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)

214 Shear, bond and torsion
SOLUTION
(a) See the derivation of eqn (6.3-8) and the Comments (c) on Step 3 of
BS 8110's shear design procedure.
(b) From eqn (6.4-2),
A
sv
= 0.4 bySy
0.87/ y v
= 0.18% of bySv for Iyv = 250 N/mm 2
Example 6.4-2
The span lengths of a three-span continuous beam ABCD are: exterior
spans AB and CD, 8 m each; interior span BC, 10 m. The characteristic
dead load G k (inclusive of self-weight) is 36 kN/m and the characteristic
imposed load Qk is 45 kN/m. The beam has a uniform rectangular section
of width b = 350 mm, and the effective depth d mar be taken as 800 mm. If
leu = 40 N/mm 2 ,/y = 460 N/mm 2 ,/yv = 250 N/mm , and ifthe longitudinal
reinforcement is as in Fig. 6.4-1, design the shear reinforcement for span
AB. Conform to BS 8110. (Note: The longitudinal reinforcement in Fig.
6.4-1 is described by the current British detaUing notation: the first figure
denotes the number of bars, the letter the type of steel-T for high yield
steel and R for mild steel-the number after the hyphen is the identification
bar mark. Thus, 2T32-1 represents two high yield bars of size 32
mm, the bars being identified by the bar mark 1; in this example, bar mark
1 refers to a straight bar of size 32 whose length is 3 m plus the projection
into the span BC. For further information on detailing notation, see
Example 3.6-3.)
SOLUTION
The design will be carried out in the steps listed previously; comments are
given at the end of the solution.
Step 1 The design shear stress
First we draw the shear force envelope. For a continuous beam, the
shear force is the algebraic sum of the simple-span shear and the shear
due to the support bending moments. The beam was previously analysed
in Example 4.9-1, and Fig. 4.9-6 shows that the redistributed support
bending moment is 768 kNm for each loading case. Loading Cases 1 and
3 (Fig. 4.9-6):
I2T16-4
Â
I
3000 3000
~ li~T32-1
2 4
2TJ2-2
~I
02112
1
800
... 1
\.3T32-3
â -1 333 350 1.-
1.
8000 J
Fig. 6.4-1 Longitudinal steel details