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)

References 245
2T
Vt = 2
hmin[hmax - (h min/3)]
Show that the equation may be obtained from the sand-heap analogy for
plastic torsion and explain whether a plastic stress distribution exists in
a concrete section at incipient failure in torsion.
6.5 BS 8110 states that the amount of torsion links should satisfy the
equation:
A sv ___ ~T~ __
->
Sv - 0.8XIYI(0.87fyv)
Using the space truss analogy, derive the equation from first principles;
relate your assumptions to research resuIts.
The equation shows that the uItimate torsional resistance is independent
of the concrete strength and that the torsional strength of a box beam is the
same as that of a solid beam. Comment.
Briefly explain the reason for the factor 0.8 in the equation.
6.6 (a) Derive the foIIowing anchorage-bond length equation and
explain your assumptions:
1 = 0.87fy cp
u 4f3Hcu
(b) Former British Codes CP 110 and CP 114 require designers to
check local bond stresses, but BS 8110 does not so require.
Comment. (Hint for Part (b): see Example 6.6-2.)
References
Evans, R. H. and Kong, F. K. Shear design and British Code CP 114. The
Structural Engineer, 45, No. 4, April 1967, pp. 153-8.
2 ACI-ASCE Committee 426. Shear strength of reinforced concrete members.
Proc. ASCE, 99, No. ST6, June 1973, pp. 1091-187. (Reaffirmed in 1980 and
published by the American Concrete Institute as Publication No. 426R-74.)
3 Kotsovos, M. D. Mechanism of 'shear' failure. Magazine of Concrete
Research, 35, No. 123, June 1983, pp. 99-106.
4 Kotsovos, M. D. Behaviour of reinforced concrete beams with a shear span to
depth ratio between 1.0 and 2.5. Proc. ACI, 81, No. 3, May/June 1984,
pp.279-98.
5 Regan, P. E. Concrete Society Current Practice Sheet No. 105: Shear.
Concrete, 19, No. 11, Nov. 1985, pp. 25-6.
6 Hsu, T. C. C. Is the 'staggering concept' of shear design safe? Proc. ACI, 79,
No. 6, Nov./Dec. 1982, pp. 435-43.
7 Kong, F. K. Shear resistance of bent-up bars (Verulam Letter). The. Structural
Engineer, 65A, No. 11, November 1987, p. 417.
8 Elzanaty, A. H., Nilson, A. H. and Slate, F. O. Shear capacity of reinforced
concrete beams using high strength concrete. Proc. ACI, 83, No. 2, March/
April 1986, pp. 290-6.