectangular beams 115
r
r2so 1
670
L 3-32mm
•••
(a)
(b)
Fig. 4.6-5
Here, feu= 40 N/mm 2 ; /y = 460 N/mm 2 •
SOLUTION
(a) Using design chart (Fig. 4.5-2).
As (three 32 mm bars) = 2412 mm 2
2412 0
e = (250)(670) = 1.44 Yo
From design chart (Fig. 4.5-2),
Mlbd 2 = 4.9 N/mm 2
M = (4.9)(250)(670 2 )(10- 6 ) = 550 kNm
xld = 0.35 approximately (by interpolation)
(b) Using BS 8110 simplified stress block (Fig. 4.6-5 (b)). With reference
to Fig. 4.6-5(b), the equilibrium condition is as given in eqn (4.6-2):
0.405/cubx = 0.87/yAs
(0.405)( 40)(250)x = 0.87( 460)(2412)
x = 238.3 mm
x/d = 0.36 < 0.5 OK
From eqn (4.6-3) (or Fig. 4.6-5(b)),
z = d - 0.45x = 670 - (0.45)(238.3)
z = 562.8 mm
M = 0.81/yAsz
= (0.87)(460)(2412)(562.8)(10- 6 ) = 543 kNm
Example4.6-9
Determine the ultimate resistance moment M and the xl d ratio of the beam
section in Fig. 4.6-6 using: